phd_all

MOISTURE MOVEMENT THROUGH EXPANSIVE SOIL AND IMPACT ON PERFORMANCE

OF RESIDENTIAL STRUCTURES

by

Heather Beata Dye

A Dissertation Presented in Partial Fulfillment of the Requirements for the Degree

Doctor of Philosophy

ARIZONA STATE UNIVERSITY

May 2008

MOISTURE MOVEMENT THROUGH EXPANSIVE SOIL AND IMPACT ON PERFORMANCE

OF RESIDENTIAL STRUCTURES

by

Heather Beata Dye

has been approved

April 2008

Graduate Supervisory Committee:

Sandra L. Houston, Co-Chair Bruno D. Welfert, Co-Chair

Claudia Zapata

ACCEPTED BY THE GRADUATE COLLEGE

iii

ABSTRACT

It is well established that damage to structures built on expansive soils is mainly caused

by changes in soil suction. Suction changes are generally attributed to changes in

environmental conditions such as change in water table depth, surface irrigation and landscape,

resulting in changes in the surface and groundwater regime. Slabs-on-grade must resist both

long-term and short-term moisture-change induced soil volume change. The design of

residential structures in arid regions is especially challenging because the soil experiences large

variations in matric suction and associated substantial volume change. As a result, a large

number of houses experience minor to severe distress.

Unsaturated soil mechanics theory is used in the determination of unsaturated soil

behavior. It is the purpose of this research work to help bridge the gap between theory and

practice in the design of residential foundations on expansive soils. One part of this study

relates to investigating the depth and degree of wetting associated with moisture flow through

expansive soils through modeling and field studies in semi-arid region for typical residential

construction development, as well as assessment of foundation performance. A number of steps

were taken towards the goal of developing a better understanding of expansive soils behavior

and field conditions leading to problems with expansive soils. These steps include: 1) numerical

modeling of moisture flow through expansive soils in one- and two-dimensions. Two extreme

surface flux conditions were considered, desert and excessively irrigated turf landscapes. The

numerical results are applicable to regions with low to moderate expansion potential and

Phoenix, Arizona environmental conditions. 2) Development of map illustration to identify

locations with low to medium swell potential in the Phoenix Valley. 3) Comparisons of the

numerical results to field evidence on depth of wetting and depth of active zone. 4) Evaluation of

stability, convergence and numerical challenges for unsaturated moisture flow through expansive

soils using Richards’ equation. Sources of numerical instabilities were identified and potential

improvements discussed. 5) Survey of Arizona region practitioners to identify current design and

construction practices, and 6) Analysis of forensic investigations to identify the nature and

common causes of residential distress.

iv

DEDICATION

To my family, who encouraged and supported me in my studies.

v

ACKNOWLEDGEMNTS

This research work was made possible through the financial support by Homebuilders

Association of Central Arizona (HBACA) and Construction Inspection and Testing Co. (CIT). The

author is very grateful for the inspiration, encouragement and support of Dr. Sandra Houston and

Dr. Bill Houston. I would like to thank Dr. Bruno Welfert for his time and unlimited patience in

explaining numerical concepts applicable to the problem considered in this research work. The

contribution of Dr. Claudia Zapata is also acknowledged, who, most importantly, was a friend in a

time of need. Additionally, I would like to express my gratitude to practitioners, Brian Juedes

(PE, Senior Vice President, Felten Group), Scott Neely (Terracon Inc.) and Dr. Kirby Meyer (PE,

Chairman, MLAW), for partial review of this research work with calculations and edits. The

development of map illustration was made possible through the collaboration with PhD students,

Drew Lucio and Sonal Singhal. Their contribution is gratefully acknowledged. This work, in part,

was made possible through the good will of numerous Arizona based companies which

interviewed with ASU and/or released their geotechnical/forensic data for research purposes.

Their contribution is gratefully acknowledged.

Finally, I would like to thank my husband Brian, who convinced me to continue with

higher education, provided moral support and was a source of fascinating discussions about

unsaturated soil mechanics and computer computations; my brother David, on whom I can

always count on; and most importantly my father and my mother who instilled in me the

appreciation for knowledge. Through their personal sacrifices I was able to immigrate to the

United States and pursue my dreams.

vi

TABLE OF CONTENTS

Page

LIST OF TABLES .......................................................................................................................... xvi LIST OF FIGURES ........................................................................................................................ xix NOMENCLATURE...................................................................................................................... xxviii CHAPTER

1 INTRODUCTION ...................................................................................................................... 1

1.1 Overview ......................................................................................................................... 1

1.2 Historical Background ..................................................................................................... 3

1.3 Research Objective and Scope ...................................................................................... 6

1.4 Research Methodology ................................................................................................... 7

1.5 Outline of Report ............................................................................................................. 9

1.6 Key Findings ................................................................................................................. 11

2 LITERATURE REVIEW ......................................................................................................... 13

2.1 Introduction ................................................................................................................... 13

2.2 Factors Affecting Swell and Moisture Migration ........................................................... 14

2.3 Moisture Variation within Soil Profile ............................................................................ 16

2.3.1 Infiltration and Wetting Front ........................................................................... 16

2.3.2 Soil Profile ........................................................................................................ 17

2.3.3 Definition of Active Zone Depth and Related Terms ....................................... 19

2.3.3.1 Active Zone Depth ..................................................................................... 21

2.3.3.2 Zone of Seasonal Moisture Fluctuation ..................................................... 21

2.3.3.3 Depth of Wetting ........................................................................................ 21

2.3.3.4 Depth of Potential Heave ........................................................................... 22

2.3.4 Edge Moisture Variation Distance ................................................................... 22

2.4 Causes of Water Content Change; Field Observations of Moisture Migration and

Heave ........................................................................................................................... 23

2.4.1 Monotonic Water Content Change .................................................................. 24

CHAPTER Page

vii

2.4.2 Seasonal Water Content Change .................................................................... 26

2.4.2.1 Field Studies of Seasonal Moisture Variations .......................................... 28

2.4.2.2 Field Studies of Seasonal Temperature Variations ................................... 30

2.4.2.3 Field Studies of Monotonic vs. Seasonal Moisture Variation and Heave .. 31

2.4.3 Accidental Changes of Water Content ............................................................ 32

2.5 Soil Response to Change in Water Content ................................................................. 35

2.5.1 Settlement ........................................................................................................ 36

2.5.2 Shrinkage ......................................................................................................... 37

2.5.3 Heave .............................................................................................................. 39

2.5.4 Fatigue of Swelling .......................................................................................... 39

2.6 Performance of Residential Construction ..................................................................... 40

2.6.1 As-built Floor Deviation from Horizontal .......................................................... 41

2.6.2 Post-Construction Slab Distortion .................................................................... 42

2.7 Mitigation measures ...................................................................................................... 43

2.7.1 Removal, replacement and recompaction ....................................................... 43

2.7.2 Mechanical Stabilization .................................................................................. 44

2.7.3 Chemical Stabilization ..................................................................................... 44

2.7.4 Stabilization of Water Content ......................................................................... 45

2.7.4.1 Passive Stabilization .................................................................................. 45

2.7.4.2 Active Stabilization ..................................................................................... 48

2.7.5 Site Drainage and Control of Landscape Watering ......................................... 48

2.8 Classification of Swell Potential Based on Soil Properties ........................................... 49

2.8.1 Mineralogical Classification ............................................................................. 50

2.8.1.1 Cation Exchange Capacity ........................................................................ 52

2.8.1.2 Cation Exchange Capacity and Soil Properties ......................................... 53

2.8.1.3 Atterberg Limits .......................................................................................... 55

2.8.2 Indirect Measurement ...................................................................................... 55

CHAPTER Page

viii

2.8.2.1 Atterberg Limits .......................................................................................... 55

2.8.2.2 Linear Shrinkage ........................................................................................ 58

2.8.2.3 Colloid Content .......................................................................................... 58

2.8.2.4 Suction ....................................................................................................... 59

2.8.3 Direct Measurement ........................................................................................ 62

2.9 Unsaturated Soil Mechanics Theory ............................................................................. 64

2.9.1 Soil Suction and Soil Moisture ......................................................................... 64

2.9.2 Measurement of Soil Suction ........................................................................... 66

2.9.3 Soil Water Characteristic Curve ...................................................................... 69

2.9.3.1 Uncertainty Band ....................................................................................... 71

2.9.3.2 Hysteresis .................................................................................................. 72

2.9.4 Unsaturated Soil Permeability ......................................................................... 74

2.9.5 Theory of Moisture Flow .................................................................................. 77

2.9.5.1 Saturated Flow ........................................................................................... 79

2.9.5.2 Unsaturated Flow ....................................................................................... 81

2.10 Numerical Methods ....................................................................................................... 85

2.10.1 Numerical Methods Used in Solution of Richard’s Equation ........................... 86

2.10.2 Available Commercial Software ....................................................................... 86

2.10.2.1 SVFlux ....................................................................................................... 87

2.10.2.2 Vadose/W .................................................................................................. 88

2.10.2.3 Hydrus ........................................................................................................ 89

2.11 Summary ...................................................................................................................... 89

3 CURRENT PRACTICE .......................................................................................................... 94

3.1 Factors Affecting Residential Building Performance .................................................... 94

3.2 Drainage Design Standards and Standard of Practice ................................................. 97

3.3 Residential Foundation Design in USA ........................................................................ 99

3.4 Residential Foundation Design in Other Countries .................................................... 105

CHAPTER Page

ix

3.5 Design and Construction Practice – Interviews with Industry .................................... 109

3.5.1 Geotechnical Engineering Interviews ............................................................ 109

3.5.1.1 Site Investigation and Soil Testing ........................................................... 109

3.5.1.2 Site Monitoring ......................................................................................... 111

3.5.1.3 Communication ........................................................................................ 111

3.5.1.4 Geotechnical Report ................................................................................ 111

3.5.1.5 Design Procedure .................................................................................... 112

3.5.1.6 Mitigation Measures ................................................................................. 112

3.5.1.7 Areas of Problems ................................................................................... 113

3.5.1.8 SWCC and Suction .................................................................................. 113

3.5.2 Structural Engineering Interviews .................................................................. 114

3.5.2.1 Occurrence of Expansive Soils ................................................................ 114

3.5.2.2 Communication ........................................................................................ 114

3.5.2.3 Geotechnical Report ................................................................................ 114

3.5.2.4 Structural Analysis and Design Procedure .............................................. 114


3.5.2.6 Areas of Problems and Concerns ............................................................ 115

3.5.3 Home Builder Interviews ................................................................................ 116

3.5.3.1 Site Assessment ...................................................................................... 116

3.5.3.2 Budget and Design .................................................................................. 117

3.5.3.3 Site Preparation Process ......................................................................... 117

3.5.3.4 Site Monitoring ......................................................................................... 117

3.5.3.5 Communication ........................................................................................ 118


3.5.3.7 Sources of Problems ................................................................................ 121

3.5.3.8 Litigation ................................................................................................... 121

3.5.4 Forensic Investigation .................................................................................... 121

CHAPTER Page

x

3.5.4.1 Failure Modes .......................................................................................... 121

3.5.4.1.1 Center Lift ........................................................................................ 122

3.5.4.1.2 Edge Lift .......................................................................................... 122

3.5.4.1.3 Settlement ....................................................................................... 122

3.5.4.2 Remediation Methods .............................................................................. 123

3.6 Failure Criteria ............................................................................................................ 123

3.7 Summary .................................................................................................................... 125

4 LABORATORY DATA .......................................................................................................... 127

4.1 Field Exploration ......................................................................................................... 127

4.1.1 Equipment ...................................................................................................... 128

4.1.2 Field Sampling ............................................................................................... 128

4.2 Soil Testing for Input Parameters ............................................................................... 129

4.2.1 Moisture Content and Dry Density ................................................................. 130

4.2.2 Atterberg Limits .............................................................................................. 131

4.2.3 Sulfate Content .............................................................................................. 131

4.2.4 Cation Exchange Capacity ............................................................................ 131

4.2.5 Specific Gravity .............................................................................................. 132

4.2.6 Expansion Index ............................................................................................ 132

4.2.6.1 Arizona Modified Expansion Index Procedure ......................................... 132

4.2.6.2 Expansion Index Procedure as per ASTM D 4829 .................................. 133

4.2.7 Constant Volume Oedometer Testing ........................................................... 134

4.2.8 Consolidation Test and Correction Factors ................................................... 135

4.2.9 Saturated Hydraulic Conductivity .................................................................. 137

4.2.10 Soil Suction .................................................................................................... 138

4.2.10.1 Pressure Plate ......................................................................................... 139

4.2.10.1.1 Equipment ..................................................................................... 139

4.2.10.1.2 Issues Associated with SWCC Testing ......................................... 142

CHAPTER Page

xi

4.2.10.1.3 One Point Method of SWCC Determination .................................. 145

4.2.10.1.4 Complete SWCC ........................................................................... 150

4.2.10.2 Filter Paper .............................................................................................. 151

4.2.10.3 Dessicator ................................................................................................ 153

4.2.11 Summary of Laboratory Results .................................................................... 153

4.2.11.1 Sampling Locations .................................................................................. 153

4.2.11.2 Summary Tables ...................................................................................... 156

4.2.12 Selection of Input for Modeling ...................................................................... 162

5 MAP OF EXPANSIVE SOIL DISTRIBUTION IN PHOENIX VALLEY ................................. 164

6 PTI RESIDENTIAL FOUNDATION DESIGN ....................................................................... 171

6.1 Introduction ................................................................................................................. 171

6.2 Historical Background ................................................................................................. 171

6.3 Definitions ................................................................................................................... 173

6.4 PTI 2nd Edition Design Procedure, 1996..................................................................... 174

6.5 PTI 3rd Edition Design Procedure, 2004 ..................................................................... 176

6.5.1 Additional Definitions Provided in the Procedure. ......................................... 177

6.5.2 Assumptions. ................................................................................................. 178

6.5.3 Procedure. ..................................................................................................... 179

6.6 Design Parameters for Arizona .................................................................................. 183

6.7 Discussion .................................................................................................................. 184

6.8 Sensitivity Analysis ..................................................................................................... 186

6.8.1 Influence of Suction Profiles on Geotechnical Parameters ........................... 187

6.8.2 Influence of Geotechnical Parameters on Slab Thickness ............................ 189

6.8.3 Sensitivity of ym to Suction Profile ................................................................. 190

6.8.4 Comparison of Different Suction Compression Index Methodologies ........... 191

6.8.5 Influence of Gravel Correction ....................................................................... 192

6.9 Conclusions ................................................................................................................ 192

CHAPTER Page

xii

7 MODELING – NUMERICAL METHODS ............................................................................. 194

7.1 Modeling Challenges .................................................................................................. 194

7.2 Selection of Program .................................................................................................. 198

7.2.1 Convergence, Stability and Accuracy ............................................................ 198

7.2.2 Experiment Set-Up ........................................................................................ 202

7.2.3 Presentation of Results ................................................................................. 203

7.2.4 Discussion and Conclusions .......................................................................... 207

7.3 Sensitivity analysis of SWCC and k(h) ....................................................................... 209

7.3.1 Uncertainty of Unsaturated Soil Functions .................................................... 210

7.3.2 Problem Set-Up ............................................................................................. 211

7.3.2.1 Soil Properties .......................................................................................... 211

7.3.2.2 Initial and Boundary Conditions ............................................................... 213

7.3.2.3 Modeling Software, Mesh Size and Time Step ........................................ 213

7.3.3 Numerical Simulation ..................................................................................... 213

7.3.3.1 Hysteresis in SWCC ................................................................................ 214

7.3.3.2 Uncertainty in k(h) .................................................................................... 215

7.3.3.2.1 Infiltration ......................................................................................... 215

7.3.3.2.2 Evaporation ..................................................................................... 217

7.3.4 Conclusions ................................................................................................... 218

7.4 SVFlux Program Behavior .......................................................................................... 219

7.4.1 Numerical Oscillations – Lessons Learned ................................................... 220

7.4.2 Numerical Challenges ................................................................................... 222

7.5 Numerical Experiments ............................................................................................... 223

7.5.1 Fixed vs. Adaptive Time Step ........................................................................ 223

7.5.2 Mixed Formulation ......................................................................................... 227

7.5.3 Normalization ................................................................................................. 228

7.5.4 Spatial Discretization - Pseudospectral Method ............................................ 228

CHAPTER Page

xiii

7.5.5 Time Discretization - Exponential Integrator ................................................. 229

7.5.6 Time Discretization - ADI ............................................................................... 229

7.6 Conclusions ................................................................................................................ 230

8 MODELING – NUMERICAL RESULTS ............................................................................... 231

8.1 Modeling Objective ..................................................................................................... 231

8.2 Design of Experiment ................................................................................................. 232

8.2.1 Problem Assumptions and Restrictions ......................................................... 233

8.2.2 Program ......................................................................................................... 234

8.2.3 SVFlux Specific Restrictions .......................................................................... 235

8.2.4 Boundary and Initial Conditions ..................................................................... 238

8.2.5 Domain Size .................................................................................................. 239

8.2.6 Soil Input Parameters .................................................................................... 240

8.2.7 Determination of Appropriate Input Flux ........................................................ 243

8.2.7.1 Evaporation .............................................................................................. 243

8.2.7.2 Desert and Low Water Use Landscaping ................................................ 248

8.2.7.2.1 Irrigation Needs of Desert and Low Water Use Landscape ............ 248

8.2.7.2.2 Irrigation Systems ............................................................................ 248

8.2.7.2.3 Input Flux for Desert and Low Water Use Landscape .................... 249

8.2.7.2.4 Average Input Flux .......................................................................... 250

8.2.7.3 Turf Landscaping ..................................................................................... 251

8.2.7.3.1 Irrigation Needs of Grass ................................................................ 251

8.2.7.3.2 Irrigation Systems ............................................................................ 252

8.2.7.3.3 Typical Water Use on Turf Landscaping ......................................... 252

8.2.7.3.4 Flux Input for Turf Landscaping ....................................................... 252

8.2.7.3.5 Average Input Flux .......................................................................... 255

8.2.8 Output Presentation - Definitions ................................................................... 256

8.3 Convergence Studies ................................................................................................. 258

CHAPTER Page

xiv

8.4 Simplification of Flux ................................................................................................... 263

8.4.1 Potential Evaporation .................................................................................... 263

8.4.2 Precipitation and Irrigation ............................................................................. 267

8.4.2.1 1-D Desert Landscape ............................................................................. 267

8.4.2.2 1-D Turf Landscape ................................................................................. 271

8.4.2.3 2-D Analysis of Average Absorbed Flux in Turf Landscape .................... 275

8.4.3 Key Findings of Flux Simplification ................................................................ 279

8.5 Depth of Influence and Suction Variation with Depth ................................................. 280

8.5.1 Desert Landscape – Dry IC ........................................................................... 280

8.5.2 Desert Landscape – Wet IC .......................................................................... 284

8.5.3 Desert Landscape - Ponding near Structure ................................................. 286

8.5.4 Turf Landscape – Dry IC ............................................................................... 290

8.5.5 Turf Landscape – Wet IC ............................................................................... 296

8.5.6 Key Findings of 1D Analysis .......................................................................... 297

8.6 Edge moisture Variation Distance Degree of Saturation ............................................ 300

8.6.1 Desert Landscape .......................................................................................... 300

8.6.2 Turf Landscape .............................................................................................. 300

8.7 Conclusions and Recommendations .......................................................................... 304

9 FIELD EVIDENCE OF WETTING/DRYING INDUCED DAMAGE ...................................... 308

9.1 Depth of Wetting and Depth of Active Zone ............................................................... 308

9.2 Forensic Investigations ............................................................................................... 322

9.2.1 Type of Data Collected .................................................................................. 323

9.2.2 Sources of Suction Change Related Distress ............................................... 324

9.2.3 Degree of Saturation and Suction Conditions below Foundations ................ 333

9.2.4 Comparison of Landscape Type to Distress Magnitude ................................ 337

9.2.5 Relative Slab Differential Data ....................................................................... 338

9.3 Comparison of forensic Investigation Incidence to Soil Properties ............................ 341

CHAPTER Page

xv

9.4 Key Findings ............................................................................................................... 341

10 CONCLUSIONS AND RECOMMENDATIONS ................................................................... 344

10.1 Scope of Research Work ............................................................................................ 344

10.2 Conclusions ................................................................................................................ 347

10.3 Future Research ......................................................................................................... 351

REFERENCES ............................................................................................................................. 353

APPENDIX

A HISTORY OF PTI GEOTECHNICAL PROCEDURE DEVELOPMENT ............................... 365

B LABORATORY DATA .......................................................................................................... 379

C DETERMINATION OF SWCC USING ONE POINT SUCTION MEASUREMENT

AND STANDARD CURVES ................................................................................................ 471

D PRESENTATION OF MODELING RESULTS ..................................................................... 488

LIST OF TABLES

xvi

Table Page

2.1. Angular Distortion Criteria Based on Design Manuals (summarized in Advanced

Foundation Repair, 2007). ...........................................................................................41

2.2. Newly constructed slab deviation from horizontal and angular distortion. ..................42

2.3. Mineral clay properties (after Woodward-Clyde and Associates, 1967). ....................53

2.4. Relation between swelling potential and PI (from Holtz and Gibbs, 1956). ................56

2.5. Expansive Soil Classification based on Atterberg Limits (Snethen et al.1977). .........56

2.6. Relationship between shrinkage and swell potential (after Altmeyer, 1955). .............58

2.7. Soil classification based on suction compression index (after McKeen, 2001). .........60

2.8. Classification of swell potential significance (after U.S. Bureau of Reclamation,

1974; surcharge of 6.9 kPa; Holtz et al., 1981). ..........................................................63

2.9. Classification of swell potential as per U.S. ASTM Standard D 4829-03 for

Expansion Index. .........................................................................................................63

2.10. Proposed empirical and theoretical equations of SWCC. ...........................................70

2.11. Proposed equations of unsaturated soil permeability as a function of suction (from

Fredlund, 1993). ..........................................................................................................75

3.1. Description of distress per Damage Category in AS2870. ........................................109

3.2. Description of distress per Damage Category in AS2870. ........................................109

3.3. Residential construction performance criteria in the first 2 years after homeowner

occupancy (AROC, 2004). ........................................................................................125

4.1. Main Equipment used for Field Sampling and Coring (after Perera, 2003). .............128

4.2. Classification of Potential Expansion based on EI (ASTM D 4829). .........................134

4.3. RH and suction per saturated salt solutions at 20°C (based on Dean, 1999). .........153

4.4. Locations of Soil Sampling. .......................................................................................154

4.5. Summary Table .........................................................................................................156

4.7. Average soil values. ..................................................................................................162

5.1. Classification of Potential Expansion (EIAZ) based on wPI. ......................................167

Table Page

xvii

6.1. Soil Index Properties Used in VOLFLO Input for Representative Soils ....................185

6.2. Design Parameters for Representative Soils ............................................................185

6.3. Design Parameters for All Soils from Chapter 4. ......................................................186

6.4. Design Parameters for Sensitivity Study. ..................................................................187

6.5. PTI 3rd 191 Edition Calculations for Example Profile for Various γh Methods ..................

7.1. Literature Review of Implemented Modeling Controls. .............................................196

7.2. Summary Table of Convergence Results .................................................................208

7.3. SWCC parameters ....................................................................................................212

7.4. Summary of Modeled Scenarios ...............................................................................214

7.5. Summary of numerical experiments, dx and dt. ........................................................227

8.1. List of Performed Analyses. ......................................................................................232

8.2. Soil Properties. ..........................................................................................................243

8.3. Potential evaporation rate for Phoenix area, Arizona (from ADWR, NOAA and

AMN 2006) and potential evapotranspiration rates for Bermuda turf landscape,

Cave Creek, Arizona (UA, from Dep. of Agriculture, 2000). .....................................246

8.4. Landscape coefficients (from Dep. of Agriculture, 2005). .........................................247

8.5. Gallons of Water needed to Wet Root Zone per Irrigation Event (from City of

Mesa, Department of Water Use, 2005). ..................................................................248

8.6. Average precipitation data from Phoenix Airport metrological station (from NCDC).249

8.7. Recommended irrigation pattern for warm season Bermuda grass (from City of

Mesa, Department of Water Use, 2005). ..................................................................251

8.8. Amount of irrigation and potential evapotranspiration used in modeling of turf

landscape. .................................................................................................................254

8.9. Average Input Flux for 2-D Analysis of CH Soil. .......................................................255

8.10. Definitions of Input and Output Quantities. ...............................................................256

8.11. Mesh spacing, time step and run times for SM-ML analyses. ..................................262

8.12. Mesh spacing, time step and run times for CH analyses. .........................................262

Table Page

xviii

8.13. HF to AF ratio of distance to 1000 kPa. ....................................................................278

8.14. Summary Table – Seasonal Depth of Influence; 1 Year Long Analysis. ..................297

8.15. Summary Table – Seasonal Surface Suction; 1 Year Long Analysis. ......................297

9.1. Saturation and Suction Variation with Depth for Undeveloped Desert. ....................320

9.2. Saturation and Suction Variation with Depth for Agricultural Land. ..........................321

9.3. Residential Construction Distress Count vs. Landscape Type (distress beyond

home owner responsibility defined by AROC). .........................................................338

9.4. Frequency of slab mode deformation occurrence and average relative slab

differential. .................................................................................................................340

9.5. Forensic investigation incidence vs. soil type. ..........................................................341

TABLE OF FIGURES

xix

Figure Page

2.1. Schematic of water front movement (after McWhorter and Nelson, 1979). ................17

2.2. Idealized water content profile (after Nelson et al., 2001). ..........................................18

2.3. Idealized suction profile of unsaturated soil (after Fredlund and Rahardjo, 1993). ....19

2.4. Slab movement, rainfall and site plan of experimental house at Vereeniging,

Transvaal Highveld (after Blight, 1965). ......................................................................25

2.5. Soil Moisture Profile for soil a) under cover and without cover, b) difference in soil

moisture profile between soil located below slab and outside of covered area (after

Tucker and Poor, 1978). ..............................................................................................26

2.6. Center lift and edge lift slab distortion due to seasonal moisture variation (after

PTI, 2004). ...................................................................................................................27

2.7. Measured vertical ground movement within soil profile of Regina clay,

Saskatchewan (after Hamilton, 1968). ........................................................................29

2.8. Typical maximum, minimum, and mean annual soil temperatures, 1959-1963 for a

typical soil cross-section in Winnipeg, Manitoba (after Hamilton, 1969). ....................31

2.9. Influence of evapotranspiration of trees on paved areas (after Snethen, 2001). ........34

2.10. Crack in residence wall due to vegetation (after Snethen, 2001). ..............................35

2.11. Sketch of crack and proximity of tree to the structure (after Snethen, 2001). .............35

2.12. Change in void ratio due to change in volumetric water content (after Nevels,

2001). ...................................................................................................................38

2.13. Effect of initial dry density on swell and shrinkage (after Chen, 1988). ......................38

2.14. Swelling and shrinkage behavior of expansive soils subject to repeated wetting

and drying (after Chen, 1988). ....................................................................................40

2.15. a) Bathtub effect of fill, b) Fat Clay cap and positive drainage to prevent the

bathtub effect of fill (SlabWorks, 2008). ......................................................................47

2.16. Typical perimeter subdrain (after Greenfield and Shen, 1992). ..................................49

Figure Page

xx

2.17. Relationship between repulsive forces of clay particles to half distance between

particles for montmorillonite (after Philip Low). Similar relationship was developed

by Warkentine et al., (1957) for swell pressure vs. half distance. ...............................51

2.18. Relationship between percentage of swell and percentage of clay (after Seed et

al., 1962). ...................................................................................................................52

2.19. Mineralogical classification (after Pearring, 1963). .....................................................54

2.20. Expansion potential based on cation exchange activity and soil activity (after

Nelson and Miller, 1992). ............................................................................................54

2.21. Mineralogical classification based on Atterberg Limits (Holtz and Kovacs, 1981). .....55

2.22. Soil swell potential in terms of activity and percent clay (Seed et al., 1962). .............57

2.23. Swell potential as a function of wPI (after Zapata et al., 2006). ..................................57

2.24. Expansive soil classification based on index soil properties (Holtz and Gibbs,

1956). ...................................................................................................................58

2.25. Soil characterization in terms of suction compression index (after McKeen, 2001). ..60

2.26. Suction compression index based on mineralogical classification of soil into six

types and soil index properties (after Covar and Lytton, 2001 and also PTI 3rd

Edition). ...................................................................................................................61

2.27. Typical Soil Water Characteristic Curve (after Fredlund and Rahardjo,1999). ...........70

2.28. Uncertainty Band of Fountain Hills, Arizona clay (Zapata, 1999). ..............................72

2.29. Ink bottle effect (after Miyazaki, 1993). .......................................................................73

2.30. Closed and open hysteresis loops developed for CH soil, Arizona. ...........................73

2.31. Typical unsaturated permeability variation with volumetric water content.

Comparison of empirical data to predicted values. (after Fredlund and Rahardjo,

1993). ...................................................................................................................76

2.32. Schematic of flow classification based on Reynolds number (after Tindall and

Kunkel, 1999). .............................................................................................................80

3.1. Matric suction at depth as a function of TMI and soil type (after Perera, 2003). ........95

Figure Page

xxi

3.2. Schematic of stem-and-footer. ..................................................................................100

3.3. Cross-section of footing in PT slab (after 3rd edition PTI, 2004). ..............................101

3.4. Schematic of ribbed PT slab (after 3rd edition PTI, 2004). ........................................101

3.5. Schematic of uniform thickness PT slab (PTI, 1998). ...............................................102

3.6. Schematic of uniform thickness PT slab (PTI, 1998). ...............................................102

3.7. Schematic of raft foundation footing. .........................................................................103

3.8. Schematic of raft foundation (AS2780, 1996). ..........................................................103

4.1. Consolidation test on a steel plug; dummy specimen. ..............................................136

4.2. Typical test results of constant volume oedometer test; correction to find swelling

pressure (after Fredlund and Rahardjo, 1993). .........................................................137

4.3. Fredlund SWCC cell schematic (after Perera, 2003). ...............................................139

4.4. Fredlund SWCC cell. .................................................................................................140

4.5. Fredlund SWCC cell set-up (grooved platen not in the picture). ...............................141

4.6. Condensation on bottom plate inside of SWCC cell. ...............................................143

4.7. Condensation on brass ring inside SWCC cell. ........................................................143

4.8. Lateral soil shrinkage during SWCC testing. .............................................................144

4.9. Soil cracking during SWCC test. ...............................................................................145

4.10. Family of SWCC Curves for Plastic Soils Developed by Perera (Perera, 2003). .....146

4.11. Pressure plate and filter paper test results, SWCC estimate. ...................................149

4.12. Filter paper calibration curve. ....................................................................................152

4.13. Sampling Locations superimposed on NRCS swell potential map. ..........................155

5.1. Natural Resources Conservation Service (NRCS) Swell Potential Map. ..................164

5.2. ASTM D 4829 Expansion Index correlation with Arizona EI test (HBACA, 2006). ...166

5.3. Modified wPI vs. EIAZ relationship. ............................................................................167

5.4. Updated Swell Potential Map for Central Arizona, Phoenix Region in the Upper 5-

ft. .................................................................................................................169

Figure Page

xxii

5.5. Updated Swell Potential Map for Central Arizona, Phoenix Region in the Upper 5-

ft with few measured EIAZ data points. ......................................................................170

6.1. Edge Moisture Variation Distance as a Function of Thornthwaite Moisture Index

(after Wray, 1978). ....................................................................................................175

6.2. Variation of Soil Suction with Thornthwaite Moisture Index (PTI, 2004). ..................179

6.3. Edge Moisture Variation Selection Chart (PTI, 2004) ...............................................182

6.4. The ym sensitivity to LL. .............................................................................................188

6.5. The ym sensitivity to PL. ............................................................................................188

6.6. The ym sensitivity to % clay. ......................................................................................189



6.9. Sensitivity Analysis of Gravel Correction Factor. ......................................................192

7.1. Comparison of modeling results with different programs, Texas site, a) cumulative

AE and domain accumulation, b) relative errors (after Scanlon et al., 2002). ..........201

7.2. Unsaturated soil properties a) SWCC and b) k(h). ....................................................203

7.3. Convergence Study for Hydrus, a) suction profile b) instantaneous flux. .................204

7.4. Convergence Study for SVFlux, a) suction profile b) instantaneous flux. .................205

7.5. Convergence Study for Vadose/W, a) suction profile b) instantaneous flux. ............206

7.6. Examples of stability issues in various software a) suction oscillation with depth, b)

actual flux oscillation at soil surface, and c) suction with depth increased

monotonically to unreasonable values. .....................................................................207

7.7. Software comparison a) Suction profile, and b) Instantaneous flux. .........................209

7.8. Unsaturated soil properties; a) SWCC and b) Unsaturated soil permeability where

F1 is drying curve fitted though experimental data, F2 is wetting curve due to

backpressure saturation, and F3 is wetting curve due to ponding. ...........................212

Figure Page

xxiii

7.9. Influence of SWCC variation for the same k(h) obtained with F1 and p=12 and

irrigation of 0.001 m/h. a) pore water pressure variation with depth, b) degree of

saturation with depth and c) instantaneous actual flux. ............................................215

7.10. Influence of k(h) variation coupled with appropriate SWCCs and irrigation of 0.001

m/h. a) pore water pressure variation with depth, b) degree of saturation with

depth and c) instantaneous actual flux. .....................................................................216

7.11. Influence of k(h) variation coupled with appropriate SWCCs and PE of 0.0002 m/h.

m/h. a) pore water pressure variation with depth, b) degree of saturation with

depth and c) instantaneous actual flux. .....................................................................217

7.12. Input flux for numerical experiment. ..........................................................................224

7.13. Implemented node spacing. ......................................................................................225

7.14. Instantaneous flux and surface matric suction for adaptive and fixed dt

formulations. ..............................................................................................................226

8.1. Analysis results: a) Input Flux, b) Net fluxes, and c) Matric suction at selected

depths. .................................................................................................................236

8.2. Analysis Results - Instantaneous flux. ......................................................................237

8.3. Boundary condition of control volume. ......................................................................239

8.4. SWCC – CH soil. .......................................................................................................241

8.5. Unsaturated Soil Permeability – CH soil. ..................................................................241

8.6. SWCC – SM-ML soil (after Pereira at al., 2005). ......................................................242

8.7. Unsaturated Soil Permeability – SM-ML soil (after Pereira at al., 2005). .................242

8.8. Relationship between AE/PE to total suction for sand, silt and clay (after Wilson,

1997). .................................................................................................................245

8.9. PE for Phoenix area, Arizona (from ADWR, NOAA and AMN 2006) and PET rates

for tall, well watered grass and Bermuda turf landscapes, Cave Creek, Arizona

(from Dep. of Agriculture, 2000). ...............................................................................246

8.10. Suction as a function of RH and T. ...........................................................................247

Figure Page

xxiv

8.11. Desert Landscape Flux. ............................................................................................250

8.12. Turf Landscape Flux. .................................................................................................254

8.13. Turf landscape, average absorbed flux per year for CH soil. ....................................256

8.14. Convergence analysis, January, PE only, desert landscape, SM-ML. .....................260

8.15. Convergence analysis, January, precipitation, desert landscape, SM-ML. ..............260

8.16. Convergence analysis, end of January, desert landscape, SM-ML. .........................261

8.17. Components of PE for PE flux simplification analysis. ..............................................264

8.18. Instantaneous and net AE for PE averaging analysis; CH soil. ................................265

8.19. Suction at depth vs. time for PE averaging analysis; CH soil. ..................................266

8.20. Suction profile at the end of the PE flux averaging analysis; CH soil. ......................266

8.21. Suction at depth vs. time for desert landscape analysis, a) CH, b) SM-ML. .............268

8.22. Suction profile at the end of analysis for desert landscape analysis, a) CH, b) SM-

ML. .................................................................................................................269

8.23. Instantaneous and cumulative flux for desert landscape analysis, a) CH, b) SM-

ML. .................................................................................................................270

8.24. Suction at depth vs. time for turf landscape analysis; a)CH, and b) SM-ML. ...........272

8.25. Suction profile at the end of analysis for turf landscape analysis; a) CH, and b)

SM-ML. .................................................................................................................273

8.26. Instantaneous and cumulative flux for turf landscape analysis; a) CH, and b) SM-

ML. .................................................................................................................274

8.27. Instantaneous flux and domain accumulation for 2D turf landscape analysis with

HF and average absorbed flux obtained from 1D analysis. ......................................276

8.28. Variation of matric suction at the soil surface with time for 2D turf landscape

analysis; a) HF, and b) average absorbed flux from 1D analysis. ............................277

8.29. Variation of suction with depth and time below the edge of the slab-on-grade for

2D turf landscape analysis; a) HF, and b) average absorbed flux from 1D analysis. 278

Figure Page

xxv

8.30. Comparison of distance of influence to 1000kPa obtained with HF and average

absorbed flux obtained from 1D analysis. .................................................................279

8.31. Suction variation with depth and time, a) CH, b) SM-ML. .........................................281

8.32. Net flux per year for CH and SM-ML soils. ................................................................282

8.33. Progression of wetting and drying fronts. ..................................................................282

8.34. Profile at wettest and driest conditions in year 6, a) CH, b) SM-ML. ........................283

8.35. Progression of wetting front for CH soil due to rainfall. .............................................284

8.36. Suction variation with time and depth for CH soil, desert landscape with moist IC. .285

8.37. Profile at wettest and driest conditions for CH soil, desert landscape with moist IC. 285

8.38. Suction variation with time and depth for CH soil zoomed in on precipitation in

December, desert landscape with moist IC. ..............................................................286

8.39. Suction variation with depth and time, a) CH, b) SM-ML. .........................................288

8.40. Profile at wettest and driest conditions, a) CH, b) SM-ML. .......................................289

8.41. SM-ML soil, plum like distribution of moisture with depth and time to maximum

depth of 1.8 m in November. .....................................................................................290

8.42. Suction variation with depth and time for CH soil, a) surface detail in 3-D , b) 2-D

plot. .................................................................................................................291

8.43. Suction variation with depth and time for SM-ML. .....................................................292

8.44. Depth of Influence for CH and SM-ML Soils. ............................................................292

8.45. Depth of influence due to irrigation a) CH (year 1), b) SM-ML (year 1). ...................293

8.46. Profile at wettest and driest conditions, a) CH (year 6), b) SM-ML (year 1). ............294

8.47. Profile at wettest and driest conditions, a) CH, b) SM-ML. .......................................295

8.48. Depth of influence due to irrigation for CH soil and moist IC. ...................................296

8.49. Monotonic Progression of Wetting Front. ..................................................................298

8.50: Suction variation at the soil surface for CH soil and desert landscape .....................300

8.51. Suction variation at the soil surface for CH soil, 2D turf landscape, average flux

analysis. .................................................................................................................301

Figure Page

xxvi

8.52. Depth of influence: horizontal inwards the slab, vertical below the edge of slab and

vertical 1-m away from the edge at landscaped conditions; 2D turf landscape,

average flux analysis. ................................................................................................302

8.53. Distance of lateral moisture migration through soil below a slab. .............................303

8.54. Suction variation at the soil surface for CH soil, 2D turf landscape, average flux

analysis. .................................................................................................................303

9.1. SWCCs and Equilibrium Conditions below Residential Foundation for Site #4;

Insitu, Undisturbed Soil Testing; Equilibrium Suction Identification Curve. ..............310

9.2. SWCC dependence on dry density; Reconstructed Soil Testing on CL with LL=29,

PI=12, and P200=63%. ...............................................................................................310

9.3. Suction Range of the Suction Identification Curve. ...................................................311

9.4. CH soil – Identification of Equilibrium Suction ...........................................................313

9.5. SM soil – Identification of Equilibrium Suction ..........................................................314

9.6. CL soil – Identification of Equilibrium Suction ...........................................................316

9.7. SC soil – Identification of Equilibrium Suction ...........................................................318

9.8. Sources of structure distress – a) courtyard and b) concentrated roof runoff. ..........325

9.9. Sources of structure distress – a corner the house creates with garage where

positive drainage away from structure is hard to maintain. .......................................326

9.10. Sources of structure distress – poor drainage, utilities in side yard, vegetation in

side yard, gutter discharge into side yard. ................................................................326

9.11. Sources of structure distress – AC condensation discharge next to foundation. ......327

9.12. Sources of structure distress – soil erosion due to roof runoff. .................................328

9.13. Sources of structure distress – soil erosion/undermining of low density soil below

homeowner installed flatwork ....................................................................................329

9.14. Sources of structure distress – poor drainage. .........................................................330

9.15. Sources of structure distress – poor drainage (positive slope), AC condensation

discharge next to foundation, turf landscape adjacent to foundation. .......................330

Figure Page

xxvii

9.16. Sources of structure distress – homeowner modified drainage and grading,

sidewalk blocks drainage, AC condensation discharge next to foundation. .............331


sidewalk/pool blocks drainage, vegetation next to foundation. .................................331


vegetable garden is a source of water. .....................................................................332


decorative boarder blocks drainage, sprinkler discharge next to foundation. ...........332

9.20. Sources of structure distress – area of potential water ponding, sprinkler discharge

next to foundation. .....................................................................................................333

9.21. Degree of saturation below residential foundations at depth between 3’-5’. ............334

9.22. Measured saturation and suction variation below slab-on-grade for a) turf

landscape, b) desert landscape, c) mixed landscape or desert landscape with

areas of potential ponding. ........................................................................................336

9.23. Equilibrium Suction below foundation. ......................................................................337

9.24. Potential Slab Shapes. ..............................................................................................339

xxviii

NOMENCLATURE Ac = Activity ratio,

AE = Actual soil evaporation mmday

,

= af

av

Fredlund and Xing SWCC fitting parameters,

= Coefficient of compressibility 2m

N

,

= bf

Ca


= ++ Calcium,

CEAc = Cation Exchange Activity,

CEC = Cation Exchange Capacity,

= cf

Ch


= Suction compression index,

= C(h) Adjustment factor which forces the SWCC through zero water content at a

suction of 106

Cs

kPa,

= Compression rebound curve

Cv = Volumetric specific heat [J/(m3

Cv

*°C)]

= Coefficient of consolidation

2cms

,

Cw = Climatic rating,

Dmy = Vapor diffusion coefficient [m3

Dv

*s/kg],

= Diffusion coefficient of water vapor through soil [kg*m/(kN*s)],

Dvap = Molecular diffusivity of water vapor in air [m2

em

/s].

= Center lift edge moisture variation distance,

e = Void ratio or

e1

exponent,

= Void ratio from the consolidation curve; the first point considered for the

calculation,

xxix

e2 = Void ratio from the consolidation curve; the second point considered for the

calculation,

EI = Expansion Index,

EIAZ = Expansion Index modified (Arizona),

em = Moisture variation distance,

F = Percent of soil passing US sieve number 200,

FF = Floor flatness,

Ff = Soil fabric factor,

FL = Local levelness,

g = Constant of gravitational acceleration29.81 m

s

.

Gs(coarse) = Specific gravity of solids,

h = u/ρ

H

g+y, total head equal to pressure plus elevation heads [m],

= + Hydrogen,

H0 = Initial height of soil specimen [in],

H2 = dr Average height of the specimen when the pressure is increased from σ1' to σ2

' ;

The value is divided by two for double drainage test [cm2

hr

],

= Total suction corresponding to the residual water content, θr [kPa],

= hr

Hs


= Depth to constant suction,

∆H = Change in height of soil specimen [in],

Δh = Height of water in a tube [m],

Change in total suction [pF],

∆H/L =

Ip

Hydraulic gradient

= Instability index,

Ipt = Instability index,

J = In PTI procedure, % of soil by weight greater than US sieve #10,

xxx

k, ks, ksat = Saturated soil permeability [m/s],

K = Absolute temperature [K],

= k(ψ) Unsaturated soil permeability [m/h],

k(h) = Unsaturated soil permeability [m/h],

k(ψ = )y Unsaturated soil permeability [m/h],

K = + Potassium,

K2SO4 = Potassium sulfate,

KCl = Potassium chloride,

kunsat = Unsaturated hydraulic conductivity,

Lv = Latent heat of vaporization for water [J/kg],

m = Fitting parameter in van Genuchten permeability equation.

m2w = 0/ ≥∂∂ uθ

Mg

, slope of SWCC in Fredlund and Sing equation,

= ++ Magnesium,

= ms Mass of dried soil [g],

= mw

n

Mass of water [g],

= Porosity,

Fitting parameter in van Genuchten permeability equation.

Na = + Sodium,

NaCl =

NH4

Sodium chloride,

= + Ammonium,

P200 = Percent passing US sieve number 200,

PE = Potential evaporation mmday

,

PIe = Effective plasticity index of the soil,

R = Universal molar gas constant 8.314 Jmole K

°

,

RH = Relative humidity [%],

xxxi

S = Source or sink in Richards’ equation [m/h],

Degree of soil saturation [%],

Slope of the total suction in pF,

t = Time [h],

T = Time factor [T90 = 0.848],

Absolute temperature [K]

TMI = Thornthwaite Moisture Index,

t90 = The time it takes to reach 90% of primary consolidation due to applied load; the

value is used when Taylor method is applied [s],

Δu = Change in total suction,

ua = Pore air pressure [kPa],

Pore air pressure [101.3 kPa],

ua – uw = Matric suction [kPa],

(ua – uw)b = Matric suction at air entry value [kPa],

uv = uvsRH, partial pore pressure due to water vapor [kPa],

uw = Pore water pressure [kPa],

uv = Partial pressure of pore water vapor [kPa],

uvs = Saturation pressure of water vapor over a flat surface of pure water at the same

temperature [kPa],

= V Total volume [ft3

Vw

].

= Specific volume of water

kgm

w

3

001.0,1ρ

,

Domain Volume of Water;The volume of water retained in the entire domain at

specified time. The output quantity is given per 1 m2 surface area.

xxxii

∆Vw = Domain Accumulation; The volume of water absorbed in or lost from the domain

within analyzed time period calculated as the difference between the final and

initial volume of water in the profile. The output quantity is given per 1 m2

surface area.

= w Gravimetric water content [%],

= w opt Optimum water content [%],

= wPI Weighted plasticity Index,

Wv = Molecular mass of water vapor

kmolkg016.18 ,

Δ = Change in quantity,

y = Elevation [m],

ym = Differential center lift movement,

Differential soil movement,

Differential swell,

ys = Differential soil movement

Zs = Active zone depth,

α = Tortuosity factor of soil,

Diffusion coefficient,

α'swell/shrink = Modified unsaturated diffusion coefficient,

α'weighted = Weighted modified soil diffusion coefficient,

β = Crossectional area of soil available for vapor flow,

λ = Thermal conductivity [W/(m*°C)],

Pore size distribution index, dimensionless,

σ = surface tension for air water interface [0.0073 N/m];

σ' = Effective stress applied to the sample [kPa],

σ1’ = Effective consolidation stress from the consolidation curve; the first point

considered for the calculation,

xxxiii

σ2’ = Effective consolidation stress from the consolidation curve; the second point

considered for the calculation,

Φ = Large relaxation constant

γw = Unit weight of water [9.81 kN/m3]

= γd Dry unit weight of soil [kN/m3]

= γd max

γh

Maximum unit weight [pcf]

= Suction Compression Index

γh swell = Swell suction compression index during swell.

γmod = Modified suction compression index

γo = Suction compression index for 100% clay

γt(wet) = Moist unit weight of soil

θ = Volumetric water content

θr = Residual volumetric water content, dimensionless,

θs = Saturated volumetric water content or porosity of the soil;

= θv Volumetric water content,

= ρd

ρw

Dry density [pcf]

= Density of water

ψ = Matric suction [kPa],

Total soil suction in the soil [kPa]

ψ T = Total suction [kPa]

% = percent

%fc = percent fine clay

Θ =

θ −θr

θs −θr

µm

, normalized water content, dimensionless,

= micro meter

1 INTRODUCTION

1.1 Overview

Problems associated with expansive soils are not widely appreciated outside the areas

of their occurrence. The amount of damage caused by expansive soils has been estimated to

exceed fifteen billion dollars annually. In years of extreme temperatures or rainfall the damage is

most severe (Wray and Meyer, 2004). The structures commonly affected by expansive soils are

residential structures, roads, irrigation canals and spillways. This report deals exclusively with

the moisture flow through expansive soils in semi-arid regions in the context of slab-on-grade

performance; however the theories presented and applications can be extended to other

engineering structures, and other environmental conditions.

Through observation and research, it was well established that the damage to structures

built on expansive soils is mainly caused by change in soil suction (water content) of soil that has

shrink/swell potential. The potential change in water content is generally attributed to the

environmental conditions, change in depth of water table, water uptake by vegetation, removal of

vegetation or excessive irrigation of landscape. Due to those factors, slab-on-grade foundations

must resist two types of expansive soil movement: short-term cyclic heave/shrinkage around the

perimeter of the foundation and long-term progressive volume change beneath the center of the

slab (Day, 1994). The slab can display three types of deformation, tilt, edge lift and edge drop.

In the first scenario, one edge of the slab is higher relative to the opposite edge with a smooth

transition between. Tilt is commonly observed in very stiff foundations where the soils below one

side of the property heaved or shrank. In edge drop deformation, the edges of the foundation

are lower relative to the center. Edge drop can be caused by number of mechanisms which are

hard to identify without benchmarked surveys before and after movement; they include

settlement, compression or shrinkage below the foundation perimeter or heave below the center

of the foundation. Based on literature review, heave below the foundation might be caused by

monotonic moisture migration or a pipe leak. Soil swell around the slab perimeter is commonly

manifested by raised edges of the slab and is described as the edge lift condition.

2

Residential foundations are typically constructed on unsaturated soils; therefore the

implementation of unsaturated soils mechanics into the slab-on-grade design is highly

appropriate. Although the theory for the analysis of geotechnical problems involving unsaturated

soils has been developed and has been known for the last four decades, and despite the well-

recognized importance of suction, unsaturated soil mechanics is not widely implemented by

practicing engineers. An investigation of practice throughout the Unites States showed that less

than 20% of commercial geotechnical laboratories performed suction measurements on a

regular basis (Zapata, 1999). This fact is attributed to several factors such as: 1) laboratory and

field testing of unsaturated soils is perceived as costly, time consuming, and difficult to conduct,

2) large uncertainty associated with the direct measurement and/or prediction of the unsaturated

soil properties (Zapata, 1999), 3) from a mathematical perspective the numerical solution of

Richards’ equation, which describes the unsaturated moisture flow through soil is a very

challenging problem characterized by stability and convergence difficulties, 4) numerical

modeling of moisture flow through unsaturated soil with any of the available public domain or

commercial software is non-trivial, and 5) the numerical solution may take a long time and

requires the use of fast computers.

Due to the above-mentioned difficulties, the Arizona Homebuilder’s Association of

Central Arizona (HBACA) sponsored a research program on expansive soils to 1) identify the

depth and magnitude of wetting below residential foundations and under free field conditions, 2)

identify factors associated with residential construction distress, and 3) assess foundation

performance under various landscape schemes. A number of steps were taken towards the goal

of developing a better understanding of expansive soils behavior and field conditions leading to

problems with expansive soils. These steps included: 1) numerical modeling of moisture flow

through expansive soils in one- and two-dimensions. Two extreme surface flux conditions were

considered, desert and excessively irrigated turf landscapes. The numerical results are

applicable to regions with low to moderate expansion potential and Phoenix, Arizona

environmental conditions; 2) development of map illustration identifying location with low to

3

medium swell potential in the Phoenix Valley; 3) comparisons of the numerical results to field

evidence on depth of wetting and depth of active zone, as well as to foundation field

performance; 4) evaluation of stability, convergence and numerical challenges for modeling of

unsaturated moisture flow through expansive soils using Richards’ equation. Sources of those

instabilities were identified and potential numerical improvements discussed; 5) survey of

Arizona region practitioners to identify current design and construction practices, and 6)

statistical analysis of forensic investigations to identify the nature and common causes of

residential distress.

1.2 Historical Background

The estimation of moisture flow through unsaturated soil for geotechnical engineering

applications is a multifaceted problem involving a combination of empiricism and unsaturated soil

mechanics theory. Due to the complexity of the problem and difficulties associated with the

implementation, the industry has adopted a semi-empirical approach to the design and mitigation

of foundations on expansive soils for residential dwellings. Many of these methodologies have

been developed based on regional environmental conditions and therefore are applicable only to

those specific regions of the world. Difficulties frequently arise when local experience is applied

to different environmental conditions and soil properties. The literature review presented

summarizes empirical findings relative to the moisture flow through unsaturated soil and the

observed impact on lightly loaded structures.

Two types of slab systems are commonly used in residential construction, conventional

stem-and-footer (with un-reinforced or lightly reinforced slab) and post-tensioned slabs. The

design methodologies, in large part, are based on the anticipated post-construction change in

the depth of wetting and degree of saturation. It is assumed that the soil suction of the

undeveloped site comes to equilibrium with the existing environmental conditions at depth

unaffected by seasonal climate variation. Thus the soil suction is referred to as the equilibrium.

Based on literature findings, the active zone depth was estimated to vary between 1.2 m to 12 m

4

(4 feet to 39 feet), depending on the definition of the term and environmental conditions of test

region (McKeen, 1980, 1981, 1985; O’Neill and Poormoayed, 1980; Thompson, 1992;

Thompson and McKeen, 1995; Wray, 1989, 1997; Durkee, 2000, Chao et al., 2006).

An introduction of an impermeable cover at the soil surface, such as a slab-on-grade or

a pavement, results in elimination of precipitation and reduction in potential evaporation (Day,

1994). Also, it is common for conditions in landscaped areas to change relative to pre-developed

conditions. With time the suction within the soil profile comes to an equilibrium with the new

environmental conditions. It is sometimes postulated that the suction below the slab is constant

with depth and equal to the initial equilibrium suction (Nelson et al., 2001). Based on empirical

evidence, the process of monotonic moisture migration due to capillary forces, moisture

condensation below the slab and temperature gradients (Chen, 1988) occurs up to six years

(Donaldson, 1965). Furthermore, it was observed that the 6-10 year long equilibration process is

followed by a uniform relative reduction in heave (Donaldson, 1965), which might be related to

fatigue of swelling. Fatigue of swelling refers to a decrease in a soil’s swelling potential as the

drying-wetting cycles repeat. Chen (1988) illustrated that swell levels off at the fifth cycle when

“relative equilibrium” is reached.

A long-term study of slab-on-grade behavior by Wray (1992) illustrated that short-term

post-construction slab movement in arid regions is attributed to seasonal climate variation

resulting in edge lift slab distortion. Continued monitoring revealed slow but increasing mound in

the center of the slab, indicating that subsequently center lift distortion might occur if soils are not

placed at the appropriate moisture content. On the other hand in humid regions, the short-term

edge lift slab distress is quickly replaced with a center lift scenario, which is likely to occur due to

edge drop (Wray, 1992).

An important parameter for slab design is the suction variation below the edges of the

slab due to environmental or human imposed conditions. It has been postulated that the suction

may vary 1) between liquid limit and shrinkage limit (conclusion based on measured gravimetric

water content data of SM and CL soils below 10 000 slab-on-grades in Houston and San

5

Antonio, Texas, (Stryron et al., 2001)), 2) between 98 kPa and 9 800 kPa (McKeen, 2001), and

3) between 33 kPa to 3 300kPa in terms of total suction (PTI, 2004).

The edge moisture variation distance, em, defined as the distance over “which moisture

will change due to wetting or drying influences around the perimeter of the foundation” (PTI,

2004), is difficult to measure experimentally. Few case studies include measured em values in

arid regions. The existing data shows that em varies between 1.75 m (study of bike trail by

Nevels, 2001) and more than 4.5 m (study of slab-on-grade where em exceeded half of the slab

width Durkee, 2000). The em might approach the active zone depth (McKeen et al., 1990),

although the PTI (2004) procedure limits the magnitude of em to 3 m (9 ft).

The slab-soil system performance is frequently evaluated in terms of slab relative

deflection, angular distortion, or overall magnitude and extent of superstructure distress. Based

on forensic engineering studies, cosmetic damage was correlated to 1.1-1.75” slab relative

deflection and 1/300 angular distortion. Structural damage was found to occur at relative

deflection larger than 3.5” and maximum angular distortion of 1/100 (Day, 1990, Skempton and

MacDonald (1956), Marsh and Thoeny (1999)). The study of as-built floor levelness, however,

suggests that these distress markers should be used with sound engineering judgement. Newly

constructed slabs were found to exhibit on average 0.5” relative slab deflection and average

angular distortion of 1/340. These values as-constructed values were found to be as large as

2.2” and 1/71 respectively, values corresponding to structural damage (Koenig, 1991, Marsh and

Thoeny, 1999, Walsh, et al., 2001, Noorany et al., 2005).

Mitigation measures are employed to minimize potential soil movement and

superstructure distress. They include 1) removal, replacement and recompaction, 2) chemical

stabilization 3) passive moisture control with moisture barriers and 4) active moisture control.

The economical feasibility of a mitigation measure depends on availability of material and

expertise of mitigation team, as well as the timing of identification of the problem. In Arizona,

active moisture control in the form of pad pre-wetting is the most commonly implemented

mitigation method. The effectiveness of these methods remains to be quantified.

6

The literature review consensus message is that the depth of moisture migration,

magnitude of suction variation with depth in open fields and below impermeable surfaces, the

distance of horizontal moisture migration below a slab, and soil-slab system behavior (with or

without mitigation measures) are highly dependent on 1) soil properties and 2) environmental

and human imposed conditions around the edges of the structure. Geotechnical engineers are

faced with the challenge of estimating design parameters for foundation system design

purposes. In general, design guidelines provide a cookie cutter methodology developed based

on a local experience in a geographic region, which may or may not be applicable to different

soil and climatic conditions. When limited empirical data is available, numerical modeling of

moisture flow through unsaturated soil can be performed to aid in selection of design

parameters.

Numerical analysis of moisture flow through unsaturated soil involves implementation of

unsaturated soil mechanics principles by solving Richards’ equation, a parabolic, stiff, advection-

diffusion partial differential equation derived from mass conservation. Stability, convergence and

time efficiency are problematic issues inherent to this class of problem. The currently

implemented standard approach to solving the PDE follows a “method of lines”, also referred to

as semi-discretization, where spatial derivatives are first approximated using a variety of (usually

low order) finite difference or finite element schemes, and the resulting discrete system of

ordinary differential equations (which also accounts for boundary conditions) is then solved using

a time integrator. Three commonly used numerical software were reviewed: SVFlux, Vadose/W

and Hydrus. It was concluded that numerical modeling of moisture flow through unsaturated soil

is a very challenging and time consuming task, but it is helpful in identification of general

moisture migration trends due to various soil and flux conditions.

1.3 Research Objective and Scope

The main objectives of this study on expansive soils include 1) identification of the depth

and magnitude of wetting below residential foundations and under free field conditions, 2)

7

identification of local practice, 3) identification of factors associated with residential construction

distress and 4) assessment of foundation performance under various landscape schemes. The

study resulted in the following research contributions:

1. Identification of challenges in numerical modeling of surface flux and associated

infiltration into unsaturated soils in arid regions.

2. Numerical modeling of infiltration into expansive soils for various landscape and surface

water control schemes.

3. Surveys of practitioners to assess Phoenix region practices used in the design of

residential foundation systems on expansive soils.

4. Development of an updated map of expansive soils distribution in the Phoenix region,

commonly used by practitioners to assess soil properties in the preliminary analysis.

5. Evaluation of the PTI procedure for slab-on-grade foundations, for Arizona soils and

climatic conditions, the predominant methodology for current practice in Arizona.

6. Study of the suction profiles beneath slabs for equilibrium conditions, using direct

suction determination and SWCC correlations.

7. Surveys of Phoenix area geotechnical firms to identify areas in the Phoenix Valley were

forensic investigations thought to be linked to the presence of expansive soils have been

conducted. This data was reviewed for determination of trends and soil expansion

potential, as well as site landscape and draining conditions.

8. Assessment of numerical modeling results through comparison for consistency with

forensic study findings and field data on depth and degree of saturation (suction).

1.4 Research Methodology

The research methodology can be divided into four major parts 1) laboratory testing, 2)

numerical modeling, 3) data collection and 4) development of maps. Soil profiles from beneath

sixteen (16) slabs were obtained for identification of soil index properties, variation of saturation

and measured suction with depth. The selected sites were located in expansive soil regions in

8

the Phoenix metropolitan area as identified from the NRCS soil map (www.nrcs.usda.gov). The

results obtained were used for 1) identification of input properties for modeling (soil properties

and initial suction conditions), 2) identification of input properties for the PTI procedure to

determine the range of potential results for Arizona soil and climatic conditions and 3)

identification of suctions below foundations.

The first research objective, identification of the depth and magnitude of wetting below

residential foundations and under free field conditions, and the fourth objective, assessment of

foundation performance under various landscape schemes were satisfied, in part, through

numerical modeling. A finite element program, SVFlux 5.80, was selected to model 1D and 2D

moisture flow through two uniform unsaturated soil types, fat clay (PI=53) and silt (PI=12).

Modeling was carried out to determine the degree of saturation, the horizontal and the vertical

distance of moisture penetration under the slab using typical Arizona environmental and human

imposed flux boundary conditions. The first flux scenario considered represents desert or low

water use landscape. In this case, the irrigation was assumed to be negligible. The appropriate

precipitation input was determined by performing statistical analysis of 24 years of precipitation

data obtained from NCDC (www.ncdc.noaa.gov). It was found that average annual rainfall of 8

inches is typical for Arizona climatic conditions. Similarly, the potential evaporation of 91 inches

per year was obtained from 1) US Weather Service, Arizona Department of Water Resources, 2)

NOAA, Western Regional Climate Center, and 3) Arizona Meteorological Network. The second

surface flux condition considered mimicked the typical watering pattern for turf landscaping,

where the irrigation and precipitation provide about 101 inches of water annually, while the

anticipated evapotraspiration is only about 46 inches annually (based on data published by

University of Arizona, Dep. of Agriculture (2000).

In order to satisfy the second objective, identification of local practice, numerous

geotechnical, structural and construction companies were interviewed. Additional firms were

solicited for geotechnical and forensic data. The geotechnical data of soil saturation and index

properties with depth were used to help complete the first objective. It was found that the

9

engineering community frequently uses the NRCS map in the preliminary assessment of soil

properties. As part of this study, an updated map, incorporating the geotechnical data obtained

in the survey was developed using ArcGIS.

The field data available from below foundations, free field undeveloped desert regions

and agricultural land were compared with the general conclusions drawn from numerical

modeling. Additionally, the forensic data of floor elevation differential, type and magnitude of

structure distress, and landscape and drainage were used together with numerical modeling to

satisfy objectives three and four, identification of factors associated with residential construction

distress and assessment of foundation performance under various landscape schemes.

1.5 Outline of Report

The first chapter is used as an introduction and for organizational purposes. Objectives

and methodologies are addressed. The main focus of Chapter 2 is literature review. The

literature review includes a wide range of topics, whose understanding was necessary for the

completion of the research objectives. It includes 1) factors affecting swell and moisture

migration; 2) field observations of moisture flow and heave; 3) the soil response to changes in

suction followed by 4) relative slab deviation from horizontal of newly constructed slab

suggesting that the magnitude of structure distress cannot be identified from floor level survey

alone, since the initial construction conditions are unknown; 5) commonly implemented

mitigation measures; 6) classification of swell potential based on soil index properties. The

presented ideas were used in the development of the PTI procedure. Also one of the

correlations developed was used in updating the NRCS swell potential map; 7) introduction to

unsaturated soil mechanics theory; 8) methods of matric suction measurement, and 9) numerical

methods and available commercial software used in the solution of Richards’ equation.

The focus of Chapter 3 is residential construction failure criteria and current practice

identified through survey of Phoenix, Arizona area geotechnical, structural and construction

professionals located in Phoenix, Arizona. A brief overview of design methodologies

10

implemented in the USA and other countries is given. Based on the interviews, the Post-

Tensioning Institute (PTI) slab-on-grade design procedure was identified as the most commonly

implemented methodology in Arizona for the design and construction of residential slab-on-grade

on expansive soils.

The soil profiles analysed are presented in Chapter 4, laboratory testing. The laboratory

testing involved the collection of sixteen (16) soil profiles from below existing slabs-on-grade.

The soils were tested for index properties, swell potential, saturated soil permeability and matric

suction. The body of the Chapter 4 gives detailed descriptions of soil testing performed and a

data summary. The detailed laboratory results are illustrated in Appendix B.

The interviews with industry revealed the significance on the Natural Resource

Conservation Service, NRCS, swell potential map in the preliminary identification of soil

properties. In Chapter 5 this map was updated using soil data supplied by practitioners and

correlations developed in this study.

Also, based on the interviews with industry, it was identified that the 3rd edition PTI

procedure is the most commonly implemented methodology for design and construction of

residential slab-on-grade on expansive soil. Chapter 6 describes this methodology in great

detail, along with presentation of a sensitivity analysis and a discussion of design values for

Arizona soil and climatic conditions.

Chapter 7 discusses numerical challenges associated with the solution of Richards’

equation. From a mathematical perspective, Richards’ equation is an advection-diffusion partial

differential equation (PDE) with stiff and parabolic characteristics. Equations in this class exhibit

stability and convergence challenges, whose solution require specially developed stiff numerical

solvers. This chapter discusses proper modeling techniques that a user of developed

commercial or public domain software should implement. The chapter concludes with future

research for implementation of more advanced solution methodologies developed by the

mathematical community.

11

Modeling results for infiltration into expansive soils for various landscape and surface

water control schemes are presented in Chapter 8. Two soil types were analysed, CH and SM-

ML representing the range of typical soils found in the Phoenix Valley region that might exhibit

shrink/swell. Results for 1-D and 2-D analysis are discussed, while details are presented in

Appendix D.

The focus of Chapter 8 is the presentation and the analysis of field and forensic data.

The field evidence on depth of wetting and active zone depth is provided, where the degree of

saturation with depth versus undeveloped desert and previously agricultural land is given. The

moisture/suction conditions below foundations, correlation of distress magnitude to landscape

type, drainage and grading, analysis of differential slab differential and identification of factors

contributing to residential construction distress are also discussed. Finally, the locations of

forensic investigations were mapped and compared to the updated NRCS map, and the

correlation between soil properties and forensic investigation incidence identified. Conclusions,

recommendation, summary of findings, and future research are given in Chapter 10.

1.6 Key Findings

The following key findings were identified from this research study:

1. Richards’ equation is a stiff parabolic PDE whose solution requires the implementation

of a stiff, implicit numerical solver. Methods typically implemented in software exhibit

instabilities suggesting an implementation of pseudo-implicit solver. The instabilities are

usually overcome by reducing mesh spacing, time step or both.

2. The solution variability due to the uncertainty of the unsaturated soil properties is large

and potentially larger than the variability associated with different software selection.

3. Flux averaging can be successfully used in the analysis of moisture flow through soil

when flux is due to atmospheric conditions (no ponding), and when no runoff occurs. On

the other hand, if runoff takes place, the flux averaging (e.i. over the period of a month)

overestimates the depth of moisture influence and degree of saturation.

12

4. Desert landscape results in very shallow moisture migration soils common to the Arizona

region; 5-cm due to precipitation; 0.5-m seasonal suction variation.

5. Edge moisture variation distance obtained from numerical modeling was limited to 10 cm

under desert landscape conditions.

6. Turf landscape results in an increased wetting front (9-m after 34 years for CH soil and

7-m after 2 years for SM-ML soil) and very shallow depth of drying (2 cm). Short-term

seasonal suction variations of 0.5 m for SM-ML soil and 1-m from CH soil was observed

in the numerical analysis.

7. Edge moisture variation distance of 35 cm was observed for CH soil under turf

landscape conditions for the conditions considered in numerical modeling. Monotonic

moisture migration below the slab leveled off during 5th year at 2.2-m.

8. The critical scenarios with respect to foundation performance are 1) poor drainage

resulting in 100% soil saturation up to the depth of 1-m. 2) initial moist conditions with

desert landscape.

9. In general, the failure mode when comparing the 2nd Edition PTI procedure to 3rd

edition is from center lift to edge lift, and increase in slab thickness.

10. In PTI procedure appears to overestimate volume change in extremely wet and

extremely dry soil, but may give reasonable results in the intermediate range.

11. Suctions below foundations depend on landscape type. For turf landscape, the

equilibrium suctions reach an average of about 500 kPa based on field measurements.

Desert landscape leads to dry suction below the foundations with an average of 1500

kPa based on field data.

12. Problems associated with foundation performance are typically caused by improper

drainage and grading.

13. Based on field evidence, for native desert profiles the average degree of saturation for

SM, SC/CL, and CH is 30%, 40%, and 70% respectively; whereas for agricultural areas

it is about 40%, 50% and 80% respectively within the upper 20'.

2 LITERATURE REVIEW

2.1 Introduction

Moisture flow through unsaturated soil is an extremely complex phenomenon consisting

of fluid transport at micro-, meso-, and macroscales. The estimation of the phenomenon is

further complicated by heterogeneity of soil medium, nonlinear unsaturated soil properties and

volume change characteristics of moisture sensitive soils at various degrees of saturation.

Although the first physically based formulation was introduced almost 100 years ago by Green

and Ampt in 1911 followed by Richard’s continuity equation in 1931 the topic continues to be

researched by engineers, soil scientists, hydrologists and mathematicians. The current research

is focused on describing soil constitutive relationships, unsaturated soil properties, physical

components of the flow phenomenon, mathematical algorithms and numerical methods needed

to solve a form of Richard’s equation, a nonlinear, parabolic, partial differential equation to which

analytical solution does not exist.

Simplified solutions to estimate the extent and degree of wetting are typically proposed

by civil engineers with an eye on practical and economical approach for design of engineered

structures. Implementation of these methodologies is especially important in arid or semi-arid

regions and moisture sensitive soil sites, where the soil might experience shrinkage, expansion

or collapse. Volume change is a response of moisture sensitive soil to a transient wetting

process. It depends on soil properties, loading conditions imposed on the soil mass and flux

conditions at the soil surface. The potential change in water content is generally attributed to

environmental conditions, human imposed irrigation, influence of vegetation and accidental

wetting due to broken pipelines.

An inadequate estimation of moisture flow has two types of economical impacts. On

one hand, it cost more to build an over-designed structure and on the other hand it is expensive

and inconvenient to fix and upgrade inadequately performing an under-designed structure. The

amount of damage caused by expansive soils has been estimated to exceed two billion dollars

annually. In years of extreme temperatures or rainfall the damage estimate reaches seven

billion dollars per year (Chen, 1988). The structures commonly affected by expansive soils are

14

residential structures of conventional construction, and impervious surfaces such as roads, and

sidewalks.

The economical impact of moisture flow through unsaturated soil is the source of

continuous search for better understanding of the phenomenon and its implementation into

engineering practice. The literature review presented here consists of an up to date overview of

proposed scientific and practical methodologies to analyze the moisture flow through soil and

access its impact on performance of residential structures. It summarizes: 1) factors affecting

moisture migration, 2) field data of depth and degree of wetting 3) classification of swell potential

4) performance of residential structures on expansive soil 5) empirically based methodologies to

estimate moisture flow 6) unsaturated soil mechanics theory and finally 7) available and

implemented numerical methods that solve a form of Richard’s equation.

2.2 Factors Affecting Swell and Moisture Migration

In general, moisture migration studies perform a function either to estimate the

magnitude of soil volume change for construction purposes or to estimate contaminant transport

for remediation purposes. Since the focus of this research is on the performance of residential

structures, the presented literature review includes relevant discussions about volume change.

The estimate of heave depends on many factors, which are not easy to quantify. Most

importantly, the heave estimate is a function of moisture migration. The major factors affecting

moisture flow though unsaturated soil, as described by Chen (1988), are listed below. The

subsequent sections provide further details about moisture migration and heave.

1. Climate.

Climatic conditions such as precipitation, evaporation and transpiration influence the

moisture content of soil. The ratio of precipitation to potential evapotranspiration is

defined as Thornthwaite Moisture Index, TMI, (Thornthwaite, 1948). A relationship was

found between TMI and moisture content of soil under free field conditions suggesting

that volume change can be determined based on this parameter alone (Hamilton, 1969).

15

One dimensional vertical ground movement study done by Sattler (1990) indicates that if

a relationship between actual and potential evapotraspiration can be established, then a

simple TMI based model can be used to determine the volume change of open-field

soils.

2. Thickness of expansive strata.

In most cases, the thickness of the expansive soil stratum extends down to a great

depth. The practical thickness is governed by the surface water penetration into the

stratum. The depth of effective soil stratum is defined in Section 2.3.2.

3. Depth to water table.

The fluctuation of water table is also a factor contributing to magnitude of net swell.

When the water table drops and then subsequently rises, the flow of water doesn’t

always follow the previous moisture flow paths. New water flow paths can develop

leading to swelling in areas previously unaffected by volume change.

4. Nature and degree of desiccation of soil.

The swell potential of soil depends on the percent and type of clay mineral present in the

soil that in turn depends on the degree of desiccation of the parent rock. Additionally,

desiccation has an impact on preferential moisture flow characteristics.

5. Permeability

The permeability of soil determines the flow rate into the soil by either gravitational flow

or diffusion. The higher the permeability, the greater the depth to which moisture

penetrates.

6.

Extraneous influences are hard to predict. They include sudden rise of perched water

table, leak from broken pipe, and the influence of vegetation. Big trees have proven to

be very problematic during draught periods.

Extraneous influence.

16

2.3 Moisture Variation within Soil Profile

When designing slabs on expansive soils, the key concerns are the amount of soil that

can contribute to the movement of the slab, the vertical depth and horizontal distance to which

the water travels under the slab. The first and second concepts are generally referred to as the

“active zone” depth. The third concept is referred to as the edge moisture variation distance.

Literature review indicates that active zone depth and edge moisture variation distance are not

clearly defined and large differences in the proposed definitions exist. The text below provides a

summary of the proposed definitions.

2.3.1 Infiltration and Wetting Front

Depending on soil type, initial soil condition and the magnitude of water available to the

soil profile, the resulting moisture variation with depth due to influx of water, called wetting front,

can have one of two possible shapes 1) sharp transition from wet to dry regions or 2) smooth

transition with depth from moist state at the soil surface to initial soil saturation at depth

(Johnson, 2006). The first scenario is illustrated in Figure 2.1, wetting front due to water ponding

at the soil surface. Below the wetting front, the water content is the same as it was prior to the

introduction of the water source. Above the wetting front, the water content is higher, and the

soil may or may not be saturated depending on soil properties and magnitude of applied flux.

This wetting front will continue to move downward as long as the total head of the soil above the

wetting front is higher than that below the wetting front or until an impermeable boundary or

water table are encountered. For considerations of expansive soils, the movement of the wetting

front may be very slow, but even small increases in water content may cause significant

amounts of heave (Nelson et al., 2001). The second scenario is illustrated in Figure 2.3, where

the soil suction increases parabolically from saturated state at the soil surface to some

equilibrium suction at depth and then decreases to saturated state at the depth of ground water

table (Fredlund and Rahardjo, 1993).

17

Figure 2.1. Schematic of water front movement (after McWhorter and Nelson, 1979).

2.3.2 Soil Profile

Extensive research has been done in the area of moisture/suction variation in the soil

profile, where suction is defined as the soil affinity for water; see section 2.9.1 for more details

(Fredlund and Rahardjo, 1993). An idealized water content profile of uniform soil at an

undeveloped arid site is presented in Figure 2.2. For nonuniform soils the profile can be

normalized by plotting wPI

with depth instead of water content alone, where w is the gravimetric

water content (%) and PI is plasticity index (%) determined with ASTM D 4318 (PTI, 1996). This

figure indicates that below some depth, Ζσ, equilibrium water content exists. Above the depth Zs

the water content decreases or increases due to environmental conditions. Profile A represents

water content loss due to evapotranspiration in an open-field soil strata located in an arid

climate. The introduction of soil cover such as a pavement or slab-on-grade cuts off the surface

water losses and with time the water content profile comes to equilibrium with the water content

below depth Zs. Profile B shows equilibrium condition under such a slab that is big enough so

that the edge effects can be neglected. Profiles C and D show the typical moisture variation

below the edges of the slab during wet and dry seasons respectively (Nelson et al., 2001).

Different range estimates of potential soil moisture conditions at the soil surface below the edges

of covered areas have been proposed 1) between liquid limit and shrinkage limit (conclusion

18

based on measured gravimetric water content data of SM and CL soils below 10 000 slab-on-

grades in Houston and San Antonio, Texas, (Stryron et al., 2001)), 2) between 98 kPa and 9 800

kPa (McKeen, 2001) and 3) between 33 kPa to 3 300kPa in terms of total suction (PTI, 2004).

Figure 2.2. Idealized water content profile (after Nelson et al., 2001).

Similar findings were presented by Fredlund and Rahardjo (1993), who expressed the

effects of the environment on soil profile in terms of matric suction. Figure 2.3 shows an

idealized variation of matric suction within homogeneous, uncovered soil profile, which depends

on environmental conditions, imposed irrigation patterns, vegetation influence, the location of the

water table, and soil permeability. Environmental conditions refer to precipitation and

evapotranspiration rates. The lack of rainfall leads to a continuously increasing suction profile

from the water table to the soil surface. On the other hand, the abundance of precipitation

results in a profile where the matric suction increases from the soil surface to an equilibrium

value. Once the equilibrium value is reached the suction decreases to zero suction at the depth

of water table.

The depth of the water table generally affects the magnitude of the matric suction profile.

The deeper the water table is the greater the magnitude of matric suction at the surface for arid

climate. The rate of migration of water due to suction changes is controlled by soil permeability.

19

The permeability of an unsaturated soil varies widely with degree of saturation. This affects the

ability of the soil to change matric suction when environmental conditions change (Fredlund and

Rahardjo, 1993).

Figure 2.3. Idealized suction profile of unsaturated soil (after Fredlund and Rahardjo,

1993).

2.3.3 Definition of Active Zone Depth and Related Terms

One of the key concerns in the design of slabs on expansive soils is the thickness of soil

strata that can contribute to slab movement. While there is number of relevant definitions, this

concept is generally referred to as the “active zone” depth. Literature review indicates that active

zone depth is not clearly defined. In fact, it has taken on several different meanings based on

techniques used for approximating its value (Durkee, 2000). The diversity of this definition is

illustrated in the wide range of reported values of "active zone" depth ranging between 1.2 m to

12 m (4 feet to 39 feet) (McKeen, 1980, 1981,1985; O’Neill and Poormoayed, 1980; Thompson,

1992; Thompson and McKeen, 1995; Wray, 1989,1997; 1991; Durkee, 2000, Chao et al., 2006).

Here are some of the “active zone” depth definitions:

20

• “Active zone depth is the upper stratum of soil in which water content changes are the

greatest” (O’Neill and Poormoayed, 1980).

• Active zone depth is the “depth of water content increase" due to placement of the slab.

The definition was derived from measurement of heave and water content changes

beneath simulated slab foundations constructed on expansive soils where the

surrounding area was not altered (Goode 1982, and Hamberg, 1985).

• Active zone depth is the "zone of seasonal fluctuation”. It can be identified in the field by

the point where the water content distribution becomes constant with time (Nelson and

Miller, 1992).

• PTI differentiates between moisture active zone and movement active zone. The

moisture active zone depth refers to the depth below the ground surface to which a

change in moisture content, and hence a change in suction value, depends on

environmental or other causes. The depth of this zone is also the location of the

equilibrium moisture content, in uniform soil characterized by 0.027 pF suction change

per ft or to other conditions such as a cemented layer or water table. The movement

active zone is usually smaller than the moisture active zone due to overburden restrain

(PTI, 2004).

• Active zone depth also referred to as the active depth of swelling is the depth at which

the overburden stress equals the swell pressure. Depths in excess of 100 feet are

obtained when typical swell pressures (10,000 psf) are considered (Fredlund and

Rahardjo, 1993).

• Nelson, Durkee, and Bonner (1998) define the active zone depth as the depth of

potential heave, which represents the maximum depth within which heave is possible.

These referenced definitions provide insight into some of the factors that must be

considered for design purposes. They are empirical approximations of active zone depth that

lack rigorous definition. Nelson at al. (2001) proposed four rigorous definitions that could be

used universally. Those definitions are:

21

2.3.3.1 Active Zone Depth

“Active zone depth is defined as the depth of soil beneath a structure that is contributing

to or has the potential to contribute to actual heave that takes place at some point at the surface

at any particular time (t). The active zone depth is time and spatially dependant parameter…The

depth of the active zone is limited by the depth of expansive soil and by the depth at which the

overburden pressure is equal to the swell pressure…Therefore, the depth at which the

overburden stress equals the swell pressure provides a method for estimating maximum

possible active zone depth” (Nelson et al., 2001).

2.3.3.2 Zone of Seasonal Moisture Fluctuation

“The zone of seasonal moisture fluctuation is the depth of soil in which water

content/suction vary due to climatic changes at the ground surface” (Nelson et al., 2001). This

parameter is sensitive to temperature fluctuations at the ground surface. Furthermore, the depth

of seasonal moisture fluctuation is related to the depth of temperature fluctuation within soil

profile (Hamilton, 1969).

2.3.3.3 Depth of Wetting

“Depth of wetting is the depth to which water content increases due to the introduction of

water from external sources, or due to capillarity after the elimination of evapotranspiration”

(Nelson et al., 2001). The introduction of soil cover such as a roadway or a slab-on-grade

significantly reduces evaporation from soil followed by water migration under the soil cover. With

time, once steady state condition is achieved, the water content increases from the soil surface

to a depth referred to as the "depth of wetting”. Factors such as irrigation, broken water pipes,

seepage from ponds or ditches, can substantially increase the depth of wetting.

22

2.3.3.4 Depth of Potential Heave

“Depth of potential heave is the depth to which the overburden vertical stress equals to

or exceeds the swelling pressure of the soil. This represents the maximum depth of Active Zone

that could occur” (Nelson et al., 2001).

The above-presented discussion is applicable to uniform soils. When strata is not

uniform, and especially when the soil layers are almost vertical the distress to structures is

concentrated and more severe. Vertical fissures in the soil provide good water flow paths

between the bedding planes. The fissures usually occur below the top layer of the soil. Nelson

(Nelson et al., 2001) found that the water contents are not uniform in the strata. The soil

adjacent to bedding planes is very wet and water migrates outward from into zones between the

bedding planes.

2.3.4 Edge Moisture Variation Distance

Damaging movement of the superstructure is generally attributed to differential soil

moisture conditions, differential swell and the distance to which water travels under the slab.

These conditions are known to vary cyclically due to evaporation and wetting events. For

example, during hot dry conditions, water can be lost from under the edges of the slab. During

rainy season the waterfront will travel under the slab to a certain distance and the wetted soil will

heave. These differential moisture conditions determine how much stress and deformation will

the slab and the structure experience. Accordingly, the differential moisture conditions are used

to design reinforcing for the slab foundations.

The distance measured inward from the edge of the slab over “which moisture will

change due to wetting or drying influences around the perimeter of the foundation” is defined by

Post Tensioning Institute (PTI, 2004) as the edge moisture variation distance, em; also known as

edge penetration distance. The unsaturated diffusion coefficient, α, is the major factor used in

the determination of em. The α parameter is a function of suction magnitude, soil permeability,

and cracks in the soils. “Roots, layers, fractures or joints in the soil increase the edge moisture

23

variation distance value” (PTI, 2004). McKeen et al. (1990) indicate that the magnitude of the

edge moisture variation distance depends on the vertical depth of moisture variation. As such,

the edge moisture variation distance can approach a distance equal to the depth of the active

zone.

Nelson and Miller (Nelson et al., 1992) point out that the edge moisture variation

distance is the most difficult parameter to estimate and it is not clearly defined for the purposes

of slab design. It should be defined in terms of measurable variation in suction, water content or

potential heave. Shear stresses within a concrete slab foundation are the result of differential

uplift forces beneath the slab. Therefore, the seasonal fluctuations in water content around the

edges of the slab represent only one factor that contributes to shear stress and cracking.

Geologic conditions, soil variability, and the time dependent progression of water from the edges

of the slab due to irrigation also contribute to differential heave over the life of the structure. In

addition, in the case of a slab type structure exposed to atmospheric conditions, such as a road

or runway, temperature fluctuations above the slab can result in significant water content

fluctuations beneath the surface.

2.4 Causes of Water Content Change; Field Observations of Moisture Migration and Heave

In uniform soil, water content changes occuring under a slab can be divided into the

following three categories: monotonic, seasonal, and accidental, which includes the influence of

vegetation. Each category depicts the manner in which the change takes place. In real

problems, the change in water content is a mixture of two or three of the above-mentioned

causes.

Moisture content beneath covered areas can increase due to gravitational migration,

capillary action, vapor and liquid thermal transfer (Chen, 1988). Water flow by gravity can occur

in all directions. If excess water is added to the system, such as rain or irrigation water, the

water content under the covered area will increase and heave will occur. Another significant

means of water transfer in fine-grained soils is capillary force. Capillary action causes moisture

24

to move upward from water table and evaporate at the surface. If structure is located on the soil

surface, it will act as moisture barrier and cause moisture to accumulate beneath it (Day, 1994).

Heaving of expansive soils may take place without the presence of free water. Water

vapor migrates from areas with high temperature toward cooler areas, generally towards

covered area where condensation takes place, and providing means for volume change of

expansive soils (Chen, 1988, Johnson and Stroman, 1976 and Hamilton 1969). The process of

water vapor movement due to thermal gradient is called thermo-osmosis and it is the most likely

mean of monotonic water content change in arid climates. Thermo-osmosis occurs in both liquid

and vapor phases.

Kraynski (1967) indicates that the transfer of water can be explained by water balance

principles in terms of potential gradient. Flow of water through unsaturated soils can be defined

in terms of hydraulic head gradient where water flows through soil from a point of high total head

to a point of low total head (Fredlund and Rahardjo, 1993).

2.4.1 Monotonic Water Content Change

Prior to construction of slab-on-grade, the soil-moisture system is in equilibrium with the

existing natural boundary conditions of evapotranspiration and precipitation. The construction of

a building imposes a new set of surface boundary conditions by cutting off both

evapotraspiration and precipitation. The soil-water system responds to the change by steady

increase in moisture until new soil-moisture equilibrium is reached. Field observation indicates

that the monotonic water content change occurs up to six years after construction of a slab. The

first cases of this phenomenon reported in literature are those of South Africa (Wooltorton, 1950,

and Jennings, 1953), where damage to houses began to appear 3 to 4 years after construction.

Three mechanisms account for the monotonic water content change. The first one is

capillary action. Capillarity causes moisture to move upward from water table and evaporate at

the surface. The presence of a slab acts as a barrier under which the moisture accumulates

(Day, 1994). The second mechanism is thermo-osmosis that is explained above in section 2.4.

25

The third mechanism includes liquid water transfer from the boundary of the slab to the center of

the structure during rainy season. Since the slab precludes evaporation, water content in the

soil under the slab in contained. The water transfer from the edge to the center of the slab

occurs only during the short rain periods through soils with low degree of saturation and

permeability (Loxton et al, 1953; Russam and Coleman, 1961; Livneh & Shklarsky, 1965;

McKeen & Johnson, 1990).

Research based on Wooltorton observations (1950) confirmed that the primary heave

under a building equilibrates in about three to six years depending on soil type and

environmental conditions where in arid climates the process takes longer than in humid ones.

The heave equilibration process is illustrated in Figure 2.4 that shows steady increase of soil

elevation under slab until equilibrium is reached. The obtained heave equilibrium is

accompanied by equilibration of moisture content under the slab.

Figure 2.4. Slab movement, rainfall and site plan of experimental house at

Vereeniging, Transvaal Highveld (after Blight, 1965).

Figure 2.5 shows the moisture equilibration process, where the moisture content of the

soil profile just below the slab approaches constant value with the water content at lower depths

26

confirming the idealized water content profile shape presented in Figure 2.3 (Tucker and Poor,

1978). Furthermore, it was observed that the equilibration process is followed by a uniform drop

in heave after 6 to 10 years from the time of construction (Donaldson, 1965).

Figure 2.5. Soil Moisture Profile for soil a) under cover and without cover, b)

difference in soil moisture profile between soil located below slab and outside of covered area (after Tucker and Poor, 1978).

It’s been assumed that at the end of the primary phase of movement, the moisture

distribution under the building will come to an equilibrium with the boundary conditions and

therefore additional significant movements will not occur. Research done by Donaldson (1965)

shows, however, that although seasonal fluctuations in the high-veld areas are insignificant,

serious distortion occurs long after the primary phase of movement has been completed. These

movements are explained by altered boundary conditions due to accidental wetting or drying.

2.4.2 Seasonal Water Content Change

Seasonal water content change within uncovered soil profile occurs due to variations in

environmental conditions. Those changes are very large in arid or semi-arid regions where rainy

and dry seasons exist. During rainy season significant amount of moisture is introduced into the

profile resulting in soil heave. During dry season water loss occurs to a depth of temperature

27

fluctuation within soil profile coupled with development of potential preferential moisture flow

path due to shrinkage cracks. Expansive soils are very common in arid and semi-arid regions. In

fact, a study done in Australia resulted in the determination of correlation between climate and

soil type (Aitchison, 1965). Theses expansive soils typically develop shrinkage cracks during dry

season. The cyclic heave and shrinkage results in soil desiccation.

For slabs-on-grade the seasonal moisture fluctuation manifests itself in the moisture

variation and heave or shrinkage under the edges of the slab. Figure 2.6 is a schematic of the

seasonal behavior of slab-on-grade constructed on expansive soil. During dry season, the

moisture content from underneath the edges of a slab is lost resulting in a dome like shape of

the slab. It is referred to as the center lift condition by design manuals (PTI, 2004). During rainy

season the opposite is true. The waterfront moves under the slab and causes heave under the

edges resulting in edge lift condition. Typically, the seasonal fluctuation affects are smaller on

the horizontal distance from the edge of the slab than the vertical depth. Refer to Appendices A

and Chapter 5 more detail.

Figure 2.6. Center lift and edge lift slab distortion due to seasonal moisture variation

(after PTI, 2004).

29

soils may impact compression and expansion properties otherwise not exhibited (Hamilton,

1969).

Figure 2.7. Measured vertical ground movement within soil profile of Regina clay,

Saskatchewan (after Hamilton, 1968).

30

Nevels (2001) performed a 4-year study to find total suction variation due to seasonal

effects under a 3.5-meter wide bicycle trail in Oklahoma City. The results were compared

against free field total suction measurements obtained from uncovered region next to the trail. It

was found that the variation and magnitude of total suction under the trail and under free field

condition were the same over the studied period of time. The results of this study can be used to

predict the behavior soil under slab-on-grade to a distance of 1.75 meters measured from the

edge of the slab; free field soil behavior should be expected under conditions specified in that

study.

Edge moisture variation distance is a parameter that is difficult to obtain. Due to

difficulties associated with the definition and measurement of this parameter, there is a limited

number of field studies aimed at this problem. One of those studies was performed by Durkee

(2000) who conducted field investigation on two simulated slabs-on-grade exposed to

environmental conditions, thus exposing the soil underneath the slabs to large temperature

variations. These slabs were located at two sites 1) Colorado State University (CSU) in Fort

Collins, Colorado, and 2) Fort Sam Houston (FSH), in San Antonio, Texas. The measured

moisture variation distance was found to exceed 4.5 m (15 ft), which was a half the slab width. It

is unclear, however, how are the proposed results influenced by temperature variations due to

environmental conditions.

2.4.2.2 Field Studies of Seasonal Temperature Variations

The consideration of temperature variation within soil profile for constructed facilities is

an important factor that influences both moisture movement and heave. Mitigation of moisture

from central to perimeter areas has been observed in crawl spaces with vapor barriers on the

ground surface. Much of this moisture movement appears to take place through the soil from

warm to cooler regions. These cases suggest that provisions of vapor barriers over the soil may

not be sufficient to maintain constant moisture distribution under crawl spaces unless insulation

is used effectively to minimize temperature gradients (Hamilton, 1969).

31

Figure 2.8 illustrates temperature variation within soil profile obtained over six years from

under a pavement located in Winnipeg, Manitoba. Similar information could be obtained for soil

located under edges of a slab-on-grade constructed in Phoenix region. The depth of

temperature variation, the minimum and maximum temperatures recorded at the surface would

vary, but the trumpet shape of the profile would be the same. Literature review indicates that the

mean soil temperature is about 7°F above the mean temperature of air. The temperature

variation with depth decreases and becomes insignificant at about 7.5 m (25 ft) (Hamilton, 1969).

Figure 2.8. Typical maximum, minimum, and mean annual soil temperatures, 1959-

1963 for a typical soil cross-section in Winnipeg, Manitoba (after Hamilton, 1969).

2.4.2.3 Field Studies of Monotonic vs. Seasonal Moisture Variation and Heave

Field studies of moisture content and heave under free field conditions, under the edges

of a slab and under slab beyond the edge moisture variation distance revealed that moisture

content variation and heave in all studied areas depend on environmental conditions. During

wet periods, both the open-field and the slab exhibited upward movement. During dry periods,

the elevation of the slab beyond the edge moisture variation distance remains constant while in

32

the open-field locations and soil under the slab edges, the soil surface exhibited downward

movement (Settler, 1990). Once the primary movement of slab is complete, only seasonal

movement and movements due to the effects of faulty drainage and garnering activities occur

under the edges of slab and in the field (Blight, 1965).

The placement conditions of slabs appear to determine the overall magnitude of heave

experienced under the structure. Wray (1992) constructed two field test sites to monitor the

behavior of slab-on-ground foundations over expansive soils, and the change in soil moisture

conditions at each site as a function of climate over the period of nine years. The test sites were

located in areas with different climatic conditions. The first one was located in humid climate

(College Station) and the second one was located in arid region (Amarillo, TX). The College

Station slab initially experienced edge lift distortion that was subsequently replaced by a uniform

heave over the entire site which turned into a center lift distortion mode at the end of a drought

period three years after construction. The Amarillo slab perimeter experienced approximately

nine annual cycles of edge lift distortion; heaved upward during cooler wet periods and flattened

during hot, dry periods. This slab continued to show a slow but increasing mound in the center

of the slab, indicating that eventually the center heave pattern governs the slab design

considerations. Wray (1995) concluded the long-term distortion mode at both sites was center-

lift distortion mode.

2.4.3 Accidental Changes of Water Content

Broken pipelines, vegetation or the presence of equipment such as boilers, furnaces or

AC units are the main sources of accidental water content changes below slab-on-grade. Trees

are the biggest cause of soil drying and subsidence resulting in foundation movement and

damage. The damage caused by trees can be very severe during drought periods (Biddle,

2001).

Vegetation has several effects on available soil moisture. “In addition to moisture

depletion by transpiration, they also shade ground surface, build up organic matter, retard

33

precipitation runoff, and form water channels from root disintegration which all influence soil

moisture patterns” (Biddle, 2001). The effect of vegetation on soil moisture depends on

environmental conditions such as sunlight, temperature, potential evaporation, relative humidity

and wind speed.

The interaction between vegetation and available moisture in expansive soils can

mobilize inactive soils to increase soil deformation from active soils (Biddle, 2001). Large broad-

leaf trees located near structures cause the greatest change in available moisture and the

greatest risk of damage to the structure whether in humid or arid climates. Most influential trees

are Popular, Elm, Willow, Oak, Bradford Pear and Ash (Bryant et al., 2001). Experience and

observation show that these types of trees should be planted 0.5 to 1.0 m beyond the anticipated

mature drip line or anticipated mature height of the tree from building foundation. Small trees,

bushes and grasses can affect available moisture at shallower depths especially in arid or

semiarid climates (Snethen, 2001).

Trees usually have 90% of the root system within 0.6 m of the soil surface and with only

small proportion of roots extending to greater depths. Structural roots, which distribute the load

of the trunk and anchor the tree to the soil are usually uniformly and radially distributed around

the trunk. Beyond the point where the tree is anchored, the root system subdivides into a mass

of fine conducting roots, which support feeder roots. The feeder roots are not distributed evenly.

They growth and distribution depend on the availability of oxygen and water and they respond to

changing conditions. Root growth is reduced in dense soils such as dry clays. The roots exploit

natural and artificial sources of water such as deep aquifers or leaky drains or moisture

condensation under a slab (Biddle, 2001).

Plants are very effective pumps that draw water from the soil and transpirate it through

their leaf system. As water is lost from the leaf, suction is developed within the leaf of magnitude

that depends on plant type. For example desert plants are capable of developing suctions in

excess of 6 000 kPa. All other plants typically develop suctions in the range between 1500 to

2000 kPa. The magnitude of suction exerted by plant roots on soil appears to be independent of

34

plant specie. It reaches maximum value of 1500 kPa and is referred to as the wilting point of

plant. When suctions in the soil mass exceed the wilting point, the plant reduces

evapotraspiration and some feeder roots start to die out (Biddle, 2001).

Figure 2.9 illustrates the influence of trees on a paved area. During drought period 5 to

10-mm wide cracks developed in the pavement with a minimal vertical displacement. The

developed cracks were circular in pattern and were located about 7 meters away from trees

(Snethen, 2001).

Figure 2.9. Influence of evapotranspiration of trees on paved areas (after Snethen,

2001).

A case study presented in Figure 2.10 and Figure 2.11 illustrate the influence of trees on

the performance of slab-on-grade. In this instance, in 1995 a Bradford Pear tree was planted

approximately 3 m from the northwest corner of the garage. By summer of 2000, during drought

period, the homeowner noticed a vertical crack through brick veneer extending the full height of

the wall. The crack was wider at the top of the wall than at the bottom. The crack developed all

at once suggesting that moisture depletion and soil shrinkage resulted in the loss of soil support

along the north portion of the west wall (Snethen, 2001).

Small plants such as herbs or grasses, on the other hand, can act as soil stabilizers.

Although these plants deplete the soil out of water, their roots reinforce the soil and to some

extend prevent soil cracking. A well-preserved lawn maintains a rather constant state of

moisture in the soil throughout the year, and typically is not the cause of differential soil

movement. (Jimenez-Salas, 1996).

35

Figure 2.10. Crack in residence wall due to vegetation (after Snethen, 2001).

Figure 2.11. Sketch of crack and proximity of tree to the structure (after Snethen, 2001).

2.5 Soil Response to Change in Water Content

The term, expansive soil is typically given to soil with plasticity index of 15% or more

which exhibits swell when exposed to water, settlement under applied load, and shrinking and

cracking during desaturation process. More recently, IBC (2003) in section 1802.3.2 introduced

a rigorous definition of expansive soil adopted by the PTI (2004) design procedure. “Soil

meeting all four of the following provisions shall be considered expansive, except that tests to

show compliance with items 1,2 and 3 shall not be required if the test prescribed in Item 4 is

conducted:

36

1. Plasticity index (PI) of 15 or greater, determined in accordance with ASTM D 4318.

2. More than 10% of the soil particles pass a No. 200 sieve (75µm), determined in

accordance with ASTM D 422.

3. More than 10% of the soil particles are less than 5 µm in size, determined in accordance

with ASTM D 422.

4. Expansion index greater than 20, determined in accordance with ASTM D 4829.”

The magnitude of the response to change in water content per particular soil depends

on initial saturation, initial dry density, and applied surcharge pressure. The influence of these

factors on swell/shrinkage behavior of soil is briefly summarized below.

2.5.1 Settlement

Settlement is the equilibration process of soil’s total stress to the applied overburden

stress which typically results in soil densification. The rate of consolidation depends on the

compressibility coefficient and the drainage conditions. The settlement of unsaturated soil can

be determined with the theory of unsaturated soil mechanics as described by Fredlund and

Rahardjo (1993). Detailed literature review of this process is not applicable to this research

project.

The search for a reliable method of predicting total have of expansive soil is probably

affected by the concept of ultimate settlement in the theory of consolidation. For many years,

engineers have been familiar with the calculation of ultimate and differential settlement of

structures founded on clay, and it was assumed that total heave can be predicted in a similar

manner. Few fundamental differences exist between settlement and heave (Chen, 1988).

Some of them are as follows:

1. Settlement of clay under load takes place without the aid of wetting, while expansion of

clay is not realized without moisture increase.

2. The total amount of heave depends on the environmental conditions, such as the extent

of wetting, the duration of wetting and the pattern of moisture migration. Similarly

37

settlement due to partial wetting depends on environmental conditions. It is challenging

to quantity the moisture migration; therefore both estimates can be errorous.

3. Differential settlement is usually described as a percent of the ultimate settlement. In

the case of expansive soil, differential heaving can equal to total heave. No correlation

between differential and total heave can be established (Chen, 1988).

2.5.2 Shrinkage

Shrinkage is the reduction in total soil volume as the response to loss of moisture. It is

generally recognized that swelling and shrinkage of expansive soils are interrelated. Over a

great portion of the world shrinkage problems pose more threat to structure damage than

swelling problems for example illite soils in China, black cotton soils in India or tree root induced

shrinkage in Britain (Chen, 1981). Shrinkage of expansive soils is typically observed in humid

climates, where precipitation exceeds the potential evaporation. Soil expansion, on the other

hand, constitutes a problem in arid and semi-arid regions (Chen, 1988).

Popescu (1980) divided shrinkage process into three stages: initial, normal, and

residual shrinkage. Critical moisture content range refers to water content range within which

shrinkage occurs. Beyond that critical moisture content range, any further change of moisture

content does not cause additional shrinkage. The work done by Nevels (2001) supports

Popescu’s claim that shrinkage ceases after reaching critical water content. This is illustrated in

Figure 2.12 where no change in void ratio is observed for soil with volumetric water content

smaller than 14%. The point where the void ratio becomes constant is referred to as the

shrinkage limit. A more extensive research in that field was done by Chen (1988) who studied

the relationship between swell and shrinkage of soil due to the variation in water content and

initial dry density.

Figure 2.13 is a plot of measured swelling and shrinkage for soil with various initial dry

densities and constant initial water content. It is seen from that figure that swelling increases

rapidly with an increase in initial dry density while shrinkage remains fairly uniform. Therefore, it

38

can be concluded that initial dry density has little effect on shrinkage behavior of soil.

Furthermore, there exists a critical dry density where the percent of swell of soil is equal to

percent of shrinkage. The critical dry density depends on soil type and initial moisture content

(Chen, 1988).

Figure 2.12. Change in void ratio due to change in volumetric water content (after Nevels, 2001).

Figure 2.13. Effect of initial dry density on swell and shrinkage (after Chen, 1988).

39

2.5.3 Heave

Heave or increase in volume is time dependant expansive soil response to increased

moisture content. The heave characteristics are quantified by 1-D swell tests described in

Sections 4.2.6 through 4.2.8. These tests represent maximum potential swell since the soil

samples are allowed to become fully saturated. The potential magnitude of swell is associated

with the initial conditions of the soil such as the initial moisture content, initial dry density and

applied surcharge pressure. Chen (1988) established that linear relationship exists between

volume change and initial soil conditions such moisture content and dry density. In general,

heave increases as the initial dry density increases, or initial water content decreases.

Therefore, heave depends on both initial water content and initial dry density.

2.5.4 Fatigue of Swelling

Fatigue of swelling refers to the decrease of soil’s swell potential as the drying-wetting

cycles continue. The dry density reaches an equilibrium conditions also called a critical value

where magnitude of swell approaches magnitude of shrinkage and the dry density of a sample

approaches a constant value. The equilibrium dry density is smaller in magnitude than the initial

dry density. Based on this observation, it can be assumed that soil will undergo equal and

minimal volume change due to swell and shrinkage when initial dry density is equal to critical dry

density. Empirical data illustrated in Figure 2.14 show that swell levels off at fifth cycle when

relative equilibrium is reached. On the other hand, shrinkage behavior is unchanged with

number of cycles (Chen, 1988).

Limited empirical information is available on heave, settlement and shrinkage due to

partial moisture content change, which reflects the difficulties associated with measurement and

analysis of unsaturated, moisture sensitive soils. Few theoretical frameworks exist that aid the

analysis and estimation of unsaturated soil behavior. They are presented by Fredlund and

Rahardjo (1993), Alonso (Alonso et al., 1990), Wheeler (Wheeler et al., 1995) and others.

40

Figure 2.14. Swelling and shrinkage behavior of expansive soils subject to repeated wetting and drying (after Chen, 1988).

2.6 Performance of Residential Construction

The performance of residential construction is typically assessed based on one of the

following criteria 1) floor levelness (American Concrete Institute, ACI, 117-90), 2) angular

distortion and 3) magnitude and extend of distress in vertical and horizontal construction, which

is the most important criteria by which to judge the significance of structure distress due to soil

movement. Various bodies developed standards for acceptable foundation movement and/or

minimum construction quality criteria. Some of the more important ones are: 1) the American

Concrete Institute (ACI), 2) the Building Research Advisory Board (BRAB), 3) the Department of

Housing and Urban Development and the Federal Housing Administration (HUD/FHA), 4) the

Post Tensioning Institute (PTI), and 5) the Uniform Building Code (UBC). Most of these

standards use language quantifying the floor levelness and the structure stiffness in terms of

angular distortion to preserve the structure severability within designed structure lifetime. The

angular distortion is defined as the maximum floor differential divided by the horizontal distance

between the measurements. Most design governing bodies limit the angular distortion at 1/240

as summarized in Table 2.1. The floor levelness is defined as the slab deviation from horizontal

over the entire area of the slab and expressed with FF values (of FL for local levelness over the

41

area of 10’) and calculated as 12.5/∆z, where ∆z is the floor differential measured in inches (ACI

117-90); see Section 3.6 for more details. As per the ACI standard, the FL is limited at 10 while

FF at 15. Local institutions, such as the Arizona Registrar of Contractors, AROC, specify the

local standard of care through publications quantifying the maximum acceptable distortions and

distress of horizontal and vertical components of the structure.

Table 2.1. Angular Distortion Criteria Based on Design Manuals (summarized in Advanced Foundation Repair, 2007).

Construction Type

Governing Body ACI 318-89

(1992), BRAB, Report No. 33

(NAC, 1968) FHA 4900.1

(1982) UBC Section 2307 (1988)

AROC (1997)

Wood 1/240 1/240 1/240 1/240 1/580 Masonry 1/240 1/300 1/240 1/240

2.6.1 As-built Floor Deviation from Horizontal

Extensive research has been inspired by the assumption made in litigations that newly

constructed slab-on-grade deviation from the horizontal is negligible. As a consequence, the

obtained manometer results are evaluated as the net post-construction movement causing

structure distress. Table 2.2 presents summary of literature review of slab deviation from the

horizontal for newly constructed conventional and PT slabs-on-grade. It illustrates that the initial

slab deviations might be as large as 2.2”, but more commonly are about 0.5”. For newly

constructed slabs the average angular distortion was found to be about 1/340. Based on the

research done by Noorany et al. (2005) the local levelness FL numbers of the newly constructed

slabs in the study ranged from 7 to 175, with a mean value of 43. These results indicate that

small percentage of newly constructed foundation systems do not comply with the acceptable

slab distortions used in the identification of expansive soil problems. More commonly, however,

the in-compliance deviation leads to overestimate of actual slab movement and potentially

misdiagnosis of structure distress as expansive soil related.

42

Table 2.2. Newly constructed slab deviation from horizontal and angular distortion.

Ref. Location # of Slabs

Slab deformation [in] Angular dist. min.-max. ave. min.-max. ave.

Koenig, 1991 San Antonio, TX 54 0.125-1.0 0.54 Marsh et al., 1999 S. CA 6 0.6-1.0 0.75 Walsh, et al., 2001 Phoenix, AZ 89 0.25-1.18 0.53 1/857-1/101 1/334 Noorany et al., 2005 CA 971 0.2-2.2 0.53 1/1000 - 1/71 1/346

2.6.2 Post-Construction Slab Distortion

Three studies of post-construction slab distortions correlated to the cosmetic and

structural structure distress were found. The results are presented in terms of the net angular

distortion and net relative deflection without the consideration for the initial state of the slab.

Skempton and MacDonald (1956) performed a long term study on numerous residential

structures to correlate the differential settlement of a foundation to building distress. The study

focused on pier foundations, not slab-on-grade. In spite of this, these results are frequently cited

in the literature concerning threshold criteria for cosmetic damage in wood frame houses

supported on slab-on-ground foundations with an argument that the interior partitions in a pier-

supported building are subjected to the same distress as interior walls supported by a slab-on-

ground foundation. Based on the Skempton and MacDonald study (1956) the cosmetic damage

occurs at angular distortion of 1/300 and maximum slab relative deflection of 1.75”.

The study of 34 slab-on-grade residences in San Diego California by Day (1990)

concluded that cosmetic damage relates to 1.15” slab differential and 1/300 angular distortion.

Structural damage was observed to correspond to 3.5” slab deformation and 1/100 angular

distortion.

The study by Marsh and Thoney (1999) consisted of 12-year long monitoring program of

400 slab-on-grade, wood-frame residences. Different threshold criteria were developed for

heave and different for settlement where distress due to heave was found to occur at smaller

angular distortions. The onset of cosmetic damage was correlated with about 1.1” floor relative

43

deflection and 1/330 angular distortion. Structural damage was correlated with relative

deflection larger than 4” and angular distortion of 1/90.

The significance of these research findings is two-fold. 1) Cosmetic damage to

residential structures occurs at about 1/300 angular distortion, a value smaller then the design

requirements for floor levelness of 1/240. 2) The angular distortion of newly constructed slabs is

on average 1/340, a value almost equal to the value assigned to correlate with cosmetic

damage. Additionally, the angular distortion of newly constructed slabs can take values as small

as 1/71, a value correlated with structural damage The obvious question here is, what is the

magnitude of movement that contributed to the distress? The identification of soil movement

related structure distress appears to be bias and incomplete when limited to relative deflection

and angular distortion. The bias is caused by unknown initial conditions. There is a need for a

comprehensive protocol for residential construction distress identification due to expansive soil

movement.

2.7 Mitigation measures

Mitigation measures are aimed at preventing or limiting potential soil movement below

foundation pre-construction or post-construction. The employed mitigation measured in part

depends on the known or assumed distress mechanism. A summary of literature review of

mitigation measures is presented below.

2.7.1 Removal, replacement and recompaction

Substitution of the active clay by an inert material eliminates the problem. However, this

procedure is viable only when the active depth is shallow (one or two meters) and the

replacement material is readily available at a low cost. In many cases, it is possible to suitably

reduce expansion problems by processing the native soil at the site to water content above

optimum and recompacting it. This approach, which is frequently implemented in Southern

California, is most effective when the resulting elevated moisture content can be maintained until

44

the completion slab construction (Greenfield et al., 1992). An alternative but related technique is

to cover the expansive soil with minimum 3-ft of non-expansive material, placing the expansive

soil at an elevated overburden stress. These methods are not economically attractive when the

site requires moving large amounts of soil for grading.

2.7.2 Mechanical Stabilization

The mechanical stabilization consists of mixing the active soil with coarser material. As

with substitution, mechanical stabilization is limited to shallow active depths. The economical

feasibility of this method depends on the availability of coarse material and the depth of

expansive soil layer (Nelson and Miller, 1992).

2.7.3 Chemical Stabilization

Chemical stabilization of the clayey soil is accomplished with the use of one of the

following additives: lime, cement, fly ash and potassium solution. These additives are introduced

into the soil through injection to depths of 4 to 8 ft or mixing or recompaction to a depth of 2 ft.

The lime addition effects on active clays are well understood. Sodium is an exchangeable base

in most clayey soils which binds with lime. The saturation with lime reduces soil plasticity and

volume change potential (Jimenez-Salas, 1996). Benefits of lime addition for already calcium-

saturated clays are not so well understood. In addition, lime treatment of expansive soils

containing soluble sulfates can actually result in swell upon the application of lime. Laboratory

testing to investigate the reactivity of clay soils is recommended when considering chemical

stabilization methods (Jimenez-Salas, 1996).

Portland cement also provides highly effective clay stabilization. Similar to lime, cement

changes the properties of clays through cation exchange, flocculation and pozzolanic reactions.

In addition, cement increases strength and durability through cementious hydration (Prusinski et

al., 1999).

45

Research on chemical stabilization with potassium solution of expansive soils in North

Central Texas by Pengelly et al. (1997) illustrated that potassium solution is a viable material for

chemical stabilization. Performance of slab-on-grade constructed on chemically treated soil

with PI of 40% is illustrated. After 7 years, the relative deformation of foundation was about 1”.

Recent research introduces the use of fly ash as a stabilizer for expansive soils (Cokca,

2001, Nalbantoglu et al., 2001, Puppala et al., 2001). The use of fly ashes is economically

attractive in regions near thermal power plants. The optimum use of fly ash requires the addition

of 20% of fly ash (Cokca, 2001). In general the introduction of fly ash increases hydraulic

conductivity, reduces PI and swelling potential of soil (Nalbantoglu et al. (2001). A reduction in

PI by 75% has been reported (Puppala et al., 2001).

2.7.4 Stabilization of Water Content

There are two ways of stabilizing water content of an expansive soil. Passive

stabilization involves maintaining soil moisture content through construction of vertical or

horizontal moisture barriers. The goal of active stabilization is to create future moisture

equilibrium conditions below the slab prior to construction by introduction of large quantities of

water to the pad.

2.7.4.1 Passive Stabilization

The purpose of a moisture barrier is to isolate the soil beneath a foundation from

seasonal wetting and drying. Horizontal moisture barriers are either in the form of a sidewalks or

geomembrane below the soil surface. Vertical moisture barriers are either concrete walls or

geomembranes below the foundation edge. The function of a moisture barrier depends on the

initial soil moisture conditions at a specific site. If the soil is initially desiccated, the barrier will

prevent access of free water through the cracks into the desiccated clay. If the soil is initially

wet, a moisture barrier will prevent seasonal moisture changes under the edges of the

foundation. Moisture barriers can also act as root barriers by preventing the roots from

46

neighboring trees from penetrating into the soil beneath a structure. Typically, vertical moisture

barrier design is based on the active zone depth. There seems to be a trend towards the use of

vertical barriers up to 2.5 m in depth. Even though the active depth is usually greater, results are

generally acceptable (Jimenez-Salas, 1996).

Moisture barriers have been used extensively and with positive results in transportation

projects in Texas and Arizona (Steinberg, 1992). Where results were not as favorable, problems

involved inadequate depth of the moisture barriers and problems with the backfill material for the

trench. A case study on effect of vertical geomembranes on pavement distress in semi-arid

region in Australia was reported by Holden (1992). He illustrated that at minimum 2.2 m deep

vertical barriers are needed to prevent seasonal moisture fluctuations below the pavement. With

a barrier constructed to a depth of 1.8 m significant moisture fluctuations were still observed.

In Texas, the use of geomembranes has recommended to residential construction. A

typical specification to use a 10 mm plastic liner attached to the outside edge of the grade beam

or slab that extends at least 6 ft away from the building. The plastic liner is covered with

landscaping soil and it conducts water away from the foundation. (Greenfield and Shen, 1992).

Similar approach is presented by Slabworks (2008). It is postulated that the expansive soil

problem is caused by water transfer through the surface soil prepared to engineered

specifications. The water collects at the surface of clay layer below the foundation where it is

allowed to pond and slowly infiltrate into the profile causing soil expansion, slab movement and

structure distress. In order to prevent this scenario, a cap consisting of fat clay is introduced at

the surface of the engineered fill. Proper site drainage would facilitate water removal from the

site and hence prevent moisture migration below the foundation system as presented in Figure

2.15. Due to the impermeable characteristics of clay, this solution is comparable to horizontal

moisture barrier. The postulated scenario is unlikely to occur in the Phoenix valley due to low

density of undisturbed soils found in this geographic region. The pad preparation effectively

increases the soil density which results in reduced saturated soil permeability. Therefore the

47

surface water might pond at the soil surface and the absorbed water will flow much easier

through the undisturbed profile layers.

Meyer et al. (2001) presented a theoretical procedure to model the effects of vertical

moisture barriers on foundation support resulting in significant reduction of the maximum vertical

differential movement (ym, a PTI design coefficient). The effects of either vertical or horizontal

moisture barrier on slab-on-grade performance are not reported yet in literature. There is a

needed to set up guidelines to effectively apply moisture barriers to expansive soils and control

the damage caused to light structures.

a)

b)

Figure 2.15. a) Bathtub effect of fill, b) Fat Clay cap and positive drainage to prevent the bathtub effect of fill (SlabWorks, 2008).

48

2.7.4.2 Active Stabilization

In arid climates, the expansive soil problem is associated with monotonic moisture

increase below the slab. An active defense against future moisture increase consists of

moisture preconditioning the pads to the anticipated equilibrium water content prior to

construction of the foundation system. This approach has been used frequently in the Phoenix

area. Although this procedure is potentially very effective, it does present some serious

challenges. Firstly, pre-wetting to the final equilibrium moisture content pre-supposes that the

final value is known. To date, methods of estimating these values have not been very reliable

and more research is needed to improve these methods. Secondly, it is difficult to wet in-situ

natural layers of expansive clay in a reasonable time due to low hydraulic conductivity inherent

to this type of soil. Flooding of the foundation area is used sometimes, with variable results

(Blight et al., 1992). A more promising procedure consists of the controlled addition of water

using borings strategically distributed over the footprint of the building. Irrigation with sprinklers is

another procedure (Williams, 1980) that has been used with some success. Even in cases

where a fill soil is placed at controlled water content during pad grading, the time of the

development often makes it difficult to maintain the elevated water content.

2.7.5 Site Drainage and Control of Landscape Watering

Frequently the residential dwelling distress related to expansive soil is caused by

homeowner modified drainage and grading around the foundation perimeter, usually for

landscaping purposes (Greenfield and Shen, 1992). Remedial measures include re-instating an

adequate slope away from the foundation on all directions. The Colorado Geological Survey

(1987) recommends a slope of 10% for vegetated areas, being 5% the minimum slope to ensure

drainage and 15% the maximum slope to prevent erosion. For paved areas a slope of 1% is

recommended. In places where rain is a significant source of water, careful installation of roof

gutters and downspouts is needed.

49

A complementary remedial measure that can be used along with site grading is the

installation of subdrains around the perimeter of the foundation to collect the water that seeps

into the soil and drain it away from the foundation (Greenfield and Shen, 1992). Subdrains are

constructed in such a way that they outfall into the storm drain system. Figure 2.16 presents an

example of a subdrain around a house. To prevent moisture migration from the trench towards

the foundation, an impermeable waterproofing material shall be installed between the structure

and the trench, as illustrated. The subdrains need to be checked periodically for clogs and

deterioration.

Figure 2.16. Typical perimeter subdrain (after Greenfield and Shen, 1992).

Houston (1996) summarizes mitigation measures especially relevant to Arizona soil and

climatic conditions.

1. Restricted irrigation watering (e.g. desert landscaping);

2. Restricted landscape vegetation adjacent to structures, unless placed in a planter;

3. Paved surfaces around the structure to the practical extent;

4. Replacement and compaction of near-surface layers to form a low permeability barrier to

water. The barrier to water should be composed of moisture-insensitive soils.

2.8 Classification of Swell Potential Based on Soil Properties

Literature review of swell potential classification based on soil properties is presented for

two reasons: 1) some of the methodologies are implemented by practitioners to estimate the

50

active zone depth for residential construction purposes, e.i. PTI manual described in Chapter 6,

and 2) as part of this research project, swell potential based on soil properties was estimated

and mapped for soils in Arizona geographical region. There are three different methods of

classifying expansive potential of clayey soils. They are mineralogical classification, indirect

measurement and direct measurement. The mineralogical classification is done directly or

indirectly where the direct methods involve X-ray diffraction, differential thermal analysis, dye

adsorption, chemical analysis or electron micrographs. The indirect measurement method of

identifying expansive soil is based on measurement of index properties of soil that are related to

swell potential. Such properties include plasticity index, activity, gradation and suction. One-

dimensional swell test is typically used as direct measurement of swell potential.

2.8.1 Mineralogical Classification

Most soil classifications systems arbitrarily define clay particles as having an effective

diameter of two microns or less. However, particle size alone does not determine clay mineral

and its properties. Mineralogical composition plays a more important role in the classification of

expansive soils than the mare determination of the percent clay composition in a soil sample.

There are three main groups of clay: montmorillonite, illites and kaolinites where montmorillonite

is responsible for majority of the expansive soil problems (Chen, 1988). The formation of

montmorillonite is associated with extreme disintegration of the parent material, strong hydration

and restricted leaching, which allows for the magnesium, calcium, sodium and iron cations to

accumulate in the soil mass. Such conditions are favorable in semi-arid regions where the

evapotranspiration exceeds rainfall. Under such conditions, enough water is available for the

alteration process, but not enough for removal of cations with flush rain (Holtz and Kovacs,

1981).

The mineralogical composition of expansive soils has an important bearing on the

swelling potential. The negative electric charges on the surface of the clay minerals, the

strength of the interlayer bonding and the cation exchange capacity, CEC, depend on clay type

51

and contribute to the swelling potential of the clay. Therefore, it is claimed by clay mineralogists

that the swelling potential of clay can be identified by recognizing the constituent mineral of clay

(Chen, 1988).

In the clay-water-air system, the water within the clay is called the adsorbed water. The

water and ions with the clay lattice constitute diffuse double layer, where two types of forces

exist, attractive and repulsive. The attractive force is quantified by electrostatic Van der Waals

force, which depends on the distance between the clay layers. The magnitude of the Van Waals

force increases as the distance between the flat plate surface and water molecules or cations

decreases. High concentration of cations near the surface of the clay particle creates a

repulsive force between the diffuse double-layer system. The magnitude of this repulsive force

has been correlated to half distance between clay particles, which is presented in Figure 2.17

(Low, 1973). Additional studies by Warketine at al. (1957) resulted in the development of

experimental curves correlating swelling pressure and interlayer half distance for

montmorillonite, which has the same shape as the shape presented in Figure 2.17. A more

practical relationship of swelling pressure, mineralogy and percent clay was developed by Seed

(1956) and is given in Figure 2.18.

Figure 2.17. Relationship between repulsive forces of clay particles to half distance

between particles for montmorillonite (after Philip Low). Similar relationship was developed by Warkentine et al., (1957) for swell pressure vs. half distance.

52

There are five techniques to identify the mineralogy of clay. They are: x-ray diffraction,

differential thermal analysis, dye adsorption, chemical analysis and electron microscope

resolution. All of these methods have proved to be cumbersome in the geotechnical engineering

practice; therefore mineralogical soil classification is almost exclusively done through indirect

measurements of such soil properties such as cation exchange capacity, activity ratio, plasticity

index and liquid limit.

Figure 2.18. Relationship between percentage of swell and percentage of clay (after Seed et al., 1962).

2.8.1.1 Cation Exchange Capacity

Clay minerals are capable of sorbing certain anions and cations and retain them in an

exchangeable state on the outside of silica-alumina clay mineral structural unit. The most

common exchangeable cations are Ca++, Mg++, H+, K+, NH4+ and Na+. The existence of such

charges is indicated by the ability of clay to absorb ions from solution. Cations are more readily

absorbed than anions; hence negative charges must be predominant on the clay surface. The

ions are temporarily attached to the clay structure. For example, clay mineral exposed to salt

53

solution will absorb Na+ ion. The same clay mineral subsequently placed in solution of

potassium chloride, KCL, will release Na+ ion and absorb K+

Cation exchange capacity (CEC) is the charge or electrical attraction for cation per unit

mass as measured in milliequivalents per 100 grams of soil. Typical ranges of cation exchange

capacities for various clay minerals are shown in Table 2.3, which shows that montmorillonite is

10 times more active in absorbing cations as kaolinite. This is caused by the large net negative

charge carried by the montmorillonite particle and greater specific surface. CEC is a significant

factor in the determination of swelling potential since swell potential is associated with increased

cation concentration and increased cation valence (Nelson and Miller, 1992).

ion. The process of replacement by

excess cations is called cation exchange, where the exchangeable reactions do not influence the

structure of the clay unit (Chen, 1988).

Table 2.3. Mineral clay properties (after Woodward-Clyde and Associates, 1967). CEC Clay Type Specific Surface Particle Diameter

[meq/100g] [m2 [microns] /g] 70-80 Montmorillonite 50-840 0.05-10 10-40 Illite 65-180 0.5-10 3-15 Kaolinite 10-20 0.5-4

2.8.1.2 Cation Exchange Capacity and Soil Properties

In general, it was observed that soil with a high plasticity index, PI, experiences greater

volume change than soils with a low PI. Pearring (1963) used that observation to develop a

correlation between cation exchange activity ratio %CECCEAc

fc

=

and activity ratio

%PIAc

fc

=

, where CEC is expressed in terms of milliequivalents per 100 grams of dry soil and

clay fraction, %fc is defined as the ratio of percent clay to percent of soil passing US sieve

number 200 , P200, expressed as a percentage. The obtained relationship is presented in Figure

2.19. The research done by Pearring (1963) inspired a follow up research, which produced the

correlation between Ac, CEC and swell potential, presented in Figure 2.20. This correlation

54

developed by Nelson and Miller (1992) is incorporated into 2nd Edition PTI slab-on-grade design

manual; see Appendices A and Chapter 6 for more detail.

Figure 2.19. Mineralogical classification (after Pearring, 1963).

Figure 2.20. Expansion potential based on cation exchange activity and soil activity

(after Nelson and Miller, 1992).

55

2.8.1.3 Atterberg Limits

Casagrande (1948) used Atterberg Limits for the mineralogical classification of clay. His

work, updated by Holtz and Kovacs (1981) is presented in Figure 2.21. The updated chart was

further used by Covar and Lytton (Covar et al., 2001) to develop a method of soil swell prediction

for slab-on-grade design purposes presented in Chapter 6.

Figure 2.21. Mineralogical classification based on Atterberg Limits (Holtz and Kovacs,

1981).

2.8.2 Indirect Measurement

Indirect measurement methods involve the estimation of parameter of interest based on

other measurements, which are either easy to perform and/or are commonly done. Indirect

swell potential estimation methods fall into two general groups, 1) index properties based, and 2)

based on fundamental soil mechanics.

2.8.2.1 Atterberg Limits

Holtz and Gibbs (1956) argued, since both liquid limit and swell potential depend on the

amount of water the clayey soil is able to absorb, these two values are related and plasticity

index alone can be used as a preliminary indication of the swelling characteristics of most clays.

56

This relation is given in Table 2.4. While it may be true that high swelling soil will manifest high

plasticity index, the converse is not true. Soils with high PI might not exhibit high swell potential

(Chen, 1988).

Table 2.4. Relation between swelling potential and PI (from Holtz and Gibbs, 1956).

Swelling Potential Plasticity Index Low 0 - 15

Medium 10 - 35 High 20 - 55

Very High 35 and Above Snethen et al. (1977) found that the soils' liquid limit, plasticity index and soil suction at

natural moisture content were the best indicators of potential swell. The resulting classification

system is shown in Table 2.5.

Table 2.5. Expansive Soil Classification based on Atterberg Limits (Snethen et al.1977). LL PI Suction Swell Swell Classification [%] [%] [pF] [%] > 60 > 35 > 4 > 1.5 High

50 - 60 25 - 35 1.5 - 4 0.5 - 1.5 Marginal < 50 < 25 < 1.5 < 0.5 Low

Seed et al. (1962) noted that two soils with the same swell potential might exhibit

different swell behavior due to different environmental conditions. He made the distinction

between swell potential and actual swell, and indicated that soil should be evaluated in two

stages. The first stage is to determine the swell potential based on the type and amount of clay

present in the soil. The second stage is to evaluate the environmental conditions to determine

the actual amount of swell that can be expected. Figure 2.22 can be used for the first stage of

analysis, where swell potential is a function of activity ratio and percent clay.

A more recent study by Zapata et al. (2006) of indirect swell determination illustrated

that PI and P200, when considered separately correlate poorly to swell potential obtained by

Arizona Modified Expansion Index. The product of these two parameters, however, wPI,

57

improves the correlation from R2

values of 0.41 and 0.27, respectively, to 0.67 as presented in

Figure 2.23. The Arizona Modified Expansion Index is a 1-D swell test performed on remolded

soil sample at 95% of maximum dry density and -1 to +4 of optimum moisture content. Low to

moderate expansive soils typical to Arizona geographic region were considered in this study.

Figure 2.22. Soil swell potential in terms of activity and percent clay (Seed et al., 1962).

EI (AZ) versus wPI

EI = 0.2014wPI + 1.682R 2 = 0.67

0

2

4

6

8

10

12

0 10 20 30 40wPI = P 200 *PI/100

Expa

nsio

n In

dex (

AZ)

(%)

Figure 2.23. Swell potential as a function of wPI (after Zapata et al., 2006).

58

2.8.2.2 Linear Shrinkage

Shrinkage limit was presumed to be related to swell potential, where linear shrinkage is

the percent linear volume change of soil from liquid limit state to oven dry. Altmeyer (1955)

suggested a relationship presented in Table 2.6. Recent research, however, failed to show a

conclusive evidence of correlation between swelling potential and shrinkage limit.

Table 2.6. Relationship between shrinkage and swell potential (after Altmeyer, 1955). Shrinkage Limit Linear Shrinkage Degree of Expansion

[%] [%] Less than 10 Greater than 8 Critical

10 - 12 5 - 8 Marginal Greater than 12 0 - 5 Non-critical

2.8.2.3 Colloid Content

Colloid content refers to percent of clay in soil sample as determined by hydrometer

testing. Percent of clay present is not sufficient to adequately predict swell potential. It needs to

be evaluated together with mineralogical classification or index properties. Figure 2.24 illustrates

the work done by Holtz and Gibbs (1956) and the dependence of swell potential on both colloid

content, plasticity index and shrinkage limit.

Figure 2.24. Expansive soil classification based on index soil properties (Holtz and

Gibbs, 1956).

59

2.8.2.4 Suction

Soil suction is a measure of a soil’s affinity for water; refer to Section 2.9.1 for rigorous

definition (Fredlund and Rahardjo, 1993). Soil suction describes the state of the soil and

indicates the intensity with which it will attract water. The drier the soil the greater the suction is.

Soil suction has two main components: matric and osmotic. The sum of matric and osmotic

suction is defined as total suction. Matric suction is the attraction of water to the soil particle

surfaces and depends on pore size distribution. The osmotic suction in clayey soils is related to

the forces from the osmotic repulsion mechanism arising from the presence of soluble salts in

the soil water. Suction changes resulting from covering an area with a slab are attributed to

changes in matric suction alone (Chen 1988). Therefore, expansive potential of soil and

moisture movement can be predicted with matric or total suction, however suction alone is

seldom used as swell potential predictor. Typically, together with soil index properties, it is

incorporated into effective stress methodologies.

An attempt was made by McKeen (2001) to develop a methodology of predicting

expansive potential of soil based on suction compression index, where the suction compression

index is defined as the change of soil volume with change in logarithm of total suction. The

magnitude of the suction compression index indicates if the soil is expansive or not. Small slope

characterizes a swelling soil while a large slope indicates a non-expansive soil. The

classification system introduced by McKeen for total suction is presented in Figure 2.25 and

Table 2.7 where the chart is divided into five sections. Each section represents soil with different

swell potential. In general, the closer the soil is to the left bottom corner, the less expansive it is.

The principle of soil suction has been utilized in number of total and differential heave

prediction methodologies. Practitioners currently implement one of these methodologies. It is

3rd edition PTI Standard for Design and Analysis of Slab-of-Grade. This method is based on

research done by Covar and Lytton (2001), who correlated index properties of 130,000 soil

samples compiled by the Soil Survey Laboratory (SSL) of the Natural Soil Survey Center to

suction compression index based on mineralogical classification. Here the suction compression

60

index is defined as the slope of volume change to logarithm of total suction change for 100% fine

clay. The result of their study was updated mineralogical classification chart introduced by

Casagrande (1948), section 2.8.1.3. The chart was partitioned into six mineralogical regions.

For each region a chart was developed that enables the determination of suction compression

index based on liquid limit, activity, P200 and percent of clay. The suction compression charts are

given in Figure 2.26 and the complete design procedure based on their work is presented in

Chapter 5, PTI, Residential Foundation Design Method.

Figure 2.25. Soil characterization in terms of suction compression index (after McKeen,

2001).

Table 2.7. Soil classification based on suction compression index (after McKeen, 2001).

Category ∆h/∆w Ch ∆H* ∆H Remarks I >-6 -0.227 15.3(6.0) 10.0 Special Case II -6 to -10 -0.227 to -.12 8.1(3.2) 5.3 High III -10 to -13 -0.120 to -.04 2.7(1.1) 1.8 Moderate IV -13 to -20 -0.040 to non expansive --- --- Low V <-20 Non-expansive --- --- Non-expansive

*∆H for f=0.5, active zone (Za)=1.5 m (5ft), ∆h=1.0 pF, s=0.9

61

Zone I

Zone II

Zone III

Zone IV

Zone V

Zone VI

Figure 2.26. Suction compression index based on mineralogical classification of soil into six types and soil index properties (after Covar and Lytton, 2001 and also PTI 3rd Edition).

62

2.8.3 Direct Measurement

The best method of predicting potential heave or potential swelling pressure of a soil

sample is to measure it directly. The measurement is typically obtained with one dimensional

oedometer test where a soil specimen is placed inside of a brass ring. The rigid brass ring is

placed inside of a confining base to eliminate lateral deformations during testing. Porous stones

are placed on top and bottom of specimen. Porous stones, which allow drainage during the

testing process, are typically made of sintered corundum and are 0.5 mm smaller than the ring.

The difference in diameter between stone and the ring prevents the stone from being dragged

along the side of the ring during consolidation test that is typically performed after the swell test.

The oedometer test can be performed by spontaneously compressing both sides of the

sample or by applying pressure from one face only. The first type of test is called floating-ring

test while the second one is referred to as fixed ring test. Soil specimen tested in the floating

ring oedometer typically experiences somewhat less friction (between the soil and the ring) than

the fixed ring test. However the advantages of the fixed ring test highly exceed the reduced

friction benefit. The primary advantage of the fixed-ring test is that drainage from the bottom

porous stone can be measured or otherwise controlled which allows for the measurement of soil

permeability (Holtz and Kovacs, 1981). The fixed ring oedometer is the most widely adopted

one-dimensional swell/compression measuring equipment.

There are three types of one-dimensional tests typically performed on expansive soils.

They are free swell test, swell pressure test and expansion index test. The free swell test

consists of applying 1 psi surcharge and submerging an undisturbed or recompacted soil sample

in distilled water. One dimensional volume change is observed and the percent swell is

calculated by dividing the change in soil height by initial height of the specimen. Table 2.8

provides a summary of values developed by U.S Bureau of Reclamation to predict the severity of

swell based on observed percent swell determined from the free swell test.

Swelling pressure is determined in a similar way to the procedure described above.

Overburden pressure is applied to an undisturbed or recompacted soil sample. The specimen is

63

submerged in distilled water, but this time the sample is not allowed to change in volume. The

tendency to swell is suppressed by applying additional load to the sample. The pressure

required to overcome the heave of soil is referred to as the swelling pressure.

Table 2.8. Classification of swell potential significance (after U.S. Bureau of Reclamation, 1974; surcharge of 6.9 kPa; Holtz et al., 1981).

Classification of Expansion

Percent Expansion (Dry to Saturated Condition)

Very High > 30 High 20-30

Medium 10-20 Low <10

Expansion Index, EI test is performed on recompacted soil samples in general

accordance with ASTM D 4829 procedure. The test is performed on 50% saturated soil where

the sample is prepared by compacting moist soil in two layers with 15 blows of 2.5 kg hammer

from distance of 12 inches per layer. The specimen is placed in consolidometer and 1-psi

surcharge pressure is applied to it. The sample is submerged in distilled water and is allowed to

swell. Dividing the observed change in height by the initial height of the sample and multiplying

it by a 1000 calculates EI. Table 2.9 gives typical expansion index values per expansion

classification.

Table 2.9. Classification of swell potential as per U.S. ASTM Standard D 4829-03 for Expansion Index.

Classification of Expansion Expansion Index Very High > 130

High 91-130 Medium 51-90

Low 21-50 Very Low 0-20

In Arizona, the standard EI procedure has been modified and is referred to as EIAZ. The

soil sample is prepared at -1% to +4% less of optimum water content and at 95% of optimum dry

density as determined from the standard compaction test. Surcharge pressure of 1-psi is

applied to the specimen that is saturated with distilled water and allowed to swell. The results

64

are expressed in terms of percentage of swell. All of the procedures described in here are given

in more detail in Chapter 4, Laboratory Testing.

2.9 Unsaturated Soil Mechanics Theory

Unsaturated soil mechanics is a relatively new discipline derived from classical soil

mechanics, mass balance and equilibrium principles, which

2.9.1 Soil Suction and Soil Moisture

in part deals with mass transport

though vadose zone. Although this theory was developed almost 50 years ago, serious

challenges limit its applicability to research, soil science and high impact environmental projects.

These challenges include and are not limited to 1) measurement of unsaturated soil properties, a

time consuming process requiring specialized equipment and expertise 2) uncertainty associated

with unsaturated soil properties, and 3) numerical modeling. Although many commercial and

public codes solving moisture flow though unsaturated soil exist, numerical modeling continues

to be an active topic of research, mainly in the area of stability and convergence, which are

challenges inherent to advection-diffusion type problems, as well as long time simulations

requiring a lot of computational effort. This section contains a literature review of transient flow

theory and its application, including definition and measurement of soil suction, estimation of

unsaturated soil properties, description of partial differential equation describing moisture flow

through unsaturated soil, overview of currently available commercial software and current

developments in numerical methods.

An unsaturated soil is commonly referred to as a three-phase system of solid, water and

air. Recently, the importance of air-water interface (i.e. contractile skin) gain a recognition as an

additional phase significant in the explanation of unsaturated soil mechanics (Fredlund and

Rahardjo, 1993). According to the theory of molecular attraction, molecules of liquid below the

surface act on each other by forces that are equal in all directions. However, molecules near the

surface have a greater attraction for each other than to molecules below the surface. This

65

produces a surface on the liquid that acts like a stretched, elastic membrane exerting tension on

objects in contact with it. Its magnitude per unit length is defined as surface tension, σ. The

effect of surface tension can be demonstrated by water rise in capillary, expressed by equation

(2.1). The relationship can be also expressed in terms air and water pressure differential referred

to as matric suction, where huuu wa ∆=−=∆= γψ (Fredlund and Rahardjo, 1993). A basic

relation between surface tension, the diameter of the capillary tube, and the rise is given by

4hdσ

γ∆ = (2.1)

where:

Δh = height of water in a tube [m];

σ = surface tension for air water interface [0.0073 N/m];

γ = specific density of water [9.81 kN/m3

Soil suction is a measure of soil’s affinity for water; it is a free energy of the pore water

which can be expressed in terms of partial vapor pressure or relative humidity (Richard, 1965).

When expressed in terms of relative humidity it is referred to as total suction.

].

( )RHWv

RTvw

T ln−=ψ

vs

v

uuRH =

(2.2)

with

ψT

(2.3)

and

- total suction [kPa];

R - universal gas constant

KmolJ31432.8

T

;

- absolute temperature [K];

vw - specific volume of water

kgm

w

3

001.0,1ρ

;

66

Wv - molecular mass of water vapor

kmolkg016.18

RH

;

- relative humidity [%]

vu - partial pressure of pore water vapor [kPa];

vsu - saturation pressure of water vapor over a flat surface of pure

water at the same temperature [kPa].

Total suction consists of matric suction and osmotic suction/ the matric suction depends

on the capillary phenomenon arising from the surface tension of water, whereas the osmotic

suction depends on the salt concentration in the pore water. The existence of salts in water

results in the reduction of the relative humidity of the water vapor pressure, which in turn causes

the reduction of total suction (Fredlund and Rahardjo, 1993).

2.9.2 Measurement of Soil Suction

Suction of soil can be measured directly or indirectly. The principle of the direct method

is to apply air pressure, causing the sample pore-water to increase or decrease until soil suction

equals the imposed air pressure. When equilibrium is reached between the pore water and the

imposed air pressures, the resultant water content is unique to this soil at this suction. Pressure

plate, tensiometer and pressure membrane are examples of direct measurement of soil suction.

Indirect measurement can be obtained with psychrometer, filter paper and thermal sensors. It is

based on thermodynamics, where the soil suction is evaluated from the measurement of relative

humidity or heat dissipation. Fredlund and Rahardjo (1993) presented a detailed description of

suction measurement methodologies with are briefly summarized below.

Total suction can be measured with psychrometers and filter paper or controlled with salt

solution in desiccators. The thermocouple psychrometers measure the total suction by

measuring the relative humidity in the air phase of the soil pores or the region near the soil. The

psychrometer consists of a semi-permeable ceramic tip protecting two metal wire conductors

welded together at the tip, which measures relative humidity by a technique called Peltier cooling

67

involving current flow, water condensation at dew point and measurement of voltage output.

Psychrometers must be calibrated prior to testing.

The filter paper method of suction measurement is based on the assumption that a filter

paper will come to equilibrium with soil suction. Equilibrium can be reached by either liquid or

vapor moisture exchange between the soil and the filter paper. When a dry filter paper is placed

in direct contact with a soil specimen in a closed container, it is assumed that water flows from

the soil to the paper until equilibrium is achieved (matric suction measurement). When a dry

filter paper is suspended above a soil specimen, vapor flow of water will occur from the soil to

the filter paper until equilibrium is achieved (total suction measurement). Upon equilibration the

water content of the filter paper is measured. The filter paper must be calibrated prior to use

which is achieved with salt solution of different molarities. When the water content of the filter

paper comes to equilibrium with the relative humidity of the solution, the water content is

determined and correlated with corresponding suction value. Filter paper is a very useful testing

methodology since wide ranges of soil suction can be determined with it. The measurement of

total suction in desiccator involves equilibrating the soil suction with the relative humidity

maintained by salt solution.

Matric suction can be measured with filter paper, tensiometer, pressure plate, pressure

membrane and thermal conductivity sensors. Tensiometer consists of fine porous stone placed

in contact with soil. A pressure gauge such as dial gauge, manometer or electronic transducer is

connected to the ceramic stone through a small bore tube to measure the pressure in the soil

water. Because the porous tip allows the migration of salts through the ceramic stone,

tensiometers measure only the matric suction component of the suction (Chen, 1988).

Matric suction can be also determined with pressure plate or pressure membrane

equipment that utilizes axis translation technique. The axis translation technique prevents water

cavitation allowing the measurement of matric suction above 101.3 kPa. Pressure plate device

consists of pressure chamber, high air entry ceramic disk, water chamber below the ceramic

disk, and water valves connected to the water chamber. The water valves allow for the

68

measurement of released or absorbed water by the soil sample located on top of the saturated

ceramic stone. The essential component of the device is the ceramic stone that is used to

separate the air and water phases. The purpose of the ceramic stone is to provide pore spaces

small enough so the air pressure required to force an air bubble through the stone is greater

than the anticipated applied air pressure. Therefore, the properties of the ceramic stone

determine the maximum allowed suction measurement; which usually is 1500 kPa. The ceramic

stone also provides a flow path for the liquid water from the soil through the ceramic stone and

into the water compartment below the stone and vice versa. The pressure membrane apparatus

is very similar to the pressure plate equipment. The pressure membrane apparatus uses

cellulose membrane instead of ceramic stone. The equipment allows for the measurement of

number of samples instantaneously up to the suction of 1500 kPa.

The measurement of matric suction can also be obtained with thermal conductivity

sensor that works on the basis of correlating the heat dissipation in a porous ceramic with its

water content. The water content, in turn is a function of the suction. Since the heat

conductivity of a porous material is lower than that of the water, the heat dissipation in a porous

material is sensitive to its water content. When a standard porous probe is inserted into a soil

sample with different pore-water suction, water passes from the area of low suction to the area

of high suction. The movement of water takes place through direct capillary flow until equilibrium

is reached. The rate of heat dissipation of the standard porous material, therefore can be

measured by supplying a precisely controlled amount of heat at a fixed rate at the center of the

porous block and by measuring the temperature rise at the same point after fixed period of time.

The temperature rise is inversely proportional to the moisture content in the standard porous

block. The measured temperature is calibrated to read matric suction (Chen, 1988).

Osmotic suction can be measured by squeezing technique. In this technique, distilled

water is added to the soil sample until the soil reaches near fluid consistency. The water is

extracted from the soil sample with fluid squeezer consisting of heavy-walled cylinder and piston

squeezer. The extracted water is subjected to electrical conductivity test. The electrical

69

conductivity of the squeezed water is used to indicate the concentration of dissolved salts that is

related to the osmotic suction of the soil.

2.9.3 Soil Water Characteristic Curve

Transient water flow problems require the relationship between soil moisture and suction

be defined. Two definitions of that relationship were found in literature. They are suction

compression index and water storage coefficient. Suction compression index defines the slope

of gravimetric water content (McKeen et al, 1990), or strain (Lytton, 1992) versus total suction.

McKeen et al. (1992) developed empirical equation presented developed using results from

CLOD test.

Ch = −0.02673 ∆h∆w

− 0.388704

∆h

(2.4)

where:

= change in total suction [pF], and

∆w = change in gravimetric water content.

Using soils from the Denver area, this equation was further modified by Perko et al.

(2000) to

Ch = −103

PL2 e + Fe +1

PL

(2.5)

where:

= plastic limit [%],

F = percent of soil passing US sieve number 200, and

e = void ratio.

Lyton and Covar (2001) presented a methodology to estimate the suction compression

index based on index properties and gradation; refer to Section 2.8.2.4 for additional details.

The water storage coefficient is a slope of the Soil Water Characteristic Curve, SWCC.

The SWCC is defined as the relationship between water content and matric suction, where the

70

water content can be expressed in terms of volumetric water content, gravimetric water content

or saturation. Figure 2.27 shows a typical plot of SWCC. It can be seen from that figure that

there exists a unique function of SWCC for adsorping and desorping process where the

difference between these two curves is about one log of suction per specific water content. The

difference can be explained by hysteresis. Most of the empirical equations were developed for

drying process, and such the equations represent the desorption relationship between water

content and suction. Numerous empirical equations have been proposed for estimation of the

SWCC. Some of them are presented in Table 2.10.

Figure 2.27. Typical Soil Water Characteristic Curve (after Fredlund and

Rahardjo,1999).

Table 2.10. Proposed empirical and theoretical equations of SWCC. Author Equation Description

Garner, 1958

Θ =1

1+ qψ n

Brooks and Corey, 1964

Θ =ψb

ψ

λ

Verified by many studies. Not valid near maximum desaturation or under fully saturated conditions.

Van Genuchten, 1980

Θ =1

1+ qψ n

m

Frequently used. The parameter m is sometimes calculated as

n11− .

Williams et al., 1983

lnψ = a1 + b1 lnθ

71

Author Equation Description

McKee and Bumb, 1984

Θ = e− ψ−a 2( )

b2 Not valid near maximum desaturation or under fully saturated conditions.

McKee and Bumb, 1987

Θ =1

1+ eψ−a 3

b3

Valid for suctions near saturation. Not suitable in the high suction range.

Fredlund, 1994

m

ns

ae

C

+

=ψ

ψθθ

ln

1)(

+

+

−=

r

r

h

hC

10000001ln

1ln1)(

ψ

ψ

Theoretical equation uniquely determines SWCC. Fits experimental data reasonably well within suction range of 0 to 106 kPa.

Θ =

θ −θr

θs −θr

θs

, normalized water content, dimensionless,

= volumetric water content at saturation, dimensionless,

θr = residual volumetric water content, dimensionless, λ = pore size distribution index, dimensionless, ψ = matric suction [kPa], hr = total suction corresponding to the residual water content, θr [kPa], a = soil parameter that which is related to the air entry value on the soil

a, m, n, p ,

= different soil parameters, a1, b1, a2, b2 = curve fitting parameters,

e = natural log base, n = controls the slope at the inflection point, and m = residual water content in the soil.

2.9.3.1 Uncertainty Band

The research done by Zapata (1999) indicates that different saturation levels can be

obtained for the same soil sample at the same suction. This phenomenon can be explained by

the variation in dry density, hysteresis, different test methodologies, variability in test procedures

and operator error. Fredlund and Rahardjo (1993) determined that when testing is done on the

same soil material with different dry density, the soil behavior will follow a different path on the

72

saturation vs. suction curve. It is further explained that the change in dry density of soil results in

a change of soil fabric and the soil at new density exhibits the behavior of a somewhat different

soil. Many of the factors are hard to quantify. Hysteresis is one exception. It is well established

that SWCC will follow one path during desaturation process and another one during saturation

(Fredlund and Rahardjo, 1993, Hillel, 1980, Scott et al., 1983).

The uncertainty band reflects the influence of the above-mentioned factors; it is also a

function of soil type. Figure 2.28 shows experimental data for Fountain Hills, Arizona clay, the

best fit function, and the 95 % confidence band developed by Zapata (1999). The data points

vary over two orders of magnitude in suction per specific water content. Similar conclusion was

presented by Gribb (2000) who reported data scatter over one order of magnitude for sandy soil.

Figure 2.28 shows that the representation of the SWCC as a single unique curve is, in general,

just an approximation.

0

0.1

0.2

0.3

0.4

0.5

0.6

1E-6 1E-4 1E-2 1E+0 1E+2 1E+4 1E+6

Matric Suction (kPa)

Vol

umet

ric W

ater

Con

tent

(cm

3 /cm

3 )

Experimental Results

Best-Estimated SWCC

95% Confidence Band

Figure 2.28. Uncertainty Band of Fountain Hills, Arizona clay (Zapata, 1999).

2.9.3.2 Hysteresis

Hysteresis is one of sources causing variability in the SWCC. Research done by Chen

(1988) provides valuable information about the variation of soil behavior during wetting and

drying cycles. He found that the drying soil follows a different path than the wetting soil on the

water content vs. dry density curve. This variation ceased at the fifth cycle in his studies and the

73

wetting and drying paths became the same. Fredlund observed similar behavior on the

saturation vs. matric suction curve presented in Figure 2.27 (Fredlund et al. 1993).

Hysteresis can be explained by an ink bottle effect. When an empty tube is placed in

water bath, the water will rise up until an equilibrium state is reached. A saturated tube with

large void below equilibrium water height, when allowed to drain, will drain to the same height.

This corresponds to drying soil behavior. If the same tube with the large void placed in the water

bath, the water will rise to a height below the void. This corresponds to wetting behavior, which

is visually presented in Figure 2.29 (Miyazaki, 1993).

Figure 2.29. Ink bottle effect (after Miyazaki, 1993).

0

10

20

30

40

50

1E-2 1E-1 1E+0 1E+1 1E+2 1E+3 1E+4 1E+5 1E+6

vwc

[%]

Suction [kPa]

Lab DataDrying CurveWetting - back pressureWetting - ponding

Figure 2.30. Closed and open hysteresis loops developed for CH soil, Arizona.

74

Closed hysteresis loop is formed when backpressure saturated soil is desaturated and

then saturated again from bottom up. The wetting curve typically has the same slope as the

drying curve and is shifted to the left of drying curve by 0.5 to 1.5 log of suction (Fredlund and

Rahardjo, 1993, Zapata, 1999 and others). When the moisture is ponded on top of the soil, the

specimen reaches lower value of saturation due to high percentage of entrapped air, which

creates an open loop hysteresis with the drying curve. The ratio of θ(sat ponding)/θ(sat Back Pressure) has

been estimated by Hillel (1980) to be about 90% and Basile at al. (2003) providing range from

78% to 95%. An idealized open and closed hysteresis loops are presented above in Figure

2.30.

2.9.4 Unsaturated Soil Permeability

In order to solve seepage of water through unsaturated soil, it is necessary to define

permeability in terms of suction. The unsaturated soil permeability, k(h), describes moisture flow

characteristics of soil with decrease in pore water pressure. As the soil desaturates, the number

of saturated pores decreases, decreasing the number of moisture flow passages, hence the soil

permeability decreases when suction increases. It was first noticed by Richards (1931) that

capillary forces describe flow through unsaturated medium and the conductivity is related to the

moisture content of the medium. Furthermore, since moisture content uniquely varies with

suction, logical conclusion follows that the unsaturated soil permeability can be expressed in

terms of suction and it can be approximated from SWCC. Table 2.11 lists historical

advancement in this area of research. Many soil parameters in the proposed equations come

from estimated SWCCs with equations from Table 2.10.

75

Table 2.11. Proposed equations of unsaturated soil permeability as a function of suction (from Fredlund, 1993).

Author Equation

( )

1

sn

a w

w

kku ua

g

ψ

ρ

= −

+

Gardner, 1958

Brooks and Corey, 1964

k(ψ) = ksat for

ua − uw( )≤ ua − uw( )b

( )( )a w b

sa w

u uk ku u

η

ψ

−= −

2 3η λ= +

for

ua − uw( )≤ ua − uw( )b

( )

( )

'

1

sn

a w

a w b

kku uu u

ψ = −

+ −

Arbhabhirama and Kridakorn, 1968

( )

( ) ( )( )( )

21

2

1 1

1

mn n

s mn

k kψ

αψ αψ

αψ

−− − + = +

van Genuchten and Maulem, 1980

( ) ( ) ( )min minp

sk k k kψ θψ= − +Modified Campbell, 1996

( )

pmn

s aekk

−

+=ψ

ψ lnLeong and Rahardjo, 1997

α = diffusion coefficient,

λ = pore size distribution index, dimensionless, θs = volumetric water content at saturation, dimensionless ρw = density of water ψ = matric suction [kPa],

= k(ψ) unsaturated soil permeability, ks = saturated soil permeability, ua = pore air pressure [kPa], uw = pore water pressure [kPa],

ua – uw = matric suction [kPa], (ua – uw)b = matric suction at air entry value [kPa],

a, m, n, n’, p = different constant soil parameters, a = Soil parameter that are related to the air entry value of the soil, e = natural logarithm, n = controls the slope at the inflection point, and m = Residual water content in the soil.

76

Typically two empirical methods are used to determine k(h). Instantaneous profile

method is used in-situ, which gives wetting curve (Watson, 1966). The evaporation method

developed by (Wind, 1968), with the modifications by Tamari et al. (1993) and Romano and

Santini (1999) is typically adopted in laboratory setting for estimation of the drying curve. In

industry, empirical methods are rarely used to estimate them due to practical challenges

associated with test procedures which include test duration, sophisticated test equipment, the

procedure know-how and analysis of data, to name few. More commonly, the unsaturated soil

properties are estimated with presented fit functions. These functions commonly estimated with

statistical model based on typically quantified soil properties such as gradation and Atterberg

Limits. As shown by van Genuchten and Nielsen (1985), Vogel et al. (2001) and Vogel and

Cislerova (1988), the choice of the analytical model for SWCC estimation can significantly affect

the predicted k(h) function. Vogel et al. (2001) illustrated that small changes in SWCC near

saturation result in large changes in k(h). The differences are more pronounced in fine textured

soils than in coarse textured ones.

Figure 2.31. Typical unsaturated permeability variation with volumetric water content.

Comparison of empirical data to predicted values. (after Fredlund and Rahardjo, 1993).

77

Limited empirical information is available about unsaturated soil permeability of clayey

soils. The available data usually illustrates k(h) only up to suction of 100 kPa. It’s been shown

that within this suction range the k(h) variation due to hysteresis is insignificant (Mualem, 1986,

Kool and Parker, 1987 and Fredlund and Rahardjo, 1993), see Figure 2.31. It should be noted

that permeability presented in terms of suction, exhibits significant hysteresis, which usually

does not exceed one log of suction (conclusion drawn based on data by Brooks and Corey,

1964). As with SWCC estimate, k(h) as a single unique curve is, in general, an approximation

which is typically based on drying SWCC estimate. Additionally, small variations in SWCC

estimate near saturation cause large differences in k(h) estimate near saturation with

consequences on numerical results, stability of solution and rate of convergence (Vogel et al.,

2001).

2.9.5 Theory of Moisture Flow

The analysis of soil response due to atmospheric conditions consists of two

components: liquid water flow, and water vapor flow. Liquid water transfer is frequently

dominated by gravity flow especially in high permeability soils or stiff clays where flow might

occur in the bedding planes, continuous fissures or shrinkage cracks. Shrinkage cracks that

develop due to surface desiccation provide an easy access of water into the deep soils. In fine-

grained soils, moisture flow due to capillary force can dominate moisture transfer mechanism.

The moisture migration can occur in all directions. For example, under artesian conditions, the

flow can be upward. The height of water rise into the capillary fringe varies inversely with the

radius of the capillary tube. In clay a theoretical rise of 1000 ft is possible (Chen, 1988).

Moisture flows from an area of high potential energy to an area of low potential energy.

The first model of moisture flow through soil was developed by Darcy (1856) followed by

universally applied mass-conservation based Richards’ equation (1931), its form implemented in

this research work. The solution of Richards’ equation requires the computational power of a

computer and a sophisticated numerical method capable of solving a stiff partial differential

78

equation, PDE. The challenges associated with the solution of mass-balance based approach

yielded the development of empirical formulations by Kostiakov (1932), Horton (1940) and

Holtan (1961) and Green-Ampt method (1911). These approaches are attractive for simple

infiltration problems, which can be solved by hand.

There are few components of gas flow: advective due to pressure or thermal gradient

and diffusive into liquid in a form of occluded air bubbles. The diffusive flow is hard to

characterize and is not significant for majority of civil engineering, hydrology and soil science

applications. Advective gas flow can occur in all directions in response to thermal gradients,

where vapor travels from high temperature to a lower one or by pressure gradients where the

gas flows from area of high potential energy to area of low potential energy. The analysis of gas

flow is important when modeling atmospheric conditions and vapor flow due to potential

evaporative fluxes. Condensation of water vapor plays a role in moisture migration and soil

heaving, which might be a significant factor in moisture migration under covered areas.

Additionally, thermal gradients can cause moisture migration in the liquid phase. Experiments

conducted at Princeton University show that the temperature differential of 1 degree C was at

least equivalent to a hydrostatic head of 1 m. Thermal gradient reaches maximum efficiency

when the moisture content in the soil is near PL (Chen, 1988).

Thermal gradient is the basis of the thermodynamic theory of moisture migration first

introduced by Edlefsen and Anderson (1943) as moisture movement initiated by a total specific

free energy gradient. It was defined in terms of surface tension, hydrostatic pressure, dissolved

material and adsorptive forces. The thermodynamic approach distinguishes between the

different water phases and prescribes the liquid flux in the direction of the higher temperature

(Ten Berge, 1990). However, it is argued that if the soil water is divided into two sub-phases,

vapor and liquid, the driving forces on the respective sub-phases caused by a temperature

gradient will cancel each other out. This might lead to the conclusion that the effect of

temperature on the driving force for water movement is smaller than previously thought (Berge,

1990). Furthermore, Corey and Klute (1985) and Durkee (2000), critiqued that the effects of

79

gravity are not taken into account in the thermodynamic approach and that it is not analogous to

Darcy’s Law. More recent work done by Wilson et al. (1994) provides a modified Richard’s

equation for advective vapor flow coupled with heat transfer which is implemented in this

research work.

2.9.5.1 Saturated Flow

Hydraulic gradient is a central concept in fluid flow mechanics. It is defined as the

energy or head loss per unit length. For laminar flow and saturated soil conditions the

relationship between flow velocity and hydraulic gradient was found to be linear. The slope of

the linear function is referred to as proportionality constant, and more commonly coefficient of

permeability, permeability or hydraulic conductivity. This relationship was first discovered

experimentally by Henry Darcy in 1856 and then proven to satisfy principles of mass

conservation. Now, this fundamental concept in soil mechanics is referred to as Darcy Law

given in equation 2.6.

yhkv

∂∂

−=

v

(2.6)

where:

= Water flow rate [m/s]

y = Distance [m]

k = Saturated soil permeability [m/s]

h = u/ρ

g+y, total head equal to pressure plus elevation heads [m]

The underlying assumption in Darcy law is that the flow velocity of water passing though

soil particles is small enough to satisfy laminar flow conditions. Figure 2.32 illustrates that as the

flux increases the hydraulic gradient increases linearly for Reynolds numbers smaller than 1,

where the Reynolds number is a measure of friction loss within a system distinguishing between

laminar and turbulent flow (see Tindall and Kunkel, 1999 for details). For Reynolds number

80

larger than 1, Darcy Law is not valid, the relationship becomes nonlinear and for Reynolds

number larger than 100 the flow becomes turbulent.

A deviation from Darcy Law was also observed in clayey soils with low permeability

under small gradient conditions. Small hydraulic gradients can cause no-flow situation or flow

rates smaller than anticipated from Darcy Law. Figure 2.32 illustrates a concept of threshold

gradient, where deviation from Darcy Law is observed for small hydraulic gradients, which is

attributed to clay microstructure and its interaction with water particles.

Figure 2.32. Schematic of flow classification based on Reynolds number (after Tindall

and Kunkel, 1999).

The first method of saturated moisture flow analysis was introduced by Cassagrande in

1937, who proposed a flow net technique, a graphical solution of Laplace’s equation in two

dimensions presented in equation 2.7, where x and y are two coordinate directions. Laplace

equation represents energy loss through any resistive medium. The flow net solution assumed

no flow in the unsaturated zone. The flow line solution is obtained through trial and error by

sketching a network of flow lines and equipotential lines spaced in such a way as to divide the

81

flow area into equal squares. The flow net technique can be only used for simple saturation

seepage problems with simple geometry, soil properties and clearly defined boundary conditions

(Holtz and Kovacs, 1981).

∂ 2h∂x2 +

∂ 2h∂y2 = 0

2.9.5.2 Unsaturated Flow

(2.7)

With the introduction of computers, numerical methods made their way into geotechnical

application. In 1967 Taylor and Brown proposed a finite element model for seepage problems

with a free “surface”. This model considered only flow of water in the saturated zone and the

phreatic line was assumed to be the upper boundary of the flow region. The model often had

convergence problems due to incorrect assumption on the upper boundary of the flow region.

More recently Butterfield and Tomlin (1972) used Boundary Element Method, BEM, for solution

of flow through saturated soil. They used direct Green function formulation that incorporates

polynomial distribution of the medium property into the free space Green’s function to obtain

solutions to steady flow in saturated heterogeneous media. The solution is obtained by iteration.

Currently there are many commercial and public domain software that implement finite element

or finite difference methodologies to solve Darcys’ equation for moisture flow through saturated

medium. The most commonly used MODLOW program uses finite difference and implicit,

backward Euler time discretization.

Unsaturated soil mechanics theory was developed as an extension of classical soil

mechanics, being a special case of unsaturated soil mechanics with its limited application to

groundwater flow and positive pore water pressures. Unsaturated soil mechanics applies to both

vadose zone and soil below ground water table providing smooth transition between them.

Unsaturated soil refers to a medium partially filled with water and partially with air. As the soil

de-saturates the pore water pressure changes from positive (compressive) to negative (tensile).

The magnitude of negative pore water pressure is a function of pore size distribution, where the

82

largest pores de-saturate first leaving tensile force acting on smaller gaps in the soil structure.

Because suction, equal to ua-uw, (Fredlund and Rahardjo, 1993) depends on the radius of pore

size, it increases nonlinearly with decrease of saturation. It is assumed that water flow can occur

only across pores filled with water. Because partially saturated soil has decreased number of

flow passages, the unsaturated soil permeability decreases with degree of saturation in a

nonlinear manner.

Unsaturated liquid moisture flow though soil in one dimension is described by Richard’s

equation, a parabolic, partial differential equation derived from mass conservation. It assumes a

continuum, homogeneous, incompressible and isothermal medium, as well as a negligible air

pressure, which is infinitely mobile in the unsaturated zone. The pressure head, h - based

formulation

( ) thmS

yhk

y ww

y ∂∂

=+

∂∂

∂∂ γψ 2

( ) 0=+

∂∂

∂∂ S

yhk

y yψ

Transient Seepage (2.8a)

y

Steady State Seepage (2.8b)

is a nonlinear advection-diffusion equation involving:

- elevation [m],

t - time [h],

h - total head [m],

γw - specific weight of water [9.81 kN/m3

m2w

],

= 0/ ≥∂∂ uθθ

, slope of SWCC

- volumetric water content

k(ψ - )y unsaturated soil permeability [m/h]

S - source or sink [m/h]

Both m2 ( )u−= ,0maxψw and k(ψ)y are functions of h via the matric suction, [kPa],

where the pore water pressure, u, is defined by

( )yhu w −= γ [kPa] (2.9)

83

Applied boundary conditions are either

h = C

C=yhky ∂

∂

prescribed pressure head (Dirichlet) (2.10a)

or

Lh =

prescribed flux (Neumann). (2.10b)

In surface runoff (or seepage) conditions, a mixture of Dirichlet and Neumann boundary

conditions is applied, depending on the value of the pore water pressure:

for 0≥u and Cxhkx =

∂∂

for 0<u , (2.10c)

where L

( ) thm

yhD

yhk

y ww

myy ∂∂

=

−

∂∂

+∂∂

∂∂ γγψ 21

represents the height of the computational domain.

For modeling of atmospheric conditions under the assumption of isothermal medium,

Richard’s equation is modified to include vapor based on from Fick’s Law as per the work of

Wilson (1994),

RTuWD

uuuD vv

w

v

a

vamy 2ρ

+=

(2.11)

RTWDD v

vapv αβ=

(2.12)

32

βα =

(2.13)

nS)1( −=β

(2.13a)

75.14

273110*229.0

+= − TDvap

(2.13b)

Dmy

(2.13c)

where:

- vapor diffusion coefficient [m3

ua

*s/kg],

- pore air pressure [101.3 kPa],

uv - uvsRH, partial pore pressure due to water vapor [kPa],

84

RH - relative humidity [%],

ρw - water density [1000 kg/m3

Dv

],

- diffusion coefficient of water vapor through soil [kg*m/(kN*s)],

α - tortuosity factor of soil,

β - crossectional area of soil available for vapor flow

S - degree of soil saturation [%]

n - porosity

Dvap - molecular diffusivity of water vapor in air [m2

A coupled model of heat, mass and vapour flow developed by Wilson et al. (1994) can

be used to describe soil behavior under anisothermal conditions. In this model, Darcy’s and

Fick’s Laws are used to describe moisture and vapour flow respectively while heat flow is

evaluated based on conductive and latent heat fluxes. Equation 2.14 gives transient liquid and

vapor water flow while equation 2.15 describes heat flow.

/s].

( ) thm

yuD

yuuu

yhk

y wwv

va

vawy ∂

∂=

∂∂

∂∂+

+

∂∂

∂∂ γψ 2

tTC

yuD

yuuuL

tT

y hv

va

vav ∂

∂=

∂∂

∂∂

+−

∂∂

∂∂ λ

(2.14)

λ

(2.15)

where:

- thermal conductivity [W/(m*°C)],

Lv - latent heat of vaporization for water [J/kg],

Cv - volumetric specific heat [J/(m3

*°C)].

The solution of Richard’s equation requires that the variation of both volumetric water

content and unsaturated permeability, k(h), with matric suction are defined. The relationship of

volumetric water content or degree of saturation to matric suction is defined as the Soil Water

Characteristic Curve, SWCC. Empirical and numerical equations estimating SWCC are listed in

Table 2.10. The unsaturated hydraulic conductivity function is a time derivative of the SWCC. A

list of researchers’ proposed k(h) is given in Table 2.11.

85

The above presented theoretical methodologies are commonly applied in commercial

and public domain software developed in Canada and US. Literature review revealed that many

theoretical approaches to the solution of liquid moisture flow through unsaturated soil exist. All

of them have a form of Richard’s equation with diversity in the description of the source term, the

change in volumetric water content with time and expression of unsaturated soil permeability in

terms of diffusivity e.i. Taigbenu, 2001, Fredlund and Rahardjo, 1993, Wray et al., 2005 and

others. There are also few published coupled vapor, heat and water flow approaches. They

include work done by Schieldge et al., 1982, Camillo et al., 1983, Witono and Bruckler, 1989,

and Thomas (1999) which are not described here. In this research work, the above presented

equations are considered to be the governing, state-of-the art equations used for 1) modeling of

atmospheric conditions and 2) illustration of advanced numerical methodologies.

2.10 Numerical Methods

Richards’ equation is a parabolic partial differential equation, PDE, with advection-

diffusion characteristics. The lack of analytical solution has led to the development and

implementation of sophisticated numerical methods requiring both time and space

discretizations. Appropriate numerical tools to analyze advection-diffusion equation include finite

difference method, FD, finite volume method, FV, and finite element method, FE. FE methods

include classical Galerkin, nonconforming, discontinuous, mixed, adaptive and multiscale

(wavelet and multigrid schemes) methods. Time discretization involves explicit or implicit

methods with or without adaptive and iterative features. Up-scaling and mass lumping are

frequently implemented. Stability, convergence and time efficiency are issues inherent to this

class of problems, hence the ongoing research in the arena of numerical methods with aim on

overcoming these challenges.

86

2.10.1 Numerical Methods Used in Solution of Richard’s Equation

Initially, the numerical solution of Richards’ equation followed a simple finite difference

method, Freeze (1971) followed by more advanced finite element work by Neuman (1972), Lam

(1987), Papagianakis and Fredlund (1984 and 1995) and Celia et al. (1990). The currently

implemented standard approach follows a “method of lines” also referred to as semi-

discretization, where spatial derivatives are first approximated using a variety of (usually low

order) finite difference or finite element schemes, and the resulting discrete system of ordinary

differential equations (which also accounts for boundary conditions) is then solved using a time

integrator.

2.10.2 Available Commercial Software

Currently, there are many commercial and public domain software for vadose zone

analysis. They vary in complexity and solution algorithms based on the intended use. Bucket

codes are typically applied in large-scale groundwater recharge problems with statistical

averaging of the main hydrological processes. The groundwater recharge occurs when the

surface precipitation exceeds runoff and PE while the seasonal moisture content changes are

handled by a root zone storage capacity referred to as a reservoir or a “bucket” (Schaake, et al.,

1996). Simplified semi-analytical solutions have been developed for large-scale analysis of

surface moisture content and surface runoff determination as input parameters for climate

estimate programs. This method is frequently coupled with real moisture data collected on

hourly bases at selected sites, such as the Walnut Gulch, Arizona monitoring station. The loop

mechanism reduces uncertainty associated with the implemented simplifying assumptions.

Rutgers at http://climate.envsci.rutgers.edu/soil_moisture/ maintains large public domain

database of soil moisture with links to related research. The third methodology involves the

numerical solution of Richards’ equation applicable to relatively small-scale problems. The

solution is progressed with sophisticated numerical tools with high computational requirements.

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Based on literature review and survey of practitioners a short list of most commonly used

programs for engineering design was established and it includes Hydrus, Vadose/W,

MODFLOW-SURFACT, Seep/W, Unsat-H, Shaw and STOMP, where Hydrus is among the most

popular ones. The choice of software frequently depends on the modeled scenario, for example

SHAW is preferred for analysis of cold climates while Unsat-H is the preferred choice in arid

regions with vegetation cover. Many commercial software for analyzing Richards’ equation

implement finite element discretizations and semi-implicit or implicit time integration schemes.

Mass lumping of soil properties is typically used to increase stability. Most software implement

some form of time step adaptivity involving the number of successful nonlinear iterations

performed in past time steps. When the maximum number of allowed iterations is reached the

step size is reduced and new solution is recomputed. A short overview of numerical methods

and numerical issues observed in the commonly used programs is given below.

2.10.2.1 SVFlux

SVFlux is a finite element program based on a FlexPDE kernel, a general software for

solving systems of PDEs in 1D, 2D or 3D. FlexPDE utilizes adaptive unstructured mesh

generation and adaptive time stepping based on an implicit Backwards Difference formula (BDF)

of low order (order 1 is implicit Euler, order 2 is “Gear's method”, a two-step method which

requires a proper initialization). By default at most 3 Newton iterations are allowed in the implicit

step, thereby transforming the implicit method into an explicit solver of predictor-corrector type

when used with a fixed time step. From an accuracy point of view this limitation can be

compensated by using smaller time steps. From a stability point of view however, such limitation

may cause local instabilities in highly refined or nearly saturated regions which may develop into

global instabilities.

Runoff boundary condition (2.10c) is handled by replacing the surface head boundary

condition by a Neumann boundary condition of the form (assuming no ponding)

88

uFkxhk xx −=

∂∂

for 0≥u

( ) 01=−+

∂∂ Lh

xh

F wγ

(2.16)

where Φ is a large relaxation constant (SVS, 2005). Using (2.9), Eq. (2.16) is equivalent to the

Robin boundary condition

for Lh ≥

2.10.2.2 Vadose/W

. (2.17)

Large values of Φ in (2.17) provide a good approximation of the head boundary

condition, but if not implemented appropriately, may introduce large coefficients, i.e. stiffness, in

the semi-discretized system of ODEs, potentially causing instabilities in the time integration.

Note that (2.16) imposes a negative surface flux (evaporation) while (2.10c) imposes a positive

surface flux in infiltration problems (Χ>0). The resulting discontinuity typically leads to oscillations

which appear in the form of excessive infiltration into or unexpected evaporation out of the soil

profile. Reducing Φ together with mesh size and time step at the soil surface typically

overcomes these instability issues, but introduces errors in the solution which are hard to

quantify.

Vadose/W 2004 is a 2D finite element program for solving (2.8a) with either structured or

unstructured user specified mesh discretization. Vadose/W works much like SVFlux, with two

exceptions: (i) a semi-implicit integration based on an implicit Euler step is used. The soil

properties are evaluated at the midpoint of the time-step using already computed values, and the

resulting linear system is solved either directly or iteratively (with at most 5 iterations by default).

The resulting scheme is, again, equivalent to an explicit scheme, albeit with an increased

stability region compared to e.g. explicit Euler; (ii) seepage boundary conditions (2.10c) are

handled by flip-flopping between flux and head boundary conditions until either condition is

satisfied (to within a given tolerance) (Geoslope, 2005). Whether such iterative process is

guaranteed to converge remains unclear.

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2.10.2.3 Hydrus

Hydrus 3.0 is a 1D software which solves a mixed form of (2.8a) obtained by defining the

time derivative in terms of volumetric water content, θ:

( ) ttu

tth

tS

yhk

y wy ∂∂

=∂∂

∂∂

=∂∂

∂∂

=+

∂∂

∂∂ θθθγψ

( )1,11,1

++++

≈− kn

nkn

hKtδ

θθ

(2.18)

Equation (2.18) is advanced in time using Picard iterations based on an implicit Euler step

( )knknww

knkn hhm ,11,12

,11,1 ++++++ −+= γθθ

(2.19)

with , starting with ∞+ == ,0,1 nnn θθθ and

∞+ == ,0,1 nnn hhh . Surface runoff is handled, as in Vadose/W, by switching between flux and

head boundary conditions until (2.10c) is satisfied.

Hydrus exhibits numerical oscillations when solving (2.18) in infiltration problems into

dry, clayey soil profiles, with large initial mass balance errors observed. Numerical oscillations

reportedly depend on both time step and mesh size, suggesting that the implemented time

discretization method is not fully implicit. These oscillations are in principle overcome by

applying upstream weighting and selecting a time step and mesh size satisfying CFL and other

appropriate criteria (UCR, 2005).

2.11 Summary

The estimation of moisture flow through unsaturated soil for geotechnical engineering

application is a multifaceted problem involving combination of empiricism and unsaturated soil

mechanics theory. Due to the complexity of the problem and difficulties associated with the

implementation of soil mechanics, the industry adopted a semi-empirical approach to the design

and mitigation of detached residential dwellings. The presented literature review summarizes

empirical findings relative to the moisture flow through unsaturated soil and the observed impact

on lightly loaded structures. Also, a brief introduction to unsaturated soil mechanics is presented

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with discussion about commercial software implemented numerical methods that solve a form of

Richard’s equation.

Two types of slab systems are commonly used in residential construction, conventional

stem and footer with un-reinforced or lightly reinforced slab and post tensioned slabs. The

design methodologies, in part, are based on the anticipated post-construction change in the

depth of wetting and degree of saturation. It is assumed that the soil suction of undeveloped site

comes to equilibrium with the existing environmental conditions at depth unaffected by seasonal

climate variation referred to as the equilibrium soil suction at active zone depth. The active zone

depth was found to vary between 1.2 m to 12 m (4 feet to 39 feet) depending on the rigorous

definition of the term and environmental conditions of test region (McKeen, 1980, 1981, 1985;

O’Neill 1980; O’Neill and Poormoayed, 1980; Thompson, 1992; Thompson and McKeen, 1995;

Wray, 1989,1997; Wray and Ellepola, 1991; Durkee, 2000, Chao et al., 2006).

An introduction of an impermeable cover at the soil surface, such as a slab-on-grade or

a pavement, results in elimination of precipitation and reduction in potential evaporation (Day,

1994). With time the suction within the soil profile below the impermeable surface comes to

equilibrium with the new environmental conditions. It is postulated that the suction below the

slab is constant with depth and equal to the initial equilibrium suction (Nelson et al., 2001).

Based on empirical evidence, the process of monotonic moisture migration due to capillary

forces, moisture condensation below the slab and temperature gradients (Chen, 1988) occurs up

to six years (Donaldson, 1965). Furthermore, it was observed that the 6-10 year long

equilibration process is followed by a uniform drop in heave (Donaldson, 1965), which might be

related to fatigue of swelling. Fatigue of swelling refers to the decrease of soil’s swelling

potential as the drying-wetting cycles continue. Chen (1988) illustrated that swell levels off at fifth

cycle when relative equilibrium is reached.

A long-term study of slab-on-grade behavior by Wray (1992) illustrated that short-term

post-construction slab movement is attributed to seasonal climate variation resulting in edge lift

slab distortion in arid regions. Continued monitoring revealed slow but increasing mound in the

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center of the slab indicating that subsequently center lift distortion might occur. On the other

hand in humid regions, the short-term edge lift slab distress is quickly replaced with a center lift

scenario (Wray, 1992).

An important parameter for slab design is the potential suction variation below the edges

of the slab due to environmental or human imposed conditions next to the foundation. It’s been

postulated that the suction may vary 1) between liquid limit and shrinkage limit (conclusion

based on measured gravimetric water content data of SM and CL soils below 10 000 slab-on-

grades in Houston and San Antonio, Texas, (Stryron et al., 2001)), 2) between 98 kPa and 9 800

kPa (McKeen, 2001), and 3) between 33 kPa to 3 300kPa in terms of total suction (PTI, 2004).

The edge moisture variation distance, em, defined as the distance over “which moisture

will change due to wetting or drying influences around the perimeter of the foundation” (PTI,

2004) is difficult to measure experimentally. Few case studies measured em in arid regions to

vary between 1.75 m (study of bike trail by Nevels, 2001) and more than 4.5 m (study of slab-on-

grade where em exceeded a half of slab by Durkee, 2000). The em might approach the active

zone depth McKeen et al. (1990) although the PTI (2004) procedure limits em magnitude at 3 m

(9 ft).

The slab-soil system performance is frequently evaluated in terms of slab relative

deflection, angular distortion or overall magnitude and extent of superstructure distress. Based

on forensic engineering studies, cosmetic damage was correlated to 1.1-1.75” slab relative

deflection and 1/300 angular distortion. Structural damage was found to occur at relative

deflection larger than 3.5” and maximum angular distortion of 1/100. (Day, 1990, Skempton and

MacDonald (1956), Marsh and Thoney (1999). The study of as-built floor levelness, however,

suggests that these distress markers should be used with sound engineering judgement. Newly

constructed slabs were found to exhibit on average 0.5” relative slab deflection and average

angular distortion of 1/340. These values were found to reach 2.2” and 1/71 respectively, values

corresponding to structural damage (Koenig, 1991, Marsh et al., 1999, Walsh, et al., 2001,

Noorany et al.2005).

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Mitigation measures are employed to minimize potential soil movement and

superstructure distress. They include 1) removal, replacement and recompaction, 2) chemical

stabilization 3) passive moisture control with moisture barriers and 4) active moisture control.

The economical feasibility of mitigation measure depends on availability of material and

expertise of mitigation team. In Arizona, active moisture control in the form of pad pre-wetting is

the most commonly implemented method. The effectiveness of these methods remains to be

quantified.

The literature review consensus message is that the depth of moisture migration,

magnitude of suction variation with depth in open fields and below impermeable surfaces, the

distance of horizontal moisture migration below a slab and soil-slab system behavior with or

without employed mitigation measures are highly dependent on 1) soil properties and 2)

environmental and human imposed conditions around the edges of the engineered horizontal

surface. The geotechnical engineers are faced with the challenge of estimating these design

parameters for foundation system design purposes. In general, design guidelines provide a

cookie cutter methodology developed based on a local experience of a geographic region, which

may or may not be applicable to different soil and climatic conditions. When limited empirical

data is available, numerical modeling of moisture flow through unsaturated soil can be performed

for the identification of case specific design parameters.

The numerical analysis of moisture flow through unsaturated soil involves

implementation of unsaturated soil mechanics by solving Richards’ equation, a parabolic, stiff,

advection-diffusion partial differential equation derived from mass conservation. Stability,

convergence and time efficiency are issues inherent to this class of problems. The currently

implemented standard approach follows a “method of lines” also referred to as semi-

discretization, where spatial derivatives are first approximated using a variety of (usually low

order) finite difference or finite element schemes, and the resulting discrete system of ordinary

differential equations (which also accounts for boundary conditions) is then solved using a time

93

integrator. Three commonly used numerical software were reviewed, SVFlux, Vadose/W and

Hydrus.

3 CURRENT PRACTICE

3.1 Factors Affecting Residential Building Performance

Determining slab movements on expansive soils is a very challenging technical problem

involving coupled unsaturated flow and unsaturated soils stress-strain analysis, as well as soil

structure interaction. The engineering community makes extensive use of local experience and

empirical procedures to address factors affecting the performance of residential structures and to

identify acceptable structure performance. These factors can be divided into two categories,

geotechnical concept based and based on physical characteristics of construction materials.

The geotechnical factors include:

• Soil type. There are two types of volume change- moisture sensitive soils, collapsible

and expansive. In Arizona, low to medium expansive soils are commonly encountered.

These soils tend to increase in volume when wetted under light load and compress

when wetted under heavy load. Shrinkage is observed when the soil is dried. The

magnitude of movement depends on the soil properties, initial and finial moisture

conditions (soil suction) and applied load (stress). The design of slab-on-grade

foundations must consider both movements of the soil and the structure, as soil-

structure interaction depends on foundation type, overall stiffness of the structure and

distribution of structure loads.

• Soil preparation prior to vertical construction. It is recognized that the magnitude of soil

expansion depends on initial dry density. In general, the expansion potential increases

with increase in initial dry density. Typically, in the Phoenix region, the foundation pads

are prepared at 95ρd max as determined from the standard Proctor tests. For sites were

problematic soils are recognized, the foundation pads are prepared at lower dry density

to reduce the magnitude of both shrinkage and swell.

• Drainage control. Problematic soils undergo volume change due to changes in the

controlling stress state variables, and for moisture sensitive soils the matric suction is the

primary variable controling the soil behavior. Matric suction is best described as

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capillary potential, and the amount of soils suction that may develop depends on the soil

grain size distribution (pore space distribution). Inadequate site drainage is often the

source of moisture which leads to changes in the matric suction stress state variable,

and consequently soil and slab movement. Ideally, residential structures are designed

and built with appropriate site and region specific drainage considerations for removal of

rainwater and landscape water from the residential structure perimeter.

• Environmental conditions. The suction at depth depends on environmental conditions

(Thornthwaite, 1948) and soil type (Perera, 2003) as illustrated in Figure 3.1 where the

weighted plasticity Index, wPI, is defined as the product of P200 in decimal times the PI in

%. Soils with higher clay content will develop higher suctions at depth in all climatic

zones which has profound consequences on slab design, where the estimated suction at

depth identifies the suction range of to which the swelling soil will be subjected. The

research by Perera (2003) is not incorporated into design manuals, however, similar

findings have been reported by other researchers.

1

10

100

1000

10000

100000

-50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90

TMI

Mat

ric

Suct

ion,

kPa

Data PointsP200=10

P200=50/w PI=0.5 or lessw PI=5

w PI=10w PI=20

w PI=50

Figure 3.1. Matric suction at depth as a function of TMI and soil type (after Perera,

2003).

96

• Initial moisture conditions. Initial moisture conditions of the foundation pad affect the

type and magnitude of soil movement. Based on the literature review presented in

Chapter 2, the soil moisture is expected equilibrate within six years of construction.

Typically, site development leads to an overall increase in soil moisture compared to

pre-development conditions. Therefore it is anticipated by the engineering community

that relatively dry initial conditions may lead to significant swell. A commonly

implemented mitigation measure involves moisture conditioning of the pad. On the other

hand, relatively wet initial moisture conditions might result in differential soil shrinkage as

equilibrium is attained at the site.

• Post construction moisture conditions are critical factors affecting the performance of

residential structures. In Arizona, the commonly implemented post construction

condition is assumed to be that associated with desert landscape for a minimum

distance of 5 ft from foundation edge. Homeowners frequently modify the perimeter

moisture conditions by planting high water use vegetation and modifying drainage to

meet vegetation needs. Although the design methodologies (e.g. PTI) account for moist

surface conditions, the actual extent and degree of wetting due to the homeowner

modifications might exceed design specifications.

• Soil structure interaction. The type and magnitude of distress depends on the

foundation type and the distribution of structure loads.

The construction based factors include:

• Temperature. Due to large temperature variation typical of Arizona climatic conditions,

concrete based materials such as flatwork, drywall and stucco will develop minor cracks.

• Slab curling and cracking due to shrinkage is common. Newly constructed slabs will

release 75 to 80% of their moisture into the atmosphere within 4-6 months after

construction. Uneven moisture release from top and bottom of the slab may lead to slab

curling, more commonly observed in thick slabs and slabs with geo-membranes. After

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the moisture release period has been completed the concrete slab will attain equilibrium

with the surround conditions. During the equilibration process, the concrete will shrink

resulting in concrete cracks, preferably at designed control joints.

• Quality of workmanship and materials. The quality of workmanship and materials may

vary and construction defects may result. The significance of this factor is hard to

quantify.

The complexity of slab-on-ground design is handled by considering simplified scenarios

presented in design manuals. These methods have been developed over time for specific

regions, based on empirical evidence of slab performance. The main design guidelines used in

the USA include BRAB, WRI and PTI described below. Additionally, general standards for

drainage and soil investigations are currently given by the IBC, and FHA.

3.2 Drainage Design Standards and Standard of Practice

Since the early 1900s, the system of building regulations in the United States was based

on three regional model code groups: (1) National Building Code, NBC, developed by Building

Officials Code Administrators International, BOCA, and used on the East Coast of the USA, (2)

Standard Building Code, SBC, developed by Southern Building Code Congress International,

SBCCI, and used in the Southeast and Uniform Building Code,(3) UBC, developed by

International Conference of Building Officials, ICBO, and used on the West Coast. By early

1990s it became obvious that there is a need for a unified standard for the entire country. In

1994 the nation’s three model code groups formed the International Code Council, ICC, to

develop International Building Code, IBC that would have no regional limitations. The first

addition was printed in 1997, the same year as the last version of UBC; therefore many

practitioners did not adopt IBC until the 2000 version.

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The UBC – 1997 version gives limited drainage recommendations:

1. “1804.7 Drainage. Provisions shall be made for control and drainage of surface water

around buildings.”

2. “1806.5.5 Foundation Elevation. On graded sites, the top of any exterior foundation

shall extend above the elevation of the street gutter at point of discharge or inlet of an

approved drainage device a minimum of 12” plus 2%.”

In Arizona, during this 1997 design period, compliance with the standard was typically

achieved by developing swales sloping 1% towards a street and located 5’-10’ away from the

foundation. The positive ground slope away from structure was typically designed at 5%, as per

the adopted FHA, Local Acceptable Standard No. 3a (FHA, 1966). The residential structures

were typically erected with the “three pure system” also referred to as the stem and footer

design.

The IBC – 2003 version defines expansive soils as soils satisfying all of the following

criteria: PI is larger then 15, more than 10% of soil passes US sieve # 200, and more than 10%

of soil particles are smaller than 0.005 mm; or a soil with expansion index greater than 20 as

determined with ASTM D4829. The standard allows for three design approached for dealing

with shallow foundations constructed on expansive clay (section 1805.8):

1. Removal of expansive soil to a depth “sufficient to ensure constant moisture content in

the remaining soil.”

2. Stabilization of soil “by chemical, dewatering, pre-saturation or equivalent techniques.”

3. Use of slab-on-grade of mat foundation designed and constructed in accordance with

the WRI/CRSI, PTI design methods or rational method accounting for soil-structure

interaction, deformed shape of the soil support, and plate action of the slab in center lift

and edge lift conditions.

This standard gives the following grading and drainage recommendations in section

1803.3 “The ground immediately adjacent to the foundation shall be sloped away from the

building at a slope of not less than 5% for a minimum distance of 10’ measured perpendicular to

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the face of the wall. Exception: Where climatic or soil conditions warrant, the slope of the

ground away from the building foundation is permitted to be reduced to not less than 2%.”

Section 1805.3.4 echoes UBC recommendation of minimum 12” plus 2% foundation elevation

above street gutter.

The IBC-2006 version did not introduce any changes into drainage, grading and dealing

with expansive soils recommendations. Currently Arizona practitioners design either 2% or 5%

positive slope away from foundations for a minimum distance of 5’. The PTI design methodology

is the most commonly used option for dealing with expansive soil in the Phoenix region.

The Arizona Registrar of Contractors, AROC, (2004) defines ponding on permeable

surface as standing water to a height of 3/16”, 30 min after flooding. Ponding on an

impermeable surface such as concrete is defined as standing water to a height of 3/32” 30 min

after flooding. Additionally, "minor ponding (up to ½" deep in small areas) is acceptable

providing the roof is dry within 48 hours after the rainfall" (AROC, 2007).

3.3 Residential Foundation Design in USA

In the United States three design methodologies are most commonly implemented:

BRAB, WRI and PTI. Although the IBC allows for other rational methods “accounting for soil-

structure interaction, deformed shape of the soil support, and plate action of the slab in center lift

and edge lift conditions” such as a finite element analysis, for example ADAPT-SOG, these finite

element based methods are infrequently used, at least in Arizona region. The foundation

manuals provide design recommendations for three types of foundation systems, three-pour-

system, post-tensioned, and mat or raft foundations.

The three-pour-system, referred to as stem-and-footer, conventional design, or free-

floating floor slab, consists of deepened footings, reinforced perimeter and an interior floor slab

that is not connected to the perimeter foundation. The 4-6” thick interior slab is sometimes

reinforced with wire mesh. This type of construction has proven to perform very well in arid

Arizona region climatic conditions and low to medium expansive soil types, where up to recently,

100

it was the most common type of foundation design. A schematic of the three-pour-system is

provided in Figure 3.2. Here two types of design are possible, continuous footings or footing

provided below the load bearing columns with deepened perimeter. In Arizona the continuous

footing design was implemented more commonly.

Figure 3.2. Schematic of stem-and-footer.

In the post-tensioned foundation design, the footing and floor slab are poured

continuously to create a slab that acts as one unit. There are three possible designs with the

PTI procedure: ribbed foundation (Figure 3.3 and Figure 3.4), uniform thickness foundation with

minimum 7.5” thickness and deepened perimeter (Figure 3.5 and Figure 3.6) and uniform

thickness foundation with continuous rib around the structure perimeter. Approximately ½”

diameter steel tendons are placed on a 5’ grid in the concrete. The tendons are stretched

compressing the concrete. It results in a unified foundation structure with fewer cracks in the

103

The evaluation of potential moisture variation with depth and soil volume change below

the foundation are components of geotechnical analyses needed for the design of residential

foundations. All discussed methodologies implement some sort of climatic based approach

coupled with simplified soil response analyses based on soil index properties or simple

laboratory tests.

Figure 3.7. Schematic of raft foundation footing.

Figure 3.8. Schematic of raft foundation (AS2780, 1996).

104

In the PTI method, providing recommendations for PT foundations only, climate is

assumed to be the main factor affecting the differential movement. The soil movements are

evaluated using the assumption of a perfectly flexible slab, but the stiffness of the structure is

considered at a different point in the design. The procedure considers two possible scenarios:

edge lift where the soil below the foundation perimeter increases in volume and center lift where

the soil below the foundation perimeter shrinks. A correlation between matric suction at depth

and Thornthwaite Moisture Index, TMI, is used to estimate the potential range of suction

variation at the soil surface. The 1st and 2nd

The more current PTI editions: Alternate Procedure for Determining Soil Support

Parameters for Shallow Foundations on Expansive Clay Soil Sites under PTI Technical Note 12

(PTI, 2003) and The 3

editions of the PTI Manual (valid for designs prior to

2003) limit the depth of moisture variation to 7’ and matric suction at depth to 3.6 pF (390kPa).

The edge moisture variation distance, em, defined as the distance inward from the edge of the

slab, over which the moisture content varies due to anticipated changes in environmental

conditions, was estimated based on empirical model. The model was developed based on

analysis of successful foundations (primarily in Texas, evaluated over 10-year period), where em

was correlated to TMI and limited to 6’. The soil response due to climatic conditions in terms of

volume change, ym, is estimated based on model correlating index properties to mineralogical

classification and permeability of clay. The charted design methodology does not consider non-

climatic factors such as drainage, slopes, cut/fill sections, soil conditions at time of construction

and vegetation, and therefore caution and engineering judgement should be exercised.

rd Edition procedure (PTI, 2004) use the same as previously TMI

relationship for estimation of active zone depth and limit the distance to constant suction at 9’.

The estimate of edge moisture variation distance is based on both TMI and soil index properties

as per work of Covar and Lytton (2001) on soil swelling and classification properties. The index

properties are related to the suction compression index, which is related to unsaturated soil

permeability and diffusivity. Therefore index properties can be used to estimate the lateral

extent of moisture variation, which is limited to 9’ in these recent PTI manuals. Similarly, ym is

105

estimated using suction compression index and estimated matric suction change. Additionally,

the design requires the soil bearing capacity to be determined. Appendix A gives a historical

development of the geotechnical PTI procedure while Chapter 6 gives design details.

The BRAB design methodology provides recommendations for conventional and mat

foundations. The design is based on soil PI and climate conditions. Two design conditions are

considered, loss of support at the edges (center lift) and loss of support at the interior (edge lift).

The amount of slab support provided by the underlying soil is called the support index, C. The

support index is a function of the climatic rating, Cw, and the effective plasticity index of the soil,

PIe. The PIe is weighted PI from the top 15’ of soil profile. The Cw indicates the intensity of dry-

moisture cycle or swell-shrink potential due to environmental conditions. In general, the higher

the climatic rating the more stable the moisture balance is. For Arizona Cw is 15-20. The BRAB

methodology also requires soil bearing capacity to be determined.

The WRI design is a modification of BRAB. It can be used to design both PT and

traditional reinforced concrete foundations. The analysis is based on PI, climate conditions and

soil bearing capacity. Additionally, a slope correction coefficient, Cs, and a consolidation

correction coefficient, Co, are introduced.

3.4 Residential Foundation Design in Other Countries

Literature review of implemented shallow foundation design methodologies in other

countries revealed that incorporation of unsaturated soil mechanics theory into standards is rare.

Design considerations of expansive soils and the extent of potential moisture variation with depth

is addressed in arid or semi-arid climatic regions such as Australia, South Africa, and Israel.

Countries in Europe started to work together in the 1970s to unify their design codes

which are now implemented in countries belonging to the European Union. Currently Eurocode 7

provides geotechnical design recommendations. Classical soil mechanics is implemented in

shallow foundation design. Limit state analysis (the structure is designed for a safety limit

required for the life of a structure) is used to check the foundation against settlement, sliding and

106

over-turning. (ENV, 2004). Similarly, Japan is developing Geo-code 21 which will unify currently

implemented different, locally developed methodologies into one national code. The foundation

types include individual stem-and-footers, continuous stem-and-footer and mat foundations.

Goe-code 21 implements limit state design presented in Eurocode 7. Sometimes countries

without codes borrow codes from other countries (Giao et al, 2002).

Radevsky (2001) compared residential construction types, remediation methods and

local acceptance of foundation movement in five countries: USA, UK, France, South Africa and

Australia. The UK and France typically have 2-3 story homes with masonry walls and plaster

finish supported on 3’-9’ deep unreinforced strip footings. Usually very small amount of

foundation movement is observed. When there is observed damage, it is commonly due to soil

shrinkage associated with an unusually dry season or large trees.

In South Africa, an arid region where expansive soil are common, single story brick and

plaster on unreinforced slab-on-ground with a 1.5’ depth of embedment is the most frequently

used residential construction method. Edge lift foundation movement and associated structural

distress are common and widely accepted. Remediation method consists of development of

articulation joints installed in the house to allow flexing when additional change in soil elevation

occurs (Radevsky, 2001).

Australia is another arid and semi-arid climatic region where expansive soils are

common. The construction methods consist of brick, or timber framework and brick veneer with

suspended timber floor on timber piles, continuous stem-and-footer with minimum footing depth

of 18”, raised floor stem-and-footer design or most common now raft foundations with footings

depth between 12” and 4’. Vapor barriers or damp-proofing membranes are required below raft

foundations. Both swelling and shrinking behavior of soil is observed. Foundation movement

and structural distress are common and widely accepted (Radevsky, 2001). When distress is

observed, the homeowner is typically advised to re-establish the moisture conditions around the

structure perimeter, which typically involves watering of the perimeter area. In areas of

107

significant distress, vertical moisture barriers are installed. Underpinning is advised against and

used only as the last resort when the structure distress is associated with expansive soils.

The Australian Standard AS2870 “Residential slabs and footings-construction” was

introduced in 1996 and continues to be revised. The design considers influence of shrinkage,

swell, and compression settlement. The AS2870 is similar to the PTI procedure in the sense

that foundations are designed for edge lift and edge drop based on calculated edge moisture

variation distance and magnitude of differential swell or shrink anticipated due to climatic

conditions. The design is based on soil shrinkage indices, and suction variation with depth due

to climatic and human imposed conditions. The standard emphasizes abnormal moisture

conditions for which the slab is not designed for, such as removal of large tree, ponding, and

excessive watering of gardens. Normal conditions include seasonal moisture variation and

properly watered garden with maintained designed grading around the foundation perimeter and

no ponding. The grading is designed for 50 mm drop over 1 m distance (5% slope). Finished

floor elevation must be a minimum of 6” above finished ground, landscaping or paved areas. No

vegetation near the foundation is allowed. Trees should be plated up to 1.5 times the mature

tree height in highly expansive soils.

The standard is very easy to implement by practicing engineers due to the site

classification system with associated assigned appropriate foundation design for each and

tabulated geotechnical parameter estimates for different climatic zones and geographic

locations. A list of estimated parameters is given:

• Site classification depends on soil type.

• The standard provides estimates of site classification based on geographic region,

climatic zone and depth of clayey material.

• The site classification is used to estimate amount of differential swell, footing

performance and slab type and design details.

• Anticipated change in soil suction, ∆u, is estimated based on geographic location. It is

estimated to be between 1.2 to 1.5 pF.

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• Depth to constant suction, Hs, depends on location and climatic zone. In moist climatic

regions, the depth does not exceed 3’, while in dry climatic regions it is 12’.

• Depth of geotechnical investigation depends on location and climatic zone. It is typically

0.75Hs.

The differential soil movement can be calculated with equation (3.1), where Ipt is

instability index obtained from laboratory testing of shrinkage. The differential center lift

movement, ym, is estimated to be 0.7ys. The differential for edge lift movement is estimated to

be 0.5ys.

dhuIy sH

pts ∫ ∆=0100

1 (3.1)

The center lift edge moisture variation distance, e, is calculated as follows:

368ms

yHe += (3.2)

where ym is in millimetres and Hs is in meters. The edge lift edge moisture variation distance is

calculated with equation (3.3) where ym is in millimetres.

256.02.0 m

yLe +≤= (3.3)

Crack width is the major assessment tool used in estimation of magnitude of soil

movement. Wall cracks smaller than 1 mm (5/128”) are considered to be acceptable and do not

require repair. The AS2870 categorizes damage in Table 3.1, where 5 categories are

discussed. Categories 0 and 1 describe insignificant damage that does not require repair.

Category 2 describes floor noticeably out of level, minor wall cracks that need to be addressed

and binding doors and windows. Category 3 or higher relates to significant damage requiring

portions of wall to be replaced. Table 3.2 provides maximum floor differentials per construction

type.

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Table 3.1. Description of distress per Damage Category in AS2870. Damage Category Wall Distress Floor Distress

Crack width [mm]

Crack width [mm]

Differential over 3m [mm]

<0.1 0 <0.3 <8 <1 1 <1 <10 <5 2 <2 <15

3 5-15 2-4 15-25 15-25 4 4-10 >25

Table 3.2. Description of distress per Damage Category in AS2870. Construction Type Max. angular distortion

[L in mm] Max. diff. footing movement

[mm] Clod frame ≤L/300 40

Articulated masonry veneer ≤L/400 30 Masonry veneer ≤L/600 20

Articulated full masonry ≤L/800 15 Full masonry ≤L/2000 10

3.5 Design and Construction Practice – Interviews with Industry

As part of this research, building professionals, geotechnical, and structural engineers

were interviewed in an effort to identify current practice in the metropolitan Phoenix area. The

interviews were performed in 2005 with homebuilders, geotechnical engineers and structural

engineers. The summary of the interviews is presented below.

3.5.1 Geotechnical Engineering Interviews

3.5.1.1 Site Investigation and Soil Testing

Geotechnical engineers often use the Natural Resource Conservation Service maps,

and geological maps for investigation planning. They also rely on experience from previous

investigations. The time lapse between the site investigation and construction varies

substantially. For public agencies the time lapse is up to five (5) years while for the private

sector, it is from two (2) months to three (3) years. It is not uncommon for the soil investigation

to continue after construction has begun. The focus of this survey was on residential

construction practices.

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The total number of samples taken per area varies widely and depends on project size

and uniformity of soil encountered. The soil investigation consists of preliminary and final

stages. During the preliminary investigation, one soil sample is taken every 20 acres. Three

values were obtained for the number of borings obtained during the final investigation. They are

1) one boring per 5 acres; 2) 8 borings per 100 homes, and 3) one boring per 600’ x 600’ area.

The depth of soil investigation varies from 5’ to 20’ depending on the company

performing the investigation. It is the industry consensus, however, that the top 4 to 5 feet of soil

are the most important for the slab design with active zone depth assumed to be within the upper

3’ to 8’ of the soil profile. Ring samples (56% area ratio samplers) are collected samples at 2’, 5’

and 10’. The soil samples are stored for one week to three months after the field investigation.

The soil samples may be either sent back to the client or stored for some period of time, up to

two years.

Soil testing is performed on bulk samples obtained with an auger and undisturbed

samples collected in brass rings at the site. The dry density of soil is estimated from blow count

(STP) or determined from undisturbed ring specimens. The moisture content and percent of silt

and clay is visually estimated in the field from disturbed soil samples obtained with a split spoon

sampler.

The bulk samples are used to obtain gradation, Atterberg Limits, Proctor compaction

test, and reconstituted (re-compacted) sample swell tests – EIAZ (see section 3.5.1.4 for

description). A few companies were found to perform additional soil testing including direct

shear, pH, resistivity, percent of chloride solvent, and soluble solids. For the reconstituted

specimen swell test (EIAZ), a token load of 100 psf is placed on top of the compacted specimen

that is contained in a ring. The specimen is given free access to water and is allowed to swell for

24 hours.

The undisturbed soil samples are used for moisture content determination and, in some

cases, density determination and response-to-wetting test. The soil with the lowest blow count is

commonly selected for the undisturbed response-to-wetting test wherein the ring specimen, at

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in-situ moisture content, is loaded to overburden stress and then given free access to water.

Depending on the geotechnical firm, the response-to-wetting test specimen may be allowed to

dry some from in-situ moisture conditions prior to testing.

Most of the laboratory work is performed by the same company that completed site

investigation. Contract labs are only used in exceptional cases when in-house lab is too busy or

for tests not performed in-house, such as hydrometer testing. Soil suction is never measured.

3.5.1.2 Site Monitoring

Pad preparation is typically monitored by a geotechnical technician for moisture content

and dry density; the soil samples obtained are typically not stored by the firm. A builder

representative is typically present during the pad preparation process. The constructed pads are

certified for construction of slab-on-ground for three (3) months. It is not uncommon for the

builder to recondition the pads in order to obtain new pad certification.

3.5.1.3 Communication

Communication between geotechnical engineers and structural engineers/builders is

generally limited to clarifications and problems. The structural engineer needs em, ym, soil

bearing capacity, subgrade modulus, and friction angle values from the geotechnical engineer.

The builder needs to know in general what kind of soil is present at the site and prevalence of

various materials, or in other words, if there is a problem with expansive soils. Additionally, the

builder needs to know and how to deal with expansive soils.

3.5.1.4 Geotechnical Report

The geotechnical report briefly describes washes and general topography of the site.

The location of underground utilities is not identified by the geotechnical engineers and their

location is not included in the report. Lot grading is discussed, and special consideration is given

when expansive soils are found at the site. General recommendations relative to expansive

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soils are to not “overconsolidate” (or densify) the soil. The soil moisture is commonly specified to

remain between -1% to +4% of optimal water content as determined by standard Proctor.

Sometimes recommendations are given to avoid irrigation or to keep vegetation away from the

structure.

The swell potential of the soil is determined and it is reported using either ASTM D 4829

EI test or the Arizona modified Expansion Index, EIAZ test. The EIAZ test is performed on

reconstituted soil samples with water content decreased by 2 from optimum water content and

dry density 95% of the maximum dry density as determined with the standard Proctor

compaction test. The results are presented as a percentage of swell. The swell potential is

categorized as small when EIAZ is smaller than 2.5%. For EIAZ between 2.5% and 4.5% the swell

potential is defined as moderate, and for EIAZ larger than 4.5%, the swell potential is referred to

as high. All surveyed companies indicated that for sites with high swell potential, only PT slab

design is recommended post approximately 2003.

3.5.1.5 Design Procedure

Depending on client needs, both PTI (1996) and stem-and-footer, or only PTI (1996)

design recommendations are given. For PTI method, additional alternative recommendations

include deepening of the perimeter beam from 12” to 24”, and lime stabilization. The PTI design

method indicates that center lift (which is actually edge drop) is the governing mode of slab

failure.

3.5.1.6 Mitigation Measures

The builder who uses a city-approved soil report is responsible for soils mitigation

(except for custom builders, who do not even need a soils report). Pre-construction mitigation

for expansive soils generally involves limiting compaction and trying to achieve the appropriate

water content (-1% to +4% of optimal moisture content is acceptable) and 95% of maximum dry

density by standard Proctor (+/- 2% is acceptable) to minimize swelling. Prior to construction,

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the pads are reconditioned by applying an undetermined amount of water through a sprinkler

system or by flooding. A less common mitigation strategy is the removal of one to two feet of

problematic soil and replacing it a with non-expansive compacted fill material. Lime treatment is

generally dismissed as ineffective, although there are cases of use of lime treatment.

Post-construction monitoring has commonly been limited to drainage inspections.

Houses are typically investigated only after problems occur. The investigation consists of a

manometer reading (level survey) to estimate differential swell. Post construction soil

investigation and testing is done only in connection with litigation.

3.5.1.7 Areas of Problems

The main cause of excessive soil swell is the initial moisture state of pads prior to

construction. The time lapse between pad preparation and vertical construction is from a few

months to a few years. Typically, the pads are not reconditioned prior to construction, resulting

in over-dried pads. The most common mode of failure observed is edge lift. Center lift is

observed only when there has been a pluming leak; however, edge drop (center lift) could also

occur in response to excessive drying at the perimeter of the structure.

3.5.1.8 SWCC and Suction

Familiarity with the soil water characteristic curve was not extensive. This was also the

case for the terms matric, osmotic, and total suction. Units used for soil suction are those of

pressure – psi, psf, and kPa. Engineers indicated that they do not work with suctions at all and

are therefore not familiar with these terms.

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3.5.2 Structural Engineering Interviews

3.5.2.1 Occurrence of Expansive Soils

The estimated number of residential subdivisions with expansive soils varies from

engineer to engineer. Expansive soils are reported to be found on between 25% to 80% of

residential projects, with swell potential typically between 3% to 4%.


Communication with geotechnical engineers is limited to identifying the variables for the

PTI program, and/or when the information is missing or unclear from the geotechnical report.

The structural engineers are in frequent contact with homebuilders and architects.

3.5.2.3 Geotechnical Report

Three values are typically given by the geotechnical engineer: em, ym and swell index

values. The typical ym values for center lift are less than ½” and for edge lift less than ¼”. The

swell index value is not used directly in the PTI structural design.

3.5.2.4 Structural Analysis and Design Procedure

Two types of slab designs are available, post tensioned slab and conventional slab. The

type of slab chosen for the design depends on the client, the builder, for whom cost is a very

relevant parameter. Currently all builders choose the PT construction when expansive soils are

encountered with swell potential larger than 3%. When the swell potential is classified as low,

both PT and conventional designs are used. The alternative to the post-tensioned design is the

stem-and-footer design, which produces a 4” thick slab. When expansive soils are found, it is

recommended to increase the standard footing depth from 18” up to 24” or 30“ Below Final

Grade (BFG).

The PTISlab 2.0 software is currently used for the design of post tensioned slabs on

expansive soil. The design is not used on collapsible soils, which were not discussed

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extensively (or encountered extensively) with the surveyed structural engineers. There is also

ADAPT software available for the design of post tensioned slabs. ADAPT is a finite element

computer program. At the time of these interviews, structural engineers were concerned about

the ADAPT program results, and engaged in review and evaluation.


The structural engineers usually recommend mitigation measures. They include but are

not limited to improved grading and drainage. It is recommended to construct the slab on soil

placed at or near optimum moisture content, and to keep water away from the slab post

construction. When a problem with expansive soil is anticipated, the geotechnical reports are

redone augmented with additional soil investigation. The removal of expansive soil is another

mitigation measure. Due to the high cost associated with the implementation of this method, it is

only employed on seldom occasions when the EIAZ exceeds 10%. Post construction mitigation

measures, due to forensic investigations, include installation of gutters, regrading of the lot, and

chemical soil stabilization (ESSL). Overall, the best approach is to prevent the moisture content

variation under the slab. The structural engineers recommend emphasizing the importance of

maintaining proper drainage to the homeowner. The pad should be placed higher than the

surroundings as development typically lead to increased moisture conditions. The homeowner

should receive a letter from the homebuilder that grading and landscaping cannot be changed;

over-watering of lawn will lead to moisture migration and soil expansion.

3.5.2.6 Areas of Problems and Concerns

Edge lift is the most common failure mode of the PT slabs observed in the field in the

Phoenix region. In the Phoenix region, those surveyed estimated that 0.5% of constructed

homes on expansive soils exhibit excessive deflections and 90% of all PT slabs exhibit to some

degree edge lift deformation. The allowable deflection criteria are as follows: L/200 for edge lift

and L/360 for center lift. The PT slabs minimize slab cracking. Local engineers expressed

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concern with the PTI method that the design is based on generalized climatic conditions only. In

general, they felt that local, in-situ conditions should be incorporated into the procedure to reflect

the actual soil/slab behaviour in the Phoenix region.

The conventional reinforced concrete slabs develop cracks during concrete curing. The

slabs are built with numerous control joints. The soil heave causes the slab to crack at the

control joint.

3.5.3 Home Builder Interviews

3.5.3.1 Site Assessment

Most builders completely rely on geotechnical engineers to perform site assessment.

Only one builder indicated that additional in-house site assessment is done by utilizing Soil

Conservation Map in conjunction with Public Reports that provide more detailed information than

the maps. The land for the subdivision construction is either purchased with or without

completed pads. When the pads are constructed by another developer, the site assessment

information comes from that selling developer. The time lapse between site assessment and

construction is reported to be up to three years.

A geotechnical engineer is employed to perform preliminary soil exploration prior to the

land purchase. Local site environment and prior issues with the site are also determined prior to

the land purchase. After the purchase, between 120 days to one year elapses before vertical

construction begins, and a more detailed site investigation (second phase, or supplemental

phase) is performed by geotechnical engineer. The structural design is based on that detailed

site investigation. It is not uncommon for the geotechnical site investigation to be augmented

after extensive soil movement due to over-lot grading. The structural design is then refined

based on the modified soils report. Such practice is meant to reduce the builder’s liability.

The site investigation is typically performed to a depth of 5’. The following geotechnical

information is important to the builders: swell potential (if less than 3%, the builder is not

concerned), location and extent of clayey material, and the existence of vertical or horizontal

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layers with problematic soil. If clayey material is found only in one lot, this particular lot alone is

treated differently.

3.5.3.2 Budget and Design

The budget for geotechnical investigation was reported as unknown. Typically more

money is spent on the construction process when expansive soils are found. In the past the

construction of PT slabs increased costs $2000 per slab compared to conventional foundation

construction. More recently, it is reported that the difference in cost is closer to $1000. Some

builders choose to construct only PT slabs, while others build PT slabs only when expansive

soils are found and the geotechnical engineer makes a recommendation to use a PT slab.

3.5.3.3 Site Preparation Process

The site preparation consists of de-vegetation, lot grading and placement of forms for

slabs. The pad preparation is followed by placement of wet and dry utility lines, and cutting of

sidewalks and streets. The lots are watered to specs the night before the slabs are poured,

however the amount of water added through sprinkling or flooding is not always monitored. ABA

is placed and slab is poured, and is post tensioned at latter time.

3.5.3.4 Site Monitoring

The site monitoring consists of three main components: pad preparation, slab

construction and lot grading. The dry density and water content of pads is monitored by

geotechnical engineers during pad preparation. The quality of concrete used in slab construction

is checked by a third party, and the placement of the tendons in the slab is monitored by a

structural engineer. The lot grading and drainage are checked by another company. This

practice appears to be voluntarily adopted by most builders, although it is not required by law. If

grading is found to be inadequate, it is redone at the end of construction. Some builders require

the homeowner to sign a contract stating that the grading and drainage cannot be modified, and

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plats cannot be planted within 24” from the house. Unfortunately this information is not required

to be turned over to the next homeowner.


The builders are communicating a lot with both structural and geotechnical engineers.

Some builders have periodic meetings with them. In addition, the geotechnical engineer is

present at the site during pad preparation, and the structural engineer is on site during post-

tensioning of slabs. Typically the same geotechnical engineer that developed the report is

monitoring the site preparation.

The builder also communicates with the homeowner through purchase document which

discusses drainage, grading and typical behavior of construction materials. Relevant highlights

of some documents are listed below:

• Soils. “The soils in Arizona are known to be expansive in nature. These expansive soils

have been analyzed by a soils engineer who has recommended the type and design of

the foundation for your home. Any changes in the foundation, the grading and the

landscaping of your home and lot can result in severe damage to your property and to

neighboring properties. Consult a professional before any such changes are made.”

• Drainage.

o “Do not alter the soil grade”

o “… your lot has been graded to keep water away from your home. The grading plan

for your lot has been engineered and graded to local, state and federal standards.

Failure to maintain grading can result in damage to your home, your lot and to

neighboring property. Any alteration of the established grade plan for your lot may

void the landscaping and drainage and termite sections of your warranty.”

o “The soil around each home site is graded to channel storm water away from the

home. Please note that the rear yard grading in some communities is designed to

retain storm water.”

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o “Berms and contours which are designed to direct the flow of water away from the

home are especially important and must not be altered.”

o “Keep water ditches or swales open and free of leaves and debris.”

o “Do not build sheds, sidewalks, hot tubs, decks, fences ,pools, or gardens in the

swales.”

o “Direct water away from the home to prevent washouts.”

• Pool. “If you choose to have a pool or spa installed, we suggest that you give careful

consideration to the eventual drainage problems that could be created.”

• Landscaping.

o “Do not plant along the foundation wall. “

o “Irrigate away from foundation, patio, porch, fence and sidewalks.”

o “Irrigation at or near the foundation will increase the likelihood of soil expansion or

settlement resulting in cracking and movement of the fence or home.”

o “We urge you to use drought resistant and drought tolerant plants.”

o “Landscaping can change the grading of your lot. The ground next to your home

should always slope away to prevent standing water.”

o “Do not allow sprinklers to wet the house or form puddles near or against the

foundation.”

o “Keep plantings in flower beds a minimum of 2’-3’ away from the foundation”

o “Improperly constructed planting beds can result in saturated soil around the

perimeter of the building, even when the soil surface nominally has positive drainage

away from the building…In this case, improperly constructed planting beds can act

to inject water directly into the select fill.”

o “Trees planted near a foundation can upset the soil moisture balance due to the

water demand of mature trees, especially during drought cycles. While it may take a

number of years before the tree gets large enough to cause structural damage, this

will eventually occur if the tree is close enough to the slab. In general, the distance

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from the tree to the foundation must be at least half the height of the tree, but the

required distance varies with tree species.”

o Do not remove trees near the vicinity of the foundation. “Trees significantly alter the

soil moisture balance of the soil, reducing the equilibrium soil moisture in their

vicinity.” After tree removal the soil will gain moisture over time and heave causing

slab movement.

• Concrete. “Do not allow water to pond near the foundation, patios, walks or driveways.

Water can cause soil expansion which can result in fractures to the concrete as well as

movement within the home.” “Small cracks, which are a result of contraction and

expansion of the concrete are characteristic of concrete and do not affect its

performance or durability.”

• Stucco. “Stucco is a cement product and takes approximately 14 days to cure. Stucco

is susceptible to cracking due to expansion and contraction. Cracks should be expected

during the lifetime of the home due to fluctuating temperatures. This is normal and does

not reduce the function of the stucco in any way. Your limited warranty does not cove

normal hairline cracks in stucco.”

• Drywall. “Nail pops and minor drywall cracks are normal and are caused by settlement

and the normal drying of stud framing and drywall materials.”


Builders report that no pre-construction mitigation measures are employed beyond

grading and drainage. The practice is to follow geotechnical and structural specs. Sometimes,

problems are observed half way through completion of a subdivision; by then it is too late to

change. Post-construction monitoring of expansive soils typically does not occur; although

builders who encounter expansive soils are beginning to informally check problematic homes

(visually inspect the foundation, walls, and driveway for cracks, etc).

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3.5.3.7 Sources of Problems

The time lapse between the pad preparation and slab construction is from a few months

to few years. During the time lapse, the pads are not covered to maintain the design soil

moisture state. In addition, the prepared pads are frequently driven over by construction trucks

to access the construction zone. Such practice leads to overcompaction of pads. The site

construction is monitored by superintendents who lack the knowledge of how s the dry density

and water content of soil influence post construction soil behavior.

3.5.3.8 Litigation

The homeowners rarely sue the homebuilder. Typically the homebuilder resolves issues

associated with expansive soils and litigation is avoided. Typically the pre-emptive action on the

part of the builder is cheaper than litigation. In most cases litigation is the result of buyer distrust

of builders rather than any negligence on the part of the builder. Emotional distress has not

been a litigious issue.

3.5.4 Forensic Investigation

3.5.4.1 Failure Modes

Forensic investigation indicates that problems with expansive soils might occur from few

months to as many as 20 years after construction. Frequently the problems are associated with

a change in landscape irrigation patterns and/or excessive rainfall. Depending on the soil

properties and irrigation conditions the following outcomes are possible:

• Soil at center swells up - common with the stem and footer design.

• Soil at center shrinks/consolidates - very uncommon, however was witnessed once.

• Soil at the edge swells up (edge lift) - common with PTI method, and

• The soil consolidates or shrinks under the edges (center lift) – observed in stem and

footer design.

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3.5.4.1.1 Center Lift

Center lift deformation is prevalent in the stem and footer design. It is speculated that

the failure occurs under following conditions. The soil stratum consists of layers of expansive soil

and more permeable sandy soil. During a wet event, the water may reach the permeable strata

through shrinkage cracks in the clay layers and travel horizontally under the slab within the

sandy layer. Once it happens, the water is trapped under the slab and the expansive soils start

to swell up. At the same time the soil under the footing is consolidating and loses water due to

the extremely hot desert conditions; the soil shrinks resulting is center lift slab deformation.

Center lift deformation is evident by more observable damage in the interior of the house such

as crushed drywall at the top of the wall next to the ceiling – although this same type of damage

pattern is consistent with edge drop. It is rare to have benchmarked surveys to determine

whether deformations appearing to be center lift are actually due to center lift or edge drop.

3.5.4.1.2 Edge Lift

Edge lift deformation is observed when soil beneath the edges of the structure expand

relative to soils in the center, for example, from excessive wetting around the perimeter. It is

attributed to poor drainage. Larger stress levels around the perimeter of the structure can help to

reduce edge lift. This is one reason why edge lift is observed most commonly in PT slabs having

more uniform distribution of loads. Evidence of edge lift movement includes distorted exterior

doors, windows and cracks in stairways. Damage is most commonly noticed for edge movement

of 2.5" or more per 5'.

3.5.4.1.3 Settlement

Settlement (shrinkage of expansive soils due to drying) of structures is observed in

areas of excessive sunshine. It is manifested through cracks in stairways and gaps between a

fence and the house. Settling soils (compression) give the same pattern of deformation.

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3.5.4.2 Remediation Methods

The following remediation methods are currently used in Phoenix region:

• Cut off walls,

• Installation of gutters,

• Change watering pattern,

• Intrusion of concrete is common where grout is pumped under sunken structure. This

solution does not perform as anticipated. The structures have a tendency to settle after

the procedure.

• Chemical treatment with lime or ESLL.

• Drying of soil with hot air. A hole is drilled in the center of the slab where hot air is

applied. It flows through the ABC layer and exits on the sides. It is effective for slabs up

to 30 ft long.

• Helical anchors or push piers. The expanded soil is removed and the house is allowed

to be supported by either push piers or anchors that are installed under the house’s

perimeter. Push piers are hydraulically driven into the soil under the slab until it locks

up. Once it locks up, it starts to push up the house to the required height. Due to the

lifting action, sometimes a significant space between the soil and the slab develops.

The space is filled with grout. In the valley the push piers are installed to a depth of 15’-

25’ and are spaced between 6’ to 8’ apart. They usually lock up at 50-60 blow count

(helical anchors locks up at 40-50 blow count). This remediation method is frequently

used in conjunction with cut off walls.

3.6 Failure Criteria

Soil movement below foundation is associated with foundation movement and structural

distress. The American Concrete Institute, ACI, and the Arizona Registrar of Contractors,

AROC, developed acceptable distortion criteria for residential construction, which are commonly

used by practitioners. The ACI 117 quantifies flatness and levelness criteria with F-Numbers, FF

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and FL respectively. Flatness refers to slabs waviness or roughness due to random bumps and

irregularities “by limiting the magnitude of successive 1’ slope changes when measured along

sample measurement lines in accordance with ASTM E 1155” (Standard Test Method for

Determining FF Floor Flatness and FL Floor Levelness Numbers). For slab-on-grade, minimum

allowable flatness is obtained with FF=15. Levelness refers to the slabs deviation from horizontal

over the entire area of the slab “by limiting differences in departure from design grade over

distances of 10 ft when measured along sample measurement lines in accordance with ASTM E

1155.” For slab-on-grade minimum local levelness (within 10’) is obtained with

zF

L ∆=

5.12

FL = 10 and

global levelness (over the entire floor) with FL=13. The Fl number can be calculated with

equation 3.4,

(3.4)

where ∆z is the floor level differential. The FL of 10 produces maximum allowable floor level

differential of 1.25” per 10’. The Arizona Registrar of Contractors, AROC, provides more

stringent requirement of ¼” differential per 12’.

Floor survey elevation (non-benchmarked) alone is not an indicator of direction or

magnitude of soil movement. Section 2.6 provides evidence from literature review that newly

constructed slab-on-grade can deviate up to 1” from horizontal. Additionally, the structural

performance of slab-and-footer foundation system is, in general, independent of the performance

of the free floating slab in the areas between footings. The thin slab is designed to act as a

separator between the building and the soil below. Developed thermal or shrinkage cracks are

not evidence of post-construction structure distress or shoddy construction. Soil movement is

associated with distress in superstructure such as diagonal cracks in drywall and stucco,

separation of baseboard and wall fixtures from the walls and cracks near soil movement. The

AROC document “Workmanship Standards for Licensed Contractors” provides guidance with

respect to unacceptable quality of construction, unacceptable post construction deformations

due to either settlement or soil movement within 2 years of homeowner occupancy and

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homeowner responsibilities which, among others, include: adjustment of doors and windows,

maintaining weather-stripping, interior and exterior caulking, leaks from plumbing fixtures and

cosmetic repair of hairline cracks on horizontal surfaces. The post construction performance

criteria are summarized in Table 3.3.

Table 3.3. Residential construction performance criteria in the first 2 years after homeowner occupancy (AROC, 2004).

Distress

Stemwall > 1/8” wide crack requires cosmetic repair > ¼” wide crack, determine cause of distress and perform

appropriate repair Stoops >1/4” differential Stucco Excessive hairline cracks or larger then 1/16” wide Drywall Excessive hairline cracks or larger then 1/16” wide Bulge or sag in walls and ceilings 3/8” in 8’ is acceptable Ceiling sag 3/8” in 8’ is acceptable

Flatwork: garage, patio, driveway > 3/32” wide cracks > 1/8” vertical differential, replace effected area > 3/8” wide control joints

Flatwork: sidewalk > 3/16” wide cracks, replace effected area

Pool deck > 1/16” wide horiz. and vert. displacements > 1/8” wide control joint separation

Levelness >1/4” in 12’ Concrete spalling unacceptable Masonry ≥ 1/8” wide stair-step crack Counter top and wall joint Caulk joint not to exceed 1/8”

Tiles Lose or cracked - Unacceptable > 1/16” joint with other material separation

3.7 Summary

In this section the industry and Arizona practice (based on informal survey data) is

presented. Up to about 10 years ago stem-and-footer foundation design was the most

commonly constructed foundation system for detached residential construction. Currently post-

tensioned slabs are selected to mitigate potential soil movement of low to medium expansive soil

typical to the Phoenix metropolitan region. The design is carried out with PTI 3rd

Interviews with industry revealed that professionals involved in construction and design

understand the importance of maintaining initial moisture conditions below the foundation by

proper grading, drainage and appropriate landscape in the vicinity of the foundation. The 5%

Edition.

126

positive slope away from the structure for a minimum of 5’ was adopted long before the

governing standards (IBC) required it. It appears that homebuilders make a lot of effort to

communicate the significance of moisture control to new homeowners who frequently do not

follow the recommendations. When problems occur, remediation methods involve re-

establishing of arid moisture conditions around the foundation perimeter by removal of

vegetation and regarding the lot. In rare cases, when significant soil movement has occurred

and the potential for future soil movement exists, additionally some or all of the following

methods are employed: vertical cut-off walls, chemical stabilization, and push-piers. The soil

moisture below the structure is assumed to come to equilibrium with the new conditions within 6

months, at which time vertical structure distress remediation is performed consisting of cosmetic

repairs, partial removal and replacement of flatwork and walls.

The Arizona Registrar of Contractors, AROC, in “Workmanship Standards for Licensed

Contractors” provides guidelines for unacceptable construction quality, unacceptable post

construction deformations due to either settlement or soil movement within 2 years of

homeowner occupancy and homeowner responsibilities. A number of researchers attempted to

identify factors signifying foundation movement such as the angular distortion and crack width,

see Section 2.6, though it is not common for geotechnical engineers to present their design

recommendations in terms of limited angular distortion. Walsh (2001) writes about newly

constructed floor levelness, using angular distortion as a guide. In the Phoenix metropolitan

area the AROC document describes the governing standard of practice.

4 LABORATORY DATA Laboratory testing was performed as a part of this research to identify typical Arizona

expansive soil properties and associated parameters employed in current foundation design

method (e.g. PTI design procedure), and to obtain transient moisture flow modelling input

parameters, which include unsaturated soil functions such as SWCC and hydraulic conductivity

and , initial matric suction profile data, and climatic and human-imposed soil surface conditions

for establishment of boundary conditions. The unsaturated soil properties, Soil Water

Characteristic Curve and unsaturated soil permeability, were either measured or estimated

based on measured index properties. The determination of initial and boundary conditions

involved the measurement of matric suction beyond the estimated active zone depth and beyond

the estimated edge moisture variation distance. To achieve these objectives, soil samples from

below slabs of 16 homes were obtained, one next to a residential property and one from

undeveloped desert conditions. The descriptions of soil testing performed and a summary data

are given below. Detailed soil profile information for each investigated site can be found in

Appendix B.

4.1 Field Exploration

The field exploration was aimed at obtaining undisturbed soil samples from under slabs-

on-grade of residential construction in Phoenix metropolitan area, Arizona, whose matric suction,

beyond that resulting from seasonal variation, had reached equilibrium. To satisfy this

requirement, structures five years old or older were chosen for the investigation. The edge

moisture variation distance was roughly estimated and the samples were taken at greater

distances from the edge of the slab. It was decided that the least inconvenient place to drill was

the garage. Before the soil samples were collected from the selected sites, special care was

taken in the gathering of related data such as landscape type, existence of gutters, quality of lot

grading, and identification of possible water sources such as pool or history of pipe leaks.

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4.1.1 Equipment

The field sampling required equipment listed in Table 4.1. The main pieces of

equipment included: coring machine capable of coring 4-inch diameter holes in concrete,

generator and hand sampling equipment for thin walled tube sampling.

Table 4.1. Main Equipment used for Field Sampling and Coring (after Perera, 2003). Item Use/Description

Coring Device

Core Bore Drilling Machine™, Model M1capable of coring 4” holes through concrete slabs (See Figure 5.1). Due to wet drilling, the top several inches of the slab was drilled with the drilling machine and the last inch was removed manually to prevent moisture contamination.

Coring Bits 4” diameter diamond coring bits for drilling through concrete.

Generator Generac™ 7000-watt portable AC generator powered the coring machine and other power tools.

Sprayer 3.5-gallon pump-up sprayer for supplying water for the coring machine.

Shop-Vac For cleaning waste (cooling water + cuttings) generated during coring.

Hand Sampling Equipment

Consisted of 1.8” and 2.8” diameter stainless steel sampling tubes (Ar≈ 10 -15%), two sampling heads, extension pipes, a 45 lb hammer, slotted wood plates to guide the pipes, and a jack.

Compaction Device

A steel rod with a cylindrical base. With the help of the compaction device, the holes were backfilled and compacted with sand and gravel mixed with excavated soil.

4.1.2 Field Sampling

After arrival at the selected site, initial information was gathered. The site information

included: site location, site description with a sketch of site details, site identification number and

type of landscape. Special care was taken to identify possible sources of severe soil moisture

variations below foundation such as existence of large trees or tree removal, swimming pools

and history of broken pipes or irrigation system.

Drilling location was established in a garage at least six feet away from the edge of the

slab; 4-inch hole was drilled in the slab up to a depth of about 2.5-inches. To avoid

contamination of subsoil with water, 1-inch of the concrete was left un-drilled. The concrete core

was retracted and the water in the cut was removed with shop-vac. The remaining concrete in

129

the hole was chiselled out and extracted. In order to prevent damage of tube samplers by large

gravel particles, the granular base material under the slab was removed by hand until natural soil

surface was reached.

Soil sampling was done continuously utilizing stainless-steel-tube samplers 3-inches in

diameter and 11-inches long. Each tube was driven manually into the soil using a 45-lb

hammer. Two slotted wood plates placed on the concrete against the pipe maintained the

verticality of the sampling tube during the driving. The sample tube was retracted from the

ground by extracting the tube with a jack. Sampling was carried out to a depth of at least 6 feet

in an effort to reach active zone depth. Five (5) to nine (9) cores were collected from each site at

consecutive depths.

The soil in retrieved Shelby tubes was trimmed to have smooth, flat surfaces at both

ends. These ends were sealed with tight-fitting rubber caps and duct tape to prevent drying of

the soil. Each tube used in sampling was stamped for identification that consisted of four

numbers: site number, sequence at which Shelby tubes were used to retrieve soil (i.e., number

one refers to the first used tube), and starting and final depths from which the soil was removed

in inches. The tubes then were taken to the laboratory for testing. The same soil sample

identification is used in the presentation of laboratory work.

The holes were backfilled with sand and gravel. The soil was placed in 6-inch lifts and

compacted with a compaction device up to the bottom level of concrete. The remaining hole

was filled with specially prepared cement slurry, that consisted of non-shrinking cement grout

with an accelerator. It was ensured that the patching material was flush with the existing

concrete. The patching required only 20 to 30 minutes of hardening before the slab could be

used again.

4.2 Soil Testing for Input Parameters

Based on unsaturated soil mechanics theory, it was determined that Soil Water

Characteristic Curve, SWCC, and unsaturated hydraulic conductivity, k(h), need to be either

130

measured or estimated in order to model transient flow through unsaturated soil. The in-situ soil

suction was measured followed by a more detailed SWCC measurement for selected

specimens. The k(h) was estimated using SoilVision 4.0 database based on SWCC and

measured Atterberg Limits. In order to benchmark obtained results to soil parameters typically

used by Arizona practitioners, additional soil testing was performed which included undisturbed

soil moisture and dry density, specific gravity, swell pressure, swell index, and Arizona modified

expansion index, EIAZ. Cation Exchange Capacity, CEC, was also determined to compare the

measured results to the answers obtained with correlation methods in the Post Tensioned

Institute, PTI, Design Manual.

4.2.1 Moisture Content and Dry Density

Most cores were tested for both water content and dry density. After plastic cap was

removed from the Shelby tube, the soil volume and soil mass were determined. Some of the soil

was extruded from the tube and the soil was cut flush with the tube. The cut off soil was broken

up and the inner part of the soil mass was removed (at least 100g), weighed, oven dried and

weigh again. The results were used in the calculation of in-situ water content with equation (4.1)

and dry density, equation (4.2), or dry unit weight, equation (4.3). Throughout this report dry

unit weight is listed as γd. The water content and dry unit weight values were verified by

repeating the calculations with soil data obtained during suction and/or swell pressure testing

where the soil was extruded into brass ring of dimensions 2.54-cm height and 6.1-cm diameter.

s

w

mm

w = (4.1)

sd

mV

ρ = (4.2)

ddgργ = (4.3)

131

where:

w - water content [%],

mw - mass of water in the sample [g],

ms - mass of dried soil [g],

ρd - dry density [pcf]

V - total volume [ft3].

g - gravitational constant [9.81 m/s2

]

4.2.2 Atterberg Limits

Atterberg limits test results, in part, were used in the evaluation of soil classification with

the Unified Soil Classification System in accordance with ASTM D 2488-93. The test was

performed based on ASTM D 4318-95 to obtain liquid limit, LL, plastic limit, PL, and plasticity

index, PI, where PI LL PL= − . Tubes number 1, 3, 5, and 7 or 8 were selected for this test,

to give an indication of soil variability with depth.

4.2.3 Sulfate Content

The IAS laboratories were contracted out to measure the sulfate content of 10 selected

soils. The ADOT method ARIZ 733 was utilized in the determination, where 60 g of distilled

water was combined with 20 g of oven dried soil. The components were mixed for five minutes

and then allowed to stand for one hour with occasional shaking of each sample by hand. The

mixture was filtered through a #2 filter paper. The filtrate was analyzed for sulfate on Coupled

Plasma Spectroscope (ICP). The results are given in terms of ppm in Table 4.5.

4.2.4 Cation Exchange Capacity

Cation Exchange Capacity, CEC, test was performed on six (6) soils. The tests were

performed based on Department of Sustainability Natural Resources, soil survey standard test

method procedure (2004). It was found that the PTI presented correlation between CEC and

index properties adequately estimates CEC for soil types common to Arizona region. The

results are provided in Table 4.5.

132

4.2.5 Specific Gravity

Specific gravity was determined for each site at selected depths, typically soil from cores

number one (1) and five (5). The test was performed by first calibrating the pycnometer. The

container was filled with de-aired water up to the 500 mL mark; its weight and water temperature

were recorded. The water was removed and replaced with mixture of soil and water. The

pycnometer was attached to an air pump in order to remove all air bubbles from the mixture.

The removal of air took about two hours and was accompanied by occasional, manual swirling of

the mixture. When the air was removed from the soil-water mixture, the pycnometer was filled

up to the 500 mL mark with de-aired water. Its weight and water temperature were measured.

In the final step, the dry mass of the solids was measured. The specific gravity was calculated

using formulas described in ASTM D 854 standard.

4.2.6 Expansion Index

In an effort to benchmark swell pressure observed during laboratory testing to expansion

potential typically determined by geotechnical practitioners in Arizona, expansion index was

measured for four selected soils. The expansion index, EI, was determined using two methods.

The first method followed ASTM D 4829-03 standard test procedure for measuring expansion

index. The second one used modified ASTM D 4829-03 standard that is used by geotechnical

engineers in the Phoenix area.

4.2.6.1 Arizona Modified Expansion Index Procedure

Optimum water content and maximum dry unit weight of soil were determined from

compaction test as per ASTM D 698 standard. Soil samples were prepared in brass rings of

dimensions: 2.54-cm height by 6.1-cm diameter with the following properties:

w = wopt – 2 (4.4a)

γd = 0.95 γd max (4.4b)

133

where,

w - water content [%],

w opt - optimum water content [%]

γd - mass of dried soil [g],

γd max -

The prepared samples were placed in the consolidometer. Sitting load of 4.8 kPa

(100psf) was applied to them. The dial gage was zeroed out and the specimens were soaked in

distilled water. The soil samples were allowed to expand. The change in height was observed

and recorded 24 hours after the beginning of the test. The expansion index was calculated

using equation (4.5).

maximum specific weight [pcf]

1000

HHEI

AZ

∆= (4.5)

where:

∆H change in height of soil specimen [in] -

H0 initial height of soil specimen [in] -

This procedure was followed by a typical consolidation test (see ASTM D 4546-96 for

details). Taylor method was used in the determination of compression curve. The results were

corrected for equipment deflection.

4.2.6.2 Expansion Index Procedure as per ASTM D 4829

The ASTM D 4829 modified sample size procedure was used to determine Expansion

Index, EI. Soil was passed through US standard sieve #4. In an attempt to achieve 50% degree

of saturation of the sample, the necessary water content of soil was approximated. The soil was

mixed with water and allowed to equilibrate for 12 hours. After equilibration, the soil-water

mixture was compacted in two layers into a metal ring of dimensions: 25.4 mm height and 101.9

mm diameter. The soil was compacted with 15 blows per layer of 5.5 lb hammer dropped from

12 in. Since the soil specimen of 101.9 mm diameter did not fit in the standard consolidation

134

apparatus, the prepared soil sample was pushed into a standard brass ring of dimensions: 2.54

cm height by 6.1 cm diameter.

The soil sample in the brass ring was placed in the consolidation apparatus and 6.9 kPa

(144 psf) was applied to it. The dial gage was zeroed out and the sample was saturated with

distilled water. The sample was allowed to expand. The change in soil height was observed

and recorded 24 hours after soil saturation. Equation (4.6) was used to calculate the expansion

index. The ASTM D 4829-03 also considers samples of saturation other than 50%. When the

expansion test is performed on a sample that is saturated between 40% to 60%, the expansion

index can be calculated using equation (4.7).

0

1000measuredHEI

H∆

= (4.6)

5065(50 )220

measuredmeasured measured

measured

EIEI EI SS

+= − −

− (4.7)

The expansion potential is classified as follows:

Table 4.2. Classification of Potential Expansion based on EI (ASTM D 4829). Classification of Potential Expansion EI

Very low 0-20 Low 21-50

Medium 51-90 High 91-130

Very High >130

This procedure was followed by typical consolidation test (see ASTM D 4546-96 for

details). Taylor method was used in the determination of compression curve. The results were

corrected for equipment deflection.

4.2.7 Constant Volume Oedometer Testing

Two cores per site were selected for swelling pressure testing with constant volume

oedometer method. Typically cores #1 and #5 were selected for this test. In this method an

135

undisturbed soil samples were directly extruded from Shelby tubes into brass rings of

dimensions 2.54-cm height by 6.1-cm diameter. The samples were weighed and placed in the

consolidometer between two porous stones. Based on soil’s moist density and depth from which

the sample was obtained, overburden pressure was calculated and applied to the sample. Next,

deformation gage was calibrated and distilled water was introduced to the sample. The

specimen was not allowed to deform in height by more or less than 0.0002-inch where the

deformation was controlled by either adding or removing weights. The system reached

equilibrium within 24 hours. The pressure required to maintain constant volume of the sample is

referred to as the swelling pressure of the soil that is further corrected for sampling disturbance

and consolidometer compressibility; see Section 4.2.7. The constant volume oedometer test

was followed by consolidation test.

4.2.8 Consolidation Test and Correction Factors

Consolidation test was performed on the same soil samples as the constant volume

oedometer test; cores #1 and #5. The test was performed in general accordance of ASTM

D4546-96 in order to determine soil compression and decompression indices. Once the swelling

pressure was determined, consolidation test was initiated by introducing an increment of load to

the specimen. Each increment typically resulted in doubling the applied load; and the first

increment would be equal to the overburden pressure.

The application of additional load was followed by recording soil compression with time,

where the readings were taken using the following increments of time: 0 sec, 6 sec, 15 sec, 30

sec, 1 min, 2 min, 4 min, 8 min, 15 min, 30 min and 1 hour. Typically 4 to 6 load increments

were applied to the soil. Once the final increment readings were completed, the rebound curve

was determined by removing an increment of load at a time. The reading of soil height was

recorded 24 hours after load removal, when recompression tendencies of soil have ceased. The

soil was maintained at saturation throughout the testing procedure.

136

The compression (consolidation for saturated specimens) at each load increment was

determined with Taylor’s method from displacement vs. square root of time curves. The

obtained results of void ratio vs. effective stress for compression and rebound curves were

determined and corrected for equipment compressibility and sampling disturbance. The first

correction, correction due to equipment compressibility, was determined by performing

consolidation test a steel plug. The system deflection was observed and plotted vs. increasing

and decreasing applied pressure on a semi-log scale. Good analytical correlations were found

between the deflections and applied load for both compression and recompression paths. The

results obtained included fitted trendlines, and are illustrated in Figure 4.1. The measured

system deflections were subtracted from the deflections measured on the tested soil to correct

for system compliance.

∆h(compression) = 1.412E-12x3 - 3.523E-09x2 + 3.581E-06x + 5.635E-03

∆h(decompression) = 2.386E-12x3 - 5.329E-09x2 + 4.312E-06x + 5.699E-03

0.0055

0.0057

0.0059

0.0061

0.0063

0.0065

0.0067

0.0069

0.0071

0.0073

0.007510 100 1000 10000

Pressure [kPa]

Cha

nge

in H

eigh

t [in

] Compression Decompression

Figure 4.1. Consolidation test on a steel plug; dummy specimen.

The following procedure was used to obtain the Fredlund and Rahardjo, 1993 correction

to the swelling pressure values. The intent of the correction is to adjust for sampling disturbance;

refer to Figure 4.2 for details.

137

1. Draw horizontal line from the point of maximum curvature.

2. Draw tangent line to the compression curve from the point of intersection.

3. Find bisector line between horizontal and tangent lines.

4. Move the recompression line to be tangent with the compression line. The point of

intersection with the bisector line indicates the corrected swelling pressure.

Figure 4.2. Typical test results of constant volume oedometer test; correction to find

swelling pressure (after Fredlund and Rahardjo, 1993).

4.2.9 Saturated Hydraulic Conductivity

The saturated hydraulic conductivity was determined for two soil samples per site; cores

#1 and #5. The consolidation test results were used to calculate the saturated soil permeability,

ksat, with equations (4.8) through (4.10).

11v w v

satc gak

eρ

=+

(4.8)

2

9090

drv

Hc Tt

= (Taylor method) (4.9)

1 2' '2 1

ve ea

σ σ−

=−

(4.10)

138

where:

Cv Coefficient of consolidation- 2cm

s

,

T time factor [T90 = 0.848], -

H2dr

average height of the specimen when the pressure is increased from σ1- ' to σ2

' ; the value is divided by two for double drainage test [cm2

t90

], the time it takes to reach 90% of primary consolidation due to applied load; the value is used when Taylor method is applied [s],

-

av Coefficient of compressibility - 2m

N

,

e void ratio, -

e1 void ratio from the consolidation curve; the first point considered for the calculation, -

e2 void ratio from the consolidation curve; the second point considered for the calculation, -

σ' effective stress applied to the sample [kPa], -

σ1’ effective consolidation stress from the consolidation curve; the first point considered for the calculation, -

σ2’ effective consolidation stress from the consolidation curve; the second point considered for the calculation, -

ρw density of water [1000- 3

kgm

at T = 20° C], and

g constant of gravitational acceleration- 29.81 ms

.

4.2.10 Soil Suction

The determination of Soil Water Characteristic Curve, SWCC, can be time consuming,

especially for clay soils. Because soil suction is such an important parameter in unsaturated soil

mechanics theory, a simplified method of SWCC determination was developed as a part of this

study. It is called One-Point Method of SWCC Determination. It is described in detail below and

in Appendix C. Tubes 1, 3, 5 and 7 or 8 were selected for this test. In order to verify the

obtained results with the proposed method, complete SWCC was performed on at least one

sample from each site. Additionally, filter paper and dessicator testing was performed on

selected soils to determine the moisture conditions corresponding to high suction values.

139

4.2.10.1 Pressure Plate

4.2.10.1.1 Equipment

In this study, matric suction was determined with pressure cells, Fredlund SWCC cells,

developed by GCTS, Tempe, AZ. This equipment is capable of testing desaturating or

saturating SWCC paths and allows for the determination of soil suction up to 1500 kPa which is

the air entry value of ceramic stone used in the cells. The schematic of the equipment is

illustrated in Figure 4.3 (after Perera, 2003). Figure 4.4 and Figure 4.5 illustrate one of the

pressure cells used in the lab set-up.

Plates

Soil Sample

Outer Cylinder

To pressure source

To volume tubes Base Plate

Ceramic Stone

Top Plate

Socket-Head Cap Screw

Inner Cylinder

Loading Pin

Loading Plate

Seal Screw

Figure 4.3. Fredlund SWCC cell schematic (after Perera, 2003).

The Fredlund SWCC pressure cell consists of pressure chamber with graduated volume

tubes attached to its base through Tygon tubing and QD valves. The pressure chamber consists

of base with room for ceramic stone, inner and outer cylinders, top plate and loading rod with

platen that goes through the top plate. The cell is equipped with four o-rings designed to prevent

air leaks. The first o-ring is located inside the base next to ceramic stone. The second one is

located between the top of the base and the outer cylinder. Another one is located between the

top of the outer cylinder and the top plate. The last o-ring is located between loading rod and top

140

plate (Perera, 2003). The soil sample is contained in a brass ring of dimensions 2.54-cm in

height and 6.1-cm in diameter. The sample is placed on top of the ceramic stone and topped

with a grooved platen transferring applied load through the loading rod. The soil suction

measurements (and associated water content and degree of saturation) are obtained by

applying air pressure to the sample and observing the amount of water released or absorbed by

the soil through the ceramic stone as well as the deformation of the specimen.

Figure 4.4. Fredlund SWCC cell.

The pressure plate device was prepared by cleaning accessible o-rings and surfaces.

The base of the cell was connected to the graduated volume tubes with Tygon tubing through

the two QD valves located on the sides of the base. The QD valves were opened and the o-ring

located inside the base was moistened to facilitate downward movement of the ceramic stone

ring. The ceramic stone ring was pressed very carefully into the well of the base; then the soil

sample was placed on top of the ceramic stone and the grooved metal platen was placed on top

Piston

Heater

Top plate

Volume Tubes

141

of the sample (not illustrated in figures). The inner and outer cylinders were placed on the base

surrounding the sample. The top plate was placed carefully observing proper alignment of top o-

ring with grove in the top plate. The top plate already contained the loading rod inserted through

the top screw and o-ring. A washer was screwed onto the bottom of the rod to prevent the rod

escaping from the cell when air pressure was applied. The top plate was tightly screwed on to

the base with four 5-inch long socket-head cap screws that sealed the cell. Air pressure was

applied to the Fredlund SWCC device set-up (Perera, 2003).

Figure 4.5. Fredlund SWCC cell set-up (grooved platen not in the picture).

Air pressure was applied through two types of regulators. Pressures up to 690 kPa were

regulated through bleeding type Fairchild™ pressure regulators. The higher pressures up to

1500 kPa were applied using nitrogen cylinder that was regulated through non-bleeding type

Fairchild™ pressure regulators. The applied pressure was measured with pressure gauges with

Inner and outer cylinders

Ceramic stone

142

0.25 or 0.50 % full-scale accuracy. Pressure gauges with ranges of 0 to 200 kPa, 0 to 690 kPa,

and 0 to 1500 kPa were used in the setup. Pressures below 10kPa were measured with water

tubes attached to one of the gages and the SWCC cell.

Very recent modifications to the Fredlund SWCC device included addition of a small

heater block on top of the cell. The heater block, obtained from Soil Moisture, is intended to

maintain constant, slightly above ambient temperature within the cell. The use of the heater

block supposed to prevent condensation of water inside the cell producing in turn more reliable

results from the volume tube read out.

4.2.10.1.2 Issues Associated with SWCC Testing

There were few challenges that needed to be overcome when measuring soil suction in

general and when working with the pressure plate apparatus. Testing of soil suction requires

draft free, constant temperature environment. Temperature variations by more than 1°C will

result in moisture condensation inside of the pressure chamber. At times the condensation

might appear on the bottom plate below cylinders, Figure 4.6, or on the brass ring containing soil

sample, Figure 4.7, or on the cylinders. Most of the condensation is observed at low suction

values. The Soil Moisture heater block has proven to be beneficial; however it did not eliminate

the condensation problem. Presented condensation pictures were obtained with SWCC cell with

attached heater block. Perez (2006) attempted to resolve this issue by introducing an insulation

sleeve around the cell. She found condensation in the pressure tube connected to the cell and

concluded that pressure plate suction testing should be conducted in an environmental chamber

capable of maintaining set temperature within 1°C. If this condition cannot be satisfied,

condensation should be anticipated in different areas of the test apparatus. Since environmental

chamber was not available for all tests conducted in this study, the condensation issue was

overcome by taking a direct measurement of soil mass once the specimen reached equilibrium

with the applied air pressure. The pressure chamber was opened, the moist specimen weight

143

and then returned to the test equipment to measure soil response to the next applied pressure

value.

Figure 4.6. Condensation on bottom plate inside of SWCC cell.

Figure 4.7. Condensation on brass ring inside SWCC cell.

Lateral soil shrinkage is another issue. In order to properly describe SWCC in terms of

volumetric water content, the total volume of soil sample is needed for each measured suction.

As an expansive soil dries, its size decreases in both horizontal and vertical directions. The

Condensation

Condensation

144

Fredlund SWCC cell is designed to monitor vertical deformation of specimen through the

displacement of plate on top of the piston. Lateral shrinkage cannot be accounted for, and yet it

is a significant factor. Figure 4.8 illustrates lateral shrinkage of initially saturated clayey soil with

its volume equal to brass ring volume and final suction of 1500 kPa. It can be further observed

that the lateral shrinkage does not occur uniformly with depth. Typically, the soil diameter is

larger at the bottom and smaller at the top. To overcome these issues, the soil volume was

measured with callipers every time the equilibrated soil with applied pressure was removed from

the pressure cell to obtain its weight. When it was possible to remove the soil from the ring,

three measurements were taken in the middle of the specimen, otherwise diameter was

measured at the top and bottom of the sample to calculate average value. The analysis of data

further revealed the sensitivity of volumetric water content or saturation to the specimen volume.

Small changes in soil volume correspond to large changes in saturation. It is the opinion of the

author that SWCC uncertainty, to a large degree, is due to errors or variability in dry density.

Figure 4.8. Lateral soil shrinkage during SWCC testing.

145

Lateral and vertical shrinkage cracks present yet another challenge. Figure 4.9

illustrates an example of this phenomenon (vertical crack), which was found to occur rather

infrequently. When large shrinkage cracks occurred, the test was redone.

Figure 4.9. Soil cracking during SWCC test.

4.2.10.1.3 One Point Method of SWCC Determination

Perera et al. (2005) provided a model to predict drying SWCC from index properties.

Figure 4.10 illustrates the developed family of SWCC curves for plastic soils based on index

properties alone. The family of curves was calculated using equations (4.11) through (4.17) for

different values of wPI. This model can be configured to give unbiased estimates of the SWCC,

but some uncertainty associated with the estimate exists. As discussed in Appendix C, a band

of uncertainty exists even when direct measurements are made, and somewhat more

uncertainty exists when index properties alone are used to get the SWCC. The uncertainty is

reduced when one direct measurement of suction and saturation is coupled with index properties

to get the SWCC. Thus the one-point method entails measuring the existing suction and

saturation on either an undisturbed sample from an in-situ location in the field or on a sample

compacted in the laboratory.

146

Figure 4.10. Family of SWCC Curves for Plastic Soils Developed by Perera (Perera, 2003).

( )

( )f

f

sv h c

b

f

C

hln e 1a

θθ =

+

(4.11)

( )r

h 6

r

hln 1h

C 110ln 1h

+= −

+ (4.12)

( )fa 32.835ln wPI 32.438= + (4.13)

( ) 0.3185fb 1.421 wPI −= (4.14)

( )fc 0.2154ln wPI 0.7145= − + (4.15)

fh 500= (4.16)

200PI*PwPI100

= (4.17)

Family of Curves

wPI = 0.4 0.5 1 2 5 10 20 50

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

0 1 10 100 1000 10000 100000 1000000

Suction [kPa]

Satu

ratio

n

147

where:

θv - volumetric water content, θs - saturated volumetric water content or porosity of the soil; e - exponent, h - matric suction [kPa];

C(h) - adjustment factor which forces the SWCC through zero water content at a suction of 106 kPa, and

The one point measurement was obtained by extruding undisturbed soil sample from

Shelby tube into a brass ring of dimensions: 2.54-cm in height and 6.1-cm in diameter. After the

initial readings of volume and weight were collected, the sample was placed in the pressure cell

on a saturated ceramic stone. Special care was taken for the soil sample not to undergo change

in volume or water content from the time it was collected from the field to the time of testing. The

soil sample was assembled inside the pressure cell and initial, trial air pressure, ua, was applied

to the specimen. This trial value can be selected by using the best available data to estimate the

initial saturation value and the best available index properties to estimate the SWCC. Then the

saturation value can be used to determine the first trial value of suction (ua) from the graph.

Alternatively, the first trial value of ua can be selected from experience and intuition.

The drainage valves were opened to expose the ceramic stone, on which the specimen

rested, to the water in the volume tubes, thus driving pore water pressure, uw to zero. The initial

air bubble flush was performed to ensure that there is no entrapped air bubbles in the system.

Weights were placed on top of the loading rod to compensate for the overburden pressure,

applied air pressure and the friction between the inner ring and the loading rod. Initial readings

of specimen height and water volume readings from volume tubes were obtained where the

initial height was measured with callipers as the distance from the top of the top plate and

bottom of the platen located on top of the loading rod.

hr, af, bf and cf are fitting parameters.

Immediately after the initial readings were collected, the volume of water in the volume

tubes was monitored to detect any tendency for water to be expelled or absorbed by the

148

specimen. Depending on soil behavior, the applied pressure was reduced or increased and

appropriate amount of weights was removed or added. The observations were conducted on a

more or less logarithmic scale; i.e., the elapsed time, at which readings were taken and ua

adjusted, from the test beginning were doubled or tripled. When the applied pressured resulted

in no change between the initial and the final water volume readings, or in other terms when

equilibrium applied pressure was found, the test was terminated. Cell drainage valves were

closed, the cell was disassembled and the specimen was removed as quickly as possible. Care

was taken to remove all of the specimen and to prevent moisture and specimen mass loss or

gain. The moist soil with ring was weighed and oven dried. The measurement of specimen

volume, water content and dry soil mass were used in the calculation of undisturbed soil

saturation. The matric suction of the undisturbed specimen was determined, and corresponds to

in-situ suction conditions of soil under the slab at tested depth. The results were used to

develop soil-water characteristic curves.

The pair of values, suction and saturation, obtained represents one value on the SWCC.

An SWCC that passes through the measured pair was estimated with equations (4.10) through

(4.16) based on an apparent wPI. If the computed suction agrees with the measured suction

then the fitting parameters are appropriate. If not, then the estimated wPI was adjusted up or

down until a match was obtained. A second SWCC estimate was obtained by varying equation

parameters in such a way as to produce a curve that goes through the measured point and

retains the slope of wPI SWCC curve. The determined suction value was further modified for

sampling disturbance. Typically, the saturation value of specimen prior to suction testing is

higher than after the test (condensation on the brass ring was observed). For this reason, the

suction value obtained may, in some cases, need to be corrected by accounting for the change

in degree of saturation. The corrected suction is simply read of from the lab-determined drying

SWCC curve.

When the insitu soil suction did exceed the testing equipment capabilities, 1500kPa, the

soil was allowed to come to equilibrium with the applied pressure. During the equilibration

149

process the soil absorbed water, potentially travelling on scanning SWCC. Filter paper testing

was performed on few soils for which direct measurement of matric suction with pressure plate

apparatus proved to be impossible. Figure 4.11 illustrates results obtained with both filter paper

and pressure plate apparatus together with fit curves for selected specimen. The measured data

points correspond to parallel SWCCs shifted by about one log cycle. The observations were

consistent with the literature review findings presented in Chapter 2.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

0.01 0.1 1 10 100 1000 10000 100000 1000000

Suction [kPa]

Satu

ratio

n [d

ecim

al]

Filter PaperPressure PlateFit through PP point (wetting curve)Fit through FP point (drying curve)wPI basedScanning Curve

Figure 4.11. Pressure plate and filter paper test results, SWCC estimate.

When both, pressure plate and filter paper results were available, the filter paper values

were reported. The in-situ soil subjected to filter paper testing was observed to loose small

amount of moisture during the testing process, therefore the obtained suction value was

corrected for sampling disturbance. The matric suction corresponding to initial soil saturation

was read off from the best fit SWCC going though the measured pair of values.

On the other hand if only pressure plate results were available for specimen that did

undergo wetting, first a wetting SWCC going through the measured pair of values was

estimated. Next, a parallel drying curve to the wetting fit was developed. These two curves

were shifted by between half to one log cycle (depending on the magnitude of saturation

150

change). The matric suction corresponding to initial soil saturation was read off from the

estimated drying SWCC.

4.2.10.1.4 Complete SWCC

For selected samples, the same sample that was used in the One Point Method was

used in the determination of complete SWCC. The soil sample was removed from the pressure

cell after the One Point test was completed. Its weight and volume were recorded and it was

placed in a distilled water bath, where the soil sample was rested on a layer of filter paper and

porous stone. The sample was covered with another layer of filter paper and porous stone.

Number of weights was placed on top of the specimen to overcome the swell potential of the

soil.

The sample was removed from water bath and its weight recorded and then transferred

into prepared pressure cell. The cell was closed and the initial pressure was applied. The

applied pressure exerted an upward thrust on the loading rod causing friction between top plate

o-ring and the loading rod. Applying correct amount of weights on the loading platen

compensated the upward thrust and the friction forces. The weights were increased until the rod

would move down under the application of light touch. Additional weights were applied to

simulate the overburden pressure the soil experienced in the field. The overburden pressure

was calculated based on the depth and moisture content of the tested sample. The pressure cell

device, at this time, was checked for air leaks by wetting the locations with o-rings. The air was

flushed from the water tubes and initial readings were collected once the water height inside

both of the volume tubes equilibrated The height of the specimen was determined by measuring

the distance between the top of the top plate and the bottom of the loading platen with a pair of

spring clippers and a Vernier calliper.

The system was left with the applied pressure until the soil reached equilibrium. It was

determined that the equilibrium was reached once the soil stopped absorbing or expelling water

which was identified by the same water volume reading obtained from the volume tubes within

151

24 hours. The equilibrium was also manifested by no variation of soil height within 24 hours. At

that time, the weights were removed and the pressure cell was opened up. The soil sample was

removed, the condensed water was wiped out from the brass ring and the mass of the moist

specimen with brass ring was recorded. The dimensions of the sample were recorded as well.

The specimen was returned to the pressure cell and the test procedure was repeated for higher

suction. Minimum of three suction measurements were obtained per specimen; 50, 500 and

1500 kPa. Once the soil came to equilibrium at 1500 kPa, final moist sample readings were

obtained. The soil sample was placed inside an aluminium container and was oven dried. The

collected values of moist and dry soil mass and volume were used to calculate soil saturation

corresponding to tested matric suction. The results are presented in Appendix B.

4.2.10.2 Filter Paper

Filter paper test with Fisherbrand filter paper #P8 was performed on selected

undisturbed and disturbed samples. Filter paper is an indirect matric and total suction

measurement method. The matric suction is obtained by placing three filter papers between two

soil samples allowing direct contact of the filter paper and the soil. The actual filter paper used

for the matric suction calculation is located between the other two filter papers preventing filter

paper contamination with soil. A piece of tape was placed on the soil and filter paper joint to

reduce the affect of air relative humidity of the matric suction results. Total suction measurement

is obtained by placing the filter paper above the soil and preventing direct contact of the filter

paper with soil with a wire mesh. The filter paper and soil set-up was placed for up to two weeks

in an air tight jar in an environmental chamber capable of maintaining set temperature to within

1°C. Once the filter paper was considered to be in equilibrium with the soil conditions the jar was

opened to retrieve the filter papers. The moist weight of filter papers was determined with a 10-4

accuracy scale. The filter papers were placed in an oven; soil mass and soil volume

measurements were collected. Within an hour, the filter papers were removed from the oven to

collect their dry mass. The suction corresponding to filter paper water content was obtained

152

from presented below calibration curve developed by ASU researchers. The calibration curve

was determined with different salt concentrations.

Filter Paper - Fitting Curve

0102030405060708090

100

10 100 1000 10000 100000 1000000Suction [kPa]

w [%

]The preparation of undisturbed soil samples for filter paper took place in an

environmental chamber. The soil was extruded from the Shelby tube and cut into 1” to 2” long

pieces with a saw. Special attention was given to the smoothness of the soil surfaces meant to

be in contact with the filter paper. The One-Point Method discussion about drying, wetting and

scanning SWCCs is relevant here. It is unknown which path is obtained with this procedure.

Figure 4.12. Filter paper calibration curve.

The preparation of disturbed soil samples consisted of soil compaction at target dry

density and prepared moisture content. The samples were prepared in standard brass rings of

dimensions: 2.54-cm in height and 6.1-cm in diameter. This methodology produces wetting

SWCC. Also on few selected samples drying SWCC was obtained with filter paper. The

compacted soil samples were placed in water bath and allowed to become saturated. In

general, the calibration time decreases with increased soil saturation. Therefore the filter papers

were placed between the prepared samples for a period of few days only. Once the filter papers

come to equilibrium with the soil, the filter papers were removed, weigh and oven dried, the soil

mass and dimensions measured. New filter papers were placed between the soil samples to

153

obtain suction values corresponding to decreased soil saturation. Fungi growth was frequently

observed with the moist soil. When this occurred, the filter paper results were discarded.

4.2.10.3 Dessicator

Total suction at higher suction range was measured with saturated salt solutions. The

saturated salt solution was placed on the bottom of a dessicator. Compacted in standard brass

rings and saturated soil samples were placed on a dessicator rack above the solution. The soil

was allowed to come to equilibrium with the salt solution over a period of 2 to 3 weeks in an

environmental chamber at approximately 20°C. Once the test was complete, the soil samples

were removed from the dessicator to measure soil mass and sample dimensions. The salt

solution was replaced with a different salt solution corresponding to a lower relative humidity.

The soil samples were returned to the dessicator and the equilibration process was repeated.

Overall three salts were used in this test, K2SO4, KCl, NaCl presented in Table 4.3. Once the

soil came to equilibrium with the final salt solution, the soil samples were oven dried.

Table 4.3. RH and suction per saturated salt solutions at 20°C (based on Dean, 1999). Salt RH

[%] Total Suction

[kPa] K2SO4 97 4540 KCL 85 24200

NaCL 75.7 43000

4.2.11 Summary of Laboratory Results

4.2.11.1 Sampling Locations

The soil samples were obtained from below 16 slab-on-grade residential properties.

One was obtained next to a property experiencing distress due to expansive soil movement and

one from an open field where expansive soils were identified. The approximate locations of

sampling is given in Table 4.4 and illustrated in Figure 4.13 where the sampling locations were

superimposed on NRCS swell potential map. This map was used to identify areas of potentially

clayey soils to target as sampling locations.

154

Table 4.4. Locations of Soil Sampling.

Soil # Cross Roads City 1 Mill Ave./Broadway Rd. Tempe 2 Kyrene Rd./Guadalupe Rd. Tempe 3 Ray / Kyrene Chandler 4 Cooper Rd./ Chandler Blvd. Chandler 5 Chandler Heights Rd./Arizona Ave. Chandler 6 Southern Ave./Stapley Dr. Mesa 7 Southern Ave./Stapley Dr. Mesa 8 Gilbert Rd. /Baseline Rd. Gilbert 9 Warner / Alma school Chandler

10 Cooper Rd./ Ray Rd. Gilbert 11 Warner / Lindsay Gilbert 12 Chandler Blvd. / Cooper Chandler 13 Baseline Rd. / Lindsay Rd. Mesa 14 Hwy 60 / Lindsay Rd. Mesa 15 Litchfield Rd. / Indian School Byp Gilbert 16 Van Buren St. / 59th Ave. Phoenix 17 Dysart Rd./ Bethany Home Rd. Litchfield 18 Meridian Dr./ 23rd Ave. Anthem

155

SOIL

SH

RIN

K/S

WEL

L PO

TSO

IL S

HR

INK

/SW

ELL

POT

3

8

9

12

10

11

5

1

2

76

14

15

13

16

17

18

Figu

re 4

.13.

Sa

mpl

ing

Loca

tions

sup

erim

pose

d on

NR

CS

swel

l pot

entia

l map

.

4.2.11.2 Summary Tables

Table 4.5. Summary Table

Sample # Soil Classification LL PL PI P200

clay [%]

ksat [cm/s] Gs CEC Sulfate

[ppm]

Consolidation Test

w γdry Cor. Ps Swell

[%] [pcf] [kPa] Index

1-1-7-18 CL 28.4 14.2 14 62.5 2.8E-07 2.738 11.8 102.4 77.2 0.0185 1-2-18-27.5 CL 31.5 20.1 11 72.1 12.3 1-3-27.5-38 CL 31.5 20.1 11 69.0 1-4-38-47 ML-CL 27.1 20.3 7 60.2

1-5-47-56.8 CL 30.1 22.3 8 59.5 4.4E-06 2.731 11.6 88.3 15.3 0.0154 1-6-56.8-66.5 ML 35.2 25.5 10 55.6 1-7-66.5-77 ML 36.2 24.9 11 52.4 1-8-77-85.5 ML 36.2 24.9 11 54.3

2-1-8.5-19 CL 30.9 19.2 12 71.2 2.5E-08 2.764 119.5 11.6 121.0 0.0150 2-2-19-27 CL 31.6 19.6 12 80.8 2-3-27-36 CL 31.6 19.6 12 74.8 9.8 2-4-36-46 CL 26.2 18.5 8 72.7 2-5-46-55 CL 26.2 18.5 8 72.7 1.1E-06 2.750 26.5 10.0 91.8 0.0111 2-6-55-66 CL 26.2 18.5 8 66.7 2-7-66-75 CL 29.9 19.3 11 68.8 2-8-75-85 CL 31.5 20.7 11 51.0

3-1-9.5-17.5 CL 28.8 17.5 11 73.6 2.7E-07 2.71 47 10.9 108 124 0.0155 3-2-17.5-25 CL 28.6 17.6 11 76.0 10.0 3-3-25-36 CL 28.6 17.6 11 76.0

3-4-36-45.5 CL 39.5 24.4 15 61.5 3-5-45.5-54.5 CL 47.7 24.5 23 52.7 6.6E-08 2.739 13.9 100 177 0.0202 3-6-54.5-64.5 CL 47.7 24.5 23 58.3 3-7-64.5-73.5 CL 47.7 24.5 23 52.7 3-8-73.5-84 SC 51.3 26.2 25 46.4

4-1-5.5-16 CL 34.5 20.5 14 67.4 1.6E-07 12.9 108.9 291.6 0.0358


clay [%]


[ppm]

Consolidation Test



4-2-16-25 CL 37.9 20.4 17 64.9 17.0 2.823 4-3-25-35.5 CL 40.6 21.7 19 57.5

4-4-35.5-45.75 SM-SC 24.3 18.0 6 36.8 4-5-45.75-55 SM-SC 24.3 18.0 6 36.8 4.8E-07 2.764 12.4 97.2 20.0 0.0088

4-6-55-65 SC 32.5 21.3 11 44.0 4-7-65-75 SC 32.5 21.3 11 29.5

5-1-8.5-16.5 SM NP NP 42.9 3.4E-07 2.784 24 6.6 103.8 10.4 0.0048 5-2-16.5-27 SC 44.5 17.6 27 41.2 18.0 3.5E-07 25 0.0067 5-3-27-36 32.8

5-4-36.5-47 5-5-47-56 SC 39.8 22.0 18 37.2 2.8E-07 2.751 9.3 98.3 15.8 0.0122 5-6-56-66

5-7-66-75.75 5-8-75.75-83.5 SC 26.7 18.7 8 28.2

6-1-7.5-17 SC 32.9 18.2 15 36.2 2.5E-07 2.742 75 10.6 97.0 42.9 0.0173 6-2-17-29.5 21.5 6-3-29.5-39 CL 46.0 24.7 21 71.1

6-4-39.5-44.5 46.0 23.2 23 76.0 6-5-44.5-48 46.0 23 23 80.8 6-6-48-52.5 CL 46.2 21.8 24 85.7 30.0 2.668 32 6-7-52.5-62 CL 43.6 22.4 21 85.0 1.4E-08 12.3 119.1 179.4 0.0304 6-8-62-65.5 50.4 23.8 27 85.0 6-9-65.5-72 CH 57.2 25.2 32 85.1 41.0

7-1-6-17 SC 7-2-17-27 7-3-27-37 CL 7-4-37-47

7-5-47-50.5


clay [%]


[ppm]

Consolidation Test



7-6-50.5-55 CL 7-7-55-60.5 CL

7-8-60.5-64.5 8-1-7-17 SM 40.2 19.3 21 49.9 5.8E-08 2.719 11.2 108.1 25.8 0.0105

8-2-17-27 CL 44.7 22.5 21.9 56.8 8-3-27-37.5 CL 49.1 25.7 23 63.6

8-4-37.5-47.5 CL 42.7 23.5 19.0 57.5 8-5-47.5-57.5 CL 36.3 21.2 15 51.3 8.0 5.3E-08 2.743 14.5 112.9 53.0 0.0201 8-6-57.5-67.5 SC 35.0 20.8 14.2 45.5 8-7-67.5-77.5 SC 33.7 20.4 13 39.6 8-8-77.5-88 36.4 8-9-88-96.5 SM NP NP 33.2

9-1-9-19 CL 28.0 16.9 11 54.3 7.1E-07 2.751 19 8.0 98.4 8.3 0.0126 9-2-19-29 SC 36.5 20.6 15.9 44.3 9-3-29-39 SC 44.9 24.3 21 34.4 6.9 9-4-39-49 SC 41.7 22.8 18.9 37.3

9-5-49-56.5 SC 38.5 21.3 17 40.3 7.0E-08 2.739 10.3 114.6 285.7 0.0241 9-6-56.5-65.5 CL 43.2 22.7 20.6 50.1 9-7-65.5-72 CL 47.8 24.1 24 59.9

10-1-7-17 SC 31.1 16.8 14 48.2 6.1E-08 2.714 11.2 124.3 154.3 0.0153 10-2-17-27.5 CL 29.7 18.9 10.7 53.4 3.7E-07

10-3-27.5-37.5 CL 28.3 21.1 7 58.6 10-4-37.5-47.5 CL 31.2 21.8 9.5 60.8 10-5-47.5-57.5 CL 34.0 22.4 12 63.0 21.0 3.3E-08 23 11.9 107.9 118.8 0.0219 10-6-57.5-68 SC 31.0 20.8 10.5 45.0 10-7-68-78 SC 28.0 19.2 9 27.1 2.736

10-8-78-84 11-1-14.5-24 CL 34.8 19.6 15 1.8E-07 2.684 40 15.2 111.2 35.2


clay [%]


[ppm]

Consolidation Test



11-2-24-34 CL 40.8 21.2 20 55.9 16.6 109 50.1 0.2288 11-3-34-46.5 CL 39.1 20.6 18

11-4-46.5-59.5 CL 49.1 24.3 25 55.8 13.0 11-5-59.5-70 CL 49.1 24.3 25 1.7E-07 2.663 14.1 110.9 73.0 0.0207 11-6-70-80 CL 49.1 24.3 25 11-7-80-90 CL 38.6 21.7 17 52.4

12-1-6-12 CL 35.1 21.2 14 1.1E-07 2.77 52 19.1 107.4 60.0 0.0242 12-2-12-24.5 CL 38.0 20.1 18 61.5

12-3-24.5-37.5 CL 38.0 20.1 18 12-4-37.5-48 SC 32.8 18.7 14 46.8 12-5-48-62 SC 36.8 23.3 13 7.1E-08 2.717 14.7 116.7 80.0 0.0203 12-6-62-75 SC 37.7 21.7 16 29.0 12-7-75-85 SC 34.5 21.1 13.5 39.8 12.0 12-8-85-96 SC 31.3 20.4 11 13-1-7-13 CL 40.9 20.0 21 65.5 24.0 1.1E-07 2.727 12 11.5 11.3 263.7 0.0298

13-2-13-23.5 CL 37.8 19.4 18.4 62.1 26.5 4.0E-07 0.0177 13-3-23.5-33 CL 34.8 18.9 16 58.7 29.0 13-4-33-42.5 CL 42.0 20.6 21.4 65.6 34.0

13-5-42.5-51.5 CL 49.1 22.3 27 72.4 39.0 5.5E-08 2.716 34 16.0 115.2 212.0 0.0262 13-6-51.5-59.5 CL 44.5 21.3 23.2 68.8 13-7-59-5-66.5 CL 39.8 20.3 19.5 65.2

13-8-66.5-71 CL 35 19.3 16 61.4 14-1-8-17.5 CL 37.8 20.4 17 64.9 28.5 9.8E-08 2.726 17.5 110.0 62.3 0.0197

14-2-18.5-34.5 CL 43.4 20.5 22.8 69.4 14-3-34.5-47.75 CL 48.9 20.7 28 73.8 44.0 2.755 33 14-4-47.75-60 CL 41.4 18.8 22.6 63.0

14-5-60-68 CL 33.8 16.9 17 52.2 2.4E-07 2.754 10.3 105.6 18.4 0.0172 14-6-68-77 CL


clay [%]


[ppm]

Consolidation Test



15-1-9-15 SM NP NP 31.5 2.726 15-2-15-21 SM 21.4 18.5 3 37.7 7.1 15-3-21-32 SC 29.1 19.0 10 48.9 15-4-32-42 SC 26.6 17.8 9.0 37.6 15-5-42-55 SC 24.1 16.5 8 26.3 4.7E-06 2.723 12.6 110.9 5.5 0.008 15-6-55-64 SC 28.1 18.5 9.8 34.0 15-7-64-73 SC 32.0 20.4 12 41.6

16-1-10.5-21 CL 29.2 17.9 11 53.7 1.5E-07 2.802 76 14.9 113.3 50.0 0.0161 16-2-21-34 CL 32.0 19.2 12.8 72.6 16-3-34-46 CL 34.7 20.4 14 91.5 20.0 16-4-46-58 CL 40.0 21.5 18.5 82.7 16-5-58-68 CL 45.3 22.6 23 73.8 30.5 4.5E-08 2.793 45 16.9 112.7 235.2 0.0316

16-6-68-77.25 CL 44.9 23.4 21.5 81.5 16-7-77.25-85 CL 44.4 24.1 20 89.1 25.4

17-1-8-16 SC 99.1 35.0 64 28.7 2.75 220 17-1-8-16 SC 37.4 13.2

17-2-16.25.5 SC 48.0 17-3-25.5-30 CH 85.1 32.5 53 62.1 19.9 2.4E-07 2.797 29.6 85.0 91.6 0.0264 17-4-30-38 SC 61.6 17-4-30-38 CH 61.6 30.1 32 83.8 17-4-30-38 CH 86.3 34.6 17-5-38-44 SC 29.1 3.78E-07 18.9 90.5 90 0.0277 17-5-38-44 2.829 17-5-38-44 CH 80.0 30.2 17-6-44-50 SC 47.2 17-6-44-50 CH 67.8 30 38 81.4 23.7 2.85E-07 20.8 90.5 361 0.0825

18-12-18 CH 55.0 26.0 26 18-14-20 CH 93.8 40.1


clay [%]


[ppm]

Consolidation Test



18-26-31 CH 2.811 18-27-32 CH 94.0 39.4 11.7 108.7 479.9 0.057 18-36-41 CH 56.6 21.4 35 6.3E-08 2.829

Footnotes: Shaded background used for estimated values

Test Type

Table 4.6. Summary Table – Response to wetting and compaction tests.

Parameter Name Soil (soil number and extruded depth range [in]) Soil 5-16.5-47 10-17-27.5 13-13-23.5 18-20-23

Corrected Swell Pressure [kPa] 10.4 154.3 263.7 479.9 Constant Volume Dry Density [pcf] 103.8 124.3 111.5 108.7 Oedometer Test Initial Water Content [%] 6.6 11.2 11.3 11.7 Saturation [%] 27.4 84.9 59.0 53.4 Expansion Index 9.0 22.5 42.6 33.0 Modified Expansion Dry Density [pcf] 110.6 110.3 104.6 108.5 Index Test Initial Water Content [%] 11.5 12.7 14.6 18.2 Saturation [%] 56.7 64.9 64.1 83.5

EI 50 6.3 12.5 41.7 77.3 Expansion Index Test Expansion Index 4.0 14.9 43.2 78.3 as per ASTM D 4829-03 Dry Density [pcf] 109.0 98.8 95.9 92.6 Standard Initial Water Content [%] 11.7 11.7 13.8 15.4 Saturation [%] 55.4 44.8 48.9 48.7

Compaction Test wopt 13.2 15 16.65 20 γmax [pcf] 116.9 117 110.31 114.2

162

4.2.12 Selection of Input for Modeling

Field investigation yielded three types of soil, CH, CL and SC with average soil properties

given in Table 4.7. The most commonly encountered soil has characteristics of low plasticity clay

or clayey sand to silty clay with PI smaller then 17. Fat clay, CH, occurs infrequently; it

represents the worst case scenario for residential construction in Arizona, therefore it was chosen

as one of the representative soils for modeling. Low plasticity clayey material with PI smaller then

15 is the second soil type of interest. Modeling of moisture flow through these two soils creates a

range of potential soil response due to typical Arizona and human imposed flux conditions on

soils found in Phoenix metropolitan region. Selected soil properties are given in Section 6.6.

Table 4.7. Average soil values. Soil Classification LL PL PI P200 %clay

CH 64 28 36 83 33 CL 38 21 17 66 23 ML to SC 33 19 13 40 11

Laboratory obtained soil profiles were used in the determination of appropriate initial

matric suction conditions. Wide range of matric suctions below a slab for different soil types and

under different landscape conditions was identified. This finding suggests that the soil samples

were obtained within edge moisture variation distance and within active zone depth; in other

words, the edge moisture variation distance exceeds the 9ft suggested by the PTI manual (PTI,

2004). The results are presented visually in Appendix B for each individual profile and in Chapter

9 per landscape type.

In the determination of initial suction profile for modeling purposes, the suction profiles

obtained for desert landscape are especially valuable since they potentially describe suction

conditions beyond the active zone depth. The active zone depth is expected to be smaller for dry

surface conditions. Suction at depth depends on soil type, where larger suctions are obtained for

lower plasticity soils. The values range between 8000 kPa for SC and 700 kPa for CL at the

approximate depth of 6.5 ft. The measured matric suction for CH soil under free field conditions

was measured only down to 2.5 ft and ranges between 2000 to 2500 kPa. Because only minor

163

volume changes are expected for suctions larger than 1500 kPa, initial suction profile of 1500kPa

was considered to be appropriate for all soil types, and subsequent data at depth obtained from

correlations between SWCC curves and degree of saturation data confirmed this to be a

reasonable range/value of suction at depth for the clay soils.

5 MAP OF EXPANSIVE SOIL DISTRIBUTION IN PHOENIX VALLEY As part of this study, regions of low, medium and moderate expansion potential were

identified by updating the NRCS “Soil Shrink/Swell Potential” map; original map illustrated in

Figure 5.1. This map is frequently used by practitioners in the preliminary analysis of the site

expansion potential. Due to the importance placed on this map by the practitioners, the ArcGIS

9.1 software was used to produce an updated map illustrating maximum potential soil expansion

determined with EIAZ (the test methodology details given in Section 4.2.6.1), The map was

created based on NRCS identified soil units, soil property data released by Arizona practitioners

(860 borings scattered throughout the Valley with reported index properties, insitu moisture,

density and EIAZ) and correlation of expansion potential to index properties presented below.

Figure 5.1. Natural Resources Conservation Service (NRCS) Swell Potential Map.

Typically geotechnical practitioners in Phoenix Metropolitan area rely on modified

Expansion Index procedure, referred to EIAZ or Arizona Swell Potential, to quantify soil response

to wetting. This procedure, described in detail in Section 4.2.6.1, is similar to the ASTM D 4829

method for Expansion Index determination; therefore the results obtained with these two

165

methods should be similar or at least correlated. A comparison of EIAZ to the ASTM EI,

developed by the ASU team as a part of the HBACE (2006) study, shows large scatter of data for

EIAZ between 0.1 and 1. The scatter is reduced for EIAZ between 1 and 10. For this range of

values, to a good approximation the ASTM EI can be obtained by multiplying the EIAZ by a factor

of 10. Limited data is available for EIAZ larger than 10, hence no conclusions can be drawn.

Refer to Figure 5.2 for details.

The Arizona Expansion Index was found to correlate with the weighted PI, wPI, defined

as the product of the percent passing US sieve # 200 in decimal and the PI in %. The

correlation, illustrated in Figure 5.3 is a continuation of research work first presented by Zapata et

al. (2006), to whom 736 data points were available. The linear correlation

EIAZ = 0.2655wPI + 0.5 (5.1)

developed with additional 124 data (mostly in the lower wPI range; previous study had limited

information for wPI less than 8) has R2 of 0.57. Based on this correlation, the following swell

potential classification was identified:

166

EIA

STM

= 0

.16E

IAZ2

+ 6

.3EI

AZ

+ 11

.7R

2 =

0.87

N =

100

110100

1000

0.1

110

100

A

EI(A

Z) [%

]

Figu

re 5

.2.

AST

M D

482

9 Ex

pans

ion

Inde

x co

rrel

atio

n w

ith A

rizon

a EI

test

(HB

AC

A, 2

006)

.

167

Table 5.1. Classification of Potential Expansion (EIAZ) based on wPI. Classification of Potential Expansion wPI EIAZ

Low < 5.65 < 2.00 Medium 5.70 – 16.95 2.01-5.00

Moderate 17 – 35.8 5.01-10.00 High >35.85 >10.01

EIAZ = 0.2655wPI + 0.5R2 = 0.5704

0

2

4

6

8

10

12

14

0 5 10 15 20 25 30 35 40wPI [%]

EI(A

Z) [%

]

Figure 5.3. Modified wPI vs. EIAZ relationship.

The updated swell/shrink map, presented in Figure 5.4 is the continuation of the HBACE

(2006) study. In that study the map was developed in collaboration with the ASU’s Geography

department which constructed the geodatabase for storing spatial data obtained from the United

States Department of Agriculture, Natural Resource Conservation Service Soil Data Mart,

located at http://soildatamart.nrcs.usda.gov/, ESRI at http://www.esri.com/data/index.html,

Maricopa County, the United States Census Bureau, GIS Data Depot at

http://data.geocomm.com/, and the Arizona Land Resource Information System at

http://www.land.state.az.us/alris/layers.html. The map developed for Central Arizona, Phoenix

http://soildatamart.nrcs.usda.gov/�

http://www.esri.com/data/index.html�

http://data.geocomm.com/�

http://www.land.state.az.us/alris/layers.html�

168

region consists of approximately 30 000 projected soil units. Note that not all soil units contained

soil information, hence grey regions on the map where soil properties were not projected. Based

on equation (5.1), soil unit maximum PI and maximum P200, the maximum swell potential was

identified and then used in the calculation of EIAZ. The engineering community provided data

were projected on top of the developed swell potential map and the soil unit information was

updated to represents the maximum potential swell within the upper 5-ft of the soil profile.

The NRCS developed map does not specify the implemented swell potential

identification methodology. Therefore only quantitative comparison can be made between the

NRCS map and the updated one. In general, Figure 5.4 identifies more regions with potentially

moderate to medium high swell potential. These types of soil properties are dominant in the East

Valley and the North Valley (up to Loop 101 and 303). High swell potential soils (EIAZ larger than

10) was found to be very rare, scattered and with small spatial extent. Based on the available

information, the soils most common to the Central Arizona have low expansion potential

characteristics.

It would be errorous to assume homogenous soil properties within each soil unit, but

rather a wide range of values with identified maximum soil response to wetting, as illustrated in

Figure 5.5. This figure presents the distribution of measured data over the identified soil unit

information. Potentially, the map could benefit from higher soil unit discretization based on the

practitioner provided data. However, a conservative approach, such as was adopted in this

study, would be to assign the maximum swell potential to the entire unit. Natural soil variability

resulting in variable expansion index supports this finding. Refer to taoofdirt.com for future

research, the swell potential map and public domain based files used in the development of the

presented map.

169

Figu

re 5

.4.

Upd

ated

Sw

ell P

oten

tial M

ap fo

r Cen

tral

Ariz

ona,

Pho

enix

Reg

ion

in th

e U

pper

5-ft

.

170

§̈¦17

Maximum Shrink/Swell Potential in Central Arizona in Upper 5-ft

Created by: Heather Dye, Drew Lucio & Sonal SinghalDye, H.B. (2008). "Moisture Movement Through Expanisve Soil and Impact on Performanceof Residential Structures." PhD Dissertation, Arizona State University, Tempe, AZ

Map Date: 05/02/08Map Projection: NAD 1983, UTM Zone 12, feet

0 1 2 30.5Miles

EI(AZ) measured data<2.0

2.01-3.50

3.51-5.00

5.01-7.50

7.51-10.00

Swell Potential*Low (<2.00)

Medium (2.01 - 5.00)

Moderate (5.01 - 10.00)

High (>10.01)

Transportation data was acquired from bothMaricopa County GIS and the U.S. CensusBureau. Soil data was derived from GIS datacreated by the USDA National ResourcesConservation Service and from contributions oflocal practitioners.

*Estimated maximum swell potential based oncorrelations with soil index properties.

Figure 5.5. Updated Swell Potential Map for Central Arizona, Phoenix Region in the

Upper 5-ft with few measured EIAZ data points.

6 PTI RESIDENTIAL FOUNDATION DESIGN

6.1 Introduction

The PTI procedure for the design of slabs-on-grade on expansive soils is currently the

most commonly used design methodology in Arizona. Several changes have been introduced in

going from the 2nd Edition to the 3rd Edition of the PTI design manual. The changes, when

applied to desert regions, tend to result in doubling of the edge moisture variation distance and a

change from center lift to edge lift design governing conditions. The new design parameters

along with the change of critical mode of slab deformation lead, in general, to somewhat thicker

slabs. It is the objective of this chapter to discuss the PTI design procedure in detail, examine

the changes in the PTI design method, Version 3, and compare the results obtained with both

the 2nd and the 3rd

6.2 Historical Background

Edition design procedures for typical Phoenix, Arizona climatic and soils

conditions presented in Chapter 4.

Wray (1978) developed a procedure for determining the edge moisture variation

distance based on the Thornthwaite Moisture Index (TMI), Thornthwaite (1948), for structures

constructed on expansive soils. This method was later adopted by the Post-Tensioning Institute

(PTI) and was kept intact in the 1st Edition of the PTI design manual that was developed for

ribbed foundations (PTI, 1980). Extensive clarifications of definitions and limitations of the

design were added into the design manual published in 1996 as the 2nd

Based on the research work done by Covar and Lytton (2001) significant changes have

been introduced into the geotechnical evaluation of the PTI design procedure published as

Alternate Procedure for Determining Soil Support Parameters for Shallow Foundations on

Expansive Clay Soil Sites under PTI Technical Note 12 (PTI, 2003). The Alternate 2

Edition PTI design

procedure (PTI, 1996). In this procedure, the soil analysis remained unchanged and the design

applicability was extended to both ribbed and uniform thickness foundations on expansive soils

with provisions also given for stable and compressible sites.

nd Edition is

applicable to sites with expansive soils and it is not applicable to soils with collapsible or

172

compressible characteristics. In this procedure, the soil analysis is based on soil index

properties that are correlated to soil mineralogy. The estimated dominant clay type and soil

index properties are both used to obtain a suction compression index for soil consisting of 100%

clay, which is modified for gradation and used to estimate an unsaturated diffusion coefficient

that is correlated to the edge moisture variation distance, em. The modified suction compression

index is also used in the prediction of differential soil movement, ym, based on the estimated

variation in total soil suction.

The 3rd Edition procedure (PTI, 2004) introduces significant changes as compared to the

2nd Edition procedure (PTI, 1996), where only the method of constant suction at depth

determination remains the same. At the same time, the 3rd Edition procedure is very similar to

the Alternate PTI 2nd Edition, first published in 2003 (PTI, 2003). The main differences include

modified sections on procedure applicability and updated figures and equations. The 3rd Edition

also contains design provisions for compressible and stable soils, as well as additional methods

of obtaining suction compression index modified for gradation. In addition, it includes an

updated suction vs. TMI relationship first presented in the PTI 1st

The 3

Edition procedure (PTI, 1980).

rd Edition PTI procedure is currently adopted by practicing engineers. From a

historical perspective and for forensic engineering purposes the difference in solutions between

different editions is significant. This chapter summarizes and provides a comparison of the

geotechnical design parameters obtained with the 3rd Edition procedure (PTI, 2004) and the

results of the former 2nd Edition version (PTI, 1996) design method. For selected soils a

comparison of slab thickness calculated with PTISlab 2.0 (implements PTI 2nd Edition), PTISlab

3.0 (implements PTI 3rd Edition) and the newest modifications to the structural design

implemented in PTISlab 3.1 is also illustrated. The geotechnical (VOLFLO) and structural

(PTISlab) software developed based on the PTI manual are available through Geostructural Tool

Kit, Inc.

173

6.3 Definitions

The definitions of edge moisture variation distance, differential swelling mode and

differential soil movement introduced in the 1st Edition (PTI, 1980) remained unchanged in the

subsequent PTI design manuals. The edge moisture variation distance, em, is a distance

measured inward from the edge of the slab over which the moisture content of the soil varies

due to wetting or drying. Prior to the 2003 publication, the magnitude of the moisture variation

distance depended mainly on climate. Starting with the Alternate Procedure (PTI, 2003) the

unsaturated diffusion coefficient was recognized as the major factor influencing the edge

moisture variation distance. Roots, fissures, fractures or joints in the soil increase em while

moisture barriers at least 2.5 ft deep can be used in to reduce em.

Differential soil movement, ym, also known in the 2nd

The swelling mode depends on the ym value. The edge lift condition often occurs when

the slab is constructed on a relatively dry pad. Due to wet environmental conditions the soil

swells around the perimeter of the structure creating a dish-shaped deformed slab. Center lift

condition often occurs when the slab is constructed on a relatively wet pad and dry

environmental conditions lead to soil shrinkage around the slab perimeter. Both conditions are

illustrated in Chapter 2 (Literature Review),

Edition as differential swell, is the

change in soil elevation between the two points separated by em. The amount of expansion or

contraction a soil stratum will undergo depends on the amount of clay minerals, thickness of

stratum, depth and uniformity of clay layer below the ground surface, surcharge pressure,

severity of climatic change, and the proximity to ground water table. It also depends on factors

such as deep tree roots and zones of high osmotic suction. Moisture barriers of at least 2.5 ft

deep can be used in to reduce ym.

Figure 2.6.

In all PTI procedures, em and ym are computed under the assumption that the slab is

perfectly flexible. Also, in all PTI chart-based procedures climate is assumed to be the main

factor affecting differential soil movement, ym, and edge moisture variation distance, em. The

factors affecting soil behavior other than climate include: vegetation requiring large amounts of

174

water, fence lines, trails and tracks which leave bare soil drier than the surrounding soil; cut and

fill sections that experience differential soil movement; poor drainage that causes runoff water to

collect near the structure; time of construction; and post construction practices. Factors not

related to climate may induce soil movements much larger than the climate dependant

movements; and the 3rd

6.4 PTI 2nd Edition Design Procedure, 1996

PTI Edition (Chapter 4 - Design Commentary) clearly states that the

design procedure is invalid when the site is influenced to any significant degree by non-climate

conditions, but special provisions allow for their consideration in Chapter 3 of the manual,

Geotechnical Investigation.

The 2nd Edition procedure (PTI, 1996) is applicable to ribbed and uniform thickness

foundations on expansive soils with Plasticity Index (PI) equal to or greater than 15%. The

applicability is extended to stable and compressible soils. In addition, this procedure is valid only

when site conditions are governed by climate and the calculated differential soil movement, ym,

does not exceed 4 inches [10.2 cm]. The input parameters needed for the PTI 2nd Edition

procedure include Liquid Limit, LL, Plastic Limit, PL, percentage of clay, %clay (defined as

percent of soil particles smaller than 0.002 mm), predominant clay material, Thornthwaite

Moisture Index for the design region, suction at the active zone depth, and the depth to constant

suction.

To determine em for both edge lift and center lift conditions, the 2nd Edition procedure

(PTI, 1996) makes use of a correlation with TMI (Figure 6.1). The TMI is determined for mean

annual climate conditions (Thornthwaite, 1948). Engineers have adopted a value of – 40 as a

representative value for the Phoenix area, Arizona. The proposed figure gives a range of

potential results, hence slab design conservatism is left up to the engineers’ discretion.

175

THORNTHWAITE MOISTURE INDEX

Figure 6.1. Edge Moisture Variation Distance as a Function of Thornthwaite Moisture Index (after Wray, 1978).

To determine ym, the following properties shall be measured or estimated based on the

following procedure:

1. Predominant clay mineral, which can be obtained from a figure presented in the PTI

manual. The clay type is a function of Activity Ratio, Ac, defined as 200

100%P PI

clay, and

Cation Exchange Activity, CEAc obtained by1.17

200

100%P PL

clay, where Plastic Limit (PL),

Plasticity Index (PI), percent soil passing US sieve # 200 (P200) and %clay are expressed

as percentages. The use of Montmorillonite is recommended if a conservative estimate

is desired (Pearring, 1963).

2. Depth to constant soil suction defined byPLw

, where w is the gravimetric water content.

It occurs at the depth of inert material, unweathered shale or high water table. When

ED

GE

MO

ISTU

RE V

ARI

ATIO

N D

ISTA

NCE

[FT]

176

sufficient data is not available, the depth to constant suction can be assumed to be 7 ft

[2.1 m].

3. Equilibrium total soil suction, which in absence of measured values is estimated based

on a correlation with TMI (Figure A3.6 in 2nd Edition PTI, 1996).

4. Moisture flow velocity defined by V = 0.5TMI, where the magnitude of TMI is used.

Though TMI is a dimensionless parameter, this is an empirical correlation that yields

velocity in units of in/year. The moisture flow velocity is limited to values not smaller

than 0.5 in/month [1.3 cm/month] or larger than 0.7 in/month [1.8 cm/month]. For

Arizona conditions, where TMI = -40, the velocity has a magnitude of 1.7 in/month [4.3

cm/month], therefore 0.7 in/month [1.8 cm/month] ought to be used.

In absence of the computer program, VOLFLO 1.0 developed by Geostructural Tool Kit

Inc., read off the magnitude of the differential soil movement from charts provided within the

manual. The charts include all parameters determined in steps 1 through 4 above. Note that in

the tables ‘Percent Clay (%)’ refers to 200

%clayP

expressed as a percentage.

6.5 PTI 3rd Edition Design Procedure, 2004

The 3rd Edition procedure is applicable to two types of slabs. The first one is a ribbed

foundation of uniform thickness slab with stiffening ribs projecting from the bottom of the slab in

both directions, schematic given in Figure 3.4. The second one is a uniform thickness slab

foundation with no interior stiffening ribs, schematic given in Figure 3.5 and Figure 3.6. This

Edition gives provisions for design on compressible and non-active soils, which are not

summarized in this chapter. In addition, it is possible to model the influence of vertical moisture

barriers, planter areas and variable soil suction profiles with a commercial computer software,

VOLFLO 1.5 developed by Geostructural Tool Kit Inc.

The 3rd Edition procedure is applicable to soils with Expansion Index, EI, greater than

20, as determined per ASTM standard D 4829, or where the following three requirements are

177

met: Plasticity Index, PI, is equal to or greater than 15 %, more than 10 % of soil passes US

sieve #200, and more than 10 % of soil particles are smaller than 0.005 mm in size. The

parameters needed in this procedure include: initial and final suction profiles, TMI, moisture

active zone depth, and mineral classification. Soil properties for each representative layer are

required: LL, PL, PI, % passing sieve #200 and %clay. In addition other soil parameters are

suggested to be determined experimentally: dry density, moisture content, cohesive strength,

confined or unconfined compressive strength, total suction, swell pressure, and Expansion

Index.

6.5.1 Additional Definitions Provided in the Procedure.

The following definitions are introduced in the 3rd Edition design procedure.

1. Moisture Active Zone Depth refers to the depth below the ground surface at which

changes in moisture content (soil suction) can be expected due to environmental

changes or other causes. This is also the location of the equilibrium moisture content.

2. Movement Active Zone Depth refers to the depth to which the soil experiences changes

in volume. The movement active zone depth is usually smaller than the moisture active

zone depth due to overburden restraint.

3. Soil Suction quantifies the energy level in the soil-moisture system. An imbalance of

total suction between adjacent soils tends to drive moisture towards regions of higher

suction. Total suction can be measured by filter paper method and psychrometers;

while pressure membranes or ceramic pressure plates measure matric suction.

4. Equilibrium (Constant) Soil Suction represents a total suction value that develops in a

soil deposit at the depth of moisture active zone as a result of multiple weather cycles at

the surface. The climate controlled equilibrium suction is expressed as a function of

TMI. The constant suction is also dependant on local site conditions such as cemented

soil, high osmotic suction, and presence of high water table or rocks, in which case the

correlation with TMI is invalid.

178

5. Suction Compression Index is a soil property that is analogous to the Compression

Index utilized in the settlement analysis of saturated soils. It is defined as the change in

volume related to a change in suction for an intact specimen of soil.

6.5.2 Assumptions.

In absence of the computer program VOLFLO 1.5, the 3rd Edition Stress Change Factor

Chart procedure solves for the following simplified conditions.

• Steady state unsaturated flow;

• The active zone is assumed to be 9 feet below the ground surface;

• Suction Compression Index does not vary by more than 10% between layers;

• The suction at active zone depth is climate controlled. Although the initial correlation of

equilibrium suction to TMI presented in 1st and 2nd Editions was developed for

homogeneous profiles, in the 3rd Edition an assumption is made that the equilibrium

suction is independent of soil type and profile homogeneity. This relationship was

updated in version 3 and it is presented in Figure 6.2 (Fig. 3.4 in PTI, 2004). Recent

studies have shown that the suction at a given TMI heavily depends on soil type (Perera,

2003), which agrees with the scatter of values and the poor statistical significance, R2

equal to 0.36, of the proposed correlation. The correlation is not valid for soils with high

osmotic suctions or where high water table is present.

• Initial suctions, hi, at the soil surface below the edge of slab and at the edge moisture

variation distance under the slab are assumed to be equal to the equilibrium suction at

the moisture active zone depth as determined from the suction vs. TMI correlation. Due

to environmental and human induced flux at the soil surface, the soil at the edge

becomes wetter or drier, resulting in different final suction values under the edge of the

slab, hf. The initial suction, hi, is based on TMI while the final suction, hf, is based on

assumed, suction variations at the soil surface. These assumptions result in constant

179

initial suction profiles at both ends of em and in a trumpet shaped final suction profile

under the edge of the slab.

Figure 6.2. Variation of Soil Suction with Thornthwaite Moisture Index (PTI, 2004).

The PTI 3rd Edition procedure is also valid for a wider range of conditions through the

use of the computer program VOLFLO 1.5. These conditions include but are not limited to

deeper active zone, significantly different suction compression index values for adjacent layers,

high osmotic suction zones, influence of vegetation, and initial soil suction profiles drier or wetter

than equilibrium.

6.5.3 Procedure.

A summarized step-by-step procedure for the 3rd Edition follows.

To calculate the edge moisture variation distance, em:

1. Determine the mineral classification zone for each significant layer. A chart that relates

the mineral classification with Atterberg limits is provided in the procedure (Covar and

Lytton, 2001).

180

2. Calculate percent fine clay, %fc, for each significant layer defined as

100Pclay%fc%200

= , where P200 is the percent soil passing US sieve # 200.

3. Calculate Liquid Limit and Plasticity Index ratios for each significant layer. These ratios

are defined as fc%

LLLLratio = and fc%

PIPIratio = respectively.

4. Calculate the Suction Compression Index, γh, for each significant layer. The 3rd Edition

PTI procedure provides four methods as presented below. When procedures 2 through

4 are used, γh shrink is read off from a figure which is based on the calculated γh swell and

which is presented in the 3rd Edition.

Procedure 1: Method based on mineralogical soil classification. A figure for each

mineralogical soil class is provided within the 3rd Edition PTI procedure. It relates LLratio

and PIratio to the suction compression index for soil consisting of 100% clay, γo. Once γo

is read off from the graph, the actual soil suction compression index for swelling and

shrinking conditions is calculated as follows:

( ) ( )0.01 %0.01 %h

fcofc eoswellγ

γ γ= (6.1a)

( ) ( )0.01 %0.01 %h

fcofc eoshrinkγ

γ γ−

= (6.1b)

Procedure 2: Expansion Index Procedure. Determine the Expansion Index, EI, per

ASTM D 4829 (ASTM, 2006) and calculate the swell suction compression index by

1700h swellEI

γ = .

Procedure 3: Consolidation Test Procedure. The γh is expressed in terms of the

slope of the compression rebound curve, Cs, and the void ratio corresponding to the

181

effective stress at the bottom of the curve, e2, obtained from a consolidation test. The

relationship reads 2

0.71

sh swell

Ce

γ =+

Procedure 4: Overburden Pressure Swell Test Procedure. In the last procedure, γh

swell is correlated to the vertical strain

HH∆ , due to increased water content and

overburden pressure, P. The following relationship is used:

101.7 logh swell

HH

Pγ

∆

+= . (6.2)

5. Calculate γh corrected if more than 10% of the soil passes US Sieve #10.

( )( )

( )

100

100hh corrected

t wet

d dry

F Fγ γ γ

γ

=+ −

(6.3)

( )

( )

100

1100

t wet

w s coarse

FJ

J Gγ

γ

= + −

(6.4)

where γt(wet) is the moist unit weight of soil when soil suction is about 2.5 pF; γd(dry) is the

dry unit weight of soil at its natural water content (optimum water content or shrinkage

limit); J is the % of soil by weight greater than US sieve #10 (2.0 mm diameter); Gs(coarse)

is the specific gravity of solids; and γw is the unit weight of water.

6. Find the modified suction compression index, γmod, for both swell and shrinkage. In this

step, γh is weighted based on the location of different layers in the soil profile; for

example: mod

3 2

6topsoil middle bottomh h hγ γ γ

γ+ +

= .

7. Calculate the modified unsaturated diffusion coefficient for each significant layer up to a

minimum of 9 ft for both swelling and shrinkage modes:

182

α'swell/shrink = (0.0029 - 0.000162*S – 0.0122*γh swell/shrink )Ff, (6.5)

where S is the slope of the total suction in pF vs. water content relationship defined by:

S = -20.29 + 0.1555*LL - 0.117*PI + 0.0684*P200, (6.6)

and Ff is defined as the soil fabric factor, which is a function of the amount of roots and

fractures present in the soil. Ff varies from 1.0 for soils with less than 1 root or fracture

per vertical foot up to 1.4 for soils with five or more roots/fissures per vertical foot.

8. Calculate the weighted modified soil diffusion coefficient for both swell and shrinkage

cases as a function of layer location within the soil profile:

( )3 (3 2 )

'18

topsoil middle bottomfweighted

F α α αα

+ += (6.7)

SCFy modm ∗= γ (6.8)

9. Read off em from Figure 6.3 for both center lift and edge lift conditions. Use values of

weighted α' and TMI for both conditions and choose the largest em value.

Figure 6.3. Edge Moisture Variation Selection Chart (PTI, 2004)

183

To find the differential soil movement, ym:

1. Measure or estimate initial, controlling soil suction. This procedure assumes that the

initial suction is the same at the soil surface at two locations separated by em and at the

moisture active zone depth, where suctions in the horizontal plane do not vary. The

magnitude and depth to constant suction is to be determined at a depth where soil

suction does not vary by more than 0.0027 pF per ft (per 0.3 m). If direct estimation is

not possible, the initial or equilibrium suction can be estimated directly from Figure 6.2,

unless scenarios unrelated to climate conditions prevail. The most common cases are:

a. When shallow water table is present and osmotic suction is negligible, the method

recommends using a suction equal to 2.0 pF.

b. When large trees are present at the site: In this case, the controlling suction should

be equal to 4.5 pF throughout the tree root zone.

c. When soil is cemented or it is known to have high osmotic suction: In this case, the

controlling soil suction must be determined experimentally.

2. Estimate the final suction at the ground surface under the edge of slab. In absence of

local measurements, final soil suction values at the ground surface are recommended to

be 2.5 pF for the wettest condition; and 6.0 pF for surfaces controlled by evaporation

from bare soil or wilted vegetation. For Phoenix conditions, limits of 2.9 pF and 4.5 pF

are commonly used.

3. Calculate the differential soil movement, ym, based on the modified suction compression

index, γmod, and the Stress Change Factor, SCF. A set of Stress Change Factors is

given in the procedure as a function of the difference between initial and final suction

values at the edge of the slab.

6.6 Design Parameters for Arizona

Three representative expansive soils collected from around the metropolitan Phoenix

area (data from Chapter 4) were used in the comparison of the 3rd Edition PTI procedure to the

184

2nd Edition in terms of em, ym and slab thickness. The 3rd Edition slab thickness was calculated

with two versions of PTISlab, 3.0 and 3.1. The 3.1 version, produced in 2007, modifies the

program for a calculation error resulting in overestimation of the slab thickness. Laboratory

testing was performed to determine typical Phoenix area input parameters needed for the

calculation of em, ym, and the slab thickness. The soil data are shown in Table 6.1 and analysis

results in Table 6.2. In the 2nd Edition analysis, 7ft [2.1 m] moisture active zone depth was used.

In the 3rd Edition analysis, 9 ft [2.7 m] active zone depth and final suctions at the edge of the slab

of 2.9 pF (78 kPa) and 4.5 pF (3100 kPa) for the edge lift and edge drop mode respectively were

used. From the PTI 2nd Edition suction vs. TMI correlation, the suction at the moisture active

zone depth is 4.36 pF (2290 kPa) and from 3rd Edition (Figure 3) it is 4.18 pF (1500 kPa). The

common practice in Phoenix is to use 4.2 pF (1555 kPa) for suction at depth, which is the value

used in this analysis.

6.7 Discussion

Several observations can be made from Table 6.1 and Table 6.2. 1) The controlling

swelling mode switches from Center lift to Edge lift in the transition from the 2nd Edition to the 3rd

Edition PTI method; 2) In the 2nd Edition, em is environment dependent while in 3rd Edition em is

also a function of the soil conductivity, i.e. the diffusion coefficient; 3) The 2nd Edition allows for a

range of possible em and ym values resulting in a range of slab thicknesses, while the 3rd Edition

estimates unique values of slab thicknesses; 4) The average (referring to the range of values

obtained with 2nd Edition) slab thickness increases for all soils in these sample calculations in

going from the 2nd Edition to the 3rd Edition PTI. The general observation is, the average slab

thickness increases as the PI increases. For Soil 1, which has the lowest average PI, the

thickness increased by 6% with 3.1 version of PTISlab (43% with PTISlab3.0), while for Soil 3,

which exhibits the largest PI, the thickness increased by 38% with 3.1 version of PTISlab (112%

with PTISlab3.0), The range of slab thicknesses increased from 7.5 to 10 inches [19 to 25 cm] to

185

a range of 12.5 to 18 inches [32 to 46 cm] with PTISlab3.0 and 9.25 to 11.75 inches [23.5 to 30

cm] with PTISlab 3.1.

Table 6.1. Soil Index Properties Used in VOLFLO Input for Representative Soils

Soil # Layer Thickness LL PL PI P200 %clay [ft/m] [%] [%] [%] [%] [%]

1

0.6/0.2 11 9 2 43 2 2.6/0.8 45 18 27 41 19 0.7/0.2 40 22 18 37 18 5.1/1.5 27 19 8 28 9

2

1.2/0.4 41 20 21 66 24 0.9/0.3 35 19 16 59 30 0.9/0.3 49 22 27 72 38 6.1/1.9 35 19 16 61 30

3

1.2/0.4 99 35 64 29 13 0.9/0.3 93 33 60 46 13 1.6/0.5 65 30 35 78 26 5.4/1.6 68 30 38 47 24

Table 6.2. Design Parameters for Representative Soils Soil

2nd Edition PTI, 1996(4) 3rd Edition PTI, 2004; PTISlab 3.1(3.0)

Number center lift(2) edge lift center lift edge lift

1 em [ft] 4.6/6.1 2.0/2.8 9 5 ym [in] 1.59/4.59 0.41/0.83 0.12 1.02

slab [in](1) 7.5/10 9.25(12.5)

2 em [ft] 4.6/6.1 2.0/2.8 9 4.6 ym [in] 2.11/6.55 0.58/1.19 0.14 1.19

slab [in](1) 8/10 9.75(14)

3 em [ft] 4.6/6.1 2.0/2.8 7 3.7 ym [in] 1.81/4.03 0.5/0.67 0.27 2.73

slab [in](1) 7.5/9.5(3) 11.75(18)

(1) Assumed sub-rectangle 40 ft x 60 ft; perimeter load 800 psf; Es = 1000 psi, μ = 1.0. (2) ym obtained with 2nd Edition PTI procedure exceeds the maximum 4" for soils 1 and 2.

Results for 4" ym value are presented. For the calculated 4.6" and 6.6" ym values, the slab thicknesses would be 10" and 10.5" respectively.

(3) The ym values for large em values from 2nd Edition procedure were obtained with computer program VOLFLO 1.0 for soils 1 and 2. The procedure charts were used in the remaining calculations. The smaller of ym values for soil 3 represent the limitations of the charts, where 3.6 pF is the maximum equilibrium suction value at depth.

In addition, PTI 3rd Edition geotechnical and structural analyses were performed on all

non-homogeneous soil profiles obtained as part of this study. The soil index based PTI analysis

186

was performed based on previously specified assumptions and initial conditions. The calculated

edge moisture variation distance has a range between 3.6-feet and 5.0-feet for the edge lift

condition and a range between 7.5-feet and 9.0-feet for the center lift condition. The differential

swell was found to vary between 0.8-inches and 2.65-inches for the design controlling edge lift

condition. The calculated slab thickness was found to vary between 9-inches and 11.0-inches

with an average of 9.8-inches. The results of the analysis (edge moisture variation distance,

differential swell and slab thicknesses) are given in Table 6.3.

Table 6.3. Design Parameters for All Soils from Chapter 4.

Soil # Center lift [inch] Edge Lift [inch]

Slab Thickness [in]

em ym em ym 3.1 1 NA 2 NA 3 9 0.09 4.5 0.97 9 4 9 0.11 4.8 1.01 9.25 5 9 0.1 5 1.07 9.75 6 8 0.14 4.1 1.54 9.75 7 8 0.14 4.1 1.54 9.75 8 9 0.11 4.6 1.37 9.75 9 9 0.1 4.7 1.22 9.75

10 9 0.08 4.9 0.8 9.25 11 9 0.14 4.4 1.67 10.5 12 9 0.11 4.8 1.19 9.75 13 9 0.12 4.6 1.25 9.75 14 9 0.12 4.6 1.17 9.75 15 NA 16 8.5 0.11 4.3 1.18 9.75 17 7.5 0.21 3.7 2.65 11 18 7 0.22 3.6 2.45 10.75

Average 8.6 0.13 4.45 1.41 9.83

6.8 Sensitivity Analysis

Five sensitivity analyses were performed to assess the influence of various parameters

on the overall solution. Influence of Soil Properties on Geotechnical Parameters.

187

6.8.1 Influence of Suction Profiles on Geotechnical Parameters

A sensitivity analysis was performed to evaluate the impact of soil parameter variability

on ym estimation. Table 6.4 gives basic soil values used in the analysis. The values of LL, PL

and % clay were varied one at a time in each soil layer and the results are plotted in Figure 6.4

through Figure 6.6. For example, in Figure 6.4, the plot for Layer 3 corresponds to holding all

parameters constant in Layers 1 and 2, and varying the LL in Layer 3 only. The figures include

results corresponding to PI larger than 15% unless the original soil values fall below it, than they

are included as well.

Table 6.4. Design Parameters for Sensitivity Study.

Layer Number

Layer Thickness LL PL P200 %clay [ft] [%] [%] [%] [%]

1 1.5 29 18 76 10 2 1.5 40 24 62 9 3 6.1 50 25 53 9

The sensitivity analysis illustrated that as LL increases the values of ym increases as well

to a certain point, and then decreases. This results is somewhat unexpected and might be

related to the correlation of LL with other input parameters, which were maintained constant. OF

course it is important to have “consistent and compatible” soil properties, and this sensitivity

analysis did not consider limitations for “natural soils conditions.” The sensitivity analysis of ym to

PL clearly illustrates points of discontinuity within the developed empirical correlation

implemented in the PTI procedure. Small changes in PL result in up to 0.2-inch drop or increase

in the ym value; see Figure 6.5. Beyond the points of discontinuity, the values or ym remain

almost constant. The ym estimate increases as the percent of clay increases up to about 15%.

For %clay larger then 15, the %clay increase results in insignificant drop in ym estimate followed

by another increase for %clay larger than 30%.

188

Overall, from geotechnical engineering perspective, it was determined that small

variations in input parameters lead to small variations in the estimate of ym. The significance of

small ym variation on slab thickness is considered next.

0.80.9

11.11.21.31.41.51.61.71.8

25 30 35 40 45 50 55 60 65LL [%]

y m [i

n]

Layer 1Layer 2Layer 3

Figure 6.4. The ym sensitivity to LL.

0.80.9

11.11.21.31.41.51.61.71.8

10 15 20 25 30 35PL [%]

y m [i

nch]


Figure 6.5. The ym sensitivity to PL.

189

0.80.9

11.11.21.31.41.51.61.71.8

5 10 15 20 25 30 35% clay [%]

y m [i

nch]


Figure 6.6. The ym sensitivity to % clay.

6.8.2 Influence of Geotechnical Parameters on Slab Thickness

The program PTISlab 3.1 was used in the sensitivity analysis of slab thickness to ym. In

this study, em of 4.5’ was assumed. It was found that for the anticipated range of ym for Arizona

soil and climatic conditions, between 0.8” and 3.0”, the thickness of slab increases almost

linearly with the increase in ym as illustrated in Figure 6.7. The minor perturbations are

associated with constant depths and widths of both longitudinal and transverse beams in the

ribbed design.

8.08.59.09.5

10.010.511.011.512.012.513.0

0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3ym [inch]

Slab

Thi

ckne

ss [i

nch]


190

6.8.3 Sensitivity of ym to Suction Profile

The sensitivity to suction was considered for two scenarios with constant initial

conditions and varying final suction conditions. The final suction has default trumpet shape with

user defined surface suction. In the first scenario, the initial condition of 3.0 pF (100kPa) was

used. In the second one, initial conditions of 4.2 pF (1555 kPa) was considered. The results are

presented in Figure 6.8. The ym increases or decreases almost linearly as the suction profile

decreases or increases, respectively. This mini-study illustrates that the PTI 3rd Edition

procedure implements linear variation of volume change with log cycle change in suction. A

better approach would be to limit the soil swell or shrinkage at volume change limiting suction

values such as the shrinkage limit (see Figure 6.8). Similarly, it is widely accepted that in

confined soil the swell will cease at some small suction value, and further decrease in suction

results in no additional volume change. Consequently, the selection of final surface suction

values for PTI design purposes should not be based on the anticipated minimum and maximum

suction variation with depth, but rather the minimum and maximum suctions corresponding to

volume change.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 1 2 3 4 5 6Final Suction [pF]

y m [i

nch]

0.1 1 10 100 1000 10000 100000Final Suction [kPa]

IC=3.0pF

IC=4.2pF


191

6.8.4 Comparison of Different Suction Compression Index Methodologies

A mini study was performed to observe the effect of alternative procedure use, included in

the PTI 3rd Edition Design Procedure, on the overall design recommendations. For this purpose

a medium expansive soil profile was chosen with the following soil properties:

• PL = 45,

• LL = 20

• PI = 25

• P200 = 94.0%

• % -2 µm = 40.0%

• EIAZ = 3.3%

• Percent swell = 2.65% at 1000 psf load.

• Cs = 0.05049.

For the edge lift condition it was determined, that depending on used methodology, the

calculated edge moisture variation distance might vary between 4.0 and 4.3 ft and the calculated

differential swell has a range from 0.68 inches to 1.54 inches. This exercise indicates that the

Index Properties method, strongly recommended by the PTI procedure, results in the most

conservative slab design, 9.75–inches thick. The least conservative design was obtained with

the EI method, which resulted in 8.25” thick slab; see Table 6.5 for details. Further research

must be performed to statistically validate the preliminary findings and conclusions presented

herein.

Table 6.5. PTI 3rd Edition Calculations for Example Profile for Various γh Methods

Method Suction Compression Index Edge Lift Center Lift

ym em Slab ym em γh swell γh γ0 [in] [ft] [in] [in] [ft]

Index Properties 0.0444 0.0426 0.1000 1.54 4 9.75 0.17 7.8 EI 0.0194 0.0190 0.0447 0.68 4.3 8.25 0.08 8.5

Overburden Swell 0.0309 0.0300 0.0704 1.08 4.2 9.25 0.12 8.0 Consolidation Swell 0.0245 0.0240 0.0564 0.86 4.3 9.0 0.10 8.3

192

6.8.5 Influence of Gravel Correction

The influence of the gravel correction given by equation (5.3) and equation (5.4) was

considered with the following values: J = 50; Gs = 2.65, γt = 125 pcf and γd = 105 pcf. The

procedure offers modest reduction for γh, as illustrated in Figure 6.9. The methodology is

insensitive to variation in Gs. In general, the reduction in moist unit weight leads to increase of

correction factor from minimum value of 0.88 to 0.97. The increase in correction factor with

increase in J is unexpected for J defined as the percent of soil by weight greater than US sieve

#10. One would expect a decrease resulting in the reduction of γh. Per values considered, a

minimum correction factor of 0.85 can be expected, which leads to very modest reduction in the

design parameters em and ym.

0.800.820.840.860.880.900.920.940.960.981.00

0 25 50 75 100 125 150Variable

Corr

ectio

n Fa

ctor

2.5 2.55 2.6 2.65 2.7 2.75 2.8Gs

Wet Unit WeightJGs

Figure 6.9. Sensitivity Analysis of Gravel Correction Factor.

6.9 Conclusions

The comparison of PTI version 2 (PTI, 1996) and PTI 3rd Edition (PTI, 2004) can be

summarized as follows: 1) The 2nd Edition provides a range in em and ym values, while the 3rd

Edition provides unique values; 2) The mode of failure changes from center lift (2nd Edition) to

edge lift (3rd Edition) for the sample Arizona conditions conducted herein; 3) The slab thickness

193

for Arizona conditions increased in going from version 2 to version 3 for the sample soils and

conditions used in this study.

Sensitivity analysis of the 3rd Edition procedure showed that 1) Discontinuities exist in

the empirically based method for γh estimation with index properties, which leads to unexpected

ym results; 2) Small changes in index properties typically lead to insignificant changes in the

design parameters, em and ym; 3) The slab thickness varies linearly with geotechnical design

parameter, ym; 4) The ym varies linearly with change in the log of the final surface suction. The

final suction values should be selected based on anticipated suction values corresponding to soil

volume change limits; 5) The index property methodology is the most conservative when

compared to other methods of suction compression index estimation provided in the manual;

and 6) The correction factor due to gravel content offers only modest reduction in suction

compression index.

The PTI 3rd Edition procedure adds some rationality to slabs-on-grade design and

covers a wider range of practical problems, with less empiricism than the PTI 2nd Edition

procedure. Hence, it may lead to more appropriate design values, although it remains to be

seen how conservative the design is and what are its limitations. Historical performance data

covering a wide range of soils and environmental conditions is needed, however, for further

evaluation.

7 MODELING – NUMERICAL METHODS The numerical analysis of the research problem required enhanced understanding of the

numerical methods used and of problem specific challenges. This chapter describes stability,

convergence and accuracy issues relevant to stiff problems, such as Richards’ equation used in

this research work, which are known to exhibit oscillatory behaviour under certain conditions. An

attempt was made to identify sources of numerical challenges and introduce ideas aimed at

increasing stability or solution efficiency as illustrated on sample problems. These ideas were

implemented using the commercial software FlexPDE 5.0.18. A discussion of program

selection, uncertainty associated with the soil properties and literature review of typical input and

program specific controls is also included. This discussion provides a good starting point for

understanding potential problems in numerical simulations.

7.1 Modeling Challenges

Unsaturated moisture flow through porous media is usually described by Richard’s

equation, a parabolic partial differential equation (PDE) presented in detail in Section 2.9.5.2.

The lack of analytical solution has led to the development of sophisticated numerical schemes by

the mathematical community. The standard approach implemented follows a “method of lines”,

where spatial derivatives are first approximated using a variety of (usually low order) finite

difference or finite element schemes, and the resulting discrete system of ordinary differential

equations (which also accounts for boundary conditions) is then solved using a time integrator.

Explicit time integrators such as forward Euler typically have strong restrictions on the

maximum time step which can be used in order to preserve stability. These restrictions largely

depend on the spatial discretization through a so-called CFL (Courant-Friedrichs-Levy)

condition. Several physical conditions severely limit this time step:

(i) strong nonlinearities in unsaturated soil properties,

(ii) abrupt changes of moisture conditions at the surface boundary,

(iii) the presence of surface runoff conditions (Scanlon et al, 2002).

195

Condition (i) can manifest itself in two ways. Sharp variations in the unsaturated soil

permeability or the Soil Water Characteristic curve (SWCC) manifested as sharp wetting front

may require locally refined grids, which may impact the overall stability of the time integration.

The slope of the SWCC also directly influences the stiffness of the ODE system, i.e., the

presence of several time scales in the solution (see Higham & Trefethen 1993 for other

definitions of stiffness), and the choice of a suitable time step.

Condition (ii) typically results in large gradients of matric suction and sharp wetting or

drying fronts, which again require a fine grid for proper modeling.

Type (i) or (ii) difficulties are especially pronounced in moisture sensitive soils such as

collapsible or expansive materials.

The stability constraints arising from condition (iii) are more subtle. As for condition (ii)

an appropriate (usually fine) mesh size must be used at the surface boundary in order to

properly capture suction or pressure head gradients. This is true in general of problems with flux

(Neumann) or flux-pressure head (Robin) boundary conditions in standard formulations, where

first-order spatial derivatives (fluxes) are directly approximated from the pressure head (or the

suction). One should note that inconsistencies between initial and boundary conditions may also

lead to local instabilities requiring small initial time steps to be resolved without long term effects.

Runoff conditions are algebraic constraints on the pressure head at the soil surface.

From a mathematical point of view the resulting differential-algebraic system of equations (DAE)

is equivalent to an infinitely stiff system, for which no explicit time integrator, even with small time

steps, can be stable in longer time windows.

The difficulties associated with (i) or (ii) are typically overcome by implementing gross

simplifications of both soil properties and surface fluxes (precipitation and irrigation are typically

averaged over a day). When field data are available, the program performance is matched to

empirical data via modification of ksat values (Chao, et al., 2006, Scanlon et al., 2002). The

solution is frequently obtained with large mesh size and large time steps, resulting in a stable,

but not always accurate or converged solution. Table 7.1 summarizes some of the literature

196

review findings, where mesh size as large as 2.5 m were reported. Smaller mesh sizes lead to

better spatial approximations but they require smaller time steps and often prohibitively long

simulation times. The solution dependence on time and space discretization is rarely discussed,

and when it is sufficient detail is not given about performed (or not) convergence studies.

Table 7.1#

. Literature Review of Implemented Modeling Controls. 1D/2D Domain

size WxH

dx dt IC Flux Type Time Modeled

Conv. study?

Code Ref.

[m] [m] [h] [kPa] [d]

1 2D 5x5 0.05 3e-10-0.03 near sat.

Pressure head 5 yes

custom based on

Celia et al., 1990

Soraganvi et al., 2003

2 1D 3 0.002-0.24

not specified 0-1100 PE, prec.,

irrig. 1095 not spec.

Hydrus, Unsat H, SHAW,

SoilCover, SWIM, VS2DTI

Scanlon et al., 2002

3 2D 12X3 0.008-0.1 not specified 400 PE 5 no SVFlux Fredlund et

al., 2006

4 2D 2x1 0.1 0.27 10 Irrig. 1 yes Seep/W Fuselier et al., 2006

5 2D 16x30 unknown not specified

500-1500

PE, prec., irrig. 36500 no Vadose/W Chao et al.,

2006

6 2D 115x30 2.5 not specified

near sat. prec. 31 no Seep/W Ng and Shi,

1998

On the other hand, implicit time integrators must be used to deal with (iii). These

methods have no CFL restriction and lead to unconditionally stable schemes (in which case the

time step is only determined by accuracy considerations), when applied to asymptotically stable

discretizations (i.e., the exact solution of the spatially discretized problem has finite energy

bounded by a constant independent of time). Note that here asymptotic stability refers to a

property of the spatial discretization, to which boundary conditions directly contribute, while

unconditional stability refers to a property of the time integration scheme. Of course one typically

needs both in order to obtain an overall stable solution.

Unfortunately, implicit integrators require the solution of (usually) nonlinear systems at

each time step, thereby increasing the complexity of the solution process. These nonlinear

equations are usually solved using a fixed-point (Picard) or Newton iteration (in either case

possibly in combination with some form of relaxation). However, the success of the time stepping

197

scheme often relies on allowing as many iterations as necessary to resolve the nonlinearities.

Because small time steps presumably lead to small changes in the solution, it is not unusual to

replace a larger cap on the number of Picard or Newton iterations by a stronger restriction on the

time-step.

In many commercial software at most a few iterations are allowed under normal settings,

with the underlying argument that too many iterations must be a sign of an inaccurate solution in

the first place (e.g. the Newton iterates wander off from the correct solution). Such a simplified

view is probably sufficient to deal with problems on a fixed mesh, with fixed pressure head

(Dirichlet) boundary conditions, and with “simple” unsaturated soil properties. In more complex

situations, such as those associated with moisture sensitive soils in dry climates and run-off

boundary conditions, this approach may however lead to unexpected stability problems. A basic

explanation is that the implicit time integrator is used in an explicit predictor-corrector mode

(each iteration corresponding to a correction on the predicted initial estimate of the nonlinear

solver) when the cap on the number of nonlinear iterations is reached, and is therefore subject

again to CFL restrictions on the time step. Even for moderately stiff problems (i.e., with relatively

distinct time scales in eigenmodes of the linearized problem) the resulting constraint on the time-

step can be so severe that it leads to a failure in the adaptive time stepping procedure.

This chapter emphasizes some of the issues discussed above, which are rarely, or only

superficially, discussed in the geotechnical engineering literature, in particular the connection

between nonlinear iterations and time-stepping. Van Dam & Feddes briefly summarize the

situation: “The result is that calculated soil water fluxes may depend largely on the structure of

the numerical scheme and the applied time and space steps.” (van Dam & Feddes, 2000), while

Tan & al. echo a similar advice: “... proper time step must be used with proper mesh size to

satisfy both stability and convergence criteria...” (Tan et al., 2004).

198

7.2 Selection of Program

In Section 2.10.2 (Available Commercial Software) numerical tools most commonly used

by practitioners were identified and described. Three of them were selected as potential

software for this research study, namely Hydrus, Vadose/W and SVFlux (with FlexPDE kernel).

Selected programs where evaluated for accuracy, convergence, stability, efficiency and user

interface on a simple 1-D problem.

7.2.1 Convergence, Stability and Accuracy

Convergence, stability and accuracy are fundamental issues in the numerical simulation

of ODEs and PDEs. In the absence of computational experience, one would not be able to

identify and mitigate issues associated with them or comprehend their significance and on the

quality of the numerical solution. Yet, these concepts set the basic criteria in any numerical

model and are the source of continuous research in numerical methods.

“Accuracy of a numerical solution is a measure of the closeness between the

approximate solution and the exact solution” (Reddy, 1993). When the exact solution is

unknown, as in most engineering problems, the accuracy is increased through reduction of mesh

size or increased order of the polynomial in the approximation function (Zienkiewicz and Taylor,

1988). Therefore, the concept of accuracy in numerical methods is closely related to

convergence and precision.

“Convergence means the tendency of a numerical solution to a particular result as the

numerical error is reduced” (Baguley and Hose, 1994). For adaptive mesh generation schemes,

the solution convergence depends on tolerance criteria. A small tolerance results in generated

small mesh size distribution, which is especially important in regions of sharp gradients.

Maximum mesh or maximum tolerance criteria requirements should be identified by performing

convergence studies, where further reduction in mesh size corresponds to negligible or no

change in the solution.

199

Precision of a solution relates the reproducibility of the answer, which may or may not be

accurate. For example, a number of software could be used in the analysis of a simple

unsaturated moisture flow problem. The obtained solutions could be very similar to each other

and yet very different from the available empirical results. One would say that these results are

precise and not accurate. Depending on the magnitude of inaccuracy, one could further state,

that the model is not robust. “A model is robust if the conclusions it leads to remain true even

through the model is not completely accurate,” or in other words, the results obtained with a

robust model are “close enough to be useful in a real-world context” (Meerschaert, 1999). The

robustness of a model is determined through sensitivity analysis to model input and initial

assumptions.

For time dependent problems, the selection of a time step discretization is just as

important as the mesh size criteria. A selection of large time step leads to numerical oscillation,

producing unstable results. Tan et al. (2004) further illustrated the correlation between mesh

size and time step. In general, small mesh size requires small time step. Most programs solving

Richards’ equation have adaptive time step generation. If the user specified criteria are not met,

the time step is reduced, until a preset tolerance is met.

Computer precision, round-off error, truncation error and loss of significance (when two

almost identical values are subtracted from each other, the difference is small and the precision

is lost) are also relevant concepts in numerical modeling. The significance of these errors can

be observed when small output quantities are acquired, such as the surface runoff in desert

landscape modeling considered in Chapter 8. In this problem, no runoff occurred, yet small

value of runoff was calculated in the mass balance analysis. This value represents the sum of

errors attributed to the above mentioned issues. These errors are also important in the analysis

of convergence studies.

A study by Scanlon et al. (2002) compared the numerical results obtained with seven

different programs designed to analyze moisture flow through unsaturated soil,

Unsat-H (SWCC and k(h) – van Genuchten fit),

200

Hydrus (SWCC and k(h) – van Genuchten fit),

Shaw (SWCC – Campbell fit, k(h) – Burdine fit),

Soil Cover (SWCC and k(h) – Fredlund fit),

SWIM (SWCC and k(h) – van Genuchten fit),

VB2DTI (SWCC and k(h) – van Genuchten fit), and

HELP (SWCC – Brooks and Corey fit, k(h) – Burdine fit),

The 1D analysed scenario consists of 3.05 m deep sandy loam profile in Texas, a semi-

arid region experiencing 1.64 m/year (64 inch/year) of PE and 0.367 m/year (14.5 inch/year) of

precipitation and irrigation specified on daily bases. The initial conditions vary from about -1100

kPa at the soil surface to about 0 kPa at the bottom boundary. The one year long analysis was

progressed with a total of 103 nodes. Fixed mesh spacing varying from 0.002 m at the soil

surface to 0.15 m at depth was applied. It is unclear if convergence studies were performed,

however, the extensive discussion about proper time stepping and mesh size imply as much.

Figure 7.1 illustrates the results of Scanlon’s analysis in terms of cumulative AE and

domain accumulation presented as magnitude and relative error. The relative error is defined as

abs(measured value-calculated value)/abs(measured value). Most of the programs calculated

zero runoff (SHAW calculated 0.1 cm, which is negligible), which matches the empirical data.

The mass balance also showed very small error in all the programs. Large discrepancies,

however, were observed in both cumulative AE and domain accumulation. Although only 0.041

m did accumulate in the profile, the calculated values varied from 0.012 m to 0.188 m which

corresponds to 17% to 360% relative error. This discrepancy is attributed to the calculation of

AE. It should be noted that not all the programs implement the same k(h) and SWCC functions,

a limitation of programs. The different estimates of k(h) and SWCC are known to diverge at both

high and low suction values, which at least in part did contribute to the total analysis error.

Comparison of results obtained with van Genuchten fit alone, still exhibit large discrepancies; the

domain accumulation relative error varies between 37% to 360% suggesting that the diversity of

unsaturated soil functions contributed very little to the overall error. Similar results were

201

obtained by Scanlon et al. (2002) for cold desert with calculated surface runoff, when none was

observed. In this case, large discrepancy were attributed to the runoff boundary condition, which

at least in part, is also due to the variability in k(h) estimates at low suction values. Other

contributing factors include different methodologies to calculate AE and surface runoff, time

discretizations and the properties of he applied numerical schemes.

a)4.1 6.7

1.24.8

2.1 2.6

18.814.2

32.6 29.735

31.534.6

34.1

17.921.5

0

5

10

15

20

25

30

35

40

Varia

ble

[cm

]

b)

63 71

1749 37

359

246

9 7 3 6 545 34

0

50

100

150

200

250

300

350

400

Mea

sure

d

Uns

at H

Hyd

rus

Sha

w

Soi

l Cov

er

SW

IM

VS

2DTI

HE

LP

Rela

tive

Erro

r [%

] Domain Accumulation

Cumulative AE

Figure 7.1. Comparison of modeling results with different programs, Texas site, a) cumulative AE and domain accumulation, b) relative errors (after Scanlon et al., 2002).

The discouraging conclusion that can be drawn from the Scanlon research is that none

of the considered programs were able to produce accurate or precise solution. Although in

some codes the discrepancy between measured and calculated cumulative AE was quite small

(3%), it did translate into significant error in domain accumulation. The literature review

202

presented in this and previous section, set proper context with which to view results of numerical

solution. The apparent diversity in answers to the same problem can be attributed to three

sources:

1) a discrepancy in unsaturated soil functions due to the use of different fits, and more

broadly, uncertainly associated with the soil properties and initial conditions,

2) the satisfied convergence and stability criteria and

3) difficulties associated with implemented numerical method.

The diversity of solutions obtained with different tools is not limited to the problem of

moisture flow through unsaturated soils, but rather to a wide range of complex, open-ended

problems ranging from climate predictions to the assessment of risk factors to human health.

This is a classic case for science of decision making that deals with prediction and unknown

uncertainty. Surprisingly, the standard approach is to choose a solution that fits ones needs best

(Sarewitz et al., 2000). The Scanlon et al. (2002) research showed that none of the considered

tools yielded accurate results, however they all lead to a similar quantitative soil response.

Therefore, the program selection is based on attributes other then accuracy, such as

computational effort, stability behavior, user interface, and required post-processing effort.

7.2.2 Experiment Set-Up

Three commercial software packages capable of handling large problems, SVFlux,

Hydrus 1D and Vadose/W, were used in the analyses of 10-hour long transient infiltration with

surface runoff into 1D, 0.5-m deep clayey soil profile with increasing initial total head from -250

m at the soil surface to -200 m at the bottom boundary. Dirichlet BC (-200 m) was applied to the

bottom boundary and flux BC (0.001 m/h) to the soil surface. The clayey soil (soil 17-3 from

Appendix B) has the following properties: LL = 85, PL = 53, Gs = 2.797, pd = 1.36 g/cm3, θw =

51.2%, Fredlund and Xing unsaturated SWCC parameters: a = 140, n = 0.6, m = 0.9, hr = 2000

and Leong and Rahardjo unsaturated soil permeability parameter p = 16 with ksat of 8.71e-6 m/h.

Van Genuchten and Mualem fit with parameters of α = 0.1 and n = 1.25 was used in analysis

203

with Hydrus 1D for which the previously described fit was not available. These two fits are

similar in the suction range of interest and are illustrated in Figure 7.2a and b.

a) b)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.1 1 10 100 1000 10000 100000

vwc

[m3 /

m3 ]

Matric Head [m]

Fredlund and Xing Fitvan Genutchen and Mualem FitMeasured Data

1E-16

1E-14

1E-12

1E-10

1E-08

1E-06

1E-04

0.1 1 10 100 1000 10000 100000

kuns

at [

m/h

]

Matric Head [m]

Leong and Rahardjo Fitvan Genutchen and Mualem Fit

Figure 7.2. Unsaturated soil properties a) SWCC and b) k(h).

7.2.3 Presentation of Results

The quality of numerical solution, in terms of matric suction and mass balance, depends

on both, space and time discretizations. Figure 7.3a to Figure 7.5a illustrate a convergence

study for the problem described above in terms of matric suction variation with depth. Through

numerical experiments it was found that mesh size needed to obtain a convergent solution

depends on both soil properties and magnitude of applied flux. An adequate solution can be

obtained with relatively large mesh for problems with small flux. Significantly smaller mesh

spacing must be used to model flux large enough to invoke surface runoff condition, which

occurs in the considered scenario. A mesh spacing of 0.005 m at the surface yielded a

convergent solution in all considered software.

Hydrus 1D has a user friendly pre-processing interface with easy, fixed mesh generation

set-up, adaptive time step and few tolerance controls, which makes it easy to modify criteria and

re-run the analysis. The program appears to be very efficient; the analysis never took longer

than one second. The available post-processing through Hydrus interface typically did not

provide sufficient information to access stability, therefore additional post-processing had to be

performed by the user. In general, very small changes in tolerance controls did result in

204

problematic, oscillatory solution in instantaneous surface flux and sometimes in suction profile.

With this program, oscillatory behavior was observed for both too large and too small mesh

spacings. Overall, it was quite difficult to obtain non oscillatory flux results. Also, a concern

about proper precision maintained throughout calculation did arise from output node

discretization truncated to second decimal place. The final concern is about identification of a

converged solution. The wetting depth does not increase or decrease consistently with a

reduction in mesh size, making it hard to determine whether the solution is converged or not.

a)

0.000.010.020.030.040.050.060.070.08

-500 0 500 1000 1500 2000 2500Suction [kPa]

Dep

th [m

]

Initial conditiondx = 0.01 0.0050.0025

b)

0.0000

0.0002

0.0004

0.0006

0.0008

0.0010

0.0012

0 1 2 3 4 5 6 7 8 9 10Time [h]

Flux

[m/h

] Applied Fluxdx = 0.010.00250.005

Figure 7.3. Convergence Study for Hydrus, a) suction profile b) instantaneous flux.

The analysis with SVFlux can be described as almost painless, at least for this simple

problem. The pre-processing user interface is straight forward with automatic mesh generation

(not implemented in this scenario) and adaptive time step feature. The program has many

tolerance controls, requiring the user to spend more time on learning the software. Another

205

benefit of SVFlux is that the analysis results are presented visually as the solution progresses.

Therefore there is no need for post-processing to access solution stability. Oscillatory behavior

was observed with large mesh spacing, perhaps as a result of larger time steps performed in the

adaptive time integration, while reduced oscillations were observed with smaller mesh

discretizations. The program robustness with respect to small mesh sizes is a great benefit. The

only concern in SVFlux has to do with the unacceptable shape of the instantaneous flux the

program outputs, as presented in Figure 7.4b. The output flux starts at the value of zero,

followed by an overestimation of the applied flux, which slowly converges to the applied value.

This behavior leads to an overestimation of absorbed water, which can be reduced by taking

smaller mesh spacing.

a)

0.000.010.020.030.040.050.060.070.08

0 500 1000 1500 2000 2500Suction [kPa]

Dep

th [m

]

Initial condition0.010.005dt= 0.001

b)

0.0000

0.0002

0.0004

0.0006

0.0008

0.0010

0.0012

0 2 4 6 8 10Time [h]

Flux

[m/h

]

Applied Flux0.010.005dx=0.001

Figure 7.4. Convergence Study for SVFlux, a) suction profile b) instantaneous flux.

206

Vadose/W was found to be the least efficient program. The pre-processing was found to

be quite cumbersome because 1) initial conditions for transient analysis can come only from a

steady state analysis with the same amount of nodes as the transient analysis, 2) artificial

division of time options into days or seconds while the preferred choice is hours, and 3)

cumbersome mesh spacing generation requiring a lot of user time. Similarly to Hydrus, the

solution stability can be assessed only during post-processing, making the program less efficient

from a user’s perspective. On a more positive note, the presentation of the results was found to

be quite nice. Finally, the reduction in mesh spacing led to an increased wetting front, and the

monotonic behaviour of the solution with a decrease in mesh size made it easy to identify a

convergence. In particular, small mesh spacings did not result in numerical oscillations more

commonly visible in calculations with Hydrus.

a)

0.000.020.040.060.080.100.120.140.16

0 500 1000 1500 2000 2500 3000Suction [kPa]

Dep

th [m

]

dx=0.0025m0.0050.010.020.05Initial Condition

b)

1E-10

1E-09

1E-08

1E-07

1E-06

0 1 2 3 4 5 6 7 8 9 10Time [h]

Flux

[m/s

] dx=0.0025m0.0050.010.020.05Initial Condition

Figure 7.5. Convergence Study for Vadose/W, a) suction profile b) instantaneous flux.

207

As discussed previously, the implementation of inadequate mesh spacing or time step

leads to numerical oscillations in the form of unexpected and large suction oscillation with depth,

Figure 7.7a, flux oscillations with time, Figure 7.7b, or monotonic increase or decrease in suction

to unexpected and unreasonable values as presented in Figure 7.7c. The second condition is

associated with handing of surface water runoff and soil properties, in particular the flatness of

one or both SWCC and k(h) functions and the existence of discontinuity at u=0.

a) b) 0.0

0.1

0.2

0.3

0.4

0.5-100000 -50000 0 50000 100000

Pore Water Pressure [kPa]

Dep

th [m

]

Solution

Initial Condition

-4E-03

-3E-03

-2E-03

-5E-04

5E-04

2E-03

0 2 4 6 8 10Time [h]

Inst

ante

nous

Flu

x [m

/h]

Applied Flux

Solution

c)

0.00

0.10

0.20

0.30

0.40

0.500 100000 200000 300000 400000 500000

Suction [kPa]

Dep

th [m

]

Initial conditiondx= 0.005

Figure 7.6. Examples of stability issues in various software a) suction oscillation with

depth, b) actual flux oscillation at soil surface, and c) suction with depth increased monotonically to unreasonable values.

7.2.4 Discussion and Conclusions

The performance of three commercial software was evaluated, SVFlux, Hydrus and

Vadose/W on a challenging problem of moisture infiltration into dry soil profile. The focus of the

evaluation was to access computational effort, stability and convergence behavior, user

interface, and required user post-processing effort. In general, it was determined that SVFlux is

the most user friendly program requiring the least amount of post-processing work from the user

208

with adequate stability and convergence behavior, therefore it was selected as the numerical tool

for this research work. Hydrus was determined to be the most computationally efficient program,

however its sensitivity to small time stepping was viewed as a liability. The actual research work

involves modeling of complex surface flux scheme. The inability to view the analysis results as

the solution progresses is a definite drawback. Potentially, at post-processing stability issues

are very likely to be discovered, which would require the modification of tolerances and starting

over the analysis. Vadose/W was found to be the least efficient program with the same

drawbacks as Hydrus.

Table 7.2#

. Summary Table of Convergence Results run time

[min] dx average dt

[h] # Newton iterations abs. water [m3]

Vadose/W 9 0.005 0.018 65.19 2.87E-05 SVFlux 0.35 0.005 0.012 2.4 9.87E-03 Hydrus >0.001 0.005 0.172 5.8 4.57E-03

In terms of performance, the nonlinearity of unsaturated soil properties and existence of

boundary condition that switches between Dirichlet and Neumann, introduces difficulties that are

not easily handled by any of the packages. The transition between unsaturated soil surface to

saturated one is typically accompanied by oscillatory behavior of flux and surface suction with

time. The numerical stability is almost always improved by decreasing time step or both time

step and mesh size.

The solutions obtained with these three packages were found to produce markedly

different results, somewhat expectedly based on literature review (Scanlon, 2002). SVFlux

produced the shallowest depth of influence (0.05 m at suction of 1000 kPa) while Vadose/W

calculated the deepest one (.0625 m at 1000 kPa) as illustrated in Figure 7.7a. Hydrus results

showed the sharpest transition from moist region to a dry one. The surface runoff was observed

to occur at different times, for Vadose/W the soil surface became saturated within the initial few

steps but around the 8th hour for SVFlux, see Figure 7.7b. It is very surprising to observe the

least amount of absorbed water to result in the largest depth of influence (Vadose/W). Similarly,

209

Hydrus absorbed about half of water volume absorbed by SVFlux and yet plotted below it. The

variability of the results can be attributed to three sources 1) discrepancy in unsaturated soil

functions due to the use of different fits, 2) handling or runoff boundary condition and 3)

difficulties associated with implemented numerical method.

a)

0.00

0.02

0.04

0.06

0.08

0.10

0.120 500 1000 1500 2000 2500

Suction [kPa]

Dep

th [m

]

Initial Condition SVFluxVadose/W Hydrus

b)

1E-06

1E-05

1E-04

1E-03

1E-02

0 1 2 3 4 5 6 7 8 9 10Time [h]

Inst

ante

nous

Flu

x [m

/h]

Applied FluxHydrusVadose/WSVFlux

Figure 7.7. Software comparison a) Suction profile, and b) Instantaneous flux.

7.3 Sensitivity analysis of SWCC and k(h)

The quality of numerical modeling solution of moisture flow through unsaturated soil, in

part, depends on properly described unsaturated soil properties. It is postulated that the

uncertainty associated with k(h) is greater than inaccuracies caused by numerical oscillation and

inaccurate convergence (Fuselier et al, 2006). The variability of SWCC is attributed to

hysteresis and difficulties associated with its measurement. The variability of unsaturated soil

210

permeability contributes to the uncertainty associated with the estimation of this parameter via fit

functions, hence a range of reasonable variation was considered. A one-dimensional analysis of

expansive soil under dry initial conditions (-1500 kPa) was performed, in which both potential

evaporation and infiltration boundary conditions were considered. It was found that small

variations in the unsaturated soil permeability function result in significantly different modeling

outputs while variations in SWCC produced almost identical soil responses in terms of soil

suction when considered independently of each other.

7.3.1 Uncertainty of Unsaturated Soil Functions

The quality of numerical solutions partly depends on properly described unsaturated soil

properties such as SWCC and unsaturated soil permeability, k(h). In industry, empirical

methods are rarely used to estimate them due to practical challenges associated with test

procedures, which include test duration, sophisticated test equipment, the procedure know-how

and analysis of data, to name a few. More commonly, the unsaturated soil properties are

estimated with fit functions such as van Genuchten, Brooks and Corey, and Fredlund and Xing

equations for SWCC and van Genuchten and Mualem, Brooks and Corey, and Leong and

Rahardjo equations for unsaturated soil permeability; see Section 2.9 for detailed descriptions.

These functions are estimated either by fitting them through few measured data points or by

statistical models based on commonly quantified soil properties such as gradation and Atterberg

Limits. As shown by van Genuchten and Nielsen (1985), Vogel et al. (1988) and Vogel and

Cislerova (1988), the choice of the analytical model for SWCC estimation can significantly affect

the predicted k(h) function. Vogel (2001) illustrated that small changes in SWCC near saturation

result in large changes in k(h) with consequences on numerical results, stability of solution and

rate of convergence. The differences are more pronounced in fine textured soils than in coarse

textured ones (Vogel et al., 2001). Section 2.9.3 (Soil Water Characteristic Curve) and 2.9.4

(Unsaturated Soil Permeability) discuss in great detail the uncertainty associated with each

parameter.

211

7.3.2 Problem Set-Up

The influence of unsaturated soil properties uncertainty on the numerical solution is

examined on a simple 1-D problem with 10-m deep soil profile. Both infiltration and potential

evaporation are considered separately on estimated ranges of SWCC and k(h).

7.3.2.1 Soil Properties

A clayey soil from Litchfield, Arizona with the following properties: LL = 85, PI = 53, Gs

= 2.797, pd = 1.36 g/cm3, θs = 51.2% and ksat = 8.71e-6 m/h was used in this analysis (the same

soil as in previous section). The drying SWCC up to 1500 kPa suction was obtained

experimentally on undisturbed specimen with pressure plate apparatus, and one filter paper test

was performed on air dried reconstructed specimen. Fredlund and Xing equation was used to

estimate SWCC while Leong and Rahardjo equation was used to define k(h).

Based on the literature review presented in Section 2.9.3 both open and closed loop

hysteretic soil behaviours were considered, which roughly includes the expected data scatter.

F1 represents a drying curve of back pressure saturated soil, F2 describes the wetting curve

obtained with soil saturated from bottom up and finely F3 represents the expected wetting curve

under ponding conditions, where a ratio θ(sat ponding)/θ(sat Back Pressure) = 0.8 was assumed. All three

curves are used in the sensitivity analysis. Table 7.3 summarised the SWCC parameters while

Figure 7.8a provides a visual representation.

Based on the literature review presented in Section 2.9.4, the data scatter of k(h) is

expected to range over two orders of magnitude for suction values smaller than 100 kPa, which

is inclusive of the k(h) variation due to hysteresis. For suctions larger than 100 kPa the

uncertainty is hard to quantify. Different values of p produce different k(h) slopes for suctions

larger than 10 kPa, with large p values producing larger k(h) slopes. The k(h) estimate with F1

and p = 12 was obtained by fitting the Leong and Rahardjo model to the k(h) slope obtained from

experimental data for similar soils available through SoilVision 4.0. Values p = 8, 20 were

considered to produce sufficient k(h) variability at high suction values. The estimate of k(h)

212

based on wetting SWCCs and the value p = 12 produced significantly different curves, with

deviations from k(h) obtained in the case F1 with p = 12 appearing at much smaller suctions, see

Figure 7.8b. The k(h) curves 1) F1, p = 8, 2) F1, p = 12 and 3) F2, p = 12 are considered to be

representative of the range of variation of this parameter and are used in this sensitivity analysis.

a)

0

10

20

30

40

50

0.01 0.1 1 10 100 1000 10000 1E+05 1E+06Suction [kPa]

vwc

[%]

-0.15

-0.10

-0.05

0.00

0.05

0.10

∆vw

c/ ∆ψ

Lab DataF1F2F3F1'F2'F3'

b)

1E-16

1E-14

1E-12

1E-10

1E-08

1E-06

1E-04

0.01 0.1 1 10 100 1000 10000 1E+05 1E+06

Suction [kPa]

kuns

at [m

/h]

F1, p=12F1, p=8F1, p=20F2, p=12F3, p=12

Figure 7.8

Table 7.3

. Unsaturated soil properties; a) SWCC and b) Unsaturated soil permeability where F1 is drying curve fitted though experimental data, F2 is wetting curve due to backpressure saturation, and F3 is wetting curve due to ponding.

Function # . SWCC parameters

Description vwc [%]

a n m hr

F1 drying 51.2 140 0.6 0.9 2000 F2 wetting from bottom up 51.2 10 0.7 0.9 200 F3 wetting from top down 41.0 40 0.7 1.1 2000

213

7.3.2.2 Initial and Boundary Conditions

Insitu matric suction measurement at depths larger then active zone depth for Arizona

climatic conditions and clayey material was determined to vary between 1000 kPa and 2500

kPa. Therefore the initial constant profile condition and bottom boundary condition are

considered to be equal to total head of -152.9 m. Two surface boundary conditions were

considered. The first one consists of constant irrigation of 0.001 m/h applied for 50 h. The

second one is a potential evaporation, PE, flux simulating average flux conditions in Jun in

Arizona where PE is 0.0002 m/h, relative humidity is 18% and temperature is 32°C. The

duration of PE flux is 500 h.

7.3.2.3 Modeling Software, Mesh Size and Time Step

Numerical analysis was performed with commercial software, SVFlux 5.80. Infiltration

flow is analysed with h-form of Richards equation. More complex atmospheric conditions

consisting of both infiltration and potential evaporation are solved with a form of Richards

equation modified for vapour flow based on the work done by Wilson (1994). Convergence

studies resulted in the application of mesh spacing varies exponentially with depth where mesh

spacing of 0.05 m was used at the bottom of the profile and 0.0005 m was applied at the soil

surface. The adaptive time step increased from 1e-7 h at the beginning of the analysis to 0.1-h at

the end with average time step of 0.1 h. Tighter mesh and time step had to be used for the

infiltration problem with wetting SWCC (F2) and k(h) based on F2 and p=12. Here dx of 0.00012

m and average dt of 4e-3-h had to be used to reduce numerical oscillations.

7.3.3 Numerical Simulation

Three sensitivity studies have been performed. The first one involved soil response in

terms of both soil suction and degree of saturation due to SWCC variation alone and irrigation

flux; Table 7.4, run 1,2 and 3. The h-formulation of Richard’s equation involves for slope of

SWCC, namely dθ/dψ, where the slope of all considered curves is almost 0 for suctions larger

214

than 100 kPa. Therefore sensitivity study due to PE flux was considered unnecessary since

identical results in terms of soil suction were expected with all SWCCs. The second sensitivity

study was aimed at quantifying the effect of k(h) variability during irrigation process; Table 7.4,

run 1,4 and 5. The last study involved sensitivity analysis due to PE and k(h) variability; Table

7.4, run 6,7 and 8.

Table 7.4#

. Summary of Modeled Scenarios Flux [m/h]

SWCC K(h) p

1 Irrigation = 0.001 F1 F1 12 2 Irrigation = 0.001 F2 F1 12 3 Irrigation = 0.001 F3 F1 12 4 Irrigation = 0.001 F1 F1 8 5 Irrigation = 0.001 F2 F2 12 6 PE = 0.0002 F1 F1 8 7 PE = 0.0002 F1 F1 12 8 PE = 0.0002 F2 F2 12

7.3.3.1 Hysteresis in SWCC

Soil response due 50-hour irrigation flux of 0.001 m/h, SWCCs described by F1, F2 and

F3 and k(h) obtained with F1 and p=12 is presented in Figure 7.9. It is observed that pore water

pressure variation with depth is almost identical in all considered scenarios, where the depth of

influence is about 0.2 m; Figure 7.9a. Similarly, the instantaneous actual flux profiles show that

soil surface saturation occurred at almost the same time (7th hour of analysis) followed by almost

identical absorption rate; Figure 7.9c. It is no surprise then that the total absorbed flux is almost

identical in all three scenarios: 0.0248-m, 0.0268-m and 0.0248-m for F1, F2 and F3

respectively. The discrepancy between runs is observed when the soil response is considered

in terms of degree of soil saturation, Figure 7.9b, which is consistent with the vwc to suction

relationships presented in Figure 7.8a.

It is concluded that soil response in terms of matric suction is independent of SWCC as

long as the slopes of SWCC derivatives remain similar. In the analyzed clayey soil, F1’, F2’ and

F3’ are almost identical and close to zero for suctions larger than 30 kPa. This finding has

215

consequence on dealing with uncertainty associated with SWCC and the assumption of non-

hysteretic k(h), where the potential variation in degree of saturation can be obtained from post

processing of numerical modeling results.

a) b) 0

0.2

0.4

0.6

0.8

1-2000 -1500 -1000 -500 0


Dis

tanc

e fro

m S

urfa

ce [m

]

F1F2F3IC

0

0.2

0.4

0.6

0.8

10 20 40 60 80 100

Degree of Saturation [%]

Dis

tanc

e fro

m S

urfa

ce [m

]

F1F2F3IC

c)

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0 10 20 30 40 50Time [h]

Inst

ante

nous

Flu

x [m

/h F1F2F3

Figure 7.9.

7.3.3.2 Uncertainty in k(h)

Influence of SWCC variation for the same k(h) obtained with F1 and p=12 and irrigation of 0.001 m/h. a) pore water pressure variation with depth, b) degree of saturation with depth and c) instantaneous actual flux.

7.3.3.2.1 Infiltration

Soil response due 50-hour irrigation flux of 0.001 m/h, and varying unsaturated soil

properties as described in Table 7.4, runs 1, 4 and 5 is presented in Figure 7.10. It is observed

that different pore water pressure variation with depth is obtained with each scenario. In

general, large k(h) slope produces smaller depth of influence and reduced effect of diffusion

component manifested in decreased spreading and sharper wetting front. The change in k(h)

has also a consequence on stability and convergence criteria. The soil characterized by

advective dominated mass transfer exhibits more numerical instabilities requiring the

216

implementation of tighter mesh and smaller time step with consequences on run time and

needed computational resources.

For modeled soil the depth of influence is 0.2 m, 0.42 m and 0.03 m for scenarios 1, 4

and 5 respectively. The instantaneous actual flux profiles show that soil surface saturation

occurred at different times as well, Figure 7.10c, with consequences on total absorbed flux:

0.0248 m, 0.0313 m and 0.0119 m for 1, 4 and 5 respectively. Figure 7.10b illustrates partial soil

wetting with depth. SWCC serves as a translation of suction, for which Richards’ equation is

solved for, into terms of engineering significance, namely degree of soil saturation. It is

observed that both scenarios 1 and 4, for which SWCC and k(h) are described with F1, start with

the same initial degree of saturation, S, profile. The final profile variations in S are attributed to

depth of influence and degree of spreading, which are the artifacts of k(h) variability.

a) b) 0

0.2

0.4

0.6

0.8

1-2000 -1500 -1000 -500 0


Dis

tanc

e fro

m S

urfa

ce [m

]

F1, p=12F1, p=8F2, p=12IC

0

0.2

0.4

0.6

0.8

10 20 40 60 80 100


Dis

tanc

e fro

m S

urfa

ce [m

]

F1, p=12F1, p=8F2, p=12

c)

00.00020.00040.00060.0008

0.0010.00120.00140.0016

0 10 20 30 40 50Time [h]

Inst

ante

nous

Flu

x [m

/h F1, p=12F1, p=8F2, p=12

Figure 7.10. Influence of k(h) variation coupled with appropriate SWCCs and irrigation of 0.001 m/h. a) pore water pressure variation with depth, b) degree of saturation with depth and c) instantaneous actual flux.

217

The presented analysis illustrates that numerical solution of moisture flow though soil is

very sensitive to variations in k(h). Unlike SWCC, the effect of k(h) variability cannot be

accessed through post-processing. It is suggested that a range of k(h) functions is modeled to

find bounds of potential soil response.

7.3.3.2.2 Evaporation

Soil response due 500 hour PE flux of 0.0002 m/h, and varying unsaturated soil

properties as described in Table 7.4, runs 6, 7 and 8 is presented in Figure 7.11. Similarly to

infiltration analysis, different pore water pressure variation with depth is obtained with each

scenario, Figure 7.11a. The profiles converge at the soil surface to about 200 000 kPa matric

suction. The depth of influence was found to be 0.25 m, 0.92 m and 0.18 m for scenarios 6, 7

and 8 respectively.

a) b) 0

0.2

0.4

0.6

0.8

11000 10000 100000 1000000

Suction [kPa]

Dis

tanc

e fro

m S

urfa

ce [m

]

F1, p=12F1, p=8F2, p=12IC

0

0.2

0.4

0.6

0.8

10 20 40 60 80 100


Dis

tanc

e fro

m S

urfa

ce [m

]

F1, p=12F1, p=8F2, p=12

c)

-0.0002

-0.00015

-0.0001

-0.00005

00 100 200 300 400 500

Time [h]

Inst

ante

nous

Flu

x [m

/h].

F1, p=12F1, p=8F2, p=12

Figure 7.11. Influence of k(h) variation coupled with appropriate SWCCs and PE of 0.0002 m/h. m/h. a) pore water pressure variation with depth, b) degree of saturation with depth and c) instantaneous actual flux.

218

Figure 7.11b, illustrates partial soil wetting with depth. The characteristics of S variation

with depth due to k(h) uncertainty are the same as for irrigation boundary flux. As before, the

presented data illustrate the significance of k(h) estimate on the numerical solution. For

engineering purposes, matric suction variation beyond 1500kPa bears no significance since it is

associated with wilting point beyond which insignificant soil volume change is expected.

However, within the context of numerical modeling, appropriate estimation of soil response due

to PE is as important as due to infiltrating flux since it determines how much water can enter the

profile for hourly discretized flux.

7.3.4 Conclusions

The quality of numerical solution of moisture flow though unsaturated soil described with

Richards’ equation, in part, depends on properly described unsaturated soil properties, namely

Soil Water Characteristic Curve, SWCC, and unsaturated soil permeability, k(h). The variability

of SWCC has been studied by many authors, see Section 2.9.3. Currently it is well understood

that the SWCC can vary over two orders of matric suction per specific saturation. On the other

hand, k(h) variability is hard to quantify, especially for clayey soils with limited available empirical

data above 100 kPa suction. For small suctions, the overall variability of k(h) can span over two

orders of matric suction and one order due to hysteresis. For the purpose of this mini study, a

range of SWCC and k(h) was considered for three sensitivity studies: 1) varied SWCC, one k(h),

irrigation flux, 2) varied k(h) with variation in SWCC for irrigation flux, and 3) varied k(h) with

variation in SWCC for potential evaporation flux.

It was found that the numerical solution in terms of matric suction is independent of

SWCC variation. SWCC serves as the translation of suction into terms of engineering

significance such as degree of saturation. This conclusion has mathematical bases. In the h-

form of Richards’ equation, the derivative of SWCC is used. For the family of considered SWCC

curves, the SWCC derivatives have almost the same slopes for suctions larger than 30 kPa,

219

hence the numerical solutions are almost identical. Since the numerical solution is independent

of SWCC, the significance of SWCC variability can be quantified with post-processing.

The numerical solution is very sensitive to k(h) variability with consequences on

numerical stability and convergence. In general, large k(h) slope produces smaller depth of

influence and reduced effect of diffusion component manifested in decreased spreading and

sharper wetting front. The soil characterized by advective dominated mass transfer exhibits

more numerical instabilities requiring the implementation of tighter mesh and smaller time step

with consequences on run time and needed computational resources. In order to determine the

range of possible soil response to implemented initial and boundary conditions it is necessary to

identify a range of potential k(h) variability followed by numerical analysis with identified

maximum and minimum k(h) functions.

7.4 SVFlux Program Behavior

The literature review presented in this work discusses the importance of using small time

and spatial discretizations, dt and dx, respectively, in practical numerical implementations. The

lack of both proper time and space discretizations may reportedly lead to unstable solutions.

The best description of what unstable solutions look like is given in the Vadose/W manual

(2004). The information missing in the literature review includes guidelines with respect to the

magnitude of appropriate dt, dx and limitations that still need future research work. Despite a

typical lack of specific dt and dx used in the available literature, a few general guidelines as

presented in Table 7.1 can nonetheless be usually derived. The following sections describe

difficulties experienced in numerical simulations of moisture flow problems and observations

related to stability and convergence issues, which point towards a need for improvements in

practical codes.

220

7.4.1 Numerical Oscillations – Lessons Learned

When stability problems exist, one of the following can be observed:

(i) Temporal oscillations in the computed instantaneous and cumulative fluxes at

the surface, almost always associated to matric suction oscillations.

(ii) Spatial oscillations of matric suction with depth at selected times.

(iii) Divergence (drift) of the matric suction to unexpected values.

(iv) Temporal and spatial oscillations in unsaturated soil permeability (more

sensitive than the matric suction to numerical perturbations).

(v) Discrepancies in mass balance. Most stability challenges were observed during

the infiltration process (more significantly during a cyclic application of

infiltration followed by PE every day, resulting in very dry and very moist

regions next to each other within the soil profile) and were overcome by

applying smaller (nonuniform) mesh discretization at the soil surface.

(vi) Sudden increases in mesh spacing with depth also resulted in oscillatory

solutions; especially in 2D problems with implemented PE flux, oscillations

were observed at the (surface) corners of the domain.

Difficulties due to mesh spacing were generally resolved by implementing an

exponential mesh discretization function in the form of )( byae −− for 1D problems with 10 m deep

profile. A minimum surface node spacing of 0.0001 m was applied to the most difficult scenario.

The adaptive time step feature determines an appropriate time step for the given mesh spacing

and tolerance controls. Typically, for small tolerances large/small mesh spacings lead to

large/small dt’s. Too small tolerances may however lead to inefficient simulations.

Stability issues also can be triggered by abrupt input flux changes such as the onset of a

precipitation or irrigation event, and manifest themselves in the form of large positive or negative

spikes in absorbed or lost flux (with similar spikes in matric suction at the soil surface). On rare

occasions, the solution can completely diverge to incorrect flux and suction values. Reduction in

dt tolerance controls typically solves this problem, however the solution is very inefficient. The

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(small) dt required to resolve sharp changes in flux is usually very expensive in terms of

computational effort and time. The adaptive time step determined by SVFlux on a sample

problem reached values of 1e-7 h, resulting in slower run time than actual implemented flux time.

An alternate and more efficient approach was to provide input flux with smooth transitions

between small and large values (say, over 15-30 minute periods).

Similarly, the surface runoff boundary condition was found to be problematic. The

transition from unsaturated soil surface condition to saturated frequently resulted in oscillatory

behavior. Oscillations in the computed surface flux were found to vary between negative and

positive values, corresponding to soil response ranging from large matric suctions to build up of

small positive pressures respectively. The runoff boundary condition is handled in 1D problems

with equation (7.1), which reads, h = Flux if u <0, and then Flux, else F*ky*(-u).

point load(h)= SWAGE(u, Flux, F*ky*(-u), w) (7.1)

The swage function is aimed at providing a smooth transition over discontinuities with a

polynomial over the width w. The difficulty in the equation arises from the alternating positive

and negative fluxes implemented as the equation (6.1) criterion is or is not met respectively.

Such handling of the boundary condition leads to oscillatory actual surface flux and matric

suction behavior. Frequently, the magnitude of these oscillations can be reduced by using

smaller dt and/or dx. If this approach fails, one should try increasing the transition width w,

decrease the F parameter or implement the boundary condition as a RAMP function. The RAMP

function, which has the same format and basic concept as the SWAGE function, reduces the

applied flux as the limits of the interval of applicability of the piecewise formulae are approached.

The modeled 2D scenario consisted of a surface region with applied zero flux below the

slab-on-grade next to a region with applied atmospheric conditions. Numerical oscillations were

observed at the junction using relatively small dx and dt. The instability was overcome by

implementing a smooth BC transition from the edge of the slab to the atmospheric BC over a

distance of 0.2 m.

222

The collapsible soil was found to be quite difficult to model. In this type of soil the

advective moisture transfer dominates. Mesh spacing and time step reductions did not improve

the stability of the solution. The observed oscillatory behavior was in fact reduced by

implementing a fixed time step (the number of Newton iterations was also increased). Due to

the advective nature of moisture flow through collapsible soil, a proper mesh spacing had to be

applied at the wetting front to avoid numerical issues. Since it is difficult to predict the depth of

the wetting front, an exponentially graded mesh spacing (as described above) was used

throughout the domain.

7.4.2 Numerical Challenges

Two scenarios were identified for which the numerical solution was not found or the

implementation of the modeling criteria was prohibitive in terms of required computational effort

and time. Both of them have to do with moisture infiltration.

. The first scenario is an infiltration into collapsible soil described in Chapter 8 with flux

into the profile large enough to invoke runoff boundary condition and soil suctions smaller than 7

kPa. Potentially, this behavior is associated with the inflection point in the derivative of the

SWCC at about suction of 7 kPa. It should be noted that the flux considered in the research

project rarely invoked surface runoff conditions in the collapsible soil, and when it did, the

surface soil suctions did not became smaller than 10kPa, hence major stability problems are not

part of the presented solution.

The 2D analysis of infiltration into clayey soil described in Chapter 8 is the second

problematic scenario. One hour long large precipitation flux (May) applied into dry profile with

adaptive time step generation took approximately four days to analyze. The obtained solution is

stable and seemingly converged. The obvious challenge here is the reduction in analysis time,

which cannot be obtained with SVFlux.

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7.5 Numerical Experiments

In this section, a number of relevant concepts to the numerical solution of Richards’

equation is presented. Some of them are illustrated on simple scenarios while others are merely

discussed setting the stage for future research.

7.5.1 Fixed vs. Adaptive Time Step

Richards’ equation is typically solved using a fixed-point (Picard) or Newton iteration (in

either case possibly in combination with some form of relaxation). The success of the time

stepping scheme often relies on satisfied CFL restrictions on the time step typically

accomplished with adaptive time discretization scheme, which should implement smooth

increase or decrease in adaptive time step as the solution progresses. The adaptive time

stepping subroutine selects the appropriate dt to satisfy user specified accuracy criteria.

Generally, the stability of the solution is not considered in commercial programs implementing

adaptive dt. Stability performance is typically evaluated for fixed time step methods. The

change in dt is comparable to a change in solution method, therefore adaptive methodologies

are more susceptible to solution instabilities which are not well understood. A range of time step

change ratios between 0.5 to 2 is typically implemented in order to more or less guarantee

stability for a time integrator which is normally stable with fixed time stepping (i.e., ratios of 1).

On a simple numerical experiment, the effect of decreased mesh spacing, decreased

adaptive time step control and increased number of Newton iterations on stability are illustrated

separately. The commercial software SVFlux was used in transient analysis of 12-hour long flux

consisting of constant PE and periodic precipitation with surface runoff into 1D, 10-m deep SM-

ML soil profile. The applied flux is illustrated in Figure 7.12. The initial conditions were obtained

from the turf landscape analysis at the end of April presented in the next chapter. The initial soil

suction decreases from 42 000 kPa at the soil surface to 10 kPa at the approximate depth of

0.05-m, then it increases to 1500kPa at about 1.5-m from the soil surface and remains constant

through the remainder of the profile. Dirichlet (h = -152.1 m) and Neumann (flux) were applied to

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the bottom boundary and soil surface, respectively. The SM-ML soil has the following properties:

LL = 29, PL = 17, Gs = 2.64, pd = 1.36 g/cm3, θw = 43%, Fredlund and Xing unsaturated SWCC

parameters: a = 4.5, n = 3.2, m = 0.35, hr = 600 and Leong and Rahardjo unsaturated soil

permeability parameter p = 16 with ksat of 0.01944 m/h. The unsaturated soil properties are

illustrated in Chapter 8, Figure 8.6 and Figure 8.7.

-0.002

0

0.002

0.004

0.006

0.008

0.01

0.012

0 1 2 3 4 5 6 7 8 9 10 11 12Time [hour]

Flux

[m/h

]

PEPrecipitation

Figure 7.12. Input flux for numerical experiment.

Four numerical scenarios are presented. The first one consists of adaptive time step

and fixed mesh spacing with depth, Mesh 1, as illustrated in Figure 7.13. For Mesh 1, the node

spacing increases from 0.00024-m at the soil surface to 0.05-m at depth of 4.9-m. The adaptive

time stepping scheme limits the number of Newton iterations to 3. Scenario 2 illustrates the

effect of reduced time stepping criterion on the set-up of Scenario 1. Scenario 3 implements

adaptive time step scheme and fixed, reduced mesh spacing, Mesh 2, where the surface node

spacing is 0.00012-m. The final scenario illustrates fixed mesh spacing, Mesh 1, and fixed time

step of 0.0002-h with 3 default Newton iterations allowed. In an effort to eliminate numerical

issues associated with sharp flux variations, the precipitation data were ramped up and down

over the period of 0.2-h. The periodic flux is representative of actual precipitation and irrigation

pattern considered in research scenarios presented in Chapter 8. The alternating infiltration and

225

evaporation events were found particularly difficult to handle for the program due to near surface

developed layers of very wet and very dry regions next to each other.

1E-04

1E-03

1E-02

1E-01

0 1 2 3 4 5 6 7 8 9 10Depth [m]

Nod

e Sp

acin

g [m

]

Mesh 1Mesh 2

Figure 7.13. Implemented node spacing.

The numerical experiments revealed that the numerical oscillations of both actual flux

and matric suction at the soil surface are highly dependent on the implemented mesh spacing.

Figure 7.14 illustrates that reducing the mesh spacing reduces the magnitude and frequency of

the numerical oscillations. As the mesh spacing decreased the average and minimum dt

increased, however the overall solution time took 50% longer; see Table 7.5. The quality of the

analysis can be aided by decreasing the time step, presented in scenario 4, or time step control

criteria, scenario 2. Table 7.5 illustrates the computed dt with time and dt ratios. The observed

stability issues might be associated with sudden increase or decrease of time step. As

discussed previously, the appropriate dt ratios are in a range between 0.5 to 2, but the observed

values sometimes go beyond this acceptable range.

In summary reducing the mesh spacing resolved SVFlux instabilities in this example

(somewhat oddly, the decrease in mesh spacing was accompanied by an increase in average

dt). The observed instabilities occured when the soil surface suctions became smaller than 4.5

kPa (for other soils this value would have been much smaller). A minimum surface node

spacing of 0.00012-m is required to resolve flux into SM-ML soil of 0.0106 m/h magnitude.

Alternately, a reduction in tolerance (TERRLIM) or the implementation of a fixed dt with larger

226

mesh size offers acceptable stability improvement. The modeling of slightly larger flux into the

soil profile results in the reappearance of the instability. A deeper understanding of this effect,

possibly due to increased stiffness associated to either under-discretization or inadequate time-

stepping control strategies, would be needed.

10

-610

-410

-210

010

2

Inst

. F

lux

[m/h

]

Adaptive dt, Mesh 1

0

0.0030.0060.0090.0120.015

Inst

. F

lux

[m/h

]

Adaptive dt, Mesh 1, decreased time cotrol

0

0.003

0.006

0.009

0.012

Inst

. F

lux

[m/h

]

Adaptive dt, Mesh 2

0 2 4 6 8 10 120

0.003

0.006

0.009

0.012

Inst

. F

lux

[m/h

]

Time [hour]

Fixed dt, Mesh 1

10

-310

-110

110

310

5

Suc

tion

[kP

a]

101

103

105

Suc

tion

[kP

a]

101

103

105

Suc

tion

[kP

a]

0 2 4 6 8 10 12

101

103

105

Suc

tion

[kP

a]

Time [hour] Figure 7.14. Instantaneous flux and surface matric suction for adaptive and fixed dt

formulations.

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Table 7.5. Summary of numerical experiments, dx and dt.

Analysis

1 2 3 4 Mesh discretization 1 1 2 1 Surface node spacing 0.000237 0.000237 0.000118 0.0002372 Fixed/Adaptive Adaptive Adaptive Adaptive Fixed ave dt [h] 0.0023 0.0013 0.0038 0.0002 min dt [h] 8E-06 5E-06 1E-04 NA #Newton iterations 3 3 3 100 terrlim 0.0001 0.00001 0.0001 0.0001 errlim 0.0001 0.0001 0.0001 0.0001 xerrlim 0.0005 0.0005 0.0005 0.0005

7.5.2 Mixed Formulation

Mixed formulation is a technique were a higher order PDE is solved as a system of first

order ODEs. For Richards’ equation the mixed formulation involves the solution of the second

order PDE

( ) thm

yhk

y ww

y ∂∂

=

∂∂

∂∂ γψ 2 (7.2)

with prescribed Robin BC, ( ( ) ( ) uFkelseCthenuifyhk yy ψψ −≤=

∂∂ 0 , where F is large

relaxation constant) at the soil surface as a system of first order equations.

thm

yf

ww

∂∂

=∂∂ γ2 (7.3a)

( ) 0=−∂∂ fyhk yψ (7.3b)

with prescribed Dirichlet BC on f. In mixed formulations the flux is considered directly. The

benefit is that fluxes are now stored and integrated in time as separate variables rather than

computed approximately from matric suction values using finite difference approximation

requiring small dx, especially near the soil surface. On the other hand, the mixed formulation

introduces an algebraic constraint (equation (7.3b)) which can be interpreted as an infinitely stiff

PDE which must be handled implicitly.

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7.5.3 Normalization

Normalization/scaling is a technique which transforms the solution of a problem into a

non-dimensionalized form. It reduces potential problems (and sometimes instabilities)

associated to the effect of round-off errors such as those occurring in calculations involving

values on different scales. Normalization can also help identify independent control parameters

in a problem.

In a similar vein change of variables/coordinate transformation can reduce the variability

of dependent or independent variables (e.g., redefining Richard’s equation in terms of the

logarithm of matric suction rather than matric suction itself) and improve problem conditioning

(e.g. via preconditioning).

7.5.4 Spatial Discretization - Pseudospectral Method

Pseudospectral methods are high order accuracy methods applicable to and frequently

implemented in the solution of PDEs. The solution with pseudospectral methods involve the

substitution with global smooth function (typically interpolating polynomial) into the PDE. The

benefit of pseudospectral methods is faster convergence. Difficulties arise however when sharp

fronts and discontinuities are part of the considered problem. “In the presence of such

phenomena the accuracy of high order methods deteriorates. This is due to the well known

Gibbs phenomenon that states that the pointwise convergence of global approximations of

discontinuous functions is at most first order. In the presence of a shock wave global

approximations are oscillatory and converge nonuniformly. Recent advances in the theory and

application of spectral methods indicate that high order information is retained in stable spectral

simulations of discontinuous phenomena and can be recovered by suitable post processing

techniques.” (Gottlieb and Gottlieb, 2003). Due to the high accuracy and fast convergence

qualities of pseudospectral methods, they still represent very attractive alternatives for the

solution of Richards’ equation, provided suitable post-processing (e.g. front reconstruction) is

available.

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7.5.5 Time Discretization - Exponential Integrator

Exponential integrators form a class of numerical methods used to integrate the solution

of a semi-linear PDE in time. The equation is usually split into linear, typically stiff part and

nonlinear, usually nonstiff part in a form

)(' yfLyy += 0tt ≥ (7.4a)

00 )( yty = (7.4b)

where L is a matrix and f(y) is a continuous function. The aim of exponential integrator is to

solve the linear part exactly and the nonlinear part using standard numerical integrator.

“Exponential integrators are especially designed to handle stiff systems, and accomplish this

goal by constructing exact integral curves for the linear part of the differential operator.

Constructing the integral curves entails the application of the matrix exponential and related

functions” (Berland and Skaflestad, 2005). The incentive of exponential integrator application,

especially exponential time differencing types, into stiff parabolic equations, such as the

Richards’ equation lies in its superior performance when compared to typically implemented

implicit numerical schemes (Berland and Skaflestad, 2005). Jackiewicz, et. al. (2006) presents

implementation of exponential integrator methods into the solution of a parabolic equation on a

sample problem. The presented methodology can be expanded into the solution of moisture

flow through unsaturated soil. Arraras et al. (2007) recently showed how such a strategy can be

successfully applied to Richards’ equation.

7.5.6 Time Discretization - ADI

Alternating direction implicit, or ADI, schemes are unconditionally stable time integration

methodologies applicable to advection-diffusion type problems (Hout and Welfert, 2007). In 2-D

or 3-D domain, the solution is integrated in time one coordinate direction at a time (1-D problem)

in a cyclic fashion. At each time step, the results from the 1-D analyses are combined to create

input for the next time step. In general, implicit time integrators are unconditionally stable, and

230

are more efficient for solving stiff parabolic PDEs. The adaptation of ADI technique makes the

implementation of implicit methods more feasible.

7.6 Conclusions

The unsaturated moisture flow though soil is analyzed by solving Richards’ equation,

a diffusion-advection PDE with stiff and parabolic characteristics. This type of equation is known

to exhibit numerical challenges in the form of errors in mass balance, numerical oscillations in

actual flux, pore water pressures at the soil surface and with depth. These difficulties are

especially pronounced for dry, moisture sensitive soils with steep unsaturated soil properties and

sharp wetting fronts. The nonlinearity of unsaturated soil properties and the existence of

boundary conditions switching between Dirichlet and Neumann introduce difficulties that are not

easily handled by any of the commercial software packages reviewed in literature and this

chapter. Additionally, the solutions obtained with different packages were reported to produce

significantly different answers (Scanlon,2002 Tan, 2004, SVS, 2000, and GeoSlope, 2004).

These discrepancies are attributed to minor differences in available unsaturated soil property fit

functions in each software, different methodologies for the calculation of AE and surface runoff

and finally different implemented numerical methodologies. These discrepancies and errors

associated with inadequate convergence and solution stability, however, are considered to be

insignificant when compared to the uncertainty associated with k(h) and its impact on the

numerical solution variability (Fuselier et al, 2006).

The consensus approach to deal with numerical difficulties is centered on the reduction

of mesh size and time step in an adaptive manner. This approach, however, may result in very

long computational times and if not handled properly may lead to unrecoverable errors and

failure of the time scheme. In this chapter few options and ideas which might improve the

accuracy and/or stability of the numerical solution of Richards’ equation were presented. A

proper study of the impact these ideas/techniques may have on this solution are out of the scope

of the present work and would need additional research.

8 MODELING – NUMERICAL RESULTS

8.1 Modeling Objective

In part, the objective of this research program was to analyze moisture movement

through unsaturated soil in the context of residential slab-on-grade construction on expansive

soil found in Arizona. The objective was satisfied by performing moisture flow analyses through

two soil types, fat clay (PI=53) and silty sand (PI=12). Modeling was carried out to determine the

suction (degree of saturation), the horizontal and the vertical distance of moisture penetration

under the slab as per typical Arizona environmental and human imposed flux boundary

conditions.

The implementation of unsaturated soil mechanics involves the use of numerical tool

such as a finite element method. Currently, few commercial programs solving the partial

differential equation of water flow through unsaturated soil, are available. SVFLUX was chosen

for this research project due to its user friendly interface and visual presentation of results while

the program performs the analysis. As a consequence, the solution stability can be visually

assessed while the program is running. In other programs, the outputs must be post-processed

to access the solution stability, hence reducing the overall efficiency of analysis.

Both 1-D and 2-D scenarios were considered in the analysis of a uniform soil profile due

to two environmental conditions. The first condition mimicked the typical desert or low water use

landscape. For this input type, it was assumed that the amount of water introduced into the soil

through irrigation is negligible, hence only the actual precipitation data were used. The

appropriate precipitation input was determined by performing a statistical analysis of 24 years of

precipitation data, where the data was obtained from Natural Climatic Data Center, NCDC. It

was found that average annual rainfall is 8.0 inches while the potential evaporation is 91 inches.

Turf landscape is the second type of flux boundary condition considered, where the irrigation

provides 93 inches of water annually, precipitation is 8 inches and the average annual potential

evapotraspiration is about 46 inches.

The results of the analyses were used to better understand the depth and extent of

wetting and suction variations that occur within expansive soils beneath residential structures.

232

Conditions for the Phoenix metropolitan area, Arizona, only were considered. To extent the

results of this research study to other climatic conditions where expansive soils of different soil

characteristic are typical, additional finite element analysis must be performed that includes

those specific soil and boundary flux conditions.

8.2 Design of Experiment

The analyses of moisture movement through unsaturated soil for residential slab-on-

grade construction on expansive soil involved the identification of appropriate modeling tool,

determination of boundary conditions, domain size, and input parameters. The input parameters

include soil characteristics obtained through laboratory testing and literature review, moisture

flux and other modeling program specific input. A list of analyses performed is provided below in

Table 8.1. The modeling results are presented in terms of matric suction and degree of

saturation (detailed modeling results presented in Appendix D). These results can be further

used to obtain the soil/slab system deformation using a stress-deformation finite element code

such as SVSolid.

Table 8.1. List of Performed Analyses. Analysis Type SM-ML CH 1-D Desert, hourly flux 6 years 6 years 1-D Desert, average flux 1 year 1year 1-D Desert, roof runoff ponding, hourly flux 1 year 1 year

1-D and 2D Desert, IC= 34th year of turf 1 year

2-D Desert 1 year, average flux 1 year, hourly flux

1-D Turf, hourly flux 2 years 11 years followed by 23 years of ave. flux analysis

1-D Turf, average flux 1 year 1 year 1-D Turf, Irrig. = PE, hourly flux 1 year 1 year 2-D Turf, hourly flux 0.35 year 2-D Turf, average flux 1 year 4 years

233

8.2.1 Problem Assumptions and Restrictions

The following general and problem specific assumptions were made in the solution of

moisture flow through unsaturated soil.

• The suction value at the bottom of the profile was determined based on insitu soil testing

and literature review that indicated a wide range of suction variation at depth from

800kPa to 10000kPa for undeveloped desert regions and below slab-on-grade

surrounded by desert landscape. From geotechnical engineering perspective, suction

values larger then 1500kPa have a limited impact on soil behavior and soil-structure

interaction; therefore in this analysis a 1500 kPa suction value was used as the base

boundary condition.

• Based on the PTI 3rd Edition procedure, the active zone depth is 9 ft. A larger depth of

30 ft (10 m) was selected as the profile depth to observe the moisture flow within the

active zone depth.

• A constant head of -153 m was assumed for initial condition resulting in 1500 kPa matric

suction at the bottom boundary and 1600 kPa matric suction at the soil surface.

• The flux into the soil profile is modeled on hourly bases and is representative of actual

precipitation and irrigation patterns.

• Soil particles and water are incompressible;

• The effect of air diffusing through water, air dissolving in water, and water condensation

are ignored;

• The model is inclusive of water vapor flow;

• The pore air pressure is constant and atmospheric;

• Air phase is assumed to be continuous;

• Soil properties such as the coefficient of volume change, m2w, vary linearly within a finite

element;

• The system is isotropic, kx = ky;

• The soil is homogeneous;

234

• Overburden pressure is negligible;

• Osmotic suction is negligible;

• Concrete slab in impermeable, zero flux is applied;

• Isothermal system; moisture flow within soil mass due to temperature gradients is not

considered.

8.2.2 Program

SVFlux 5.80 is a finite element program designed to solve Richard’s equation for

moisture flow through unsaturated soil. It is based on a FlexPDE kernel, a general software for

solving systems of PDEs in 1D, 2D or 3D. FlexPDE utilizes adaptive unstructured mesh

generation and adaptive time stepping based on an implicit Backwards Difference formula (BDF)

of low order (order 1 is implicit Euler, order 2 is “Gear's method”, a two-step method which

requires a proper initialization). The program runs under Microsoft Windows NT/2000/XP

operating system and requires a minimum of 128 MB RAM and 150 MB hard drive space. More

space is needed for the storage of large output files, where the amount of that space is

determined by the complexity of the problem and the type of output specified by the user. The

generated input and output data are stored with Microsoft Access.

The required input parameters consist of the following soil properties: SWCC, kunsat

function, Gs, saturated volumetric water content, and saturated soil permeability. The required

problem set up consists of domain size, boundary and initial conditions. The boundary

conditions can be entered in terms of hydraulic head or flux where the flux can be positive

(infiltration) or negative (evaporation). The flux can be entered as a constant value, in terms of

equation or as a step flux. The program is also capable of calculating evaporative flux by using

the Penman (1948) formulation or the Ward Wilson method (Wilson et al., 1994).

The type of output is specified by the user. It is possible to obtain initial or final pore

water pressures as well as the difference between them. The analysis results can also be

displayed in terms of total or pressure head, volumetric or gravimetric water content, unsaturated

235

hydraulic conductivity, gradient, final water storage coefficient, void ratio, porosity, total unit

weight, total or dry density, and degree of saturation. When the evaporation option is used

additional variables can be obtained as well: volumetric air content, diffusion coefficient, vapor

gradient, relative humidity, and pore-air pressure.

8.2.3 SVFlux Specific Restrictions

In the process of moisture flow modeling with SVFlux some program restrictions

(limitations) were identified. These limitations and the methods used to overcome them are

described below.

1. SVFlux automatically removes entries in output files when the output files become

relatively large. It was observed that initially reported results at small time increments of

0.02 h are output using time increments of up to 2.5 h. This difficulty was overcome by

subdividing the analysis into shorter run-time parts. The input for each part of the

analysis was taken as the output from the preceding analysis (part). For a one year

long analyses, 2 to 8 time subdivisions were used.

2. The following Figure 8.1 illustrates the unexpected consequence of automatic output file

reduction described above. The results of 1D, hourly flux, desert landscape CH are

presented, where unmodified analysis of 10-h input (0.02-h time increments) is

compared to the modified file after 4380-h of analysed input (increased to 0.75-h time

increments). It was observed that the quality of the solution appeared to deteriorate,

appearing oscillatory about the unmodified solution for all outputs: matric suction,

instantaneous and net fluxes.

The significance of this complication lies in a suggestive lack of stability, which is

not actually present in the internal computations of the program – although the

automatically reduced data typically oscillated about the non-reduced solution. This can

be seen in Table 8.1, where the reduced output results are plotted along with the

unmodified files.

236

a)

b)0 1 2 3 4 5 6 7 8 9 10

-2

0

2

4

6

8x 10

-4

Var

iabl

e [m

/h]

Time [h]

PrecipitationPotential Evaporation

0 2 4 6 8 10-1

0

1

2

3

4

5x 10

-3

Net

Flu

x [m

]

Time [h]0 2 4 6 8 10

0

0.2

0.4

0.6

0.8

1

1.2

1.4x 10

-3

Net

AE

[m/h

]Time [h]

Automatically Reduced DataNot Reduced Data

c)

0 1 2 3 4 5 6 7 8 9 100

500

1000

1500

2000

Suc

tion

[kP

a]

Time [h]

Dist=0, Automatically Reduced DataDist=0,Not Reduced DataDist=0.03, Automatically Reduced DataDist=0.03,Not Reduced Data

Figure 8.1. Analysis results: a) Input Flux, b) Net fluxes, and c) Matric suction at

selected depths.

237

3. A small error is introduced into the actual instantaneous flux calculation from program

overshooting the solution and then converging to the applied value, which can be

observed in Figure 8.2. This error is reduced with reduction of both time step and mesh

size, which is computationally time-expensive. In part, the goal of stability and

convergence studies was to reduce this error by implementing the optimal mesh grid

and time step.

Figure 8.2. Analysis Results - Instantaneous flux.

4. The automatic mesh generation feature was found to be unsatisfactory. This SVFlux

feature is controlled with two tolerances, errlim and xerrlim. The reduction in these

controls results in reduction of mesh spacing to a certain value. It was observed that

further reduction in those controls did not lead to a further reduction in space

discretization, yet convergence studies did identify the need for smaller mesh spacings.

As a consequence, the numerical results obtained with the automatic mesh generation

feature almost always displayed stability issues.

In addition to the automatic mesh generation, the SVFlux program has two built-

in user specified mesh generation features, constant dx at specified depth, and dx as a

function of depth. The first feature, constant dx, was applied to the soil surface while the

238

mesh generation at depth was progressed with the automatic method. It was observed

that the mesh size increases very rapidly from the surface to some other, default mesh

size value shortly below the surface. This sudden increase was correlated to increased

solution instability in general and significant oscillatory behavior near the domain

boundaries. This challenge was overcome by introducing an exponential function to

control the gradual increase in mesh spacing with depth. For 1-D analyses, the function

alone was used. For 2-D problems, two mesh controls were utilized. The first one

involved specified, usually uniform mesh within an expected area of moisture movement.

The second control involved utilizing the soil surface mesh spacing control, where the

mesh spacing was increased with horizontal distance beneath the slab.

5. A large discrepancy was observed between the actual net flux provided in SVFlux output

and the change in domain accumulation of water volume (Δvw), while it is expected that

these values be identical. It was further observed that this discrepancy occurs when the

applied flux out of the profile, PE, exceeds the flux into the profile. In the absence of

runoff the net flux computed by SVFlux is correct and matches that computed from ΔVw.

Due to this limitation, the cumulative flux presented in this dissertation was obtained

from the change in domain accumulation. This is not an error in the program results, but

rather an error in output reporting.

8.2.4 Boundary and Initial Conditions

Figure 8.3 illustrates applied boundary conditions to the 2-D domain. In an effort to

simulate symmetry lines, the vertical boundary conditions were set to zero flux. Zero boundary

flux was also applied to the region directly under the slab. Neumann BC simulating

environment/human imposed flux was applied to the remaining portion of the domain along the

top boundary. It consists of precipitation, typically applied irrigation, potential evaporation,

relative humidity and temperature parameters representative of Arizona climatic conditions (see

section 8.2.7 for details). The bottom boundary consists of a constant head value determined

239

from soil testing beyond the estimated active zone. The initial profile of matric head was

assumed to be constant with depth and equal to 153 m. The water table in Arizona is commonly

very deep, and therefore its inclusion in shallow moisture migration analyses was not

considered.

The 1-D analyses simulated the moisture flux beyond the distance of structure influence.

This is achieved by applying “Specified Input Flux” to the top boundary, matric suction of 1500

kPa to the bottom boundary (as for 2D analysis) and constant initial matric head condition of 153

m.

Flux = 0Flux = 0

Constant Head

Specified Input Flux Flux = 0

x

y

Figure 8.3. Boundary condition of control volume.

8.2.5 Domain Size

Stepped flux consisting of positive and negative values was applied to the above-

mentioned control volume of relatively permeable soil, SM-ML. The size of the control volume,

CV, was determined by an iterative process, where the bottom and both vertical boundaries

were moved in and out from the edge of the slab one at a time. With each iteration, the suction

output was compared to the previous suction output. The distance from the edge of the slab that

did not influence the output results by more than 1 % was considered to be the correct length

and the iteration process was stopped. It was found that a 5 meter deep profile with a 5 meter

wide slab region and 2 meter wide “Specified Input Flux” region were sufficient domain size

dimensions for the slab-on-grade on expansive soil modeling. The 1-D analyses were

performed on a 10 m deep profile.

240

8.2.6 Soil Input Parameters

SVFLUX required the following parameters to be specified: equilibrium soil suction at

the bottom of the profile, specific gravity, saturated hydraulic conductivity, volumetric water

content of saturated soil, SWCC and unsaturated soil permeability function. Field exploration

and soil testing were carried out in an effort to determine the typical range of soil properties

found in Phoenix region and to obtain the necessary input data. The summary of both activities

are described in Chapter 4.

In an effort to identify the range of potential moisture migration depth and degree of

saturation, two soil types were selected based on plasticity index and saturated soil permeability,

The CH soil with PI of 53 was expected to produce maximum em and minimum depth of

influence, SM-ML soil with PI of 12, was expected to produce minimum em and maximum depth

of influence. The properties of the CH were obtained experimentally, where SWCC was

performed on undisturbed sample with pressure plate apparatus and filter paper. The k(h) curve

was estimated based on experimental data for similar soils available through SoilVision (SVSb,

2005). The Leong and Rahardjo fit with Fredlund and Xing SWCC parameters were used to

estimate k(h) function such that the curve slope matched the slope of the k(h) of experimental

data, which was accomplished by varying the parameter p. The available experimental data

were limited to suction of 100 kPa, therefore some uncertainly exists for the unsaturated soil

permeability function corresponding to matric suction larger than 100 kPa. The soil properties

are presented in Table 8.2 while the unsaturated curves are illustrated in Figure 8.4 and Figure

8.5.

The properties of the SM-ML soil were obtained from literature review rather than in-

house experimental data because well documented unsaturated soil properties, including

experimental k(h), were found (Pereira at al., 2005). The soil properties are presented in Table

8.2, Figure 8.6 and Figure 8.7. The figures also illustrate the derivatives of SWCC, S’. It is

postulated that the shape of the S’ has a consequence on convergence and stability criteria of

the numerical solution when the soil surface becomes saturated and the surface runoff boundary

241

condition is invoked. The S’ for the CH soil converges exponentially from value smaller then -

0.05 1/kPa at suction of 0.01 kPa to zero value at suction of 1000 kPa. The S’ for the SM-ML

soil has a value of zero 1/kPa for small and large values of suction. The function reaches a

minimum of -0.047 1/kPa at suction of 5 kPa. Coincidentally, the SM-ML soil was observed to

present numerical challenges at suction values smaller than 10 kPa.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

0.01 0.1 1 10 100 1000 10000 100000 1000000

Suction [kPa]

Satu

ratio

n [d

ecim

al]

-0.050

-0.045

-0.040

-0.035

-0.030

-0.025

-0.020

-0.015

-0.010

-0.005

0.000

0.005

dS/d

ψ [1

/kPa

]

Laboratory Data - DryingFredlund and Xing FitS'

Figure 8.4. SWCC – CH soil.

1E-16

1E-15

1E-14

1E-13

1E-12

1E-11

1E-10

1E-09

1E-08

1E-07

1E-06

1E-05

1E-04

0.01 0.1 1 10 100 1000 10000 100000 1000000

Suction [kPa]

k uns

at [m

/h]

Figure 8.5. Unsaturated Soil Permeability – CH soil.

242

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

0.01 0.1 1 10 100 1000 10000 100000 1000000

Suction [kPa]

Satu

ratio

n [d

ecim

al]

-0.050

-0.045

-0.040

-0.035

-0.030

-0.025

-0.020

-0.015

-0.010

-0.005

0.000

0.005

dS/d

ψ [1

/kPa

]

Experimental Data - Wetting Experimental Data - DryingFredlund and Xing fit S'

Figure 8.6. SWCC – SM-ML soil (after Pereira at al., 2005).

1E-11

1E-10

1E-09

1E-08

1E-07

1E-06

1E-05

1E-04

1E-03

1E-02

1E-01

0.01 0.1 1 10 100 1000 10000 100000 1000000

Suction [kPa]

k uns

at [m

/h]

Leong and Rahardjo Fit

Experimental Data - 1



Experimantal Data - 4

Figure 8.7. Unsaturated Soil Permeability – SM-ML soil (after Pereira at al., 2005).

243

Table 8.2. Soil Properties.

Classical Soil Properties

Soil Type CH SM-ML LL 85 29 PL 32 17 PI 53 12 P200 86 48 %clay 33 13 Gs 2.797 2.64 γd [pcf] 85 85

SWCC a 140 4.5 (Fredlund and b 0.6 3.2

Xing Fitting Equation) c 0.9 0.35 h 2000 600 θw [%] 51.2 48.3 mv (Default) 1.00E-07 1.00E-07 Transition width (Default) 0.02 0.02

Permeability Function kx sat [m/h] 8.71E-06 1.94E-02 (Leong Fitting Equation) ky sat [m/h] 8.71E-06 1.94E-02 p 12 16

Vapor Diffusion Dmy 1 1 α 0 0

Sink/Source none none

8.2.7 Determination of Appropriate Input Flux

Expansive soil supporting slab-on-grade in the Phoenix metropolitan area can

experience a wide range of flux conditions consisting of precipitation, potential evaporation and

irrigation. Two extreme flux conditions typical for the Phoenix region were identified. They are

turf landscaping, were the lawn is irrigated every day, and desert landscaping or xeriscape

where negligible amount of water is introduced to the soil surface. Landscape professionals and

government employees were surveyed in an effort to determine the appropriate and typically

applied irrigation patterns in the Valley. This information was used to develop input flux applied

in the finite element modeling requiring four flux components to be described, flux onto the soil

such as irrigation or precipitation, potential evaporation, relative humidity and temperature.

8.2.7.1 Evaporation

Wilson et al. (1995) demonstrated through laboratory drying tests that actual evaporation

rate from bare soil is a function of total soil suction at the soil surface. The actual evaporation

244

from soil depends on temperature and relative humidity, where the relative humidity can be

expressed in terms of total soil suction. These relationships are given in equations 8.1 and 8.2.

The SVFLUX computer program utilized these equations to calculate actual evaporation based

on potential evaporation rates with modified Richards’ equation for vapor flow, Equation 2.11.

11

vWRTeAE PE

RT

ψ − = −

(8.1)

vWRTRH e

ψ

= (8.2)

where:

AE - actual soil evaporation mmday

,

PE - potential evaporation mmday

,

K - absolute temperature [K],

R - universal molar gas constant 8.314 Jmole K

°

,

RH - relative humidity of the air above the soil surface [%],

ψ - total soil suction in the soil [kPa], and

Wv - molecular weight of water 0.018 kgmole

.

Figure 8.8 illustrates, for three different soil types, the dependence of actual evaporation

on total suction at the soils surface, where the ratio of actual evaporation to potential

evaporation, AE/PE, is plotted on a semi-log scale against total suction. The value of AE/PE

begins to decline when the suction exceeds 3000 kPa for all tested soils. The decline is

attributed to the decline of surface vapor pressure to below the saturated vapor pressure; and

thus the relative humidity declines as well. The ratio of AE/PE continues to decline and

approaches zero as the soil surface suction increases toward 100,000 kPa; a value that

corresponds to applied 50% relative humidity and the evaporation ceases. Figure 8.8 further

245

indicates that the relationship between AE/PE to suction is independent of soil type, hence the

relationship developed for sand, silt and clay produces very similar results.

Figure 8.8. Relationship between AE/PE to total suction for sand, silt and clay (after

Wilson, 1997).

The potential evaporation data for the Phoenix region were obtained from three internet

sources 1) US Weather Service, Arizona Department of Water Resources (2006), 2) NOAA,

Western Regional Climate Center (2006), and 3) Arizona Meteorological Network (2006).

Measured data for one year were available from source 1 and 2, while source 3 provided 6 years

of estimated PE based on measured relative humidity, RH, and temperature data, T. The

average from all three sources was used to develop PE flux used in the desert landscape

analysis presented in Table 8.3 and Figure 8.9. The 6-year averages of RH and T from source 3

were further used to develop RH and T program input, Table 8.3.

The potential evapotranspiration data, PET, for tall, well watered, cool season grass

were obtained from University of Arizona for a golf course in Cave Creek, Arizona (UA, 2000).

Based on Table 8.4, the evapotranspiration rates were modified by a 0.6 landscape coefficient to

simulate the evapotraspiration experienced by warm season Bermuda grass, a plant commonly

used in Phoenix landscapes. The plant evapotranspiration rate is, in part, a function of leaf

length, since PET was determined for long leaf vegetation, the correction was necessary to

246

adequately describe typical site conditions (UA, 2000). The applied PET is presented in both

Figure 8.9 and Table 8.3.

Table 8.3. Potential evaporation rate for Phoenix area, Arizona (from ADWR, NOAA and AMN 2006) and potential evapotranspiration rates for Bermuda turf landscape, Cave Creek, Arizona (UA, from Dep. of Agriculture, 2000).

Month PE - Potential Evaporation 0.6PET - Evapotranspiration of RH T warm season, Bermuda grass

[in/mo] [m/h] [in/mo] [m/h] [%] [C] 1 -3.3 -1.16E-04 -1.3 -4.45E-05 52.7 11.9 2 -4.1 -1.46E-04 -1.8 -6.35E-05 49.5 13.1 3 -6.4 -2.26E-04 -2.7 -9.59E-05 44.9 16.6 4 -8.7 -3.07E-04 -4.0 -1.39E-04 33.9 21.0 5 -11.3 -4.00E-04 -5.1 -1.81E-04 25.7 27.0 6 -11.9 -4.20E-04 -6.0 -2.11E-04 24.5 31.3 7 -12.3 -4.35E-04 -6.1 -2.16E-04 32.4 33.8 8 -10.3 -3.62E-04 -5.6 -1.97E-04 42.2 32.2 9 -8.7 -3.06E-04 -4.9 -1.72E-04 39.3 29.9 10 -6.6 -2.32E-04 -3.9 -1.38E-04 49.6 22.4 11 -4.2 -1.50E-04 -2.8 -9.75E-05 49.5 14.9 12 -2.8 -9.84E-05 -1.6 -5.75E-05 51.5 10.3

Sum -91 -2.3 -46 -1.2 [ in(m)/year]

-13

-11

-9

-7

-5

-3

-1

0 1 2 3 4 5 6 7 8 9 10 11 12Time [month]

Rate

[in/

mo]

PEPET of tall, well watered grassPET of Bermuda grass

Figure 8.9. PE for Phoenix area, Arizona (from ADWR, NOAA and AMN 2006) and PET

rates for tall, well watered grass and Bermuda turf landscapes, Cave Creek, Arizona (from Dep. of Agriculture, 2000).

247

Table 8.4. Landscape coefficients (from Dep. of Agriculture, 2005). Grass Type Coefficient

Cold season grass 0.8 Warm season grass - Bermuda 0.6

Based on equation 8.2, and available RH and T data, the maximum potential soil surface

suction can be calculated. For both desert and turf landscape scenarios the minimum RH of

24.5% occurs in Jun, which corresponds with the maximum anticipated soil surface matric

suction of 198 000 kPa at T = 31.3°C. Figure 8.10 illustrates that the soil suction is highly

dependent on RH, where small changes in RH translate into large suction changes for RH larger

than 90%. For RH smaller than 90%, which corresponds to about 14 000 kPa, small RH

changes translate into insignificant suction changes from the perspective of engineering

application. On the other hand, the surface soil suction is almost independent of air

temperature. For suctions smaller than 10 000 kPa, the calculated RH is almost identical for

a range of temperatures between 5 and 40°C. For suctions larger then 10 000 kPa the potential

change in T corresponds to a maximum RH change of 4% at 100 000 kPa suction, resulting in

potential suction variation between 90 000 to 100 000kPa, a difference which again is

insignificant for engineering application.

0102030405060708090

100110

10 100 1000 10000 100000 1000000

RH

[%]

Suction [kPa]

T = 40 C 20 5

Figure 8.10. Suction as a function of RH and T.

vWRTRH e

ψ

=

248

8.2.7.2 Desert and Low Water Use Landscaping

8.2.7.2.1 Irrigation Needs of Desert and Low Water Use Landscape

Desert landscaping consisting of native Arizona plants does not require irrigation. A

landscape consisting of low water use plants also referred to as “xeriscape” is recommended to

be irrigated once to twice a month. The amount of water applied should match and not exceed

plant water needs specified in Table 8.5 (“Landscape Watering by the Numbers”, 2005). Special

care should be exercised to apply only as much water as the plant needs since over watering

can lead to wilting of the plants. The water should be applied infrequently to ensure deep root

system development.

Table 8.5. Gallons of Water needed to Wet Root Zone per Irrigation Event (from City of Mesa, Department of Water Use, 2005).

Plant Type Diameter of Plant Canopy [ft] 1 2 3 4 5 6

Trees 1.5 5 11 16 22 26 Shrubs 1 4 8 12 17 20

Ground Cover/Cacti 0.5 2 3.5 5 7 9

8.2.7.2.2 Irrigation Systems

Irrigation of xeriscape is typically managed with water drip system which produces 1

gal/h of water. The drip system must be maintained and regulated frequently to perform as

designed. Irrigation professionals report that drip systems in Arizona are often poorly installed

with substandard materials, which leads to the development of leaks. Because the tubing is

installed below ground surface, those leaks are rarely caught in a timely manner. As a result, in

some instances, the system was found to use more water than the sprinkler system. The lack of

education about the proper use and maintenance of the drip system and the fact that the amount

of water provided to the plants is not easily observable are the main causes of water overuse.

249

8.2.7.2.3 Input Flux for Desert and Low Water Use Landscape

The amount of water typically applied to desert or low water use landscape is negligible.

Therefore, for modeling purposes, desert flux is exclusively based on the amount of water

applied to the soil surface from precipitation and potential evaporation. For the purpose of

developing a reasonable input flux, 24-year daily precipitation data and 9-year hourly

precipitation data was obtained and analyzed for Phoenix Airport meteorological station from

NCDC. Statistical analysis revealed that average rainfall in Phoenix is 8.04 in/year with standard

deviation of 3.0 in/year. The maximum rainfall was found to be 15.1 in/year and the minimum

was 0.06 in/year. Further analyses indicated that, for the most part, rainy days within a month

occur close to each other and rainy hours within a day occur consecutively. Therefore the

precipitation data was applied in the model on the beginning of each month for the specified

number of rainy days and for the duration of rainy hours per day. The precipitation input was

further modified for potential evaporation. This modification simplified the potential evaporation

input from numerous PE intervals applied between the rain events to a constant PE per month.

Table 8.6. Average precipitation data from Phoenix Airport metrological station (from NCDC).

Month Average

Precipitation Average Number

of Rainy Desert Input [ m/h]

Precipitation applied as per PE [in/mo] Days Hours Prec. Scheme Ave. flux per mo.

1 0.98 6 7 7.20E-04 4.00E-05 -1.16E-04 2 0.9 6 8 6.40E-04 4.44E-05 -1.46E-04 3 1.1 7 8 7.30E-04 5.45E-05 -2.26E-04 4 0.32 4 5 7.00E-04 1.98E-05 -3.07E-04 5 0.15 3 1 1.65E-03 6.73E-06 -4.00E-04 6 0.03 2 1 7.80E-04 2.23E-06 -4.20E-04 7 1.02 8 5 1.06E-03 5.82E-05 -4.35E-04 8 0.82 9 2 1.45E-03 3.67E-05 -3.62E-04 9 0.7 5 3 1.49E-03 3.11E-05 -3.06E-04

10 0.58 4 4 1.17E-03 2.48E-05 -2.32E-04 11 0.69 4 6 9.00E-04 2.93E-05 -1.50E-04 12 0.78 5 6 7.70E-04 3.06E-05 -9.80E-05

250

A mini study was performed to observe if the application of PE during rain event

increased by PE value modified the output results when compared to the results obtained due to

rain event alone. It was found that the soil response in terms of suction was identical for both

cases justifying the use of modified rain data for potential evaporation values. The applied

precipitation and PE data are given in Table 8.6 as well as presented in Figure 8.11.

8.2.7.2.4 Average Input Flux

As part of this research work, flux simplification was performed and its consequences on

the quality of the numerical solution were observed. It was accomplished by substituting the

hourly discretized flux with average monthly flux. The simplified average flux scheme consists of

the same PE, RH and T input data and averaged precipitation over the period of each month.

The value of averaged precipitation was increased by the amount that would evaporate during

the rainy hours. Consequently, the net average applied flux is equal to 10.6 inches/year. The

data are given in Table 8.6 and illustrated in Figure 8.11.

-0.0005

0

0.0005

0.001

0.0015

0.002

0 30 60 90 120 150 180 210 240 270 300 330 360Time [day]

Flux

[m/h

]

PrecipitationPEAverage Flux

Figure 8.11. Desert Landscape Flux.

251

8.2.7.3 Turf Landscaping

8.2.7.3.1 Irrigation Needs of Grass

Proper irrigation of turf landscape consists of a yearly flux equal to the yearly

evapotranspiration rate. Therefore, the warm season Bermuda grass requires 46 in/year of

water. The grass is semi-dormant in the wintertime (November through February) when a

reduced watering regimen is required when compared to the summer months. The local

irrigation recommendation is to apply 0.75-in of water during every irrigation event. In general,

the warm season grass should be provided with about 1-in of water once a month between

November through February and 2 to 3-in of water a week from May through September when

the plants are irrigated once every few days; see Table 8.7 for proper irrigation schedule. For

turf landscapes developed on clayey soils, that are known to absorb only about 0.1 in/hour of

water, the irrigation pattern presented in table 4 is still valid. The frequency of watering during

the scheduled irrigation day should be appropriately increased to provide the soil with the

recommended dosage of absorbable water. This kind of infrequent watering pattern encourages

the plants to develop deep root systems and produces hardy plants (McCaleb, 2005 and City of

Mesa, 2005).

Table 8.7. Recommended irrigation pattern for warm season Bermuda grass (from City of Mesa, Department of Water Use, 2005).

Month Frequency once every

January 4 weeks February 21 days

March 14 days April 7 days May 4 days June 3 days July 3 days

August 4 days September 6 days

October 6 days November 14 days December 4 weeks

252

Sometimes people choose to over-seed their lawns with cold season grass for the winter

growth. The new seeds are introduced to the landscape from September to October. The new

plants require watering of up to six times a day for a few minutes at a time to ensure germination

and maintenance of the new plants (City of Mesa, 2005).

8.2.7.3.2 Irrigation Systems

There are two watering systems commonly used in Phoenix: pop-up sprinklers and

rotors. The pop-up sprinklers produce 1.6-1.87 in/hour of water while the rotors output 0.2-0.8

in/hour of water depending on the manufacturer of the product. The pop-up sprinkle system is

about 70% efficient while the rotor system is 90% efficient. Because the watering system is not

100% efficient, the yard must be over-watered by the deficiency factor to ensure that all the

plants in the lawn are provided with a sufficient amount of water.

8.2.7.3.3 Typical Water Use on Turf Landscaping

Based on information obtained from the landscape professionals and Phoenix area

government agencies, it is estimated that the turf landscapes are often over-watered by 2 to 5

times the above recommended amount. The mismanagement of water use is mainly attributed to

homeowner’s lack of knowledge about grass needs. Landscapes are typically irrigated every

day where the water is applied once or twice a day. The common once a day option consists of

a 15-20 minute watering period while the twice a day watering pattern typically last 5 to 10

minutes per application.

8.2.7.3.4 Flux Input for Turf Landscaping

Based on the investigation of typical irrigation patterns and amount of water used per

day in the Phoenix area on turf landscaping, it was concluded that large variability exists in the

amount of water applied per irrigation event. This variability is associated with the diversity of

253

available watering equipment and the variability of time the equipment is used for. Due to those

factors, the following assumptions were necessary to develop a reasonable turf flux:

• It was determined that the most commonly applied irrigation pattern is to water once per

day throughout the year; therefore irrigation is assumed to be applied once a day;

• The total amount of water applied to the turf landscaping is 2.2 PET; that translates to

103 in/year.

• It is reasonable to assume that the amount of water applied per day in the winter time is

much smaller than the amount of water applied per day during the summer months

when the grass shows signs of distress very easily. Winter irrigation is assumed to be

1.5 of corrected PET(February) (0.0023 m/day) and summer irrigation is 2.0 of corrected

PET(Jun) (0.005 m/day).

• Drainage from the landscaped lot is assumed to be fairly good. Most of Arizona turf

landscapes are surrounded by a curb, where the difference between the curb and the

soil surface is about 0.3”; measurement performed by the author on 47 turf landscapes.

Therefore, it is assumed that some of the excess water will be available for absorption

up to one hour from the onset of the irrigation event. This is accomplished by applying

constant flux for a period of one hour. The use of runoff option ensures that only water

absorbed within the irrigation period is utilized by the computer program.

• Assume 0.4 in/hour (0.0102 m/h) rotor water system is used; 0.5 h in winter and 1h in

summer.

The applied turf landscape scheme for the numerical models in this study consists of

half an hour to one hour of irrigation every day followed by 23 hours of evapotranspiration.

There are two magnitudes of applied irrigation. The first flux has magnitude of 0.2 in/hour and is

applied between November through April; it is referred to as the Winter irrigation. The second

flux, also called the Summer irrigation is applied during the remaining portion of the year and has

magnitude of 0.4 in/hour. The evapotranspiration rate increases from winter months to the mid-

summer and then it decreases towards December. The available evapotranspiration rate varies

254

parabolicly with time, but for the purpose of modeling, the rate was simplified to vary on monthly

basis. The applied flux consists of precipitation and irrigation where the precipitation data are

given in Table 8.6, while the irrigation and PET data are provided in Table 8.8 as well as plotted

in Figure 8.12. In addition, a flux scenario was considered, where the applied irrigation

constitutes 1.3 of PE, the input data are also given in Table 8.8.

-0.0010.0000.0010.0020.0030.0040.0050.0060.0070.0080.0090.0100.011

0 30 60 90 120 150 180 210 240 270 300 330 360Time [day]

Flux

[m/h

]

Irrigation Potential EvapotranspirationAverage Flux Precipitation

Figure 8.12. Turf Landscape Flux.

Table 8.8. Amount of irrigation and potential evapotranspiration used in modeling of turf landscape.

Month

Irrigation Magnitude of Irrigation Magnitude of Irrigation Average Flux PET Period Flux = 2.2PE Flux = 1.3PE per mo.

[h] [m/h] [m/h] [m/h] [m/h] 1 0.5 0.0046 0.0031 1.32E-04 4.45E-05 2 0.5 0.0046 0.0031 1.35E-04 6.35E-05 3 0.5 0.0046 0.0031 1.42E-04 9.59E-05 4 0.5 0.0047 0.0032 1.13E-04 1.39E-04 5 1 0.0106 0.0054 4.41E-04 1.81E-04 6 1 0.0106 0.0054 4.37E-04 2.11E-04 7 1 0.0106 0.0054 4.82E-04 2.16E-04 8 1 0.0106 0.0054 4.68E-04 1.97E-04 9 1 0.0106 0.0054 4.63E-04 1.72E-04

255

Month

Irrigation Magnitude of Irrigation Magnitude of Irrigation Average Flux PET Period Flux = 2.2PE Flux = 1.3PE per mo.

[h] [m/h] [m/h] [m/h] [m/h] 10 1 0.0105 0.0053 4.57E-04 1.38E-04 11 0.5 0.0046 0.0031 1.25E-04 9.75E-05 12 0.5 0.0046 0.0031 1.25E-04 5.75E-05

8.2.7.3.5 Average Input Flux

Similarly as for the desert landscape, consequences of flux simplification were analysed

for the turf landscape by averaging both irrigation and precipitation over each month. In addition,

PET with RH and T input data were used. The implemented average flux is presented in both

Table 8.8 as and in Figure 8.12.

Table 8.9. Average Input Flux for 2-D Analysis of CH Soil. Average Flux [m/h]

month Year 1 Year 2 Year 3 Year 4 Year 5 1 5.32E-05 2.96E-05 2.95E-05 2.86E-05 2.78E-05 2 2.77E-05 1.40E-05 1.04E-05 1.04E-05 9.73E-06 3 6.25E-06 -2.11E-06 -3.90E-06 -4.78E-06 -6.58E-06 4 -1.85E-05 -2.46E-05 -2.65E-05 -2.78E-05 -2.80E-05 5 8.83E-06 1.76E-06 -6.45E-07 -1.61E-06 -2.33E-06 6 -1.95E-06 -6.58E-06 -8.42E-06 -9.43E-06 -1.00E-05 7 1.11E-05 6.47E-06 5.23E-06 3.91E-06 4.24E-06 8 9.44E-06 5.20E-06 4.33E-06 3.00E-06 2.13E-06 9 1.21E-05 6.64E-06 3.90E-06 6.25E-06 3.84E-06

10 1.90E-05 2.71E-05 3.21E-05 3.13E-05 2.45E-05 11 1.85E-06 -4.93E-06 -7.49E-06 -9.74E-06 -6.20E-06 12 2.72E-05 2.64E-05 2.22E-05 2.29E-05 2.30E-05

In addition, an average absorbed flux was used to analyse CH 2-D scenario and

efficiently obtain an estimate of edge moisture variation distance. This input was derived from 1-

D output analyses and consists of only one flux component summarized in Table 8.9. The

results of 11 years 1-D analyses were also used to develop an average flux to estimate long-

term depth of influence. Figure 8.13 illustrates that after 5th year of analysis the yearly flux levels

off, in this particular case to a value of 0.022 m/year, which was applied to subsequent 23 years

of analysis.

256

0

0.02

0.04

0.06

0.08

0.1

0.12

0 1 2 3 4 5 6 7 8 9 10 11Time [year]

Flux

[m/y

ear]

Figure 8.13. Turf landscape, average absorbed flux per year for CH soil.

8.2.8 Output Presentation - Definitions

The numerical results are mainly illustrated in terms of matric suction, in kPa, and

degree of saturation, as a percentage, calculated based on matric suction results and soil

properties. The quality of the numerical solution, in part, is judged based on the mass balance.

Therefore, the presentation of the numerical results requires that the following input and output

quantities are clearly defined:

Table 8.10. Definitions of Input and Output Quantities.

Quantity Name Units Quantity Description

Instantaneous Precipitation/ Precipitation/ Precipitation Rate

m/h Rainfall rate is the positive flux into the profile obtained from

historical data and applied on hourly bases to simulate the actual precipitation pattern and magnitude.

Cumulative Precipitation m Total applied precipitation within modeled time period. The

applied volume of water is given per 1 m2 surface area.

Instantaneous Irrigation/ Irrigation / Irrigation Rate

m/h

Turf irrigation rate is the positive flux into the soil profile estimated based on recommendations of landscape professionals and government officials; applied on hourly bases to simulate the actual irrigation pattern and magnitude applied by residents of Phoenix valley.

Cumulative Irrigation m Total applied irrigation within modeled time period. The applied volume of water is given per 1 m2 surface area.

257


Cumulative Irrigation and Precipitation m Sum of applied positive soil fluxes into the soil profile within

considered time period given per 1 m2 surface area.

Instantaneous PE/ PE/ PE Rate m/h

Potential evaporation or evapotranspiration rate is the applied negative flux out of the profile. It is obtained from historical data and applied on hourly bases to simulate the average monthly potential PET or PET magnitude.

Cumulative PE m Total applied PE or PET within modeled time period. The applied volume of water is given per 1 m2 surface area.

RH % The average monthly relative humidity obtained from historical data.

T °C The average monthly temperature obtained from historical data.

Flux m/h Generic term used in describing instantaneous applied flow

rate which might include all or some of the applied flux components.

Net Cum. Flux/ Net Cum. Applied Flux m Sum of all applied fluxes: net precipitation, net irrigation and

net PE given per 1 m2 surface area.

Average Flux m/h

The average applied flux either into or out of the profile. It either represents the average irrigation and/or precipitation applied over the period of each month (in this case PE is also applied) or it constitutes one and only one applied flux component varying on monthly bases and obtained from 1-D output analysis as the absorbed or lost volume of water per modeled period of time.

Instantaneous AE/ AE/ AE Rate m/h Actual Evaporation rate is the negative flux out of the profile

calculated by the program based on PE, RH and T.

Cumulative AE m Total volume of water lost from the soil profile within modeled

time period due to evaporation. The program output quantity is given per 1 m2 surface area.

Domain Volume of Water/ Vw m The volume of water retained in the entire domain at specified

time. The output quantity is given per 1 m2 surface area.

Instantaneous Flux m/h

Term used to in describing net flux at the soil surface in response to the applied precipitation, irrigation and PE; quantity calculated by the program. This is the rate of water absorption or loss from the domain per 1 m2.

Domain Accumulation/ ∆Vw

m or m3

The volume of water absorbed in or lost from the domain within analyzed time period calculated as the difference between the final and initial volume of water in the profile. The output quantity is given per 1 m2 surface area in 1D analysis and as

258


volume (m3) in 2D analysis.

Cumulative Runoff m The volume of water that did not get absorbed by the domain.

Calculated as the applied precipitation + irrigation – AE- ∆Vw. It is given per 1 m2 surface area.

8.3 Convergence Studies

The research done by Thiam-Soon among others illustrated that two important issues

are found to create difficulties in the finite element analysis of moisture flow through unsaturated

soils (Thiam-Soon et al., 2004). They are oscillations of pore water pressures within the soil

profile and solution convergence to the correct answer. Both of these problems are caused by

the implementation of improper mesh size, dx or dy, and/or time step, dt. Thiam-Soon further

illustrated that an appropriate ratio between the element size and time step exists that will

ensure a nonoscillatory, convergent solution, which is a valid assessment of numerical solution

behavior per the applied numerical method. Refer to Section 2.9 for detailed discussion about

stability, convergence and accuracy.

Through numerical experiments performed for this study, it was further observed that the

mesh size and time step requirements change with a change in applied flux magnitude. In

general, the larger the inward flux, the smaller the required dx and dt. Additionally, initial

conditions and steepness of flux (e.i. a transition from small or zero value to a large value over a

short period of time) have a consequence on convergence and stability criteria. Since the flux

considered in this analysis consists of periods of precipitation discretized hourly followed by

prolonged periods of potential evaporation, the convergence and stability experiments were

performed on characteristic problem segments. The desert landscape was divided into

precipitation and evaporation periods in each month, while the turf landscape was analysed on

monthly bases. The solution convergence was observed on domain accumulation, net AE, soil

surface matric suction and depth of influence. Only stable results, typically achieved by reducing

dt, were used in the convergence analysis. They are characterized by lack of matric suction

259

oscillations with depth and at the soil surface with time. The determined maximum dx for the

most challenging flux period was then used in the entire analysis, while maximum dt was allowed

to change from one flux period to another based on the results of convergence studies.

Convergence studies were not performed on average flux scenarios. It was assumed that the

stringent convergence criteria developed for the hourly flux analyses are sufficient for the

average flux scenarios; the anticipated program runtime with average flux is smaller than the

time required for convergence study.

An illustrative example of convergence analysis is presented in Figure 8.14, through

Figure 8.16. They show results obtained with 1-D analyses of the SM-ML soil for January desert

landscape flux. The solution of SM-ML soil required the implementation of constant dt with

increased number of Newton iterations (adaptive dt generation lead to unstable behavior during

precipitation events). The mesh discretization for the 10-m deep profile was implemented with

an exponential function, )( byae −− with origin of the domain at the base boundary. The results are

presented in terms of the node spacing at the soil surface.

For problems involving only evaporation, Figure 8.14a, convergence criteria require dx

smaller than 0.00048-m. Implementation of larger mesh size results in overestimation of both,

domain accumulation and cumulative AE. When the applied flux consists of PE only, for 1-D

problems the domain accumulation and cumulative AE should be identical. Figure 8.14 further

illustrates that these values differ when the solution is obtained with large mesh spacings, and

converges to a single value as the mesh size decreases. Figure 8.14b shows that modeling of

evaporation (PE) alone is insensitive to dt. Time step of 0.5 h was found to be adequate.

Figure 8.15 illustrates the convergence study performed on precipitation period in

January for 1-D analyses of the SM-ML soil. The flux consists of precipitation and PE. The

figure shows that when AE is almost equal to PE (this is always true when flux into the soil

exceeds PE), AE result is insensitive to considered variation in both dx and dt. As the mesh

spacing decreases for constant dt, the domain accumulation values approach a converged value

exponentially. A reduction in dt produces similar results, where these two solutions plot parallel

260

to each other; see Figure 8.15a. The same general behavior was observed when keeping dt

constant and varying dx. When a small enough dx is used, the curves obtained overlap and vary

with dt in the same way. Based on the results presented in Figure 8.15b, it was determined that

dt of 0.01-h and dx of 0.00024-m are required to obtain a stable and convergent solution for this

particular soil type and applied flux scheme.

a) b)

-0.040

-0.035

-0.030

-0.025

-0.020

-0.015

0.00001 0.0001 0.001 0.01 0.1

Node Spacing [m]

Var

iabl

e [m

]

Net AE

Domain Accumulation

0 0.1 0.2 0.3 0.4 0.5 0.6

Time Step [h]

Figure 8.14. Convergence analysis, January, PE only, desert landscape, SM-ML.

a) b)

0.0138

0.0140

0.0142

0.0144

0.0146

0.0148

0.0150

0.0001 0.001Node Spacing [m]

Varia

ble

[m]

ICum. AEI ΔVw, dt = 0.001h ΔVw, dt = 0.01h

ΔVw, dt = 0.025h ΔVw, dt = 0.05h ΔVw, dt = 0.075h

0.0001 0.001 0.01 0.1

Time step [h]Cum. AEI ΔVw, dx = 9e-4

ΔVw, dx=5e-4m ΔVw, dx = 2e-4

ΔVw, dx = 1e-4

Figure 8.15. Convergence analysis, January, precipitation, desert landscape, SM-ML.

261

Initially, both soil surface matric suction and the depth of influence where tracked for

convergence purposes. Figure 8.16 plots results for end of January, desert landscape, 1-D SM-

ML soil. It was determined that these two parameters are not good indicators of solution

convergence. The domain accumulation is the best indicator; therefore convergence analysis

was focused on domain accumulation, while the matric suction output was used to access

solution stability; in other words the selection of appropriate dt per applied dx.

a) b)

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.55

0.00001 0.0001 0.001 0.01 0.1Node Spacing [m]

Dep

th o

f Moi

stur

e In

fluen

ce [m

]

InfiltrationEvaporation

1

10

100

1000

10000

100000

0.00001 0.0001 0.001 0.01 0.1Node Spacing [m]

Mat

ric S

uctio

n at

sur

face

[m]

Infiltration

Evaporation

Figure 8.16. Convergence analysis, end of January, desert landscape, SM-ML.

Table 8.11 and Table 8.12 summarize analyses run time, dx and dt used in both 1-D and

2D scenarios. In general, the most efficient way of analysing desert landscape was to specify

one large maximum dt for the entire problem (dt all) and smaller maximum dt for irrigation

periods (dt(prec.)). For SM-ML soil, stable and convergent solution was easier to obtained with

fixed dt formulation and increased number of Newton iterations, while analysis of CH soil

progressed smoother with the adaptive dt generation. Even in the adaptive analyses, different

output dt was specified for the PE periods and different for the precipitation events to facilitate a

better selection of dt, which is especially problematic for the program during the transition from

evaporation to precipitation.

262

Table 8.11. Mesh spacing, time step and run times for SM-ML analyses.

Analysis Type dx equation

dx at

surface dt

generation

dt all

dt(prec.)

Run time per year

( )3−− yae [m] [10-5 m] [h] [h] [h] 1-D Desert, hourly flux a = 1.1 24 fixed 0.5 0.01-0.05 67

1-D Desert, average flux a = 1.1 24 adaptive 0.017-0.5 NA 10

1-D Desert, roof runoff ponding, hourly flux

a = 1.1 24 fixed 0.5 0.0025-0.06 131

2-D Desert, average flux

1-D Turf, hourly flux a=1.1&1.2 12-24 fixed 0.0025-0.01 NA 360 1-D Turf, average flux a = 1.1 12-24 adaptive 0.012-0.5 NA 14

1-D Turf, Irrig. = PE, hourly flux a=1.1&1.22 10.3-24 fixed 0.0002-0.02 NA 141

2-D Turf, average flux

Table 8.12. Mesh spacing, time step and run times for CH analyses.

Analysis Type dx equation

dx at

surface dt

generation

dt all

dt(prec.)

Run time per year

( )3−− yae [m] [10-5 m] [h] [h] [h] 1-D Desert, hourly flux a = 1 48 adaptive 0.5 0.0013-0.03 48

1-D Desert, average flux a = 1 48 adaptive 0.014-0.5 NA 13

1-D Desert, roof runoff ponding, hourly flux

a = 1.15 17 adaptive 0.5 (0.054-9)e-3 47

1-D Desert, IC= 34th year of turf a = 1 48 adaptive 0.5 0.0013-0.03 40

2D Desert, IC= 34th year of turf

0.03 throughout

profile 125 adaptive 0.005-0.5 NA

2-D Desert 0.03

throughout profile

125 adaptive 0.005-0.5 NA 379

1-D Turf, hourly flux a = 1.15 17 adaptive 2.7e-6-0.1 NA 59 1-D Turf, average flux, years 12-34 a = 1.15 17 adaptive 0.5-1 NA 6

1-D Turf, average flux, year 1 a = 1 48 adaptive 0.05-0.5 NA 5.5

1-D Turf, Irrig. = PE, hourly flux a = 1.15 17 adaptive 0.00027-0.1 NA 69

2-D Turf, hourly flux 0.03

throughout profile;

250 adaptive 7.6e-6-0.1 NA 1965

2-D Turf, average flux

0.0375 throughout

profile; 500 adaptive 0.02-0.1 NA 31

263

8.4 Simplification of Flux

The quality of the numerical solution of moisture flow through unsaturated soils for the

purpose of depth of moisture influence determination depends, in part, on properly described flux

boundary conditions including appropriate environmental factors and inclusion of the

microclimate created by human activity. Rigorously described surface flux boundary conditions

were used in the analyses of CH and SM-ML soils, and simplifications to these conditions were

systematically made to determine the impact of simplified boundary conditions on the final

solution. The problem set-up is described in Section 8.2. It was found that major simplifications,

through averaging of flux conditions and increased time-steps for application, result in only

negligible difference in computed matric suction compared to more detailed simulations of flux

when the capacity of the soil to absorb applied surface water is not exceeded, such as for the

desert landscape conditions of this mini-study. Otherwise, as observed for the turf irrigation

case of this study, averaging surface flux can result in significant over-estimate of the extent and

degree of wetting in the profile.

8.4.1 Potential Evaporation

Simplification of potential evaporation flux alone was considered in this part of the study

on CH soil. Based on AZMET data the potential evaporation rate increases as the air

temperature increases and relative humidity decreases (2006). Figure 8.17 presents the

estimated hourly and average values for January 2000, Phoenix airport, with cumulative PE of

0.09-m. The PE hourly data fluctuate daily from a maximum value at mid afternoon each day to

a minimum value at night. During the winter months, the RH fluctuates between 12% during the

daytime hours to 100% at night while the minimum PE reaches a value of zero. The complexity

of the PE flux discretized on hourly bases presents the modeler with already discussed in

Chapter 7 numerical challenges requiring the implementation of small mesh and time steps,

which is computationally expensive. On the other hand, the implementation of flux averaging

provides a very attractive, time efficient alternative. The presented mini-study illustrates that PE

264

flux simplification is an appropriate method yielding similar soil response in terms of matric

suction.

The one-month long PE analysis revealed that results obtained with average PE are

very similar to the results obtained with hourly discretized PE. Figure 8.18 illustrates that the

hourly discretized instantaneous AE fluctuates about the average instantaneous AE, as

expected. As the soil surface becomes desaturated, the oscillations decrease resulting in

cumulative AE of -0.0149 m as compared to -0.0160 m lost from the domain due to the average

flux. For hourly discretized flux, in general, diffusion of soil moisture from inside of the domain

towards the soil surface occurs when PE is at minimum. The increased moisture content of the

soil surface provides larger amount of water available for evaporation during the day time hours

resulting in increased domain moisture loss when compared to the average flux analysis.

-1.3-1.2-1.1-1.0-0.9-0.8-0.7-0.6-0.5-0.4-0.3-0.2-0.10.00.10.20.30.40.50.60.7

0

12

24

36

48

60

72

84

96

108

120

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750

PE [m

m/h

]

RH

[%] a

nd T

[°C

]

Time [h]RH, hourly RH, average T, hourly T, average PE, hourly PE, average

Figure 8.17. Components of PE for PE flux simplification analysis.

The most important parameter, to judge the moisture flow analysis with is matric suction.

In terms of matric suction, the soil surface values obtained with hourly flux fluctuate about the

265

average PE soil response as presented in Figure 8.19. Both flux scenarios produce profiles

where suction decreases gradually from the maximum suction of 90 000 kPa at the soil surface

to initial suction profile at approximate depth of 0.3 m from the soil surface, see Figure 8.20. A

slight discrepancy between these two profiles is observed below the soil surface. The average

flux solution plots parallel and above the hourly discretized flux solution.

Based on the PE flux simplification study it was concluded that PE averaging is an

adequate flux modeling methodology. A small discrepancy was observed in both outputs, net

AE and matric suction. This quantifiable discrepancy, however, should be considered against

the unquantifiable uncertainty associated with hourly measured RH and T data, and estimated

PE based on the measured RH and T data. The hourly discretized flux took approximately 9-

times longer to analyze then the average flux. Due to these factors, average PE is implemented

in this entire study.

-2

-1

0

x 10-4

Inst

. AE

[m/h

]

Hourly FluxAverage Flux

0 100 200 300 400 500 600 700-0.02

-0.015

-0.01

-0.005

0

Cum

. AE

[m]

Time [hour] Figure 8.18. Instantaneous and net AE for PE averaging analysis; CH soil.

266

0 100 200 300 400 500 600 70010

3

104

105

106

Mat

ric

Suc

tion

[kP

a]

Time [hour]

Hourly Flux, x=0 mAverage Flux, x=0 mHourly Flux, x=0.07 mAverage Flux, x=0.07 m

Figure 8.19. Suction at depth vs. time for PE averaging analysis; CH soil.

103

104

105

Matric Suction [kPa]10 20 30 40 50 60

0

0.05

0.1

0.15

0.2

0.25

0.3

Dist

ance

from

sur

face

[m]


Initial ProfileHourly FluxAverage Flux

Figure 8.20. Suction profile at the end of the PE flux averaging analysis; CH soil.

267

8.4.2 Precipitation and Irrigation

8.4.2.1 1-D Desert Landscape

Both CH and SM-ML soils were used in the desert landscape flux simplification analysis.

The desert or low water use landscape consists of 2.3 m of PE and 0.2 m of rainfall annually.

The analysis with hourly discretized flux, HF, produced large matric suction variations at the soil

surface ranging from 190 000 kPa at the end of dry period in Jun to 10 kPa after a precipitation

event for SM-ML soil and 20 kPa for CH soil. These suction swings are not present in the

average flux, AF, analysis as expected.

For CH, the soil surface suctions approach the values calculated with HF analysis

except for very shallow depth. Just below the surface, the soil response in terms of suction is

similar for both types of analysis as illustrated in Figure 8.21a. Figure 8.22a (suction variation

with depth at the end of year) further shows that the discrepancy between these two approaches

exists only in the initial 0.2 m of the profile. At larger depths the solutions are almost identical.

Similar soil response was observed for the SM-ML soil. A discrepancy in profiles due to

the HF fluctuations is observed to a depth of 0.2 m., Figure 8.22b. Both profiles merge with the

initial condition plot at about 1.3 m from the soil surface. In general, the AF overestimates the

cumulative water loss resulting in suction profile, which plot parallel and below the suction profile

obtained with the HF.

The cumulative flux, as calculated by the computer program for 1 m2 surface area, is

presented in Figure 8.23 for both HF and AF analyses. The domain accumulation is similar for

HF and AF runs, and approaches -0.0561 m and -0.0555 for CH soil HF and AF respectively at

the end of one year. For SM-ML soil the domain accumulation is -0.0457 and -0.0494 for HF and

AF respectively. This helps explain why the results for CH soil obtained with both approaches

produce similar results and why a small discrepancy is observed in SM-ML soil. Although

surface runoff boundary condition was utilized for the desert landscape flux (i.e. well-

graded/sloped soil surface), the surface flux conditions are such that essentially no runoff

occurred for either hourly or monthly averaged flux steps.

268

a)

Mat

ric

Suc

tion

[kP

a]

Time [day]

0 50 100 150 200 250 300 35010

1

102

103

104

105

106

Hourly Flux, x=0 mAverage Flux, x=0 mHourly Flux, x=0.1 mAverage Flux, x=0.1 mHourly Flux, x=0.2 mAverage Flux, x=0.2 m

b)

Mat

ric

Suc

tion

[kP

a]

Time [day]

0 50 100 150 200 250 300 350

101

102

103

104

105

106

Hourly Flux, x=0mAverage Flux, x=0mHourly Flux, x=0.5mAverage Flux, x=0.5mHourly Flux, x=1.0mAverage Flux, x=1.0m

Figure 8.21. Suction at depth vs. time for desert landscape analysis, a) CH, b) SM-ML.

269

a)

103

104

105

Matric Suction [kPa]0 10 20 30 40 50 60

0

0.2

0.4

0.6

0.8

1

Dist

ance

from

sur

face

[m]



b)

103

104

105

Matric Suction [kPa]0 10 20 30 40

0

0.5

1

1.5

2

Dis

tanc

e fr

om s

urfa

ce [m

]



Figure 8.22. Suction profile at the end of analysis for desert landscape analysis, a) CH, b) SM-ML.

270

a)

-5

0

5

10

15x 10

-4

Inst

. Flu

x [m

/h]

0 50 100 150 200 250 300 350-0.06

-0.04

-0.02

0

0.02

Dom

ain

Acc

umm

[m]

Time [day]


b)

-5

0

5

10

15

20x 10

-4

Inst

. Flu

x [m

/h]

0 50 100 150 200 250 300 350-0.06

-0.04

-0.02

0

0.02

Dom

ain

Acc

um. [

m]

Time [day]


Figure 8.23. Instantaneous and cumulative flux for desert landscape analysis, a) CH, b) SM-ML.

271

8.4.2.2 1-D Turf Landscape

Both CH and SM-ML soils were used in the turf landscape flux simplification analysis.

The turf landscape consists of 1.16-m of PE, 0.2-m of precipitation and 2.37-m of irrigation per

year. The hourly discretized flux was applied daily per half an hour during the winter regiment

and per one hour during the summer irrigation schedule. The analysis with hourly discretized

flux, HF, produced large matric suction variations at the soil surface ranging from 50 000 kPa at

the end of April to 5 kPa after precipitation or irrigation event at the soil surface of SM-ML soil

and between 50 000 kPa to about 0 kPa for CH soil as illustrated in Figure 8.24.

The results obtained with monthly average flux are very different from the results

obtained with hourly discretized conditions for both analysed soils. For the average monthly flux

and CH soil, the surface matric suction decreases from the initial condition to near 0 kPa,

increases to about 200 kPa in April and goes back to 1 kPa after April, where it remains

essentially constant. In contrast, the surface suction varies widely for the HF input. The depth of

influence obtained with AF is 2.5-m, compared to 1.9-m with HF, Figure 8.25a, and the AF

results in higher degree of saturation. The increased depth of wetting is associated with larger

amount of water absorbed in the AF scheme, Figure 8.26a. After one year, the domain

accumulation is 0.33-m for AF and 0.11-m for HF. The difference is attributed to runoff and

reduced time for infiltration in the HF analyses.

Similarly, the AF analysis overestimates the depth and degree of wetting in SM-ML soil.

The advective character of this material results in a very sharp wetting front, with suctions behind

the front maintained at about 10kPa throughout the analysis for both flux scenarios. The depth

of influence obtained with AF is 7.1-m, compared to 5.6-m with HF, Figure 8.25b. The difference

is attributed to surface runoff in HF, which is completely nonexistent in the AF analysis. It is

reflected in the domain accumulation of 0.93 for HF and 1.34 for AF analyses as illustrated in

Figure 8.26b. In conclusion flux simplification through averaging for turf landscape analysis is

not recommended since the depth and magnitude of wetting are overestimated.

272

a)

Mat

ric

Suc

tion

[kP

a]

Time [day]

0 50 100 150 200 250 300 35010

-2

10-1

100

101

102

103

104

105

Hourly Flux, x=0mAverage Flux, x=0mHourly Flux, x=1mAverage Flux, x=1mHourly Flux, x=2mAverage Flux, x=2m

b)

Mat

ric S

uctio

n [k

Pa]

Time [day]

0 50 100 150 200 250 300 35010

0

101

102

103

104

105

Hourly Flux, x=0mAverage Flux, x=0mHourly Flux, x=3mAverage Flux, x=3m

Figure 8.24. Suction at depth vs. time for turf landscape analysis; a)CH, and b) SM-ML.

273

a)

10-1

100

101

102

103

104

Matric Suction [kPa]40 50 60 70 80 90 100

0

0.5

1

1.5

2

2.5

3

3.5

4

Dist

ance

from

sur

face

[m]



b)

100

101

102

103

104

Matric Suction [kPa]

20 30 40 50 60 70 80

0

1

2

3

4

5

6

7

8

Dis

tanc

e fro

m s

urfa

ce [m

]



Figure 8.25. Suction profile at the end of analysis for turf landscape analysis; a) CH, and b) SM-ML.

274

a)

Inst

. Flu

x [m

/h]

0

5

10

15x 10

-3

0 50 100 150 200 250 300 3500

0.1

0.2

0.3

0.4

Dom

ain

Acc

um. [

m]

Time [day]


b)

Inst

. Flu

x [m

/h]

-3

0

3

6

9

12x 10

-3

0 50 100 150 200 250 300 3500

0.5

1

1.5

Dom

ain

Acc

um. [

m]

Time [day]


Figure 8.26. Instantaneous and cumulative flux for turf landscape analysis; a) CH, and b) SM-ML.

277

Figure 8.28. Variation of matric suction at the soil surface with time for 2D turf landscape analysis; a) HF, and b) average absorbed flux from 1D analysis.

a)

b)

Edge

of S

lab

278

Figure 8.29. Variation of suction with depth and time below the edge of the slab-on-grade for 2D turf landscape analysis; a) HF, and b) average absorbed flux from 1D analysis.

Table 8.13. HF to AF ratio of distance to 1000 kPa. Distance to 1000 kPa Ratio Horizontal distance measured inward from the edge of the slab 1.7 Vertical distance below the edge of the slab 1.3 Vertical distance in side yard 1.1

a)

b)

279

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.90 20 40 60 80 100 120

Time [day]

Dist

ance

[m]

Horiz. Dist to 1000kPa, HF Horiz. Dist to 1000kPa, AF

Vert. Dist to 1000kPa below Edge of Slab, HF Vert. Dist to 1000kPa below Edge of Slab, AF

Vert. Dist to 1000kPa 1-m aw ay from Slab,HF Vert. Dist to 1000kPa 1-m aw ay from Slab,AF

Figure 8.30. Comparison of distance of influence to 1000kPa obtained with HF and average absorbed flux obtained from 1D analysis.

8.4.3 Key Findings of Flux Simplification

The flux simplification analysis of potential evaporation revealed that the averaging of

PE produces adequate approximation of soil response. Similarly, the analysis of desert

landscape revealed that simplification of precipitation data by averaging produces adequate

approximation of soil behavior. This finding is applicable to flux conditions dominated by

evaporation. However, the flux simplification scheme, wherein averaging of flux over each

month is employed, is not appropriate for irrigation or precipitation dominated scenarios such as

the turf landscape example of this mini-study. The averaging overestimates both the degree of

saturation and the depth of wetting for cases where excessive surface runoff occurs. On the

other hand, if the amount of surface runoff is known or can be estimated, flux averaging

developed with the absorbed water provides adequate soil response in 1-D analysis. In the slab-

on-grade 2-D scenario, flux averaging with absorbable water (determined from HF 1-D analysis)

underestimates both degree of saturation and distance of wetting. This is a result of using 1-D

280

runoff estimates for a 2-D analysis, which is clearly not appropriate and leads to error as shown

herein.

It is recommended that the effect of simplification of surface flux conditions be carefully

considered on a case-by-cases basis. While there is a high price to pay with regard to run-times

for detailed modeling of actual surface flux conditions, it is clear that there are many important

problems for which highly detailed flux input is required to achieve reasonable simulation of field

conditions. For the purpose of this research study, PE averaging is employed while precipitation

and irrigation are modeled on hourly bases.

8.5 Depth of Influence and Suction Variation with Depth

8.5.1 Desert Landscape – Dry IC

Both CH and SM-ML soils were used in 1D, six year long desert landscape analysis.

Both soils were observed to experience large matric suction variations at the soil surface ranging

from 193 000 kPa at the end of dry period in Jun to 10 kPa after a precipitation event in January

for SM-ML soil and 62 kPa after precipitation in March for CH soil. Figure 8.31 illustrates very

shallow moisture infiltration depths for both soils. The wetting front (distance to 1000 kPa matric

suction) is limited to 0.025-m for CH soil and 0.04-m for SM-ML soil, while the progression of

drying front continuously increases in the modeled time period for both soils suggesting that

equilibrium conditions have not been reached yet. The rate of domain moisture loss significantly

decreases after the first 2 years of analysis and then varies linearly with time as illustrated in

Figure 8.32.

The progression of both wetting and drying fronts is very well illustrated in Figure 8.33.

The drying front reaches approximate depth of 2.5-m in SM-ML soil and only about 1.6-m in CH

soil. The difference is attributed to larger volume of water retained in CH soil. On the other

hand, for both soils the wetting front occurring after precipitation events reaches approximately

the same depth each time. The progression of the wetting front with precipitation for the CH soil

is shown in greater detail in Figure 8.35. Initially, the moisture flow is characterised by a very

281

sharp transition from moist to dry soil conditions. With time the wetting front takes on diffusive

characteristics with surface suctions reaching only 70 kPa, which approximately corresponds to

80% degree of saturation for this soil, based on the drying curve SWCC. Overall, the deviation

of wetting and drying suction profiles within a precipitation period occurs only to a depth of 0.08-

m for the CH soil.

a)

b)

Figure 8.31. Suction variation with depth and time, a) CH, b) SM-ML.

282

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0.00

0 1 2 3 4 5 6Time [year]

Flux

[m/y

ear]

SM-ML CH

Figure 8.32. Net flux per year for CH and SM-ML soils.

0

0.5

1

1.5

2

2.5

30 1 2 3 4 5 6

Time [year]

Dept

h fro

m s

urfa

ce [m

]

SM-ML (2000kPa)SM-ML (1000kPa, Dec.)CH (2000kPa)CH (1000kPa, Dec.)

Figure 8.33. Progression of wetting and drying fronts.

Desert landscape modeling on range of typical Arizona soil properties illustrates that

under desert preconstruction conditions, maintained desert landscape and properly maintained

grading and drainage conditions around residential property, issues associated with moisture

migration are essentially non-existent. Suction variation with depth due to precipitation events is

very shallow and never exceeds 0.05-m. The seasonal suction variation with depth is also very

283

shallow. For the CH soil it is observed to a depth of 0.4-m and 0.6-m for SM-ML soil as

illustrated in Figure 8.34.

a)

101

102

103

104

105


0 20 40 60 80 100

0

0.5

1

1.5

2

2.5

3

3.5

4

Dis

tanc

e fro

m s

urfa

ce [m

]


Initial ProfileYear 6 - JunYear 6 - Wettest Cond. (March)

b)

101

102

103

104

105


0 10 20 30 40 50 60 70 80

0

0.5

1

1.5

2

2.5

3

3.5

4

Dis

tanc

e fro

m s

urfa

ce [m

]


Initial ProfileYear6-Jun.Year6-Wettest Cond. (Jan.)

Figure 8.34. Profile at wettest and driest conditions in year 6, a) CH, b) SM-ML.

284

101

102

103

104

105


0 20 40 60 80 100

0

0.05

0.1

0.15

0.2

Dis

tanc

e fro

m s

urfa

ce [m

]


Initial ProfileBefore Prec. in Nov.After first rain in Nov.After all Rain in Nov.

Figure 8.35. Progression of wetting front for CH soil due to rainfall.

8.5.2 Desert Landscape – Wet IC

The influence of initial conditions on soil response to desert landscape was considered

on the CH soil only. The suction profile obtained after 34 years of turf landscape analysis

(presented below in section 8.5.4.) was used as initial conditions. The matric suction gradually

increases from 80 kPa at the soil surface to 293 kPa at the depth of 5-m and 1195 kPa at 10-m.

This modelling scenario represents either the existence of turf landscape for prolonged period of

time followed by change in landscape scheme or abandoned agricultural activity for residential

development using desert landscape.

As in the previous analysis, the matric suction at the soil surface undergoes significant

variations from 180 000 kPa at the end of Jun to about 73 kPa during precipitation after summer.

Prior to summer the minimum matric suction of 0.2 kPa was observed. The moist initial

conditions resulted in very shallow drying front. In the first year of analysis, the short-term drying

front does not exceed the depth of 0.17-m (depth to 2000 kPa), as illustrated in Figure 8.36. In

this scenario, the monotonic moisture loss with depth bears more engineering significance than

285

in the desert pre-construction conditions considered previously. Figure 8.37 shows that beyond

the depth of seasonal moisture variation, which is less than 0.2-m, an increase in matric suction

up to 100% is observed to a depth of 1.5-m from the soil surface. This soil response has

consequences on soil volume change.

Figure 8.36. Suction variation with time and depth for CH soil, desert landscape with

moist IC.

10

110

210

310

410

5


0 20 40 60 80 100

0

0.5

1

1.5

2

2.5

3

Dis

tanc

e fro

m s

urfa

ce [m

]


Initial ProfileJun-driest conditionDecember after rain

Figure 8.37. Profile at wettest and driest conditions for CH soil, desert landscape with

moist IC.

286

The wetting front due to precipitation is very shallow and does not exceed 0.024-m

(depth to 1000 kPa). In clayey material, the absorbed water very quickly diffuses with depth.

which results in a characteristic plum matric suction distribution with time and depth as illustrated

for December precipitation in Figure 8.38. The large PE and low RH typical to Arizona

environmental conditions result in loss of all the absorbed water within a few days of the

precipitation.

Figure 8.38. Suction variation with time and depth for CH soil zoomed in on

precipitation in December, desert landscape with moist IC.

8.5.3 Desert Landscape - Ponding near Structure

Frequently, lot drainage of a single family Arizona dwelling consists of a properly

designed swale. The roof runoff is designed to flow into the side yard swale, which provides the

water with an access into the street and off the property. This type of drainage system is

expected to perform very well under Arizona environmental conditions, removing the need for

more expensive gutter system. Practicing engineers and building professionals report that the

designed swale drainage system is often modified by the homeowner who installs sidewalks and

287

planters in the vicinity of the foundation. This type of lot modification has a potential of trapping

the roof runoff on site and developing areas of potential water ponding.

A numerical simulation was performed to access the impact of impeded roof runoff

drainage on moisture flow through unsaturated soil in 1-D domain on two soil types, namely SM-

ML and CH. The amount of roof runoff was calculated based on an assumed 10-meter wide

total roof area. The ponding scenario was modeled by applying desert flux boundary conditions

without runoff option and with precipitation magnitude increased by a factor of 6. The initial

conditions were obtained from 6th year of desert landscape analysis for the CH soil and 5th year

for the SM-ML soil, discussed in section 8.5.1. Figure 8.39 illustrates the migration of moisture

with depth and time. The initially dry soil conditions at depth are quickly eliminated by the

progressing wetting front in both soil profiles. Due to ponding, the CH soil has the potential of

becoming essentially completely saturated up to an approximate depth of 0.8-m (based on the

assumed drying SWCC). Beyond this depth, the suctions increase gradually up to the initial soil

conditions, see Figure 8.40. The maximum depth of wetting front (distance to 1000 kPa) was

observed to occur in December at the depth of 1.9-m.

In general, the selection of minimum suction profile is hard to identify due to plum like

moisture distribution with depth and time as illustrated for SM-ML soil in Figure 8.41. Figure

8.40b gives the suction distribution for SM-ML soil shortly after precipitation event. In this figure

the minimum surface suction of 4.5 kPa increases to about 8 kPa at the depth of 0.8-m from the

soil surface, however, due to diffusion, the suction of 8 kPa is observed down to a depth of 1.8-m

sometime after the precipitation. The SM-ML soil is characterised by sharp wetting fronts and

very moist soil conditions behind the front with approximate suctions of 10 kPa. The maximum

depth of influence (depth to 1000kPa) was observed to occur in December at the depth of 3.2-m.

The drying front for both soils is very shallow with maximum depth of influence in Jun.

The depth to 2000 kPa is 0.126-m for the CH soil and 0.194-m for the SM-ML soil. The

modeling of ponding scenario illustrated that although the PE exceeds the contribution of water

288

from roof runoff, under poor drainage conditions significant moisture migration within typical

Arizona soils should be anticipated.

b)

Figure 8.39. Suction variation with depth and time, a) CH, b) SM-ML.

289

a)

10-3

10-1

101

103

105


0 20 40 60 80 100

0

1

2

3

4

5

Dis

tanc

e fro

m s

urfa

ce [m

]


IC-End of Year 6, Desert FluxDriest Cond. - JunWettest Cond. (Dec.)

b)

100

101

102

103

104

105


0 20 40 60 80 100

0

1

2

3

4

5

Dis

tanc

e fro

m s

urfa

ce [m

]


IC-End of Year 5, Desert FluxDriest Cond. - JunWettest Cond. - Dec.

Figure 8.40. Profile at wettest and driest conditions, a) CH, b) SM-ML.

290

Figure 8.41. SM-ML soil, plum like distribution of moisture with depth and time to

maximum depth of 1.8 m in November.

8.5.4 Turf Landscape – Dry IC

Both CH and SM-ML soils were used in 1-D, turf landscape analysis, where precipitation

and irrigation approximately exceed PE by a factor of 2.2. Long-term moisture migration in CH

soil was analysed (34 years), while short-term (only 2 years) of simulation with SM-ML were

performed. Both soils were observed to experience large matric suction variations at the soil

surface ranging from 37 700 kPa at the end of dry period in Jun to 0.001 kPa after a precipitation

event for the CH soil and 42 600 kPa at the end of dry period in April to 4.6 kPa for SM-ML soil.

The progression of moisture through the soil should be considered on three time scales,

daily, seasonal and long-term monotonic suction change dictated by annually dominating surface

fluxes. Figure 8.42 illustrates very shallow moisture gain or loss with depth for CH soils due to

short-term daily precipitation, irrigation and evaporation events. The short-term cyclic depth of

moisture variation is better illustrated in Figure 8.45, where the suction profiles obtained before

and after irrigation events diverge only in the upper 0.01-m for both types of soil. The influence

of PE (depth to 2000 kPa) is limited to shallow depths and does not exceed 0.004-m for CH soil

291

and 0.02-m for SM-ML soil. The seasonal suction variation is limited to 1.2-m for CH soil and

0.5-m for SM-ML soil as illustrated in Figure 8.46. Overall, the excessive irrigation results in a

monotonic progression of wetting front in both soils. Within the first year of the analysis the

maximum depth of wetting front is 1.07-m for CH soil (Figure 8.42) and 4.6-m for SM-ML soil

(Figure 8.43). The depth of influence due to monotonic moisture migration continues to increase

after 34 years of CH soil analysis and reaches almost 9-m. After 2 years of the SM-ML soil

analysis the depth of influence reached 7-m and also continues to increase.

a)

b)

Figure 8.42. Suction variation with depth and time for CH soil, a) surface detail in 3-D , b) 2-D plot.

292

Figure 8.43. Suction variation with depth and time for SM-ML.

0

1

2

3

4

5

6

7

8

9

100 5 10 15 20 25 30 35

Time [year]

Dept

h fro

m s

urfa

ce [m

]

SM-ML (2000kPa)SM-ML (1000kPa)CH (2000kPa)CH (1000kPa)

Figure 8.44. Depth of Influence for CH and SM-ML Soils.

293

a)

b)

101

102

103

104

105


0 20 40 60 80 100

0

0.01

0.02

0.03

0.04

0.05

Dis

tanc

e fro

m s

urfa

ce [m

]


Initial ProfileBefore Irrig. (April)After Irrig. (April)

Figure 8.45. Depth of influence due to irrigation a) CH (year 1), b) SM-ML (year 1).

294

a)

100

101

102

103

104


0 20 40 60 80 100

0

1

2

3

4

5

6

Dis

tanc

e fro

m s

urfa

ce [m

]


Initial ProfileWettest Cond. - March.Driest Cond. - Jun

b)

100

101

102

103

104

105


0 20 40 60 80 100

0

1

2

3

4

5

6

Dis

tanc

e fro

m s

urfa

ce [m

]


Initial ProfileDriest Cond. - AprilWettest Cond. - Dec.

Figure 8.46. Profile at wettest and driest conditions, a) CH (year 6), b) SM-ML (year 1).

Additionally, the soil response due to more appropriate irrigation was considered for both

soils. In this scenario, the magnitude of precipitation and irrigation is approximately equal to 1.3

PE. The short-term daily moisture migration has very similar pattern to the soil response

obtained with the excessive irrigation described above. The surface suctions were observed to

295

vary between 0.005 kPa after irrigation or precipitation event to 75770 kPa at the end of April for

CH soil. Similarly, suction variation between 5.0 kPa and 86160 kPa at the end of April occurs

for the SM-ML soil. The depth of seasonal moisture influence is approximately 0.5-m for both

soils (Figure 8.47), while the monotonic wetting front is 1.0-m for CH soil and 1.7-m for SM-ML

soil on the end of the first year as illustrated in Figure 8.49.

a)

100

101

102

103

104

105


0 20 40 60 80 100

0

0.5

1

1.5

2

2.5

3

Dis

tanc

e fro

m s

urfa

ce [m

]


Initial ProfileWettest Cond. - March.Driest Cond. - April

b)

100

101

102

103

104

105


0 20 40 60 80 100

0

0.5

1

1.5

2

2.5

3

Dis

tanc

e fro

m s

urfa

ce [m

]



Figure 8.47. Profile at wettest and driest conditions, a) CH, b) SM-ML.

296

8.5.5 Turf Landscape – Wet IC

The influence of initial conditions on moisture migration through soil was considered on

CH profile with precipitation and irrigation equal to 1.3PE. This scenario illustrates the effect of

proper irrigation on previously agricultural land or change in irrigation magnitude. The initial

suction conditions were obtained from the 34-year turf landscape analysis, where the applied

flux into the soil profile was equal to 2.2PE. In general, the daily moisture migration exhibited

similar pattern as the overwatered turf landscape scenario with large surface suction swings

between 0.0001 kPa after irrigation or precipitation event to 57278 kPa at the end of Jun. The

seasonal moisture migration occurs to an approximate depth of 0.5-m. In this modelling

scenario, the initial suction conditions are smaller than 1000 kPa, hence the identification of the

depth of influence as the depth to 1000 kPa is inappropriate. The moisture loss due to PE

(depth to 2000 kPa) is limited to 0.005-m, which is illustrated in Figure 8.48. The partial drying

with depth is very consequential on soil volume change behavior. Note that a 100% increase in

suction occurs to a depth of 0.5-m. The moist initial soil conditions will result in soil shrinkage as

the suction increases.

100

101

102

103

104

105


0 20 40 60 80 100

0

0.5

1

1.5

2

2.5

3

Dis

tanc

e fro

m s

urfa

ce [m

]


Initial ProfileWettest Cond. - March.Driest Cond. - Jun

Figure 8.48. Depth of influence due to irrigation for CH soil and moist IC.

297

8.5.6 Key Findings of 1D Analysis

The objective of 1D modeling was to determine the depth of suction variation (wetting

and drying), at equilibrium or pseudo-equilibrium, for desert and turf landscapes for a range of

soils typical for Arizona geographic region. The modeling results were considered on three time

scales, daily, seasonal and monotonic moisture loss or gain. In general, it was found that the

daily suction fluctuations are limited to 5 cm from the soil surface independent of soil type and

type of analysis (i.e. desert or turf landscapes). The depth of wetting and drying front due to

seasonal moisture migration is summarized in Table 8.14, while the values of suction variation at

the soil surface are provided in Table 8.15. The wetting front (defined as the depth to 1000 kPa)

due to monotonic moisture migration is illustrated in Figure 8.49.

Table 8.14. Summary Table – Seasonal Depth of Influence; 1 Year Long Analysis.

Landscape Scenario

Depth to Suction [m] CH SM-ML

1000 kPa 2000 kPa 1000 kPa 2000 kPa Desert, IC1 0.025 0.67 0.04 1.030 Desert, IC2 0.024 0.17 Ponding, IC1 1.9 0.126 3.22 0.194 Turf, Irrig = 2.2PE, IC1 1.065 0.004 4.63 0.019 Turf, Irrig = 1.3PE, IC2 NA, IC<1000kPa 0.005 Turf, Irrig = 1.3PE, IC1(3) 0.600 0.047752 (1.68) (0.077) IC1 - const head=-153m, IC2 - after 34 years of turf landscape, IC3 - after 5 or 6 years of desert landscape.

Table 8.15. Summary Table – Seasonal Surface Suction; 1 Year Long Analysis.

Landscape Scenario

Surface Suction [kPa] (Saturation [%]) CH SM-ML

min max min max Desert, IC1 62.5015 191671 10 193262 Desert, IC2 73 180000 Ponding, IC1 0.001 206388 4.5 179463 Turf, Irrig = 2.2PE, IC1 0.001424 37725 4.6 42683 Turf, Irrig =1.3 PE, IC2 0.001 57278 Turf, Irrig =1.3 PE, IC1(3) 0.005 75770 (5) (86160) IC1 - const head=-153m, IC2 - after 34 years of turf landscape, IC3 - after 5 or 6 years of desert landscape.

298

0 1 2 3 4 5 60

5010

015

020

025

030

035

0Ti

me

[day

]

D

SM-M

L, D

eser

tSM

-ML

Dese

rt, P

ondi

ngSM

-ML,

Tur

f, Fl

ux=2

.2PE

SM-M

L, T

urf,

Flux

=1.3

PECH

, Des

ert

CH, D

eser

t, Po

ndin

gCH

, Tur

f, Fl

ux=2

.2PE

CH, T

urf,

Flux

=1.3

PE

Figu

re 8

.49.

M

onot

onic

Pro

gres

sion

of W

ettin

g Fr

ont.

299

A six-year long analysis was performed for desert landscape. The highest suctions at

the soil surface and at depth were found to occur in June while the lowest suctions were found to

occur at the end of March for the CH soil and the end of January for the SM-ML soil. The

analysis revealed that for desert landscape and a well-drained site the drying front continues to

increase after six years of analysis, however, the depth of influence of wetting (i.e. reduced

suction that would result in swell/edge lift) is only about 5 cm. Although the monotonic drying

front continues to increase, the seasonal moisture loss is limited to 0.7-m for the CH soil and

about 1-m for the SM-ML soil. The consequence on constructed facilities of moisture migration

through soil exposed to desert landscape and good drainage is insignificant. That is of course

true only for desert pre-construction conditions. Moist preconstruction conditions, resulting from

agriculture, for example, might be related to some shrinkage with depth. Up to 100% increase

(100 kPa to 200 kPa) in soil suction can be expected to a depth of 1.5-m from the soil surface.

The effect of poor drainage on progression of wetting and drying fronts was considered

next. When a site is characterized by poor drainage and the accumulation of the roof runoff

water can be expected, deep wetting fronts develop in both soil types; up to 1.9-m for the CH soil

and up to 3.2-m for the SM-ML soil. In this case, the drying front is very shallow and does not

exceed 20 cm. A soil/slab system built on desert pre-construction conditions and post-

construction conditions consisting of poor drainage will experience severe moisture migration

potentially resulting in significant soil volume increase and slab movement. This finding is

consistent with the forensic studies gathered to date in that desert landscape sites with poor

drainage seem to be susceptible to expansive soil damage in regions of high expansion potential

soils.

The seasonal moisture migration due to turf landscape is limited to 1-m for the CH soil

and 0.5-m for the SM-ML soil. The soil profile exposed to turf landscape should be expected to

experience continuous monotonic progression of wetting front. The CH soil was used in a 34-

year long study. The wetting front reached the approximate depth of 9-m and had not yet fully

300

attained equilibrium. Depending on the initial, pre-construction, conditions, the soil profile might

gain of loose moisture resulting in either soil swell or shrinkage.

8.6 Edge moisture Variation Distance Degree of Saturation

8.6.1 Desert Landscape

The CH soil was used in 2D desert landscape analysis to identify the seasonal

horizontal distance of moisture variation. Figure 8.50 illustrates that within the first year of

analysis, the depth of influence, both wetting and drying are limited to 10 cm from the edge of

the slab. Such shallow distance of influence has no consequence on the performance of

residential structures.

10

-1

101

103

105

Mat

ric S

uctio

n [k

Pa]

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.10

20

40

60

80

100

Deg

ree

of S

atur

atio

n [%

]

Distance from Edge of Slab [m]

Initial Cond.Wettest - MarchDriest - JunEnd of Year

Figure 8.50: Suction variation at the soil surface for CH soil and desert landscape

8.6.2 Turf Landscape

The CH soil was used in 2D turf landscape analysis to identify the seasonal and

monotonic horizontal distance of moisture variation. This modeling scenario was particularly

301

difficult to model therefore flux averaging was implemented. Section 8.4.2.3 describes the

performed flux averaging where results obtained with hourly discretized flux are compared to

results obtained with average flux over 123 days. The average flux was obtained from the

domain accumulation of 1D turf landscape analysis. Due to lateral moisture migration in the 2D

analysis, a discrepancy between these two methods (i.e. AF and HF) was observed. Correction

factors for the average flux analysis were identified and are given in Table 8.13. Uncorrected

average flux results are given in both Figure 8.51 and Figure 8.52.

Under turf landscape condition, seasonal moisture fluctuation up to 0.34-m should be

expected. The analysis illustrates that monotonic moisture migration starts to level off in the fifth

year of analysis and reaches horizontal distance of 2.2-m (corrected distance to 1000kPa). This

finding qualitatively matches literature review and forensic engineering observations, where slab

movement levels of in about 5th year post-construction.

10

1

102

103

104

Mat

ric S

uctio

n [k

Pa]

-2 -1.5 -1 -0.5 0 0.520

40

60

80

100

Deg

ree

of S

atur

atio

n [%

]

Distance [m]

Initial Cond.Wettest Cond. - January (Year 5)Driest Cond. - April (Year 5)

Figure 8.51. Suction variation at the soil surface for CH soil, 2D turf landscape, average

flux analysis.

302

0

0.5

1

1.5

2

2.5

30 1 2 3 4 5

Time [year]

Dist

ance

[m]

Horiz. Dist to 1000kPa

Vert. Dist to 1000kPa below Edge of SlabVert. Dist to 1000kPa 1-m away from Slab

Figure 8.52. Depth of influence: horizontal inwards the slab, vertical below the edge of

slab and vertical 1-m away from the edge at landscaped conditions; 2D turf landscape, average flux analysis.

Similar, the SM-ML soil was used in the identification of lateral moisture migration

through soil below a foundation due to turf landscape. Only 1.8 year was analysed with the

average absorbed flux, obtained from the domain accumulation of 1-D analysis. Based on the

numerical modeling results, it was observed that the lateral moisture migration levels off in the

second year of the analysis at the approximate distance of 1.5-m from the edge of the slab, as

illustrated in Figure 8.53. The magnitude of soil suction within the distance of moisture migration

is approximately 20 kPa. As expected, the lateral transition width between the wetting front and

the initial conditions, which is approximately 0.5-m, is much larger than the transition width

observed in the vertical direction. In highly permeable soils such as the SM-ML material

considered in this study, the vertical moisture flow is dominated by advection, while the lateral

mass transfer is mostly occurs due to diffusion.

The distance of seasonal moisture migration is insignificant for this type of soil and turf

landscape. Figure 8.54 illustrates that this distance is limited to approximately 20-cm. Directly

below the edge of the foundation, soil suctions were found to vary between 7 kPa and 100kPa,

which potentially is inconsequential on the soil/structure interaction.

303

Figure 8.53. Distance of lateral moisture migration through soil below a slab.

10

1

102

103

104

105

106

Mat

ric S

uctio

n [k

Pa]

-2 -1.5 -1 -0.5 0 0.5 1

20

40

60

80

100

Deg

ree

of S

atur

atio

n [%

]

Distance from the Edge of Slab [m]

Initial Cond.Wettest Cond. - Dec. (Year 1)Driest Cond. - April (Year 2)End of Analysis (Day 275 of year 2)

Figure 8.54. Suction variation at the soil surface for CH soil, 2D turf landscape, average

flux analysis.

Edge

of S

lab

304

8.7 Conclusions and Recommendations

Moisture flow through unsaturated soil is a complex modeling problem whose solution

requires large computational resources and a lot of available time. Towards the goal of

enhanced understanding of the matric suction variation within the soil profile, and the horizontal

and vertical distance of moisture penetration for residential construction, modeling efforts

utilizing current unsaturated soil mechanics theory and the latest developments in computer

programming geared towards the solution of the unsaturated flow were pursued. The results of

the analyses were used to better understand the influence of climatic conditions, drainage, and

landscape scheme on performance of residential structures constructed on expansive soils in

Arizona specific region.

The analyses were performed on two soils with low and medium expansion potential

typical of the Phoenix region. An appropriate control volume size was determined to be 10-

meters for one-dimensional analysis and 7-meter length by 5-meter depth for two-dimensional

problems with 5-meter long slab. In the analysis, an initial, equilibrium suction value of 1500 kPa

was used. This value was obtained through laboratory testing of insitu soil at depth. Landscape

professionals and government employees were surveyed in an effort to determine the

appropriate as well as the commonly applied irrigation patterns in the Valley; as a result two

dominant flux conditions were identified. They are turf landscaping, were daily one-hour long

irrigation is followed by potential evaporation as provided by Department of Agriculture, and

desert or “Xeriscape” landscaping where negligible amount of water is introduced to the soil

surface. The appropriate precipitation input was determined by performing a statistical analysis

of 24 years of precipitation data, where the data was obtained from NCDC. It was found that

average annual rainfall is 8.0 inches while the potential evaporation is 91 inches. The desert

landscape was modeled by applying average monthly precipitation per average number of rainy

days and average hourly rain duration and discretized on hourly bases. The rain events were

assumed to occur on the beginning of each month and were followed by potential evaporation,

as obtained from Arizona Department of Water Resources, US Weather Service.

305

The objective of 1D modeling was to determine the depth of suction variation (wetting

and drying), at equilibrium or pseudo-equilibrium, for desert and turf landscapes. A six-year long

analysis was performed for desert landscape. The highest suctions at the soil surface and at

depth were found to occur in June while the lowest suctions were found at the end of March for

the CH soil and January for the SM-ML soil. The analysis revealed that for desert landscape

and a well-drained site the seasonal suction variation is limited to about 0.5-m from the soil

surface, however, the depth of influence of wetting (i.e. reduced suction that would result in

swell/edge lift) is only about 10 cm. The monotonic drying front continues to move downwards

within the 6 years of analysis to a depth of 1.6-m in the CH profile and 2.5-m in the SM-ML

profile. Because the monotonic suction variation with depth occurs over a range of suctions that

do not correspond to soil volume change, the consequence on soil/slab system would be

expected to be insignificant. Findings from the 2-D desert flux modeling are consistent in that

they show significant suction variation only within about 0.1 m of horizontal distance measured

inward from the edge of the slab after one year of application of desert flux surface conditions.

Such shallow moisture migration has no consequence on soil/slab system. The conclusion from

this modeling study is that the depth of influence of surface flux (precipitation and evaporation) is

quite shallow, provided the drainage conditions at the site are good and provided recommended

desert irrigation practices are followed (i.e. negligible additional water is added to the site over

and above normal precipitation).

The same conclusion cannot be drawn, if the initial conditions are representative of

previously agricultural use of land. In this scenario, the seasonal moisture migration is very

shallow as well (within 20 cm) and inconsequential to the behavior of constructed facilities. The

monotonic moisture loss with depth is the governing mechanism resulting in 100% suction

increase to a depth of 1.5-m within the first year of analysis. The suction variation with depth

occurs over a range of suctions that do correspond to soil volume change, hence soil shrinkage

and slab movement should be anticipated.

306

The influence of wetting is quite different when desert landscape is combined with poor

site drainage. When roof runoff was allowed to concentrate at the soil surface after a rainfall

event, the depth of wetting became quite significant. The effect of poor drainage and roof runoff

water ponding near residential structure is the worst case scenario resulting in high soil

saturation (100% for the assumed SWCC) to a great depth of 0.8-m for the CH soil. The

suctions gradually increase with depth to the initial suction values with maximum 1.9-m depth of

influence (depth to 1000kPa). Similarly the SM-ML soil has a 3.2-m deep depth of influence.

The conclusion from this modeling study is that uncontrolled drainage and water ponding near

the foundation lead to significant suction reduction to great depths which will result in differential

soil swell and slab movement. This finding is consistent with soil/slab system behavior reported

by practicing engineers.

The turf landscape analyses were completed for 1-D conditions to assess the depth of

suction variation resulting from typical Phoenix-area lawn watering practices, and for

assumptions of good site drainage. These analyses show that the seasonal suction variation

occurs to a depth of 1.2-m for CH soil and 0.5-m for SM-ML soil. The excessive watering

scheme results in monotonic moisture increase with depth. After the first year of analysis the

depth of influence (depth to 1000 kPa) is 1.07-m for the CH soil and 4.6-m for the SM-ML soil.

The analysis with the CH soil was continued for 34 years. The wetting front continues to

increase and reaches the approximate depth of 9-m. Greater depths of influence would be

experienced with poor drainage conditions. Findings from the 2-D desert flux modeling show

significant seasonal suction variation only within about 0.34-m of horizontal distance measured

inward from the edge of the slab. The monotonic moisture migration occurs to a depth of 2.2-m

and levels of during 5th year of analysis. Again these findings are consistent with reported

soil/slab behavior by practitioners.

General conclusions from the modeling study include: (1) It is very important to

accurately model the flux boundary condition so that both duration and intensity of wetting and

evaporation episodes are accurately represented, (2) It is very important to accurately model

307

surface drainage conditions with respect to their influence on surface flux, (3) When equilibrium

is reached the net surface flux (water that actually goes into and out of the soil) is, on average,

zero. Steady state of equilibrium, in this context, does not mean constant rainfall or irrigation or

evaporation, but it does mean that the same pattern is repeated year after year – the pattern

does not have to be identical, just similar in important parameters such as inches of

rain/irrigation, site grading, duration of rain/irrigation event, actual evaporation. Drought and

unusually wet years will cause fluctuations about this equilibrium (mean), (4) At points beneath

the slab, and at some depth, these fluctuations are very small.

In arid and semi-arid regions, actual evaporation will exceed rainfall. Reasonable

landscaping will add some to the soil moisture state, but at a degree of wetting that is well below

saturation. The high soil storage capacity helps keep water from going to great depth. There is

a “Shut-off” suction that has been found to occur. Once total suction reaches about 3000 kPa

the actual evaporation begins to shut off as the kunsat goes very low, and in spite of high gradient,

flow is seriously restricted into very dry surface soils. Suction at the surface is further controlled

by the relative humidity of the air.

9 FIELD EVIDENCE OF WETTING/DRYING INDUCED DAMAGE The discussion presented about field evidence of wetting/drying induced damage was

made possible through the contribution of data from numerous Arizona based engineering

companies. The data on soil index and moisture conditions with depth under free field

conditions was used in the identification of the depth of wetting, the depth of active zone and

equilibrium suction at depth. The data on soil index and moisture conditions with depth under

slab-on-grade foundations were used in the identification of saturation and suction conditions

below residential structures. The spatial distribution of the data was further used in the

development of the updated swell potential map illustrated in Chapter 5. The map together with

the collected soil index properties were used in the identification of forensic investigation

incidence to soil type. Additionally, the forensic investigation data formed the bases for

identification of sources of suction change related distress, types of slab deformation, magnitude

of relative slab differential and impact of landscape and drainage to distress magnitude.

9.1 Depth of Wetting and Depth of Active Zone

The local community of geotechnical engineers was solicited for information on

moisture, dry density, soil classification and index properties data with depth. The information

from 575 borings was compiled. The data were group based on the soil classification, CH, GC,

CL, SC and low plasticity or NP soils (SM, SW, ML, SP, GM and GP). Note that only visual soil

classification was performed on many of the soils. The data was further subdivided based on

depth. The information was used in the identification of average degree of saturation, range of

saturation, and corresponding average wPI and average γd. When insignificant variability in

terms of degree of saturation beyond the depth of 10’ was observed, the values obtained below

this depth were averaged and then used in the estimation of equilibrium matric suction.

An empirical method of equilibrium matric suction determination was developed based

on laboratory obtained SWCCs, insitu matric suction and saturation measurement obtained

below residential foundations located in Phoenix Valley (discussed in Chapter 4 and presented

in Appendix B). The need for new methodology is rooted in SWCC variability due to 1)

309

hysteresis; in general, it is unknown whether the equilibrium point lies on the drying, wetting or

scanning path. The measured one-point suctions obtained from below residential foundations in

the Phoenix region almost always did plot below the drying curve, indicating scanning curve

behavior. Most SWCC estimation methodologies were developed for the drying path, therefore

one should anticipate an error up to one order of magnitude in the estimated matric suction,

expressed in kPa; 2) dry density; the sensitivity of SWCC to dry density was identified during

laboratory testing. Figure 9.1 illustrates SWCCs with up to one order of matric suction

magnitude difference between them for the same saturation level. The curves were developed

on undisturbed soil samples obtained from consecutive depths with very similar soil index

properties and different initial dry density values. Similarly, Figure 9.2 presents SWCCs

obtained on recompacted specimens. Again, a difference of up to one order of matric suction

magnitude in kPa was observed. Typically, the available SWCC estimation methodologies do

not include the contribution of dry density, hence it is unknown how is the resulting suction

estimate effected; and 3) soil structure (i.e. undisturbed vs. compacted soil); the majority of

SWCC estimation methods were developed based on results obtained from recompacted

specimens. The soil recompaction homogenizes the soil structure by destroying preferential

flow paths and exposing more clay particles to water absorption. As a result, recompacted soils

are capable of retaining higher water content per the same suction when compared to an

undisturbed specimen, or in other words, the SWCC of recompacted soil has characteristics of a

soil with higher wPI (weighted Plasticity Index; a product of PI and the percent passing US sieve

#200 expressed as a decimal). Due to these challenges, the estimate of equilibrium suction at

depth for Arizona climatic and soil conditions was based on SWCCs developed with the One-

Point Method (see Appendix C) on undisturbed, insitu samples extruded from beneath

residential foundations (i.e. equilibrium conditions have been reached), hence matching the

model conditions to the prediction scenario and reducing the uncertainty associated with the

hysteresis (measured data are on scanning curve), dry density (the measured data are in a dry

310

density range common to the region) and soil structure (the measured data represent insitu,

undisturbed conditions).

0

20

40

60

80

100

0.01 0.1 1 10 100 1000 10000 100000 1000000


Deg

ree

of S

atur

atio

n [%

]

Depth [in] wPI Dry Unit Weight [pcf] 8 9.4 11910 9.4 105 30 10.9 11644 10.9 110 50 2.2 10154 2.2 93 72 3.2 99Suction Identification Curve

Figure 9.1. SWCCs and Equilibrium Conditions below Residential Foundation for Site

#4; Insitu, Undisturbed Soil Testing; Equilibrium Suction Identification Curve.

0

10

20

30

40

50

60

70

80

90

100

0 1 10 100 1000Matric Suction [kPa]

Satu

ratio

n [%

]

dry unit weight = 106 pcf

dry unit weight = 80pcf

Figure 9.2. SWCC dependence on dry density; Reconstructed Soil Testing on CL with

LL=29, PI=12, and P200=63%.

311

Analysis of the laboratory data revealed that the equilibrium suction is a function of soil

index properties, which was previously reported by Perera (2003). In general, as the wPI

increases, the equilibrium suction and saturation increase. For all sites, a straight line could be

drawn through the points as illustrated in Figure 9.1 (note that SWCC is on a semi-log scale).

This line is referred to as the Suction Identification Curve, which was found to have a matric

suction range over one to three orders of magnitude. The range depends on soil index

properties and the starting matric suction value of the Suction Identification Curve. The matric

suction range increases as the wPI decreases or as the starting point on the Suction

Identification Curve decreases; see Figure 9.3.

y = -0.728x + 3.015R2 = 0.4553

0

1

2

3

4

0 1 2 3 4Starting Point of Curve, log(Suction) [kPa]

Cur

ve R

ange

log(

Suct

ion)

[kPa

]

Figure 9.3. Suction Range of the Suction Identification Curve.

Based on the findings above, an empirical model was developed in the following way:

1. The laboratory obtained SWCCs were group and plotted based on the soil classification,

CH, CL, SC and SM.

2. The equilibrium degree of saturation was identified from geotechnical data per each soil

category and each field condition (i.e. undeveloped desert and agricultural land).

312

3. The suction Identification Curve was constructed in such a way as to pass through the

degree of saturation identified in (2) and the center of the family of curves developed in

(1). The corresponding matric suction was read off. It represents the average matric

suction per the soil classification under identified environmental conditions.

4. The minimum and maximum matric suctions were read off at the points where the

Suction Identification Curve crosses the outer most and the inner most SWCCs. These

suction values usually correspond very well with the identified through range of degree

of saturation from the field data.

The developed plots are illustrated in Figure 9.4 through Figure 9.7. Additionally, based

on the average wPI, the Fredlund and Xing fit for wetting and drying paths are plotted. In all

considered scenarios, these two curves plotted below and above the identified average

equilibrium condition. This indicates that the implemented methodology estimated suction on the

scanning curve, as expected.

313

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110

100

1000

1000

010

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1000

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Suct

ion

[kPa

]

S

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124

32 9

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118

29 8

824

109

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314

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7.6

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7.9

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8.5

113

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8.8

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8.8

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8.9

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316

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soil

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318

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319

The analysis of field data revealed that the degree of saturation with depth remains

approximately constant for all soil types under undeveloped desert conditions. The range of

values observed varies between 30% for low plasticity soils to about 70% for fat clays as

provided in Table 9.1. This data suggests that under undeveloped desert conditions the depth of

active zone is very shallow. Based on numerical modeling presented in Chapter 8, the depth of

active zone and the depth of wetting are limited to the upper one meter under natural climatic

conditions. The available field data is not discretized enough to verify this finding, however the

lack of variation in the soil saturation with depth suggests as much.

Only one value of average matric suction was calculated per each soil classification. For

this purpose the average saturation and average wPI beyond the depth of 10’ was used. An

average equilibrium suction of 2550 kPa was identified for CH soil, about 5000 kPa for CL and

SC and approximately 500 kPa for low plasticity or NP material. Under undeveloped desert

conditions it is possible to obtain suctions as small as 230 kPa (SM soil) or as large as 18 000

kPa (SC soil).

A similar analysis was performed on soil profiles obtained from agricultural land or land

used for agriculture in recent months prior to the soil testing. It was determined that the degree

of saturation increases with depth from about 40% (SM soil), to 50% (CL and SC) within the

upper 10’ to a range from 46% (SM) to 70% (SC and CL) at depth. (Note that limited data was

available for CH soils and no data below 5'. The average surficial degree of saturation for CH

soil was found to be about 86%). The data suggest moisture accumulation beyond the depth of

10’. This data, presented in Table 9.2, further provides evidence that the depth of wetting

exceed 15’ under moist surface flux conditions, while the evaporative fluxes have consequence

on the soil moisture in the upper 10’. This finding supports the results presented in Chapter 8,

where the depth of wetting of CH soil under excessively irrigated turf landscape was found to

reach 9-m (27’) after 34 years of analysis.

The average equilibrium matric suction for all soils was identified beyond the depth of

10’. Agricultural use of land leads to decreased suction at depth for all types of soil found in

320

Arizona to a range between 220 kPa for SM soils to approximately 500 kPa for CL soils. The

maximum estimated suction value does not exceed 1300 kPa for CL soil. On the other hand, it

is possible to obtain suctions as small as 70 kPa (SC soil).

Table 9.1. Saturation and Suction Variation with Depth for Undeveloped Desert.

Average Degree of Saturation [%]

Count 0'-2' 2'-5' 5'-10' 10'-15' 15'-20' 20'-30' >30' CH 11 69.1 61.1 68.5 70.8 GC 15 45.1 29.5 36.7 37 27 18 CL 72 45.5 40.7 44.7 40.5 35.1 36.8 57.1 SC 111 39.5 33.3 44.0 39.2 38.7 35.0 32.9 SM, ML, SP 135 30.4 38.5 37.8 26.3 37.3 29.7 40.1

Range of Degree of Saturation [%]

Count 0'-2' 2'-5' 5'-10' 10'-15' 15'-20' 20'-30' >30' CH 11 62-76 50-81 68-68 66-76 GC 15 38-57 17-41 36-36 25-50 23-31 18-18 CL 72 25-71 12-80 19-80 23-69 25-65 19-72 25-85 SC 111 11-92 12-85 21-95 15-57 17-84 15-65 18-86 SM, ML, SP 135 10-61 6-93 10-81 10-50 17-64 16-45 9-86

Average wPI

Count 0'-2' 2'-5' 5'-10' 10'-15' 15'-20' 20'-30' >30' CH 29.8 27.9 23.3 21.2 GC 2 6.8 2.6 CL 27 6.3 8.3 9.1 8.3 6.9 14.9 SC 44 3.5 4.9 4.3 6.7 10.4 9.1 SM, ML, SP NA NA NA NA NA NA NA NA

Average γd [pcf]

Count 0'-2' 2'-5' 5'-10' 10'-15' 15'-20' 20'-30' >30' CH 111.1 103.4 GC 15 104.0 108.3 108.6 115.1 98.8 97.6 CL 75 98.7 98.6 100.2 95.1 100.7 99.3 103.0 SC 112 107.1 106.4 106.7 108.2 100.4 104.1 101.3 SM, ML, SP 135 111.6 105.7 106.3 105.8 108.7 110.4 106.7

Equilibrium Conditions at Depth

S [%] Average Suction Min. Suction Max. Suction [%] [kPa] [kPa] [kPa]

CH 69 2550 1000 4580 CL 42 5200 2800 10 000 SC 36 4900 2100 18 000 SM, ML, SP 32 470 230 1200

321

Table 9.2. Saturation and Suction Variation with Depth for Agricultural Land.

Soil Classif.

Average Degree of Saturation [%], Agricultural Land

Count 0'-2' 2'-5' 5'-10' 10'-15' 15'-20' 20'-30' >30' CH 6 82 86 GC 0 CL 92 50.0 56.7 49.5 73.7 63.1 SC 62 46.6 51.6 47.6 68.7 71.6 SM, ML, SP 77 37.0 39.0 42.4 46.8 21.4 30.0

Soil Classif.

Range of Degree of Saturation [%]

Count 0'-2' 2'-5' 5'-10' 10'-15' 15'-20' 20'-30' >30' CH 6 82-82 78-86 GC 0 CL 92 14-97 22-92 17-87 21-100 43-84 SC 62 25-90 15-99 24-84 45-97 52-88 SM, ML, SP 77 7-86 12-82 10-91 14-92 16-33 8-92

Soil Classif.

Average wPI

Count 0'-2' 2'-5' 5'-10' 10'-15' 15'-20' 20'-30' >30' CH 5 31.7 30.5 GC 0 CL 32 10.2 9.7 11.0 11.8 SC 17 6.6 4.4 2.6 10.6 SM, ML, SP NA NA NA NA NA NA NA NA

Soil Classif.

Average γd [pcf]

Count 0'-2' 2'-5' 5'-10' 10'-15' 15'-20' 20'-30' >30' CH 6 96.3 93.4 GC 0 CL 93 99.4 96.0 98.0 95.3 106.5 SC 62 98.8 101.3 101.3 100.2 108.7 SM, ML, SP 77 103.3 97.5 103.5 105.8 114.1 109.8

Soil Classif.

Equilibrium Conditions at Depth

S Average Suction Min. Suction Max. Suction [%] [kPa] [kPa] [kPa]

CH 84 380 180 700 CL 68 480 150 1260 SC 70 350 70 1200 SM, ML, SP 43 220 100 450

322

Through this study it was determined that the degree of saturation under undeveloped

desert conditions averages about 30%, 40%, and 70% for SM, SC/CL, and CH respectively,

which is reached within the upper 1-m (3’). The corresponding equilibrium matric suctions are

470 kPa / 5000 kPa / 2500 kPa. Agricultural land use modifies the surface flux conditions

resulting in increased degree of saturation for all plastic type of soils. In the upper 3-m (10’) the

saturation values were found to be 40%, 50% and 80% for SM, SC/CL and CH respectively.

The degree of saturation increases with depth up to 45% and 70% for SM and SC/CL. These

increased saturation values correspond to decreased suctions (when compared to the desert

surface flux) to 200 kPa for SM soil and about 500 kPa for CL soil.

More detailed analysis is needed to develop initial suction recommendations for the use

in the slab-on-grade design methodology. The presented observations illustrate the general

dependence of the soil suction on both soil properties and surface flux conditions with potential

consequences on post-construction soil movement. Under initial dry conditions, poor drainage

and turf landscape are critical design scenarios resulting in potential soil swell or consolidation of

low density soils. On the other hand, slab-on-grade constructed on previously agricultural land

might experience movement associated with soil shrinkage in addition to soil movement caused

by poor drainage and turf landscape.

Soil topography, surface slope, vegetation and the surficial soil properties, which dictate

the amount of water that can enter the profile during precipitation events, play a role in the

equilibrium suction at depth for undeveloped sites. On the other hand, the equilibrium suction

appears to be independent of the depth to water table (Perera, 2003). Future research should

focus on identification and quantification of factors that significantly alter the suction at depth as

well as the development of methodology to estimate the equilibrium suction.

9.2 Forensic Investigations

The local community of geotechnical, structural engineers and homebuilders was

solicited for information on forensic investigations thought to be related to expansive soils. The

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response to this solicitation, which was issued by ASU researchers as well as the HBACA staff,

was very impressive. The input from multiple geotechnical firms which consisted of 742 different

forensic investigations became available for this research study. The data obtained is not non-

uniform in detail. For many, only location of investigation is known while for others (163

investigations) all information obtained during the forensic investigation became available,

including soil data obtained from underneath the slab-on-grade. The forensic data was used 1)

in correlating moisture conditions below foundations to soil type and landscape conditions, 2) to

identify landscape, drainage and grading conditions associated with unacceptable residential

structure distress, 3) to identify sources of suction change related distress, and 4) to analyse

floor level surveys, identify dominant slab shape and range of relative slab differential. 5)

Additionally, the forensic investigation incidence was correlated to soil type and swell potential.

For this purpose, the forensic data was coupled with the NRCS soil unit data and soil properties

obtained during the forensic investigation.

9.2.1 Type of Data Collected

Different degree of detail is available for the collected forensic data. Most of the

performed forensic investigations are limited to visual observations of distress, landscape and

drainage conditions. Some investigations in addition to the visual observations include some of

the following information: slab-on-grade level manometer results, lot grading monometer results,

post-construction soil profiles below and adjacent to the foundation, initial soil conditions

(preconstruction geotechnical report and pad construction data) and post construction history

such as the existence of leaks, change in landscape scheme and previously performed chemical

stabilization with data from the previously performed forensic evaluations. None of the data

included all of the discussed details, but rather one or two additional sets of information.

The data based on visual observations included locations and magnitudes of distress.

The evidence of superstructure movement includes and is not limited to 1) cracks in slab-on-

grade, 2) diagonal drywall, stucco and ceiling cracks, 3) cornerbead separation, 4) wall and

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ceiling separation, 5) baseboard or cabinetry and wall separation, 6) cracks in ceramic tile or

grout separation, 7) door and windows binding, 8) horizontal or vertical sidewalk panels

separation, 9) flatwork cracks, 10) stair step block separation in perimeter fence and 11) pillar

and wall separation. Additionally, the quality of drainage including existence of sidewalks, areas

of potential ponding, and existence of gutters were identified and collected. Analyses were

performed on the data to identify general trends.

9.2.2 Sources of Suction Change Related Distress

The soil volume change and soil/structure interaction related sources of distress are not

discussed here. The identification of these factors would require much more detailed analysis

with postulated potential distress mechanisms. The author is very reluctant to speculate on the

potential sources of soil volume change related distress based on very limited physical evidence.

Rather, the conclusions based on sufficient facts are given and are limited to sources of suction

change related distress, which can be categorized into three groups design considerations,

quality of construction and post construction modifications.

The first category, design considerations, deals with architectural design concept,

location of utilities, location of AC condensation discharge, location of roof runoff discharge from

gutters, designed drainage and location of perimeter walls and weep screeds. Two problematic

architectural roof designs have been identified, the first one includes small courtyard, where up

to 1/3 of the roof runoff can concentrate, see bird’s eye view of residence with courtyard in

Figure 9.8a. The second, more common design leads to the roof runoff concentration from

about ¼th of the roof area in one spot, typically the front or the back of the property, as

illustrated in Figure 9.8b. Inadequate drainage and grading in those locations might potentially

result in relatively substantial increase of soil moisture causing soil volume change and structure

distress.

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Figure 9.9. Sources of structure distress – a corner the house creates with garage

where positive drainage away from structure is hard to maintain.

Figure 9.10. Sources of structure distress – poor drainage, utilities in side yard,

vegetation in side yard, gutter discharge into side yard.

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Figure 9.11. Sources of structure distress – AC condensation discharge next to

foundation.

In Arizona, swale is the most commonly implemented drainage system. The roof runoff

is designed to fall next to the foundation, drain into the side yard swale and migrate at about 1%

slope to the street in front of the property or into a small retention basin in the property backyard.

The roof runoff has the potential of eroding the soil and creating areas of potential ponding.

Figure 9.12 illustrates the roof runoff eroded area parallel to the foundation with accumulated

precipitation. It is recommended to install a gutter system in place of the swale drainage

mechanism for regions with moisture sensitive soils. If this solution is not feasible, it is

recommended to construct the swale system with larger slope towards the street and cover the

side yards with sufficient amount of gravel, which should reduce the soil erosion. Although as

designed, unmodified by homeowner drainage conditions appear to work properly for a period of

time, unexpected long-term performance was observed in many forensic investigations. Soil

erosion creates areas of potential ponding directly next to the foundation and with time reduces

the slope of the swale.

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Figure 9.12. Sources of structure distress – soil erosion due to roof runoff.

The adequate quality of construction (soil density, drainage and grading) is very

important for the proper performance of residential dwellings. Typically, the as-constructed

quality of drainage and grading is hard to identify during forensic investigations. The difficulty is

commonly caused by homeowner modified surface conditions. Soil erosion or slab undermining

is sometimes observed at homeowner installed flatwork. It is mostly caused by construction on

low density, improperly compacted soils and/or negative drainage next to the flatwork, see

Figure 9.13. The existence of low density soils, in general, is problematic when next to the

foundation. Regions with loose, high permeability soils allow moisture infiltration to great depths.

The absorbed moisture has the potential of lateral migration from the infiltration region to area

below the foundation. The moisture migration might occur either due to capillary forces or along

interbed layers. Depending on the soil type and insitu conditions, the soil below the foundation

might respond to decrease in matric suction as soil volume reduction (compression) or increase

(swell). The existence of low density soils next to the foundation was rarely reported in the

forensic investigations.

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Figure 9.13. Sources of structure distress – soil erosion/undermining of low density

soil below homeowner installed flatwork

The maintenance of adequate grading and drainage are essential for proper

performance of residential structures. Homeowners typically lack the basic understanding that

modifications of grading, drainage and surface flux conditions lead to soil suction changes

associated with soil volume change and structure distress; hence the landscape and surface

conditions are frequently modified. The various modifications resulting in poor drainage are

illustrated in Figure 9.14 through Figure 9.20. The typical modifications include constructed

flatwork (mostly sidewalks), pools, planters, decorative boarders and vegetation planted next to

the foundation or vegetation with berms further impede the drainage. The introduction of a pool

into the backyard is especially problematic. The pool deck, commonly sloped towards the

residential property, causes additional moisture to flow from the pool deck area into the area of

potential ponding developed directly next to the foundation.

The acceptable levels of ponding on site and next to the foundation are quantified by

AROC (2007) and summarized in Section 3.6 of this dissertation. For residential construction in

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Arizona, the discussed grading and drainage challenges should be viewed in the context of

those tolerances.

Figure 9.14. Sources of structure distress – poor drainage.

Figure 9.15. Sources of structure distress – poor drainage (positive slope), AC

condensation discharge next to foundation, turf landscape adjacent to foundation.

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Figure 9.16. Sources of structure distress – homeowner modified drainage and grading, sidewalk blocks drainage, AC condensation discharge next to foundation.

Figure 9.17. Sources of structure distress – homeowner modified drainage and

grading, sidewalk/pool blocks drainage, vegetation next to foundation.

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grading, vegetable garden is a source of water.


grading, decorative boarder blocks drainage, sprinkler discharge next to foundation.

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Figure 9.20. Sources of structure distress – area of potential water ponding, sprinkler

discharge next to foundation.

9.2.3 Degree of Saturation and Suction Conditions below Foundations

Two sets of data were available for saturation or suction determination below residential

foundations. In the first set, obtained from practitioners, the soil samples were typically obtained

2-5’ away from the edge of the slab and to a depth of about 5’ below the soil surface. This set

consists of 99 borings with measured soil index properties, gravimetric water content and dry

density. The available information was group based on the soil classification, CL, SC, SM to

identify the range of degree of saturation found at depth (CH soil data were not available). The

deepest value in a profile was used for the analysis, typically located between 3’-5’ below the soil

surface. Large data scatter was observed for all soil types as illustrated in Figure 9.21. For the

CL soil, the degree of saturation varies between 29% and 89% with an average of 65%. For the

SC soil, the degree of saturation varies between 19% and 85% with an average of 47%. For the

SM and ML soil, the degree of saturation varies between 16% and 55% with an average of 33%.

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0

1

2

3

4

5

6

7

8

9

10

15-2

0

20-2

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25-3

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30-3

5

35-4

0

40-4

5

45-5

0

50-5

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55-6

0

60-6

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65-7

0

70-7

5

75-8

0

80-8

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85-9

0


Occ

uran

ce F

requ

ency

CLSCSM

Figure 9.21. Degree of saturation below residential foundations at depth between 3’-5’.

The calculation of the equilibrium suction at depth for this set of data was considered to

be inappropriate. Many of the forensic investigations were performed only few years after the

construction, hence the equilibrium conditions have not been reached yet as characterized by

large saturation variability at different slab locations and with depth. Additional information

needed for comprehensive equilibrium suction determination include pre-construction land use

and the post-construction human imposed flux conditions. This information was available for

limited number of sites.

The second set of data consists of soil testing performed on 16 profiles obtained from

beneath slab-on-grade foundations constructed at least 10 years prior to sampling. The soil

samples were typically obtained 5’ away from the edge of the slab and to a depth of about 8.5’.

The soil testing included the measurement of index properties, gravimetric water content, dry

density and insitu matric suction. The matric suction and degree of saturation profiles were

divided based on and landscape type surrounding the location of the boring. Three major

landscapes were identified, turf, desert and mixed. The mixed landscape is defined as the

desert landscape with large irrigated desert trees or shrubs, location of potential ponding such as

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sidewalks or combination of turf and desert landscape. The soil profiles were further subdivided

based on dominating soil classification. It is important to note that the majority of the profiles

encountered were not homogeneous, with CL and SC layers within the same profiles. Therefore

the profile classification identifies the dominating soil type. The results are presented in Figure

9.22.

Three profiles are available for turf landscape. Turf landscape conditions result in moist

soil profile. Near the soil surface the degree of saturation varies between 20-95% for all soil

types. Below the depth of 60-inches the degree of saturation decreases to an approximate

range between 40 to 80% as illustrated in Figure 9.22a. In terms of matric suction, at the soil

surface, below the slab, the values vary between 10 kPa to 2000 kPa. At depth, the matric

suction range decreases to between 50 kPa and 350 kPa. Conclusions based on soil type

cannot be drawn based on the available information.

Four profiles are available for desert landscape. Under desert conditions SC soils

remain relatively dry with depth. Filter paper testing and One-Point Method, scanning curve

methodology produced 1200 kPa to 15 000 kPa suction range at the soil surface and about 8000

kPa suction at depth. For SC soil, the degree of saturation was found to vary between 27 % to

70 %. For the CL material, suctions at the soil surface, below the slab, were found to vary

between 250 kPa and 1600 kPa and converge to about 700 kPa at depth; in terms of degree of

saturation the values vary between 40 and 90% without any particular pattern.

A large data scatter was observed under mixed landscape scenario. For this type of

surface flux condition 6 CL and 2 SC profiles are available. The degree of saturation in CL

material varies between 30 to 90% without any particular pattern, in terms of matric suction, the

variation is between 120 kPa to 15 000 kPa at the soil surface. The variability decreases with

depth to a range between 200 kPa and 1600 kPa with an average of about 600 kPa. Matric

suction in SC soil varied between 1900 kPa and 4000 kPa at the soil surface and between 200

kPa and 600 kPa at depth which corresponds to 16 to 70% degree of saturation range at the soil

surface and about 30% at depth.

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a)

0

10

20

30

40

50

60

70

80

90

1000 20 40 60 80 100

S [%]

Dep

th [i

n]

wPI soil classif.

6.5 SC

8.8 SC

14.0 CL


b)

0

10

20

30

40

50

60

70

80

90

1000 20 40 60 80 100

S [%]

Dep

th [i

n]

wPI soil classif.

6.4 SC

8.4 SC

11.0 CL

13.5 CL


c)

0

10

20

30

40

50

60

70

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1000 20 40 60 80 100

S [%]

Dep

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wPI soil classif.

3.2 SC

5.8 SC

5.3 CL

6.4 CL

7.2 CL

11.3 CL

12.6 CL

17.6 CL


Figure 9.22. Measured saturation and suction variation below slab-on-grade for a) turf

landscape, b) desert landscape, c) mixed landscape or desert landscape with areas of potential ponding.

The measured suction data were further used in the identification of relationship

between equilibrium suction to soil type and landscape scheme. The suction data measured

below 3’ were plotted against wPI and an exponential relationship was identified as illustrated in

Turf Landscape

Desert Landscape

Mixed Landscape

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Figure 9.23. In general, under desert landscape scenario, the matric suction decreases from

above 10 000 kPa to about 800 kPa as the wPI increases. Under turf landscape the matric

suction increases from about 60 kPa for NP soil to about 800 kPa as the wPI increases. The

majority of the analysed soils were collected from below foundations surrounded by mixed

landscape. The equilibrium suctions obtained from those sites plot mostly between the two

identified curves.

Desert Landscape: Suction = 288wPI-1.15

R2 = 0.4061

Turf Landscape: Suction = 83.82wPI0.598

R2 = 0.569

10

100

1000

10000

100000

0 5 10 15 20 25 30 35wPI

Suct

ion

[kPa

]

Desert Landscape Turf Mixed

Figure 9.23. Equilibrium Suction below foundation.

9.2.4 Comparison of Landscape Type to Distress Magnitude

The frequency of occurrence and the magnitude of distress were compared to

landscape type on 134 properties under forensic investigation. Six of those residences were

surrounded by turf landscaping, including the side yards. Only 19 properties had desert

landscape with no irrigation system installed. The remainder was qualified under mixed

landscaping. It was identified that about 95% of the properties under forensic investigation did

exhibit poor drainage in the vicinity of the slab. It was further determined that there is no

correlation between landscape type and residential construction distress under poor drainage

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conditions. The results are presented in Table 9.3. Based on the numerical modeling presented

in this dissertation, the influence of the roof runoff and poor drainage are much more

consequential on the depth of moisture migration and the magnitude of degree of saturation than

an excessively irrigated turf landscape. Therefore, it is concluded that the residential

construction distress is mostly caused by improper, typically homeowner modified drainage. The

most commonly observed distress is excessive hairline drywall and stucco cracking, up to 1/32”

wall/wall and wall/ceiling separations, and within tolerance (as per AROC) flatwork cracking and

control joint separations. Note that the age of the properties under forensic investigations varied

between 0.5 to 20 years. The AROC criteria identifying unacceptable distress tolerances apply

to residential properties that are two years old or newer. In the analysis presented, the AROC

guidelines are simply used as a benchmark.

It was identified that about 50% of the residences under investigation exhibited distress

within AROC tolerance for homes two years old or newer. The remaining 50% mostly did

experience excessive cosmetic distress. More than 2 excessive cracks or separations where

identified in about 18% of the properties.

Table 9.3. Residential Construction Distress Count vs. Landscape Type (distress beyond home owner responsibility defined by AROC).

All Data Desert Landscape Turf Landscape

All

Exceeds AROC tolerance for

homes 2 years old or newer. All

Exceeds AROC tolerance for homes

2 years old or newer. All

Exceeds AROC tolerance for

homes 2 years old or newer.

Average 16 2 20 2 17 1 Max 55 12 46 12 51 3 Min 0 0 1 0 2 1

Count 134 19 6

9.2.5 Relative Slab Differential Data

In general, the post-construction slab movement is very difficult to identify mainly due to

limited knowledge about the initial and pre-construction conditions. Based on the post-

construction manometer results, location and magnitude of structure distress and visual

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observation of landscape, drainage and grading, number of possible soil/slab interaction

scenarios might be identified. Additional soil testing of stress state, however, must be performed

to postulate on the most likely distress mechanism or the combination of distress mechanisms.

It is most likely that a combination of swell, shrinkage, and compression occur simultaneously at

each site with one mechanism dominating over the others in time.

In forensic engineering practice, manometer testing is a commonly used tool in the

identification of potential magnitude of slab movement and distress mechanism. The limitations

of the results are well understood by practitioners. The reported results are frequently discussed

in the context of Walsh (2001) research about relative slab differential of newly constructed

slabs, which is on average about 0.5”.

Three major slab shapes were identified, tilt, center lift and edge lift. The compiled

forensic engineering data were used in the identification of the frequency with which each post-

construction slab deformation occurs under Arizona soil and climatic conditions along with the

distribution of relative slab differential per each identified shape. The data mostly consists of

conventional stem-and-footer design. Only ten (10) post tensioned slabs were available for

analysis. The cross-sections of the identified shapes are given in Figure 9.24, while the

frequency of occurrence and the corresponding relative slab deformation is tabulated in Table

9.4.

Tilt

Center Lift

Edge drop

Dome

Edge Lift

Figure 9.24. Potential Slab Shapes.

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The tilt deformation is characterized by a smooth transition from one edge of the

property to the other. It might be caused by dominating swell or shrinkage on one side of the

property. It is also possible that the foundation was constructed out of level with negligible post-

construction movement. The tilt deformation is the most commonly encountered slab shape

(32%) with an average relative slab differential of 1.3”, which is slightly above the average

relative slab differential of 1.2” calculated with all available data.

Table 9.4. Frequency of slab mode deformation occurrence and average relative slab differential.

slab shape % of occurrence average rel. ∆ min. rel. ∆ max rel. ∆ tilt 32% 1.3" 0.6' 3.7"

center lift 29% 1.2" 0.7" 1.7" edge lift 17% 1.2" 0.5" 1.9"

no pattern 22% 0.9" 0.4" 1.3"

Center lift (edge drop) is the second most commonly encountered slab shape occurring

29% of the time with an average relative slab deformation of 1.2”. This deformation can be

further subdivided into 1) classical center lift condition characterised by gradual slab transition at

low points at the edges to high points in the center. This deformation is potentially caused by

shrinkage, settlement below footings and/or expansion below the center of the slab. 2) The edge

drop condition typically exhibits sharp transition from low points at the slab perimeter high points

some distance away from the edges. This deformation can be caused by shrinkage or

settlement below the foundation perimeter. In this scenario the soil expansion is not a significant

factor; and 3) The dome may be caused by a leak from a pipe below the foundation. It is

characterized by a sharp transition from high point somewhere in the center of the slab to low

points nearby.

Edge lift slab deformation, most likely caused by swell around the slab perimeter, is

observed in 17% of forensic investigations, with an average relative slab differential of 1.2”. A

large portion (22%) of the analysed slabs do not exhibit any pattern. The average relative slab

differential in this group is 0.9”, which is not large when compared to as-constructed conditions.

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Limited conclusions can be drawn about the post-construction distribution of post-

tensioned slab shapes and the associated average relative slab differentials. Only ten (10)

manometer results were available for this study. The small number of case studies is linked to

the limited use of this methodology up to approximately five year ago. Based on the available

data, the average relative PT slab differential is 1.6” with range from 0.9” to 3.7”. Tilt was found

to be the most common deformation shape.

9.3 Comparison of forensic Investigation Incidence to Soil Properties

Quantitatively, the forensic investigation incidence was compared to the existence of

expansive soils in Arizona. The forensic data were plotted using GIS as another map layer in

the updated Expansion Potential map given in Figure 5.5. Visual assessment of the data

revealed that CH soils are quite rare in the Phoenix area of Arizona; hence forensic

investigations associated with the existence of moderately to high expansion material below

foundations is rare as well. In general, forensic investigations occur more commonly on SC

soils (51%), which are very prevalent in the Phoenix Valley. The second most common soil type,

CL, is responsible for 36% of forensic investigations. The remainder of the forensic work occurs

on SM soils, most likely associated with its collapsible properties, rather than expansion.

Table 9.5. Forensic investigation incidence vs. soil type. Soil

Type % of occurrence in

forensic investigations Occurrence of soil type in

the Valley CH 4.0 Rare CL 36.4 Common SC 50.5 Most Common SM 9.1 Common

9.4 Key Findings

Based on the analysis of forensic engineering data of single family residences located in

the Phoenix Valley, it is concluded that:

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1. Structure distress is correlated to improper drainage and grading, typically modified by

the homeowner. The modifications include and are not limited to sidewalks and other

flatwork, pools, boarders, and introduction of vegetation next to the foundation.

2. When areas of potential ponding exist, the frequency and extent of distress was found to

be independent of landscape around the foundation.

3. Only 50% of forensic cases exhibit distress requiring repairs beyond homeowner

responsibilities set forth by AROC (2004).

4. The most commonly observed post-construction slab shape is tilt with average relative

slab differential of 1.3”.

5. Under turf landscape conditions the suctions below foundation (measured at about 5’

from the edge) were found to vary between approximately 10 kPa to 1000 kPa with and

average of about 200 kPa at depth.

6. Under desert landscape conditions the suctions below foundation (measured at about 5’

from the edge) were found to vary between approximately 250 kPa to 15 000 kPa with

an average of about 2000 kPa at depth.

7. The soil saturation and suction below residential foundations depend on soil clay

content. The higher the clay content, the higher the saturation and the lower the matric

suction.

8. The performance of the residential structures can be improved with the following

recommendations:

• Use of gutters in areas of moisture sensitive soils.

• Gutter discharge and AC condensation should outlet far away from the foundation.

• Eliminate the empty spaces between the structure and a sidewalk.

• Increase the minimum distance between landscape and foundation to 7’ (based on

modeling).

• Increase side yards to 10’.

• Do not install utilities in the side yards.

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• Place weep screed in many locations to promote moisture drainage away from the

property.

• Increase the slope of the swale.

10 CONCLUSIONS AND RECOMMENDATIONS

10.1 Scope of Research Work

Performance of unsaturated soil as an engineering material is strongly related to the

changes in moisture content that occur over the life of the structure. Some of these soil moisture

content changes occur incidentally (e.g. watering of a nearby golf course) or through natural

processes such as the precipitation. Other changes in moisture content result from more direct

human interaction such as landscape irrigation. Development brings about changes in both

surface and groundwater flows, with the typical impact being an overall increase in soil moisture.

In general, precautions such as good site drainage and diversion of roof run-off reduce the

amount of moisture introduced into the soil over the life of the structure. It is critical that the

moisture conditions and moisture content changes of unsaturated soil are taken into

consideration in the geotechnical site investigation and foundation design.

Problems associated with geotechnical practice for unsaturated soils can usually be

placed into one of two categories: (1) unconservative designs and procedures that lead to

failures or construction difficulties, or (2) over-conservatism that leads to much higher than

necessary construction costs. A common example of the second category is the modeling of

initially unsaturated soils as saturated soils. This approach is often rationalized with the

assumption that the material may become saturated in the future. In a few cases this

assumption is justified, but in a great majority of cases it is not justified. The inattention to the

fundamental aspects of unsaturated soil behavior and the relatively limited investigations of

response-to-wetting of unsaturated moisture sensitive soils has typically resulted in great over-

conservatism, with a few cases of unconservative practice. The focus of this particular study is

on unsaturated soils that tend to swell upon wetting and shrink upon drying. These soils are

commonly referred to as Expansive Clays.

Volume change in response to wetting is most simply evaluated through one-

dimensional oedometer testing to assess expansion potential. Performance of such oedometer

response-to-wetting tests is common practice for investigation of volume change resulting from

increased moisture content. For example, in a test commonly called the overburden swell test

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the undisturbed specimen, confined in a ring, is subjected to dry loading up to the vertical stress

level anticipated in the prototype and then given free access to water, thereby bringing the soil

suction to zero or near zero. The typical result from such a test is the percent swell resulting from

wetting from in-situ moisture conditions to full saturation at the stress level expected in the field

after construction. Although this simple test is very valuable for detecting the presence of

swelling soils, it provides information only on the full wetting response of the soil. Another

commonly performed oedometer test, used as an index or indicator of swelling soils, is the

Expansion Index test, EI, performed on a remolded specimen, and also taken from an initial

condition of about 50% saturation to a fully wetted state. In Arizona, the most commonly

performed response to wetting test, EIAZ, entails 1-D volume change measurement of a soil

specimen prepared at 0.95ρd max and wopt –(1 to +4) obtained with standard proctor test and fully

saturated.

In the actual field situation the amount of expansion, or shrinkage, is a function of the

degree of differential wetting (or drying in the case of shrinkage). Many investigators have

reported field strains much lower than those obtained for the fully wetted lab specimen. The use

of response to wetting tests wherein the specimen is fully wetted is conservative for many

situations. Of course the real challenge is to understand the relationship between soil moisture,

stress level, and volume change, as well as the prediction of the actual degree of wetting that will

occur in the field.

Although it is common for geotechnical engineers to assess the change in moisture

content of the soil that may occur over the life of the structure, it is important to realize that it is

the more fundamental parameter, soil suction, which is critical in predicting soil response. In the

absence of gradients due to soil salts, and for the typical field situation where pore air pressure

is atmospheric, the soil suction is simply the negative pore water pressure.

Determining slab movements on expansive soils is a very challenging technical problem

involving coupled unsaturated flow and unsaturated soils stress-strain modeling, as well as soil

structure interaction. A literature review on the geotechnical practice for expansive soils is

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attached as Chapter 1. Construction on expansive soils is challenging, and thus prone to some

problems and litigation. The engineering community makes extensive use of local experience

and empirical procedures to address these problems. As part of this study, a substantial

database of residential construction performance was developed for the Phoenix region.

The tasks performed in this study are as follows:

1. Conducted surveys with practitioners to assess Phoenix region practices used in the

design of residential foundation systems on expansive soils.

2. Determination of representative expansive soils properties for a range of expansive soils

across the Valley. These properties are derived from field sampling and laboratory

testing performed by ASU and include information needed for modeling moisture

movement in expansive soils and also information needed for application of the current

PTI method (geotechnical part). Included in the information are soil water characteristic

curves, insitu soil suction, expansion index, swell pressure, hydraulic conductivity,

gradation properties including hydrometer results, and Plasticity Index.

3. Study of the suction profiles beneath slabs for equilibrium conditions, using direct

suction determination and SWCC correlations.

4. Developed updated NRCS (Natural Resource Conservation Service) map of expansive

soils distribution in the Phoenix region, commonly used by practitioners to assess soil

properties in the preliminary analysis.

5. Based on the findings that the PTI procedure for slab-on-grade foundations was the

predominant methodology for current practice, evaluated PTI method for Arizona soils

and climatic conditions.

6. Survey of landscape professionals and government agencies concerned with water use

to determine typical homeowner landscape water use in the Phoenix Valley.

Assessment of the amount of typical homeowner landscape over-watering was made.

This information was used, together with regional climatic records, to determine typical

surface flux conditions for the Phoenix region.

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7. Identification of challenges in numerical modeling of surface flux and associated

infiltration into unsaturated soils in arid regions.

8. Based on finding above, modeled the problem of infiltration into expansive soils for

various landscape and surface water control schemes.

9. Conducted survey of Phoenix area geotechnical firms to identify areas in Phoenix Valley

were forensic investigations of expansive soils have been conducted. This data was

reviewed for determination of trends with soil expansion potential, site landscape and

draining conditions.

10. Assessment of numerical modeling results through comparison for consistency with

forensic study findings and field data on depth and degree of saturation (suction).

11. Recommendations for future studies and future cooperative efforts.

10.2 Conclusions

Foundations placed on expansive soils are vulnerable to distress, especially in arid or

semi-arid regions. Based on geotechnical firm interviews, it appears that the Arizona local

practice is moving in the direction of use of the new, 3rd Edition, PTI method for computation of

differential heave and edge moisture variation distance. Local structural engineers are also

often recommending the use of PT slabs designed with slab thickness as determined by the 3rd

Edition PTI method.

Based on the interviews on current practice, discussions with many local professional

groups on residential home performance, and the findings from the forensic studies, it appears

that generally good performance has been realized with current and past approaches, which

were, to a large extent, based on geotechnical design parameters obtained from the less

conservative 2nd Edition PTI method, and for conventionally designed concrete foundation

systems. However, there are still some problems, and cases of litigation, surrounding expansive

soil issues. When problems arise, the sources of problems include poor drainage, construction

problems, homeowner activity, landscape scheme, and expansive soil -- and most likely some

348

combination of two or more of these sources. The findings of this study imply that current

methods of dealing with expansive soils are good, but somewhat higher reliability may be

desirable. The solution is to develop a greater understanding of the factors affecting

performance, and to improve understanding of input parameters required for design.

One often-posed question is whether this new 3rd Edition PTI methodology is appropriate

for Arizona conditions. The 3rd edition procedure is more conservative compared to the former

2nd Edition PTI method, and also leads to more conservative foundation design compared to the

past conventional practice. One must consider that the design values of differential movement,

ym, and edge moisture variation, em, which in turn lead to the slab thickness, vary depending

upon the model input parameters. Thus, a better understanding of the design inputs in terms of

soil properties such as suction compression index and unsaturated hydraulic conductivity (or

diffusivity), as well as improved understanding of soil suction profiles for both pre- and post-

construction conditions, is essential for improved analysis and design of residential foundation

systems. The findings of this study should be useful to practicing geotechnical engineers in

selection of input parameters for the PTI model, and other models, for estimation of differential

movement and pre- and post-construction soils suction profiles.

Overall, the key findings of this research study are as follows:

Numerical Modeling:

1. Numerical analysis of moisture flow through unsaturated soil is typically carried out

through the solution of Richards’ equation. The Richards’ equation is a stiff parabolic

PDE whose solution requires the implementation of a stiff, implicit numerical solver.

Methods typically implemented in software exhibit instabilities suggesting an

implementation of pseudo-implicit solver. The numerical challenges arise under surface

runoff conditions. The instabilities are usually overcame by reducing mesh spacing, time

step or both.

349

2. The numerical solution variability due to the uncertainty of the unsaturated soil

properties is large and potentially larger than the variability associated with different

software selection.

3. Flux averaging can be successfully used in the numerical analysis of moisture flow

through soil due to atmospheric conditions (no ponding) when no runoff occurs. On the

other hand, if runoff takes place, the flux averaging overestimates the depth of influence

and degree of saturation.

4. Desert landscape results in increasing monotonic drying front and very shallow moisture

migration for all soil common to Arizona region; 5-cm due to precipitation; 0.5-m

seasonal suction variation.

5. Edge moisture variation distance is limited to 10 cm under desert landscape conditions.

6. Turf landscape results in increasing wetting front (9-m after 34 years for CH soil and 7-m

after 2 years for SM-ML soil) and very shallow depth of moisture loss (2 cm). Short term

seasonal suction variation of 0.5 m for SM-ML soil and 1-m from CH soil was observed.

7. Edge moisture variation distance of 35 cm was observed for CH soil under turf

landscape conditions. Monotonic moisture migration below the slab levels off during 5th

year at 2.2-m.

8. The critical scenarios are 1) poor drainage resulting in essentially 100% soil saturation

up to the depth of 1-m; 2) initial moist conditions with desert landscape.

PTI Slab Design:

1. In general, the failure mode when moving from 2nd Edition PTI procedure to 3rd edition

is from center lift to edge lift and increase in slab thickness.

2. In PTI procedure overestimates volume change in extremely wet and extremely dry soil

but may give reasonable results in the intermediate range.

350

Soil Characteristics for Central Arizona Geographic Region:

1. Low expansion potential soils are very common to the Central Arizona geographic

region. Based on visual analysis of the updated swell potential map, approximately 50%

of the Phoenix Valley region consists of medium to moderate soil material within the

upper 5-ft of the soil strata. High expansion potential soils are not common in the

Phoenix region.

2. Field evidence suggests that the degree of saturation for native desert profiles of clayey

soil averages about 30%, 40%, and 70% for SM, SC/CL, and CH whereas the average

degree of saturation for agricultural areas averages about 40%, 50% and 80% for SM,

SC/CL, and CH within the upper 20’.

3. The estimated equilibrium matric suctions are approximately 470 kPa for SM soil and

5000 for SC and CL soils and undeveloped desert conditions typical to the Phoenix

region. Agricultural use of the land results in a decrease in matric suction to

approximately 200 kPa for SM soil and about 500 kPa for SC and CL soils.

Field Evidence:

1. Suctions below the foundations depend on landscape type. For turf landscape the

equilibrium suctions reach an average of about 500 kPa. Desert landscape leads to dry

suction below the foundations with an average of 1500 kPa.

2. Problems associated with foundation performance are typically caused by improper

drainage and grading commonly modified by the homeowner.

3. The incidence of forensic investigations correlates very well to the location of medium to

moderate expansively soils. Based on the site data collected during forensic

investigations, the litigation incidence correlates very well with SC and CL soils.

4. The findings from the unsaturated flow modeling are consistent with the findings from

the forensic investigations of this study in that the site drainage was found to be

extremely important to good foundation performance.

351

10.3 Future Research

Three topics for future research have been identified, 1) challenges arising from

numerical modeling of moisture flow through unsaturated soil, 2) identification of soil properties

for the state of Arizona through the development of map illustrations and 3) development of

slab-on-grade design methodology that implements unsaturated soil theory and local

experience.

The research work presented herein illustrated that numerical modeling of moisture flow

through unsaturated soil is very challenging, time consuming task. The nonlinearity of

unsaturated soil properties and the existence of boundary condition that switches between

Dirichlet and Neumann, introduces difficulties that are not easily handled by any of the

commonly implemented numerical methodologies for geotechnical and hydrology use.

Sophisticated methodologies developed by the mathematical community, such as exponential

integrators, spectral methods and alternating direction implicit, ADI, schemes show great

potential for the solution improvement.

During the preliminary soil analysis, the practicing engineers routinely use the NRCS

developed map illustration of soil swell potential distribution within the Central Arizona region.

As part of this study, the map was updated based on NRCS identified soil units and soil

properties supplied by Arizona region geotechnical practitioners. Similar map for the entire state

of Arizona could be developed.

Several commonly used methods for estimating heave employ the assumption that the

soils in the field will be fully wetted to considerable depth at some point after construction.

However, direct field observations show that the degree of wetting is almost always well short of

full saturation. It is extremely important to include partial wetting because assuming saturation

overpredicts the amount of swell (Walsh et al., 2006). Practitioners and researchers alike

routinely point this out, but because many existing methods are unable to deal with partial

wetting the practice is to assume total wetting and claim conservatism, even though it is

recognized that this is over-conservative. There are many case studies where the amount of

352

swell is less than predicted using full wetting. The PTI method does try to incorporate partial

wetting in a very approximate way, and it does provide more flexibility on partial wetting

assumptions through the use of the program VOLFLO. New research using unsaturated soils

theories has lead to models that allow for better characterization of soil properties and response

as well as methods that allow for better estimation and improved methods of application of

partial wetting concepts (Fredlund and Pham, 2006). What is needed, however, are models that

are consistent with these more advanced unsaturated soils theories, but which utilize routine

testing methods and are sufficiently simplified for routine adoption into practice. One could

argue that the PTI method uses partial wetting and is simple, but there remains a need for a

method that incorporates results of site-specific testing with a constitutive model that is

benchmarked/calibrated to performance at a regional scale.

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APPENDIX A

HISTORY OF PTI GEOTECHNICAL PROCEDURE DEVELOPMENT

Research leading up to 2nd Edition PTI

1. Research done by Thornthwaite (1948) lead to the development of climate index, TMI.

∑

∑ ∑

=

= =

−= 12

1

12

1

12

160100

nn

n nnn

PE

dsTMI (1)

(1a) PEPPEP

forforPEP

s≤>−

=0

(1b) PPEPPE

forforPPE

d≤>−

=0

The water surplus, s, and the water deficiency, d, are calculated on month-to-month

basis in centimeters or inches. The calculation is based on potential evaporation, PE,

and precipitation, P, data. The obtained values of TMI for the US were plotted on a

map, see Figure 1.

Figure 1. Thornthwaite moisture Index for US (after PTI, 2004).

367

2. Holtz and Gibbs (1956) used Atterberg limits as predictors of soil behavior. In general, it

was observed that soil with a high plasticity index, PI, experience greater volume change

than soils with a low PI.

Figure 2. Expansive soil classification based on index soil properties (Holtz and Gibbs, 1956)

3. Russam and Coleman (1961) correlated soil suction beyond active zone depth to TMI,

see Figure 3.

Figure 3. Relationship between soil suction at depth and TMI (PTI, 1996).

368

4. Seed (1962) developed a chart correlating Ac and %clay to swell potential. The percent

clay is defined as the percent of soil faction smaller then 0.002 mm.

Figure 4. Soil swell potential in terms of activity and percent clay (Seed et al., 1962).

5. Pearring (1963) developed a correlation between mineralogical classification and index

properties. He introduced two new parameters: cation exchange activity ratio

%CECCEAc

fc⎛ ⎞

=⎜⎝ ⎠

⎟ and activity ratio%PIAc

fc⎛ ⎞

=⎜⎝ ⎠

⎟ , where CEC is expressed in terms of

milliequivalents per 100 grams of dry soil and clay fraction, %fc, is defined as the ratio of

percent clay to percent of soil passing US sieve number 200 expressed.

369

ACTIVITY RATIO

MONTMORILLONITE

INTERSTRATIFIED

HALLOSITE

ILLITE�CHLORITE�KAOLINITE

ATTAPULGITE

CA

TIO

N E

XC

HA

NG

E A

CT

IVIT

Y (C

EA

c)

0.1 0.2 0.4 0.6 0.8 1.0 1.5 3.0

1.5

1.0

0.8

0.6

0.4

0.2

0.1

2.0

Figure 5. Mineralogical classification (after Pearring, 1963).

6. Edge moisture variation distance, em, is a distance measured inward from the edge of

the slab over which the moisture content of the soil varies due to wetting or drying. In the

procedure, the magnitude of em is determined based correlation developed with TMI

based on successful performance of 10 year old slabs in Texas (Wray, 1978). The

correlation is presented in Figure 6. Differential swell, also referred to as differential soil

movement, ym, is the change in soil elevation between the two points separated by em.

The amount of expansion or contraction that a soil stratum will undergo was correlated

to mineralogical classification, permeability of clays and total potential of soil water

(Wray, 1978). In the procedure ym is determined based on %clay, mineralogical

classification, depth to constant suction, em and moisture flow velocity, V = 0.5*TMI,

where the magnitude of TMI is used. Though TMI is a dimensionless parameter, this is

an empirical correlation that yields velocity in units of in/year. The moisture flow velocity

is limited to values not smaller than 0.5 in/month [1.3 cm/month] or larger than 0.7

in/month [1.8 cm/month].

370

7. 1980 publication of 1st edition PTI procedure for ribbed PT foundation design.

8. 1996 publication of 2nd edition PTI procedure which expands its application to uniform

thickness PT slab with provisions given to stable and compressible sites. The authors

provide larger commentary on the development and implementation of the method.

EDG

E M

OIST

URE

VARI

ATIO

N DI

STAN

CE [F

T]

THORNTHWAITE MOISTURE INDEX

Figure 6. Edge Moisture Variation Distance as a Function of Thornthwaite Moisture Index (after Wray, 1978).

371

Research Leading up to 3rd edition PTI

1. Lytton (1977) presented an equation to estimate the potential volume change

⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛−=

Δ

i

f

i

fh h

hVV

σσ

γγ σ 1010 loglog (2)

where:

γh is the suction compression index, where the suction compression index is defined as

the change of soil moisture with change in logarithm of total suction;

γσ is the mean principal stress compression index;

hf and hi are initial and final water suctions respectively;

σf and σi are final and initial stress terms.

2. McKeen and Hamberg (1981) developed a chart where suction compression index is

correlated to CEAc and Ac. The suction compression index was obtained from

Coefficient of Linear Extensibility, COLE, test.

Figure 7. Classification of COLE values with Ac and CEAc (McKeen and Hamberg, 1981).

372

The COLE test gives is a ratio of the difference between the moist and dry

lengths of a clod to its dry length, (Lm-Ld)/Ld when Lm is the moist length at 33kPa and

Ld is the air-dry length. This is a drying test developed by Brasher et. al. (1966). The

established relationship between volume and water content (or suction) from the COLE

test is a constitutive function of a particular expansive soil. Such a relationship can be

used to quantify volume change characteristics of soil upon wetting and drying (McKeen

1985).

The values in the chart correspond to suction compression coefficient values for

soil consisting of 100% clay. The actual suction compression index can be obtained

with equation (3).

200

100%Pclay

h γγ = (3)

3. Cassagrande used Atterberg Limits for the mineralogical classification of clay. His work,

updated by Holtz and Kovacs (1981) is presented in Figure 8. The updated chart was

further used by Covar and Lytton (2001) to develop a method of soil swell prediction for

slab-on-grade design purposes.

Figure 8. Mineralogical classification based on Atterberg Limits (Holtz and Kovacs, 1981).

373

4. The updated mineralogical classification chart is presented below.

Figure 9. Soil classification based on Atterberg Limits (PTI, 2004).

5. McKeen et al. (1990) indicate that the magnitude of the edge moisture variation distance

depends on the vertical depth of moisture variation. As such, the edge moisture

variation distance can approach a distance equal to the depth of the active zone.

6. An attempt was made by McKeen (2001) to develop a methodology of predicting

expansive potential of soil based on suction compression index. The magnitude of the

suction compression index indicates if the soil is expansive or not. Small slope

characterizes a swelling soil while a large slope indicates a non-expansive soil. The

classification system introduced by McKeen for total suction is presented in Figure 6

where the chart is divided into five sections. Each section represents soil with different

swell potential. In general, the closer the soil is to the left bottom corner, the less

expansive it is.

374

Figure 10. Soil characterization in terms of suction compression index (after McKeen, 2001).

7. Suction compression index can be correlated to mineralogical soil classification and soil

index properties. Covar and Lytton (2001). obtained 130 000 soil samples compiled by

the Soil Survey Laboratory (SSL) of the National Soil Survey Center. The data were

filtered for data sets containing the following information:

• LL,

• PI,

• CEC

• CLOD

• %clay

• P200.

375

Zone I

Zone II

Zone III

Zone IV

Zone V

Zone VI

Figure 11. Suction compression index based on mineralogical classification of soil

into six types and soil index properties (after Covar and Lytton, 2001).

376

The 6400 records were used in the development of the presented correlation between

index properties and suction compression index, where suction compression index was

obtained from COLE test as follows:

⎥⎥⎦

⎤

⎢⎢⎣

⎡−⎟

⎠⎞

⎜⎝⎛ += 11

100

3COLEswellingγ ;

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ +−=

−3

1100

1 COLEswellingγ (4)

They developed a correlation between suction compression index and mineralogical

classification. Here the suction compression index is defined as the slope of volume

change to logarithm of total suction change for 100% fine clay. Preliminary work was

published in 2000 by TBPE. The suction compression index is used in the estimation of

both em and ym in the updated version of PTI procedure.

8. Em depends on TMI and unsaturated diffusion coefficient, α. Diffusivity is correlated with

soil index properties and suction compression index. The relationship was established

by running Jayatilaka et al. program (1992) for 9 selected climatic zones and one year of

input.

Figure 12. Edge Moisture Variation Selection Chart (PTI, 2004).

377

9. Alternate Procedure for Determining Soil Support Parameters for Shallow Foundations

on Expansive Clay Soil Sites under PTI Technical Note 12 (PTI, 2003) was printed.

10. The 3rd Edition procedure was printed (PTI, 2004). It is very similar to the previous

version. The differences lie in the estimation of suction compression index equations

and updated suction compression index charts.

References:

Brasher, B. R., D. P. Franzmeier, V. Valassis and S. E. Davidson. (1966). Use of Saran Resin to Coat Natural Soil Clods for Bulk-Density and Water-Retention Measurements. Soil Science, 101, 108.

Cover, A.P. and Lytton, R.L. (2001). Estimating Soil Swelling Behavior Using Soil Classification

Properties. ASCE Geotechnical Publication 115, ASCE, 44-63. Holtz, W. G. and Gibbs, H. J. (1956). Engineering properties of expansive clays. Transactions

ASCE, 121, 641-677. Holtz, R. D. and Kovacs, W. D. (1981). An Introduction to Geotechnical Engineering, Prentice-

Hall, Englewood, NJ. Jayatilaka, R. Gay, D. A., Lytton, R. L. and Wray W. K. (1992). Effectiveness of controlling

pavement roughness due to expansive clays with vertical moisture barriers. Research Report 1165-2F, Texas Transportation Institute, College Station.

Lytton, R.L. (1977). Engineering properties of expansive soils. Presentation to the American

Geophysics Union, Conference, San Francisco. McKeen, R.G. (1981), Design of airport pavement on expansive soils. Dept. of Transportation,

Federal Aviation Administration, Rep. No. DOT FAA/RD-81/25. McKeen, R.G. and Hamberg, D. J. (1981), Characterization of expansive soils. Transportation

Research Record 790, Transportation Research Board, 73-78. McKeen, R. G. (1985), Validation of Procedures for Pavement Design on Expansive Soils,

DOT/FAA/PM-85/15, Program Engineering and Maintenance Service, Federal Aviation Administration, Washington DC.

McKeen. R. G. and Johnson, L. D. (1990). Climate controlled soil design parameters for mat

foundations. Geotechnical Engineering Division Journal, ASCE, Vol. 116, 1073-1093. Pearring, J.R. (1963). A study of basic mineralogical, physico-chemical and engineering index

properties of laterite soils. PhD Dissertation Texas A&M University, College Station. Russam, K. and Coleman, J.D. (1961). The effect of climatic factors on subgrade moisture

conditions. Geotechnique, 11(1). 22-28.

378

Seed, H.B., Mitchell, J.K. and Chan, C.K. (1962). "Studies of swell and swell pressure characteristics of compacted clays", Highway Res. Board Bulletin 331, 12-39.

TBPE. (2000). Residential Foundation Design Subcommittee. Advisory Report, Texas Board of

Professional Engineers, Austin, TX. Wray, W. K. (1978). Development Procedures for Residential and Light Commercial Slab-on-

Ground Constructed Over Expansive Soils. PhD Dissertation, Texas A&M University at College Station, Tx.

APPENDIX B

LABORATORY DATA

TABLE OF CONTENTS

Page Site # 1 .........................................................................................................................................382 Site # 2 .........................................................................................................................................387 Site # 3 .........................................................................................................................................392 Site # 4 .........................................................................................................................................397 Site # 5 .........................................................................................................................................402 Site # 6 .........................................................................................................................................408 Site # 7 .........................................................................................................................................413 Site # 8 .........................................................................................................................................414 Site # 9 .........................................................................................................................................419 Site # 10 .......................................................................................................................................424 Site # 11 .......................................................................................................................................430 Site # 12 .......................................................................................................................................435 Site # 13 .......................................................................................................................................440 Site # 14 .......................................................................................................................................446 Site # 15 .......................................................................................................................................451 Site # 16 .......................................................................................................................................456 Site # 17 .......................................................................................................................................461 Site # 18 .......................................................................................................................................467

Site # 1

Table 1. General Site Information

Soil # 1 City Tempe Cross Roads Mill Ave./Broadway Rd. Year of Construction 1977 Date of Sampling 2/2003 Lot Size [ft2] 11100 House Size [ft2] 2272 Construction Type wood frame Foundation Type stem and footer Slab Thickness [in] 3 Thickness of Gravel Layer [in] 4 Landscape near sampling area Paved, large trees Distance from slab edge to core location [ft] 10 Pool no History of Leaks no

Figure 1. Bird’s-Eye View.

383

Table 2. Index Properties.

Soil Sample #

Classification

LL PL PI P200 clay ksat [cm/s] Gs CEC Sulfate

[ppm]

1-1-7-18 CL 28.4 14.2 14 62.5 2.8E-07 2.738 1-2-18-27.5 CL 31.5 20.1 11 72.1 12.3 1-3-27.5-38 CL 31.5 20.1 11 69 1-4-38-47 ML-CL 27.1 20.3 7 60.2

1-5-47-56.8 CL 30.1 22.3 8 59.5 4.4E-06 2.731 1-6-56.8-66.5 ML 35.2 25.5 10 55.6 1-7-66.5-77 ML 36.2 24.9 11 52.4 1-8-77-85.5 ML 36.2 24.9 11 54.3

Footnotes: Shaded used for estimated values

Table 3. Moisture Conditions.

Depth Water

Content γdry Saturation Suction Sample # [in] [%] [pcf] [%] [kPa]

1-1-7-18 10 11.8 102.4 48.6 845 1-1-7-18 14 11.9 102.7 49.3 792 1-1-7-18 15 14.7 1-1-7-18 16 14.2

1-2-18-27.5 20 13.9 1-2-18-27.5 23 13.1 97.4 47.9 399 1-2-18-27.5 27 14.4 1-3-27.5-38 29 13.3 1-3-27.5-38 33 12.8 96.5 45.9 508 1-3-27.5-38 37 11.3 1-4-38-47 42 11.5 92.0 36.9 156 1-4-38-47 46 12.1

1-5-47-56.8 49 12.1 1-5-47-56.8 50 11.6 88.3 34.1 292 1-5-47-56.8 54 12.1 87.9 35.4 261 1-5-47-56.8 56 11.8

1-6-56.8-66.5 58 13.1 1-6-56.8-66.5 62 12.6 93.7 42.3 146 1-6-56.8-66.5 65 17.6 1-7-66.5-77 70 17.5 1-7-66.5-77 72 13.3 98.5 49.9 187 1-7-66.5-77 75 10.7 1-8-77-85.5 78 12.7 1-8-77-85.5 80 12.7 98.5 48.0 222 1-8-77-85.5 85 12.8

Footnotes: Shaded background used for estimated values Suction test description – Section 4.2.9.1.3 and Appendix D.

384

Table 4. Consolidation Tests.

Test 1 Test 2

Sample Ps Cor. Ps w γdry Sample Ps

Cor. Ps w γdry Swell Sample #

Type [kPa] [kPa] [%] [pcf] Type [kPa] [kPa] [%] [pcf] Index 1-1-7-18 R 77.2 77.2 11.8 102.4 0.0185

1-2-18-27.5 1-3-27.5-38 1-4-38-47

1-5-47-56.8 R 12.9 15.3 11.6 88.3 0.0154 1-6-56.8-66.5 1-7-66.5-77 1-8-77-85.5

Footnotes R - reconstructed test I - insitu test See section 4.2.7 for test description, submerged test

0

20

40

60

80

100

0.0010.010.1110

Grain Diameter [mm]

% P

assi

ng

1-2-18-25 1-4-36-45

1-6-55-64 1-8-74-84

Figure 2. Gradation and Hydrometer Test.

385

050

010

00

Suct

ion

[kPa

]0

5010

0

S [%

]0.

00.

51.

0

w/P

L

Figu

re 3

. Pr

ofile

.

1015

20

w [%

]85

9510

511

5γ d

[pcf

]

8 M

L

7 M

L

6 M

L

5 C

L

4 M

L-C

L

3 C

L

2 C

L

1 C

L

Gra

vel

Con

cret

e

Cor

e #

Soi

l Cla

ssif.

0 10 20 30 40 50 60 70 80 90

Depth [inch]

386

0.40

0.45

0.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00

1 10 100 1000 10000

Pressure [kPa]

Voi

d Ra

tio1-1-7-18 Reconstructed

1-5-47-56.8 Reconstructed

Figure 4. Consolidation Test

0

20

40

60

80

100

0.01 0.1 1 10 100 1000 10000 100000 1000000Matric Suction [kPa]

Degr

ee o

f Sat

urat

ion

[%]

1-1-14 (dry spec. w eight = 103)1-2-23 (97)1-3-33 (97)1-4-42 (92)1-5-54 (88)1-6-62 (94)1-7-72 (98)

Figure 5. SWCC. S vs. matric suction

387

Site # 2

Table 5. General Site Information.

Soil # 2 City Tempe Cross Roads Kyrene Rd./Guadalupe Rd. Year of Construction unknown Date of Sampling 4/2003 Lot Size [ft2] unknown House Size [ft2] 29 795 Construction Type wood frame, commercial Foundation Type stem and footer Slab Thickness [in] 4 Thickness of Gravel Layer [in] 4.5 Landscape near sampling area paved, few trees near foundation Distance from slab edge to core location [ft] 10 Pool no History of Leaks no


388


Soil Sample # Classification


[ppm]

2-1-8.5-19 CL 30.9 19.2 12 71.2 2.5E-08 2.764 2-2-19-27 CL 31.6 19.6 12 80.8 2-3-27-36 CL 31.6 19.6 12 74.8 9.8 2-4-36-46 CL 26.2 18.5 8 72.7 2-5-46-55 CL 26.2 18.5 8 72.7 1.1E-06 2.750 2-6-55-66 CL 26.2 18.5 8 66.7 2-7-66-75 CL 29.9 19.3 11 68.8 2-8-75-85 CL 31.5 20.7 11 51

Footnotes: shaded used for estimated values


Sample # Depth Water

Content γdry Saturation Suction [in] [%] [pcf] [%] [kPa]

2-1-8.5-19 11 11.6 121.0 75.8 1410 2-1-8.5-19 14.5 11.8 120.3 75.6 1425 2-1-8.5-19 17.5 12.1 112.7 63.7 1595 2-2-19-27 25 11.5 97.6 41.7 2-3-27-36 33 10.2 95.9 35.5 1550 2-3-27-36 35 10.0 96.5 35.6 2-4-36-46 45 11.5 91.9 36.7 2-5-46-55 48 10.0 91.8 31.9 2-5-46-55 52 9.6 93.1 31.5 1151 2-5-46-55 54 10.1 93.6 33.6 2-6-55-66 65 10.6 94.3 35.8 2-7-66-75 70 10.2 95.8 35.6 846 2-7-66-75 71 11.3 99.1 42.8 2-8-75-85 82 13.3 88.0 38.6 470 2-8-75-85 84 13.6 91.5 42.9 354



Test 1 Test 2



Type [kPa] [kPa] [%] [pcf] Type [kPa] [kPa] [%] [pcf] Index 2-1-8.5-19 R 75.9 119.5 11.6 121.0 0.0150 2-5-46-55 R 20.7 26.5 10.0 91.8 0.0111

Footnotes R - reconstructed test See section 4.2.7 for test description, submerged test

389

8 CL

7 CL

6 CL

5 CL

4 CL

3 CL

2 CL

1 CL

Gra

vel

Conc

rete

Core

# S

oil C

lass

if.85

9510

511

512

5γ d

[pcf

]

0 10 20 30 40 50 60 70 80 90

Depth [inch]

510

15

w [%

]0.

00.

51.

0

w/P

L0

5010

0

S [%

]0

1000

2000

Suct

ion

[kPa

]

Figu

re 7

. Pr

ofile

.

390

0

20

40

60

80

100

0.0010.010.1110

Grain Diameter [mm]

% P

assi

ng

2-2-18-25 2-3-27-36

2-6-55-64 2-8-74-84

Figure 8. Gradation and Hydrometer Tests.

0.35

0.40

0.45

0.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

1 10 100 1000 10000

Pressure [kPa]

Voi

d Ra

tio

2-1-8.5-19 Reconstructed

2-5-46-55 Reconstructed

Figure 9. Consolidation Test.

391

0

20

40

60

80

100


Degr

ee o

f Sat

urat

ion

[%]

2-1-14.5 (dry spec. w eight = 120 pcf)

2-1-17.5 (112.7)

2-3-33 (95.9)

2-5-52 (93.0)

2-7-70 (95.7)

2-8-82/84 (88/91.5)

Figure 10. SWCC: S vs. matric suction.

392

Site # 3


Soil # 3 City Chandler Cross Roads Kyrene Rd./Ray Rd. Year of Construction unknown Date of Sampling 5/2003 Lot Size [ft2] unknown House Size [ft2] unknown Construction Type wood frame, commercial Foundation Type stem and footer Slab Thickness [in] 4 Thickness of Gravel Layer [in] 5.5 Landscape near sampling area paved, gravel area near foundation Distance from slab edge to core location [ft] 30 Pool no History of Leaks no

Table 10. Visual soil description.

Core # Soil Description 0-4.0 Concrete 4-9.5 Granular base 3-1-9.5-17.5 Brown sandy clay, traces of organic matter (dry leaves) 3-2-17.5-25 Brown sandy clay. 3-3-25-36 Brown sandy clay, lens of silty sand on the top of sample, root holes 3-4-36-45.5 Brown sandy clay, root holes 3-5-45.5-54.5 Dark brown and light brown sandy clay 3-6-54.5-64.5 Dark brown and light brown sandy clay, some gravel on top of sample 3-7-64.5-73.5 Clayey sand 3-8-73.5-84 Sandy clay

393




[ppm]

3-1-9.5-17.5 CL 28.8 17.5 11 73.6 2.7E-07 2.71 47 3-2-17.5-25 CL 28.6 17.6 11 76.0 10 3-3-25-36 CL 28.6 17.6 11 76

3-4-36-45.5 CL 39.5 24.4 15 61.5 3-5-45.5-54.5 CL 47.7 24.5 23 52.7 6.6E-08 2.739 3-6-54.5-64.5 CL 47.7 24.5 23 58.3 3-7-64.5-73.5 CL 47.7 24.5 23 52.7 3-8-73.5-84 SC 51.3 26.2 25 46.4

Footnotes: Shaded used for estimated values




3-1-9.5-17.5 16.6 10.8 108.1 52.0 1527 3-2-17.5-25 3-3-25-36 35 10.5 95.3 36.9 1551

3-4-36-45.5 3-5-45.5-54.5 50 13.6 100.3 53.2 1278 3-6-54.5-64.5 3-7-64.5-73.5 72.5 7.1 106.9 32.9 571 3-8-73.5-84 83 14.9 105.1 65.7 726

Footnotes: Suction test description – Section 4.2.9.1.3 and Appendix D.


Test 1 Test 2

Sample Ps Cor. Ps w ρdry Sample Ps

Cor. Ps w ρdry Swell Sample #

Type [kPa] [kPa] [%] [pcf] Type [kPa] [kPa] [%] [pcf] Index 3-1-9.5-17.5 R 48.5 100.0 10.6 108.1 R 70 124 11 108 0.0155 3-2-17.5-25 3-3-25-36

3-4-36-45.5 3-5-45.5-54.5 R 68.5 114.0 13.3 100.6 R 90 177 14 100 0.0202 3-6-54.5-64.5 3-7-64.5-73.5 3-8-73.5-84

Footnotes R - reconstructed test I - insitu test See section 4.2.7 for test description, submerged test

394

8 SC

7 CL

6 CL

5 CL

4 CL

3 CL

2 CL

1 CL

Gra

vel

Conc

rete

Core

# S

oil C

lass

if.85

9510

511

5γ d

ry [p

cf]

0 10 20 30 40 50 60 70 80 90

Depth [inch]

510

15

w [%

]0.

00.

51.

0

w/P

L0

5010

0

S [%

]0

1000

2000

Suct

ion

[kPa

]

Figu

re 1

1.

Prof

ile.

395

0

20

40

60

80

100

0.0010.010.1110

Grain Diameter [mm]

% P

assi

ng

3-2-17.5-253-4-36-45.53-6-54.5-64.53-8-73.5-84


0.40

0.45

0.50

0.55

0.60

0.65

0.70

0.75

10 100 1000 10000

Pressure [kPa]

Voi

d Ra

tio

3-1 9.5-17.5Reconstructed3-5-45.5-54.5Reconstructed


396

0

20

40

60

80

100


Deg

ree

of S

atur

atio

n [%

]

3-1-16.6 (dry spec. w eight = 108)

3-3-35 (80)

3-5-50 (100)

3-7-72.5 (106)

3-8-83 (105)


397

Site # 4


Soil # 4 City Chandler Cross Roads Cooper Rd./ Chandler Blvd. Year of Construction 1999 Date of Sampling 4/2003

2Lot Size [ft ] 4 813 2House Size [ft ] 1 208

Construction Type wood frame, commercial Foundation Type stem and footer Slab Thickness [in] 3 Thickness of Gravel Layer [in] 2.5 Landscape near sampling area desert, desert trees Distance from slab edge to core location [ft] 12 Pool no History of Leaks no


398



LL PL PI P200 [%]

% clay


[ppm]

4-1-5.5-16 CL 34.5 20.5 14 67.4 1.6E-07 4-2-16-25 CL 37.9 20.4 17 64.9 17 2.823

4-3-25-35.5 CL 40.6 21.7 19 57.5 4-4-35.5-45.75 SM-SC 24.3 18.0 6 36.8 4-5-45.75-55 SM-SC 24.3 18.0 6 36.8 4.8E-07 2.764

4-6-55-65 SC 32.5 21.3 11 44 4-7-65-75 SC 32.5 21.3 11 29.5





4-1-5.5-16 8 12.51 119.1 74.4 1880 4-1-5.5-16 10 12.62 105.0 53.0 1648 4-2-16-25 24 14.00

4-3-25-35.5 30 12.88 115.7 70.1 1640 4-3-25-35.6 34 12.70 116.3 70.2 1615

4-4-35.5-45.75 40 9.20 4-4-35.5-45.75 44 10.77 109.9 50.8 521 4-5-45.75-55 50 10.81 101.3 42.8 254 4-5-45.75-55 53 14.35 93.1 46.8 135

4-6-55-65 64 13.29 4-7-65-75 72 8.39 99.0 31.5 262 4-7-65-75 74 8.34 99.0 31.2 215



Test 1 Test 2



Type [kPa] [kPa] [%] [pcf] Type [kPa]

[kPa] [%] [pcf] Index 4-1-5.5-16 R 217 291.6 12.9 108.9 0.0358

4-5-45.75-55 R 12.5 20.0 12.4 97.2 R 10 10.4 13.2 96.7 0.0088 Footnotes

R - reconstructed test I - insitu test See section 4.2.7 for test description, submerged test

399

010

0020

00

Suct

ion

[kPa

]0

5010

0

S [%

]

7 SC

6 SC

5 SM

-SC4 SM

-SC3 C

L

2 C

L

1 C

L

Gra

vel

Con

cret

e

Cor

e #

Soi

l Cla

ssif.

8595

105

115

γ dry

[pcf

]

0 10 20 30 40 50 60 70 80

Depth [inch]

510

15

w [%

]0.

00.

51.

0

w/P

L

Figu

re 1

6.

Prof

ile

400

0

20

40

60

80

100

0.0010.010.1110

Grain Diameter [mm]

% P

assi

ng

4-1-5.5-164-2-16-254-3-25-35.54-5-45.75-554-7-65-75


0.40

0.45

0.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

1 10 100 1000 10000

Pressure [kPa]

Voi

d R

atio




401

0

20

40

60

80

100


Degr

ee o

f Sat

urat

ion

[%]

4-1-8 (dry spec. w eight = 119)

4-1-10 (105)

4-3-30 (116)

4-4-44 (110)

4-5-50 (101)

4-5-54(93)

4-7-72 (99)


402

Site # 5


Soil # 5 City Chandler Cross Roads Chandler Heights Rd./Arizona Ave. Year of Construction 2000 Date of Sampling 5/2003


Construction Type wood frame Foundation Type stem and footer Slab Thickness [in] 6 Thickness of Gravel Layer [in] 2.5 Landscape near sampling area desert, sidewalk potentially impedes drainage Distance from slab edge to core location [ft] 14 Pool yes History of Leaks no Previous Land Use Undeveloped desert




LL PL PI P200 [%]

% clay

ksat [cm/s]

Sulfate [ppm] Gs CEC

5-1-8.5-16.5 SM NP NP 42.9 3.4E-07 2.784 24 5-2-16.5-27 SC 44.5 17.6 27 41.2 18 3.5E-07 25 5-3-27-36 32.8

5-4-36.5-47 5-5-47-56 SC 39.8 22.0 18 37.2 2.8E-07 2.751 5-6-56-66

5-7-66-75.75 5-8-75.75-83.5 SC 26.7 18.7 8 28.2

403


Sample # Depth Water Content γdry Saturation Suction [in] [%] [pcf] [%] [kPa]

5-1-8.5-16.5 12 6.60 103.8 27.4 5-1-8.5-16.5 15.5 7.28 96.7 25.6 7300 5-2-16.5-27 18.5 9.55 125.1 69.1 1564 5-3-27-36 35 5.97 107.8 27.4 9900

5-4-36.5-47 38.5 7.05 108.3 33.4 1225 5-5-47-56 50 9.27 98.3 34.4 5400 5-5-47-56 54 9.35 96.9 33.5 5915 5-6-56-66 58 7.65 105.3 33.7 3250

5-7-66-75.75 60 5-8-75.75-83.5 78 6.33 109.0 30.5 9216F

Footnotes: Gray background - values estimated with w and γd only, Black background - values estimated with scanning curve based on measured suction F Filter Paper Test Suction test description – Section 4.2.9.1.3 and Appendix D.


Test 1 Test 2



Type [kPa] [kPa] [%] [pcf] Type [kPa] [kPa] [%] [pcf] Index 5-1-8.5-16.5 I 10 10.4 6.6 103.8 R 3.5 3.46 7.8 96.2 0.0048 5-2-16.5-27 R 0.0067 5-5-47-56 I 14.2 15.8 9.3 98.3 R 17 20 9 96.9 0.0122

Footnotes R - reconstructed test I - insitu test See section 4.2.7 for test description, submerged test.

Table 22. Compaction and EI Tests.

Test Type Parameter Name Value Expansion Index 9.0

AZ Modified Expansion γd [pcf] 110.6 Initial Water Content [%] 11.5 Index Test

Saturation [%] 56.7 EI 50 6.3

Expansion Index Test Expansion Index 4.0 as per ASTM D 4829-3 γd [pcf] 109.0 Standard Initial Water Content [%] 11.7 Saturation [%] 55.4

wopt [%] 13.24 Compaction Test γmax [pcf] 116.90

404

050

0010

000

Suct

ion

[kPa

]0

5010

0

S [%

]

8 SC

7 SC

6 SC

5 SC43

2 SC

1 SM

Gra

vel

Conc

rete

Core

# S

oil C

lass

if.90

100

110

120

130

γ dry

[pcf

]

0 10 20 30 40 50 60 70 80 90

Depth [inch]

510

15

w [%

]0.

00.

51.

0

w/P

L

Figu

re 2

1.

Prof

ile.

405

0

20

40

60

80

100

0.0010.010.1110

Grain Diameter [mm]

% P

assi

ng

5-1-8.5-16.55-2-16-275-3-27-365-5-47-565-8-75.75-83.5


0.40

0.45

0.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

1 10 100 1000

Pressure [kPa]

Voi

d Ra

tio

5-1-8.5-16.5 Reconstructed

5-1-8.5-16.5 Insitu

5-2:4-16.5-47 EI test


406

0.40

0.45

0.50

0.55

0.60

0.65

0.70

0.75

0.80

1.0 10.0 100.0 1000.0

Pressure [kPa]

Voi

d Ra

tio

5-5-47-56 Insitu



5-2:4-16.5-47

wopt = 13.24%

γd max = 116.9 pcf

109

110

111

112

113

114

115

116

117

118

11 12 13 14 15 16 17 18

Gravimetric Water Content [%]

Dry

Spe

cific

Wei

ght [

pcf]

Figure 25. Compaction Test.

407

0

20

40

60

80

100


Degr

ee o

f Sat

urat

ion

[%]

5-1-15.5 (dry spec. w eight = 97)

5-2-18.5 (125)5-3-35 (108)

5-4-38.5 (108)5-5-54 (97)

5-6-58(105)5-8-78 (108)

Figure 26. SWCC: S vs. Matric Suction.

408

Site # 6


Soil # 6 City Mesa Cross Roads Southern Ave./Stapley Dr. Year of Construction 1979 Date of Sampling 6/2003


Construction Type wood frame Foundation Type stem and footer Slab Thickness [in] 3 Thickness of Gravel Layer [in] 4.5 Landscape near sampling area paved, sidewalk, large desert trees Distance from slab edge to core location [ft] 11 Pool Yes History of Leaks No Previous Land Use Unknown


409



LL PL PI P200 [%]

% clay


[ppm]

6-1-7.5-17 SC 32.9 18.2 15 36.2 2.5E-07 2.742 75 6-2-17-29.5 21.5 6-3-29.5-39 CL 46.0 24.7 21 71.1

6-4-39.5-44.5 46.0 23.2 23 76 6-5-44.5-48 46.0 23 23 81 6-6-48-52.5 CL 46.2 21.8 24 85.7 30 2.668 32 6-7-52.5-62 CL 43.6 22.4 21 85 1.4E-08 6-8-62-65.5 50.4 23.8 27 85 6-9-65.5-72 CH 57.22 25.21 32 85.1 41




6-1-7.5-17 8.5 7.50 104.5 32.5 15100 6-1-7.5-17 10 10.94 96.5 39.1 7900 6-1-7.5-17 12 10.26 96.8 36.9 9700 F

6-1-7.5-17 14.5 10.62 96.6 38.0 8800 6-2-17-29.5 16 10.94 96.5 39.1 7900 6-3-29.5-39 33 11.63 107.27 55.3 9100 F

6-3-29.5-39 38 11.63 107.3 55.3 9100 6-4-39.5-44.5 6-5-44.5-48 46 11.90 109.0 60.7 3700 F

6-6-48-52.5 49 12.04 116 74.5 6-6-48-52.5 51.5 12.16 116.2 75.7 2188 6-7-52.5-62 54 12.27 119.1 83.1 6-7-52.5-62 60 13.79 116.4 86.3 3400 6-8-62-65.5 6-9-65.5-72 71 14.65 116.5 91.8 1590

Footnotes: Gray background - values estimated with w and γd, Black background - values estimated with scanning curve F Filter Paper Test Suction test description – Section 4.2.9.1.3 and Appendix D.

410


Test 1 Test 2 Cor. Ps

Cor. Ps Sample Ps w γdry Sample Ps w γdry Swell Sample #

Type [kPa] [kPa] [%] [pcf] Type [kPa] [kPa] [%] [pcf] Index 6-1-7.5-17 I 20 42.9 10.6 97.0 I 76 93.3 7.5 105 0.0173

6-7-52.5-62 I 130 179.4 12.3 119.1 I 627 7.7 120 0.0304 Footnotes

I - insitu test See section 4.2.7 for test description, submerged test.

0

20

40

60

80

100

0.0010.010.1110

Grain Diameter [mm]

% P

assi

ng

6-1-7.5-17

6-3-29.5-39

6-6-48-52.5

6-9-65.5-72


411

9 C

H8

CL

7 C

L

6 C

L5

CL

4 C

L

3 C

L

2 SC

1 SC

Gra

vel

Con

cret

e

Core

# S

oil C

lass

if.90

100

110

120

γ dry

[pcf

]

0 10 20 30 40 50 60 70 80

Depth [inch]

510

15

w [%

]0.

00.

51.

0

w/P

L0

5010

0

S [%

]10

010

000

Suct

ion

[kPa

]

Figu

re 2

9.

Prof

ile.

412

0.30

0.35

0.40

0.45

0.50

0.55

0.60

0.65

0.70

0.75

0.80

1 10 100 1000 10000

Pressure [kPa]

Voi

d Ra

tio6-1-7.5-17 in situ

6-1-7.5-17 in situ

6-7-52.5-62 in-situ


0

20

40

60

80

100


Degr

ee o

f Sat

urat

ion

[%]


6-3-33 (107)

6-5-45 (109)

6-6-51.5 (116)

6-9-71 (116) & 6-7-54 (116)


413

Site # 7

The property is located next to site #6. Both sites have similar site conditions in terms of

human imposed surface conditions, soil type, construction type and structure age. Soil testing

was not performed. Initially the extruded cores were kept as a duplicate of site #6, and then

additional soil testing was deemed unnecessary.


Soil # 7 City Mesa Cross Roads Southern Ave./Stapley Dr. Year of Construction 1979 Date of Sampling 7/2003 Lot Size [ft2] 12 650 House Size [ft2] 1 672 Construction Type wood frame Foundation Type stem and footer Slab Thickness [in] 3.5 Thickness of Gravel Layer [in] 2.5 Landscape near sampling area desert, paved Distance from slab edge to core location [ft] 12 Pool no History of Leaks no Previous Land Use Unknown

Table 28. Visual Soil Description.

Core # Soil Description 0-3.5 Concrete 3.5-6.0 Granular base 7-1-6-17 Dry, light brown sandy clay 7-2-17-27 Dry, light brown sandy clay 7-3-27-37 Dry, light brown sandy clay 7-4-37-47 Dry, hard, brown clay 7-5-47-50.5 Dry, hard, brown clay 7-6-50.5-55 Dry, hard, brown clay 7-7-55-60.5 Dry, hard, brown clay 7-8-60.5-64.5 Dry, hard, brown clay

414

Site # 8


Soil # 8 City Gilbert Cross Roads Gilbert Rd. /Baseline Rd. Year of Construction 1987 Date of Sampling 6/2003


Construction Type wood frame Foundation Type stem and footer Slab Thickness [in] 3.5 Thickness of Gravel Layer [in] 3.5 Landscape near sampling area turf irrigated every 30 min., large trees Distance from slab edge to core location [ft] 9.8 Pool no History of Leaks no Previous Land Use Unknown


415



LL PL PI P200 [%]

% clay


[ppm]

8-1-7-17 SM 40.2 19.3 21 49.9 5.8E-08 2.719 8-2-17-27 CL 44.7 22.5 21.9 56.8

8-3-27-37.5 CL 49.1 25.7 23 63.6 8-4-37.5-47.5 CL 42.7 23.5 19.0 57.5 8-5-47.5-57.5 CL 36.3 21.2 15 51.3 8 5.3E-08 2.743 8-6-57.5-67.5 SC 35.0 20.8 14.2 45.5 8-7-67.5-77.5 SC 33.7 20.4 13 39.6 8-8-77.5-88 36.4 8-9-88-96.5 SM NP NP 33.2

Footnotes: shaded used for estimated values.




8-1-7-17 9 6.24 100.8 25.0 8-1-7-17 11 10.63 107.0 49.8 1600 8-1-7-17 13 11.18 108.12 53.8 8-1-7-17 15 13.18 116.9 80.0 1004

8-2-17-27 8-3-27-37.5 34 18.50 8-3-27-37.5 35.5 17.56 102.5 72.9 495.5

8-4-37.5-47.5 8-5-47.5-57.5 50 13.74 112.6 73.0 8-5-47.5-57.5 53.5 14.54 112.91 77.9 8-5-47.5-57.5 55.5 13.67 114.4 76.2 251.6 8-6-57.5-67.5 8-7-67.5-77.5 73 12.57 8-7-67.5-77.5 75 11.80 106.0 53.0 253.0 8-8-77.5-88 8-9-88-96.5 94.5 6.04 8-9-88-96.5 95.5 9.88 98.2 36.7 44.0


416


Test 1 Test 2 Cor. Ps

Cor. Ps Sample Ps w γdry Sample Ps w γdry Swell Sample #

Type [kPa]

[kPa] [%] [pcf] Type [kPa] [kPa] [%] [pcf] Index 8-1-7-17 I 22 25.8 11.2 108.1 I 19 18.8 6.2 101 0.0105

8-2-17-27 8-3-27-37.5

8-4-37.5-47.5 8-5-47.5-57.5 I 24.2 53.0 14.5 112.9 I 86 143 13.7 113 0.0201 8-6-57.5-67.5 8-7-67.5-77.5

8-8-77.5-88 8-9-88-96.5

Footnotes R - reconstructed test I - insitu test See section 4.2.7 for test description, submerged test.

0

20

40

60

80

100

0.0010.010.1110

Grain Diameter [mm]

% P

assi

ng

8-1-7-178-3-27-37.58-5-47.5-57.58-7-67.5-77-58-9-88-96.5


417

010

0020

00

Suct

ion

[kPa

]0

5010

0

S [%

]

9 SM8

7 SC

6 SC5 CL

4 CL

3 CL

2 CL

1 SM

Gra

vel

Conc

rete

Core

# S

oil C

lass

if.90

100

110

120

130

γ dry

[pcf

]

0 10 20 30 40 50 60 70 80 90 100

Depth [inch]

510

1520

w [%

]0.

00.

51.

0

w/P

L

Figu

re 3

4.

Prof

ile.

418

0.40

0.45

0.50

0.55

0.60

0.65

0.70

1 10 100 1000 10000

Pressure [kPa]

Void

Rat

io

8-1-7-17 Insitu8-1-7-17 Insitu8-5-47.5-57.5 in situ8-5-47.5-57.5 in situ


0

20

40

60

80

100


Degr

ee o

f Sat

urat

ion

[%]

8-1-15 (dry spec. w eight = 117)8-1-11 (107)8-3-35.5 (102)8-5-55.5 (114)8-7-75 (106)8-9-95.5 (98)


419

Site # 9


Soil # 9 City Chandler Cross Roads Warner/ Alma School Dr. Year of Construction 1983 Date of Sampling 5/2003


Construction Type wood frame Foundation Type stem and footer Slab Thickness [in] 4 Thickness of Gravel Layer [in] 5

areas of desert and very green turf near boring location Landscape near sampling area

Distance from slab edge to core location [ft] 8.7 Pool no History of Leaks no Previous Land Use Unknown


420



LL PL PI P200 [%]

% clay


[ppm]

9-1-9-19 CL 28.0 16.9 11 54.3 7.1E-07 2.751 19 9-2-19-29 SC 36.5 20.6 15.9 44.3 9-3-29-39 SC 44.9 24.3 21 34.4 6.9 9-4-39-49 SC 41.7 22.8 18.9 37.3

9-5-49-56.5 SC 38.5 21.3 17 40.3 7.0E-08 2.739 9-6-56.5-65.5 CL 43.2 22.7 20.6 50.1 9-7-65.5-72 CL 47.8 24.1 24 59.9

Footnotes: shaded used for estimated values.



9-1-9-19 11 7.18 105.0 31.3 14400 9-1-9-19 16 8.03 98.4 29.9 9-1-9-19 18 8.85 103.8 37.5 7750 F

9-2-19-29 9-3-29-39 32 12.00 111.0 61.1 6000 F

9-3-29-39 38 13.02 109.4 63.6 2500 9-4-39-49

9-5-49-56.5 51 9.35 112.0 49.1 9-5-49-56.5 53 10.30 114.6 57.9 8900 F

9-5-49-56.5 55 10.70 111.4 55.3 2900 9-6-56.5-65.5 9-7-65.5-72 68 13.55 110.0 67.5 10500F

9-7-65.5-72 71 14.66 109.4 71.9 7400 Footnotes:

Gray background - values estimated with w and γd, Black background - values estimated with scanning curve based on measured suction F Filter Paper Test Suction test description – Section 4.2.9.1.3 and Appendix D.


Test 1 Test 2



Type [kPa] [kPa] [%] [pcf] Type [kPa] [kPa] [%] [pcf] Index 9-1-9-19 I 6 8.3 8.0 98.4 0.0126

9-5-49-56.5 I 210 285.7 10.3 114.6 0.0241 Footnotes:

I - insitu test See section 4.2.7 for test description, submerged test.

421

1000

1000

010

0000

Suct

ion

[kPa

]0

5010

0

S [%

]

7 C

L

6 C

L

5 SC

4 SC

3 SC

2 SC

1 C

L

Gra

vel

Con

cret

e

Cor

e #

Soi

l Cla

ssif.

9010

011

012

013

0γ d

ry [p

cf]

0 10 20 30 40 50 60 70 80

Depth [inch]

510

15

w [%

]0.

00.

51.

0

w/P

L

Figu

re 3

8.

Prof

ile.

422

0

20

40

60

80

100

0.0010.010.1110

Grain Diameter [mm]

% P

assi

ng

9-1-9-19

9-3-29-39

9-5-49-56.5

9-7-65.5-72


0.40

0.45

0.50

0.55

0.60

0.65

0.70

0.75

0.80

1 10 100 1000 10000

Pressure [kPa]

Voi

d Ra

tio

9-1-9-19 Insitu

9-5-49-56.5 Insitu


423

0

20

40

60

80

100


Degr

ee o

f Sat

urat

ion

[%]


9-3-32 (111)

9-3-38 (109)9-5-55 (111)

9-5-52 (112)

9-7-68&71 (110&109)


424

Site # 10


Soil # 10 City Gilbert Cross Roads Cooper Rd./ Ray Rd. Year of Construction 1995 Date of Sampling 5/2003


Construction Type wood frame Foundation Type stem and footer Slab Thickness [in] 4 Thickness of Gravel Layer [in] 3

gravel and turf areas, sidewalks and few small trees Landscape near sampling area

Distance from slab edge to core location [ft] 9 Pool no History of Leaks no Previous Land Use Unknown


425



LL PL PI P200 [%]

% clay


[ppm]

10-1-7-17 SC 31.1 16.8 14 48.2 6.1E-08 2.714 10-2-17-27.5 CL 29.7 18.9 10.7 53.4 3.7E-07

10-3-27.5-37.5 CL 28.3 21.1 7 58.6 10-4-37.5-47.5 CL 31.2 21.8 9.5 60.8 10-5-47.5-57.5 CL 34.0 22.4 12 63 21 3.3E-08 23 10-6-57.5-68 SC 31.0 20.8 10.5 45.0 10-7-68-78 SC 28.0 19.2 9 27.1 2.736 10-8-78-84

Footnotes: shaded used for estimated values,



10-1-7-17 9 10.03 10-1-7-17 11 10.85 10-1-7-17 12 11.21 124.3 84.9 2450 10-1-7-17 15 11.44 127.0 94.2 665

10-2-17-27.5 10-3-27.5-37.5 33 14.80 100 58.0 10-3-27.5-37.5 35 15.11 100.0 59.2 231 10-4-37.5-47.5 10-5-47.5-57.5 53 14.52 110.6 73.6 268 10-5-47.5-57.5 55 12.61 109.0 61.4 10-5-47.5-57.5 56 11.91 107.9 56.4 10-6-57.5-68 10-7-68-78 72 8.87 104.83 38.9 443 10-7-68-78 76 10.28 100.44 40.5 453.5

10-8-78-84 80 10.56 100 41.1 10-8-78-84 83 13.97 Footnotes:

Gray background - values estimated, Suction test description – Section 4.2.9.1.3 and Appendix D.

426


Test 1 Test 2 Sample Ps Cor. Ps w γdry Sample Ps Cor. Ps w γdry Swell Sample #

Type [kPa] [kPa] [%] [pcf] Type [kPa] [kPa] [%] [pcf] Index 10-1-7-17 I 31 154.3 11.2 124.3 0.0153 10-5-47.5-

57.5 I 80.9 118.8 11.9 107.9 0.0219 Footnotes:

I - insitu test, See section 4.2.7 for test description, submerged test




Saturation [%] 64.9 EI 12.5 50



0

20

40

60

80

100

0.0010.010.1110

Grain Diameter [mm]

% P

assi

ng

10-1-7-17

10-3-27.5-37.5

10-5-47.5-57.5

10-7-68-78


427

010

0020

0030

00

Suct

ion

[kPa

]0

5010

0

S [%

]

8

7 SC

6 SC5 CL

4 CL

3 CL

2 CL

1 SC

Gra

vel

Conc

rete

Core

# S

oil C

lass

if.90

100

110

120

130

γ dry

[pcf

]

0 10 20 30 40 50 60 70 80 90

Depth [inch]

510

15

w [%

]0.

00.

51.

0

w/P

L

Figu

re 4

4.

Prof

ile.

428

0.30

0.35

0.40

0.45

0.50

0.55

0.60

1 10 100 1000 10000

Pressure [kPa]

Voi

d Ra

tio 10-1-7-17 Insitu

10-5-47.5-57.5 Insitu


0.50

0.55

0.60

0.65

0.70

0.75

1.0 10.0 100.0 1000.0 10000.0

Pressure [kPa]

Voi

d R

atio

10-2-17-27.5 EI

10-2-17-27.5 EI(AZ)

Figure 46. Consolidation Test – EI Data.

429

10-2-17-27.5

wopt = 15.0%

γd max = 117 pcf

104105106107108109110111112113114115116117118

10 11 12 13 14 15 16 17 18 19 20


Dry

Spe

cific

Wei

ght [

pcf]


0

20

40

60

80

100


Degr

ee o

f Sat

urat

ion

[%]

10-1-15 (dry spec. w eight = 127)

10-3-32 (100)

10-5-53 (111)

10-7-76 (100)

10-7-72 (105)


430

Site # 11


Soil # 11 City Gilbert Cross Roads Warner Rd./ Lindsay Rd. Year of Construction 1999 Date of Sampling 6/2003


Construction Type wood frame Foundation Type stem and footer Slab Thickness [in] 6 Thickness of Gravel Layer [in] 8.5 Landscape near sampling area gravel, few trees Distance from slab edge to core location [ft] 10.8 Pool no History of Leaks no Previous Land Use Unknown


431



LL PL PI P200 [%]

% clay


[ppm]

11-1-14.5-24 CL 34.8 19.6 15 1.8E-07 2.684 40 11-2-24-34 CL 40.8 21.2 20 55.9

11-3-34-46.5 CL 39.1 20.6 18 11-4-46.5-59.5 CL 49.1 24.3 25 55.8 13 11-5-59.5-70 CL 49.1 24.3 25 1.7E-07 2.663 11-6-70-80 CL 49.1 24.3 25 11-7-80-90 CL 38.6 21.7 17 52.4

Footnotes: Shaded used for estimated values,



11-1-14.5-24 18 15.19 111.24 81.3 169.0 11-1-14.5-24 22 15.45 111.36 83.0 139.0 11-2-24-34 32 16.91

11-3-34-46.5 43 13.75 105.77 64.2 263.0 11-4-46.5-59.5 58 15.47 11-5-59.5-70 63.5 14.06 110.89 75.7 124.0 11-5-59.5-70 65 11.46 110.88 61.7 411.5 11-6-70-80 79 11.92 11-7-80-90 83 9.53 106.56 45.7 237.3

Footnotes: Gray background - values estimated with w and γd, Suction test description – Section 4.2.9.1.3 and Appendix D.


Test 1 Test 2

Sample Ps Cor. Ps w γdry Sample Ps Cor. Ps w γdry Swell Sample #

Type [kPa] [kPa] [%] [pcf] Type [kPa] [kPa] [%] [pcf] Index 11-1-14.5-24 I 19 35.2 15.2 111.2 11-2-24-34 R 26 50.1 16.6 109 0.2288

11-3-34-46.5 11-4-46.5-59.5 11-5-59.5-70 I 45.0 73.0 14.1 110.9 R 109 209 12.4 110 0.0207 11-6-70-80 11-7-80-90

Footnotes: R - reconstructed test I - insitu test, See section 4.2.7 for test description, submerged test.

432

100

1000

Suct

ion

[kPa

]0

5010

0

S [%

]

7 C

L

6 C

L

5 C

L

4 C

L

3 C

L

2 C

L

1 C

L

Gra

vel

Con

cret

e

Core

# S

oil C

lass

if.90

100

110

120

130

γ dry

[pcf

]

0 10 20 30 40 50 60 70 80 90

Depth [inch]

510

1520

w [%

]0.

00.

51.

0

w/P

L

Figu

re 5

0.

Prof

ile.

433

0

20

40

60

80

100

0.0010.010.1110

Grain Diameter [mm]

% P

assi

ng

11-2-24-34

11-4-46.5-59.5

11-6-70-80


0.40

0.45

0.50

0.55

0.60

0.65

0.70

0.75

1 10 100 1000 10000

Pressure [kPa]

Voi

d Ra

tio

11-1-14.5-24 In situ


11-5-59.5-70 in situ



434

0

20

40

60

80

100


Degr

ee o

f Sat

urat

ion

[%]

11-1-19 (dry spec. w eight = 111)

11-3-43 (106)

11-5-65 (111)

11-7-83 (107)


435

Site # 12


Soil # 12 City Chandler Cross Roads Cooper Rd. /Chandler Blvd. Year of Construction 1995 Date of Sampling 5/2003


Construction Type wood frame Foundation Type stem and footer Slab Thickness [in] 2.75 Thickness of Gravel Layer [in] 3.25 Landscape near sampling area turf, sidewalk, few small trees and paved area Distance from slab edge to core location [ft] 9 Pool no History of Leaks no Previous Land Use Unknown


436



LL PL PI P200 [%]

% clay


[ppm]

12-1-6-12 CL 35.1 21.2 14 1.1E-07 2.77 52 12-2-12-24.5 CL 38.0 20.1 18 61.5

12-3-24.5-37.5 CL 38.0 20.1 18 12-4-37.5-48 SC 32.8 18.7 14 46.8 12-5-48-62 SC 36.8 23.3 13 7.1E-08 2.717 12-6-62-75 SC 37.7 21.7 16 29 12-7-75-85 SC 34.5 21.1 13.5 39.8 12

12-8-85-96 SC 31.3 20.4 11 Footnotes: Shaded used for estimated values,



12-1-6-12 9 19.11 107.4 87.6 12-1-6-12 11 15.30 112.0 78.6 89

12-2-12-24.5 23 19.48 12-3-24.5-37.5 35.5 16.81 111.8 87.4 29.5 12-4-37.5-48 47 15.58 12-5-48-62 57 14.65 116.7 88.7 12-5-48-62 60 18.19 97.2 66.8 52.8 12-6-62-75 74 19.00 12-7-75-85 12-8-85-96 93 16.44 106.8 76.6 85.6



Test 1 Test 2



Type [kPa] [kPa] [%] [pcf] Type [kPa] [kPa] [%] [pcf] Index 12-1-6-12 I 17 60. 19.1 107.4 R 28 74.4 18.8 108 0.024

12-2-12-24.5 12-3-24.5-37.5 12-4-37.5-48 12-5-48-62 I 40.9 80. 14.7 116.7 R 33 66.3 18.3 97.2 0.020 12-6-62-75 12-7-75-85

12-8-85-96 Footnotes:

R - reconstructed test I - insitu test, See section 4.2.7 for test description, submerged test.

437

050

100

Suct

ion

[kPa

]0

5010

0

S [%

]0.

00.

51.

0

w/P

L

Figu

re 5

5.

Prof

ile.

1015

20

w [%

]90

100

110

120

130

γ dry

[pcf

]

8 SC

7 SC

6 SC

5 SC

4 SC

3 C

L

2 C

L

1 C

LG

rave

lC

oncr

ete

Core

# S

oil C

lass

if.

0 10 20 30 40 50 60 70 80 90 100

Depth [inch]

438

0

20

40

60

80

100

0.0010.010.1110

Grain Diameter [mm]

% P

assi

ng

12-2-12-24.5

12-4-37.5-48

12-6-62-75

12-7-75-85


0.35

0.40

0.45

0.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

1 10 100 1000 10000

Pressure [kPa]

Voi

d Ra

tio

12-1-5-12 Insitu12-1-5-12 Reconstructed12-5-48-62 Insitu12-5-48-62 Reconstructed


439

0

20

40

60

80

100


Degr

ee o

f Sat

urat

ion

[%]

12-1-11 (dry spec. w eight = 112)

12-3-35.5 (112)

12-5-50 (97)

12-8-93 (107)


440

Site # 13


Soil # 13 City Mesa Cross Roads Baseline Rd. / Linday Rd. Year of Construction 1982 Date of Sampling 12/2003


Construction Type wood frame Foundation Type stem and footer Slab Thickness [in] 3.5 Thickness of Gravel Layer [in] 3.5 Landscape near sampling area desert, few desert trees Distance from slab edge to core location [ft] 16 Pool no History of Leaks no Previous Land Use Unknown


441



LL PL PI P200 [%]

% clay


[ppm]

13-1-7-13 CL 40.9 20.0 21 65.5 24 1.1E-07 2.727 12 13-2-13-23.5 CL 37.8 19.4 18.4 62.1 26.5 4.0E-07 13-3-23.5-33 CL 34.8 18.9 16 58.7 29 13-4-33-42.5 CL 42.0 20.6 21.4 65.6 34.0

13-5-42.5-51.5 CL 49.1 22.3 27 72.4 39 5.5E-08 2.716 34 13-6-51.5-59.5 CL 44.5 21.3 23.2 68.8 13-7-59-5-66.5 CL 39.8 20.3 19.5 65.2 13-8-66.5-71 CL 35 19.32 16 61.4 Footnotes: Shaded used for estimated values.


Test 1 Test 2


Type [kPa] [kPa] [%] [pcf] Type [kPa] [kPa] [%] [pcf] Index 13-1-7-13 I 143 263.7 11.5 11.3 0.0298

13-2-13-23.5 R 0.0177 13-5-42.5-51.5 I 174 212.0 16.0 115.2 0.0262 Footnotes








442


Sample # Saturation Suction Depth Water Content γdry

[in] [%] [pcf] [%] [kPa] 13-1-7-13 8 11.45 13-1-7-13 9 11.00 116.5 65.7 4500 13-1-7-13 11 11.27 111.5 58.8 1045

13-2-13-23.5 22.5 12.58 13-3-23.5-33 30 10.62 13-3-23.5-33 31 10.94 110.2 55.5 1564 13-4-33-42.5

13-5-42.5-51.5 46 15.95 13-5-42.5-51.5 47 15.09 115.6 88.7 1150 13-5-42.5-51.5 49.5 15.99 115.2 92.9 600 13-6-51.5-59.5 13-7-59-5-66.5 13-8-66.5-71 67 10.34 13-8-66.5-71 69 9.99 106.2 45.9 675

Footnotes: , Gray background - values estimated with w and γd

Black background - values estimated with scanning curve, Suction test description – Section 4.2.9.1.3 and Appendix D.

0

20

40

60

80

100

0.0010.010.1110

Grain Diameter [mm]

% P

assi

ng

13-1-7-1313-3-23.5-3313-5-42.5-51.513-8-66.5-71


443

100

1000

1000

0

Suct

ion

[kPa

]0

5010

0

S [%

]

8 CL

7 CL

6 CL

5 CL

4 CL

3 C

L

2 C

L

1 CL

Gra

vel

Con

cret

e

Core

# S

oil C

lass

if.90

100

110

120

130

γ dry

[pcf

]

0 10 20 30 40 50 60 70 80

Depth [inch]

510

1520

w [%

]0.

00.

51.

0

w/P

L

Figu

re 6

1.

Prof

ile

444

0.40

0.45

0.50

0.55

0.60

0.65

0.70

1 10 100 1000 10000Pressure [kPa]

Void

Rat

io13-1-7-13 Insitu

13-2-13-23.5 EI(AZ)

13-5-42.5-51.5 Insitu


13-2-13-23.5

wopt = 16.65%

γd max = 110.3 pcf

103

104

105

106

107

108

109

110

111

15 16 17 18 19 20 21 22 23


Dry

Spe

cific

Wei

ght [

pcf]


445

0

20

40

60

80

100


Degr

ee o

f Sat

urat

ion

[%]


13-3-31 (110)

13-5-47 (116)

13-8-69 (106)


446

Site # 14


Soil # 14 City Mesa Cross Roads Lindsay Rd./US 60. Year of Construction 1981 Date of Sampling 12/2003


Construction Type wood frame Foundation Type stem and footer Slab Thickness [in] 3.5 Thickness of Gravel Layer [in] 4.5 Landscape near sampling area grass Distance from slab edge to core location [ft] 16 Pool no History of Leaks no Previous Land Use Unknown


447


Soil Sample # Classif.

LL PL PI P200 [%] % clay ksat [cm/s] Gs CEC Sulfate [ppm]

14-1-8-17.5 CL 37.8 20.4 17 64.9 28.5 9.8E-08 2.726 14-2-18.5-34.5 CL 43.4 20.5 22.8 69.4

14-3-34.5-47.75 CL 48.9 20.7 28 73.8 44 2.755 33 14-4-47.75-60 CL 41.4 18.8 22.6 63.0

14-5-60-68 CL 33.8 16.9 17 52.2 2.4E-07 2.754 14-6-68-77 CL

Footnotes: shaded used for estimated values,



14-1-8-17.5 11 18.06 111.2 93.7 10 14-1-8-17.5 13 17.26 14-1-8-17.5 14 15.13 112.3 80.8 310 14-1-8-17.5 16 17.45 110.0 87.6

14-2-18.5-34.5 14-3-34.5-47.75 42 18.41 110.1 91.1 575 14-3-34.5-47.75 44 18.36 14-3-34.5-47.75 45.5 17.75 111.2 90.3 649 14-4-47.75-60

14-5-60-68 64 10.90 14-5-60-68 66 10.33 105.6 45.6 1090 14-6-68-77 73 12.61 14-6-68-77 75 12.99 106.32 58.5 350




Type [kPa] [kPa] [%] [pcf] Type [kPa] [kPa] [%] [pcf] Index 14-1-8-17.5 I 16 62.3 17.5 110.0 0.0197

14-2-18.5-34.5 14-3-34.5-47.75 14-4-47.75-60

14-5-60-68 I 18.4 18.4 10.3 105.6 0.0172 14-6-68-77

Footnotes: I - insitu test, See section 4.2.7 for test description, submerged test.

448

6 CL

5 CL

4 CL

3 CL

2 CL

1 CL

Gra

vel

Conc

rete

Core

# S

oil C

lass

if.10

011

012

0γ d

ry [p

cf]

0 10 20 30 40 50 60 70 80

Depth [inch]

1015

20

w [%

]0.

00.

51.

0

w/P

L0

5010

0

S [%

]10

100

1000

1000

0

Suct

ion

[kPa

]

Figu

re 6

6.

Prof

ile.

449

0

20

40

60

80

100

0.0010.010.1110

Grain Diameter [mm]

% P

assi

ng

14-1-8-17.5

14-3-34.5-47.75

14-5-60-68


0.40

0.45

0.50

0.55

0.60

0.65

1 10 100 1000

Pressure [kPa]

Voi

d Ra

tio

14-1-8-17.5 Insitu

14-5-60-68 Insitu


450

0

20

40

60

80

100


Degr

ee o

f Sat

urat

ion

[%]

14-1-14 (dry spec. w eight = 112)14-3-45.5 (111)14-6-75 (106)14-1-11 w etting and drying14-3-42 drying curve


451

Site # 15


Soil # 15 City Gilbert Cross Roads Elliot Rd./ McQueen Rd. Year of Construction 1994 Date of Sampling 5/2003


Construction Type wood frame Foundation Type stem and footer Slab Thickness [in] 5 Thickness of Gravel Layer [in] 4 Landscape near sampling area desert, small tree Distance from slab edge to core location [ft] 8 Pool no History of Leaks no Previous Land Use Unknown


452



LL PL PI P200 [%]

% clay


[ppm]

15-1-9-15 SM NP NP 31.5 2.726 15-2-15-21 SM 21.4 18.5 3 37.7 7.1 15-3-21-32 SC 29.1 19.0 10 48.9 15-4-32-42 SC 26.6 17.8 9.0 37.6 15-5-42-55 SC 24.1 16.5 8 26.3 4.7E-06 2.723 15-6-55-64 SC 28.1 18.5 9.8 34.0 15-7-64-73 SC 32.0 20.4 12 41.6

Footnotes: Shaded used for estimated values.



15-1-9-15 10 4.65 15-1-9-15 11 5.17 91.8 16.6 3950

15-2-15-21 17 4.61 104.4 20.1 2700 15-2-15-21 19 6.89 15-2-15-21 20 6.90 103.8 29.6 393 15-3-21-32 28 10.90 15-3-21-32 29 9.26 15-3-21-32 30 10.90 94.3 37.2 289.2 15-4-32-42 15-5-42-55 46 12.56 110.9 64.8 15-5-42-55 51.5 7.58 97.4 27.9 431 15-5-42-55 53 7.69 99.1 29.5 363 15-6-55-64 15-7-64-73 70 8.42 15-7-64-73 71 8.46 15-7-64-73 72 8.42 97.8 31.3 606

Footnotes: Gray background - values estimated with w and γd, Black background - values estimated with scanning curve, Suction test description – Section 4.2.9.1.3 and Appendix D.


Test 1 Test 2


Type [kPa] [kPa] [%] [pcf] Type [kPa] [kPa] [%] [pcf] Index 15-5-42-55 I 1.9 5.5 12.6 110.9 0.008

Footnotes: I - insitu test, See section 4.2.7 for test description, submerged test

453

7 SC

6 SC

5 SC

4 SC

3 SC

2 SM

1 SM

Gra

vel

Conc

rete

Core

# S

oil C

lass

if.90

100

110

120

γ dry

[pcf

]

0 10 20 30 40 50 60 70 80

Depth [inch]

05

1015

w [%

]0.

00.

51.

0

w/P

L0

5010

0

S [%

]10

010

0010

000

Suct

ion

[kPa

]

Figu

re 7

1.

Prof

ile.

454

0

20

40

60

80

100

0.0010.010.1110

Grain Diameter [mm]

% P

assi

ng

15-1-8-18.515-2-15-2115-3-21-3215-5-42-5515-7-64-73


0.15

0.20

0.25

0.30

0.35

0.40

1 10 100 1000

Pressure [kPa]

Voi

d Ra

tio

15-5-42-55 Insitu


455

0

20

40

60

80

100


Degr

ee o

f Sat

urat

ion

[%]

15-2-20 (dry spec. w eight = 104)

15-2-17 (104)

15-3-30 (94)15-5-51.5 (97)

15-7-72 (98)

Figure 74. SWCC: S vs. Matric Suction

456

Site # 16


Soil # 16 City Phoenix Cross Roads Van Buren St. / 59th Ave. Year of Construction 1983 Date of Sampling 5/2004


Construction Type block Foundation Type stem and footer Slab Thickness [in] 4 Thickness of Gravel Layer [in] 6.5 Landscape near sampling area desert Distance from slab edge to core location [ft] 8 Pool no History of Leaks no Previous Land Use Unknown


457


Soil Sample # Classifi.

LL PL PI P200 [%]

% clay


[ppm]

16-1-10.5-21 CL 29.2 17.9 11 53.7 1.5E-07 2.802 76 16-2-21-34 CL 32.0 19.2 12.8 72.6 16-3-34-46 CL 34.7 20.4 14 91.5 20 16-4-46-58 CL 40.0 21.5 18.5 82.7 16-5-58-68 CL 45.3 22.6 23 73.8 30.5 4.5E-08 2.793 45

16-6-68-77.25 CL 44.9 23.4 21.5 81.5 16-7-77.25-85 CL 44.4 24.1 20 89.1 25.4 Footnotes: Shaded used for estimated values.



16-1-10.5-21 12 14.51 113.5 75.8 250 16-1-10.5-21 16 10.66 118.6 63.6 232 16-1-10.5-21 19.5 14.91 113.3 77.5 190 16-2-21-34 16-3-34-46 40 19.85 16-3-34-46 43 18.14 95.0 61.0 580 16-4-46-58 16-5-58-68 60 16.43 16-5-58-68 62 17.52 109.4 83.1 1167 16-5-58-68 65.5 16.94 112.7 87.2

16-6-68-77.25 16-7-77.25-85 83 20.39 100.0 77.2 569




Type [kPa] [kPa] [%] [pcf] Type [kPa] [kPa] [%] [pcf] Index 16-1-10.5-21 I 17 50.0 14.9 113.3 0.0161 16-5-58-68 I 152 235.2 16.9 112.7 0.0316


458

100

1000

1000

0

Suct

ion

[kPa

]0

200

400

S [%

]0.

00.

51.

0

w/P

L

Figu

re 7

6.

Prof

ile.

1015

2025

w [%

]90

100

110

120

130

γ dry

[pcf

]

7 C

L

6 C

L

5 CL

4 CL

3 CL

2 CL

1 C

L

Gra

vel

Conc

rete

Core

# S

oil C

lass

if.

0 10 20 30 40 50 60 70 80 90

Depth [inch]

459

0

20

40

60

80

100

0.00010.0010.010.1110

Grain Diameter [mm]

% P

assi

ng

16-1-10.5-2116-3-34-4616-5-58-6816-7-77.25-85


0.40

0.45

0.50

0.55

10 100 1000 10000Pressure [kPa]

Voi

d Ra

tio 16-1-10.5-21 Insitu

16-5-58-68 Insitu


460

0

20

40

60

80

100


Degr

ee o

f Sat

urat

ion

[%]

16-1-13 (dry spec. w eight = 119)16-1-13 drying curve16-1 (114)16-3-43 (95)16-5-62 (109)16-7-83 (100)


461

Site # 17


Soil # 17 City Litchfield Cross Roads Dysart Rd./ Bethany Home Rd. Construction Type wood frame Foundation Type stem and footer

Landscape near sampling area Sample obtained from area of recently removed turf landscape 5' away from foundation.

Pool no History of Leaks no Previous Land Use Agricultural Land

Table 68. Visual soil description.

Core # Depth [in] Soil Description

8.0-15 Gravel size decomposing granite very well mixed with light brown, hard clay. 17-1-8-16

15-16 Light brown, hard clay

17-2-16-25.5 16-25.5 Very loose sand mixed with gravel. Vertical layers of dark brown clay.

25.5-26" Light brown clay mixed with gravel. 26-28" Light brown clay; small amount of decomposed rock on one side. 28-28.5" Sandy silt; there is a small amount of decomposed rock on one side.

17-3-25.5-30

28.5-30" Light brown, easy to break clay with white spots 30-31.5" Six layers of clayey sand and silty sand

17-4-30-38 31.5-38"

There is decomposing rock on one side of the profile. On the other side there is dark brown, hard clay with white spots that look like completely decomposed rock; currently it is a very soft material. On the furthest edge, there is a vertical layer of loose sand.

38-41" Decomposed light brown rock with horizontal and vertical seams of clay. 17-5-38-44

41-44" Very hard dark brown clay. There is a vertical layer of white clay on the side of the tube.

17-6-44-50 44-50 A half of the sample is decomposing granite and the other half is medium dark brown, very hard clay. The soil varies vertically.

462

Figure 80. Profile – Visual Soil Description.

463



LL PL PI P200 [%]

% clay


[ppm]

17-1-8-16 GC 99.1 35.0 64.1 28.7 2.75 220 17-1-8-16 GC 37.4 13.2 17-2-16.25.5 GC 48.0 17-3-25.5-30 CH 85.1 32.5 52.6 62.1 19.9 2.4E-07 2.797 17-4-30-38 SC 61.6 17-4-30-38 CH 61.6 30.1 32 83.8 17-4-30-38 CH 86.3 34.6 17-5-38-44 SC 29.1 4E-07 17-5-38-44 2.829 17-5-38-44 CH 80.0 30.2 17-6-44-50 SC 47.2 17-6-44-50 CH 67.8 30 37.8 81.4 23.7 3E-07 Footnotes: Shaded used for estimated values,



17-1-8-16 9 11.51 17-1-8-16 14 30.28 83.8 79.9 408 17-1-8-16 15 22.37 99.7 85.8

17-2-16.25.5 20 18.96 83.2 49.3 17-3-25.5-30 26.5 29.57 85.0 78.9 94.5 17-3-25.5-30 28.5 27.39 88.3 78.8 95.5 17-4-30-38 32 26.11 17-4-30-38 35 24.77 98.7 90.6 17-4-30-38 37 23.42 17-5-38-44 39 18.92 17-5-38-44 41 28.17 90.4 84.1 1370 17-5-38-44 42 30.38 17-5-38-44 43 32.39 89.7 95.2 285 17-6-44-50 47 20.78 103.3 83.5


464


Test 1 Test 2 Cor. Ps Sample Ps w γdry Sample Ps Cor. Ps w γdry Swell Sample #

Type [kPa] [kPa] [%] [pcf] Type [kPa] [kPa] [%] [pcf] Index 17-3-25.5-30 I 37.4 91.6 29.6 85.0 0.0264 17-5-38-44 I 29 90 19 90.5 0.0277 17-6-44-50 R 231 361 21 90.5 0.0825 Footnotes


0

20

40

60

80

100

0.00010.0010.010.1110100

Grain Diameter [mm]

% P

assi

ng

17-1-8-16 17-1-8-1417-2-16-25.5 17-3-25.5-3017-4-30-38 clay, rocks, sand layer 17-4-30-38 clay, rocks17-5-38-44 bottom 17-5-38-44 top17-6-55-62 clay 17-6-44-50 granit


465

6 SC

&

CH

5 SC

&

CH

4 SC

&

CH

3 C

H

2 SC

1 SC

Core

# S

oil C

lass

if.80

9010

011

0γ d

ry [p

cf]

0 5 10 15 20 25 30 35 40 45 50

Depth [inch]

1015

2025

3035

w [%

]0

5010

0

S [%

]0

1000

2000

Suct

ion

[kPa

]

Figu

re 8

2.

Prof

ile.

466

0.80

0.85

0.90

0.95

1.00

1.05

1.10

1 10 100 1000 10000

Pressure [kPa]

Voi

d Ra

tio

17-3-24-38 Insitu

17-5-38-44 Insitu

17-6-44-50 Reconstituted


0

20

40

60

80

100


Degr

ee o

f Sat

urat

ion

[%]

17-1-14 (dry spec. w eight = 84)17-3-28.5 (88)17-5-43 (90)17-1-10 drying curve17-3-30 drying curve17-5-53 drying curve


467

Site # 18

Soil # 18 is a light brown very hard clayey material obtained with 4 separate borings

located next to each other. The sampling location is a region of undeveloped desert near a

roadway covered with scattered native vegetation. The soil was found to be uniform with depth in

texture and color. To simplify the presentation of the data, only soil number followed by range of

depths in inches from which the soil was extruded are provided; for example 18-12-18.


Soil # 18 City Anthem Cross Roads Meridian Dr./ 23rd Ave. Date of Sampling 3/2005 Landscape near sampling area Undeveloped desert Previous Land Use Undeveloped Desert

Figure 85. Bird’s-Eye View (● – location of sampling).



LL PL PI P k200 [%] % clay sat

[cm/s] Sulfate [ppm] Gs CEC

18-12-18 CH 55.0 26.0 26 18-14-20 CH 93.8 40.1 18-26-31 CH 2.811 18-27-32 CH 94 39.4 18-36-41 CH 56.6 21.4 35 6.3E-08 2.829

Footnotes: Italics and shaded used for estimated values.

468



18-12-18 15 14.99 112.8 76.5 1400 18-14-20 16 13.31 110.3 63.9 1740 18-14-20 18 13.40 109.3 62.8 2000 18-26-31 27.5 12.15 117.7 70.3 2500 18-27-32 29 11.50 106.6 50.5 7700 18-26-31 30 12.60 105.2 53.4 5800 18-27-31 31 11.65 108.7 53.7 5500 18-29-36 34 12.20 123.7 81.5 550




Type [kPa] [kPa] [%] [pcf] Type [kPa] [kPa] [%] [pcf] Index 18-27-32 I 318 479.9 11.7 108.7 0.057


Table 76. Compaction and EI Tests for 18-20-23.

Test Type Parameter Name Value Expansion Index 33





469

100

1000

1000

0

Suct

ion

[kPa

]0

5010

0

S [%

]0.

00.

51.

0

w/P

L

Figu

re 8

6.

Prof

ile.

1012

1416

w [%

]10

011

012

013

0γ d

ry [p

cf]

0 5 10 15 20 25 30 35 40

Depth [inch]

470

0

20

40

60

80

100

0.00010.0010.010.1110

Grain Diameter [mm]

% P

assi

ng

18-2-27-32

18-3-14-20


0.40

0.45

0.50

0.55

0.60

0.65

1 10 100 1000 10000

Pressure [kPa]

Voi

d Ra

tio

18-27-32 Insitu


471

18-20-23

wopt = 20.00%

γd max = 114.2 pcf

90

92

94

96

98

100

102

104

106

108

10 15 20 25 30


Dry

Spe

cific

Wei

ght [

pcf]


0

20

40

60

80

100


Degr

ee o

f Sat

urat

ion

[%]

18-18 (dry spec. w eight = 109)18-27.5 (118)18-34 (124)18-34 drying and w etting curves18-18 drying curveFilter Paper Test


APPENDIX C

DETERMINATION OF SWCC USING ONE POINT SUCTION MEASUREMENT AND

STANDARD CURVES

(PAPER PRESENTED IN GEOTECHNICAL SPECIAL PUBLICATION NO. 147, ASCE,

PROCEEDINGS OF THE FOURTH INTERNATIONAL CONFERENCE ON UNSATURATED

SOILS, APRIL 2-6, 2006, CAREFREE, ARIZONA, 1482-1493 ; AUTHORS: W. N. HOUSTON,

H.B. DYE, C. E. ZAPATA, Y. Y. PERERA, A. HARRAZ)

Abstract

During the last decade several researchers and practitioners have stressed the

importance and the need of adopting unsaturated soil mechanics in the analysis of problems

associated with swelling clays and other problematic unsaturated soils. To accomplish this goal,

the determination of the soil-water characteristic curve (SWCC) becomes essential. However,

practitioners perceive the SWCC determination as a time consuming and expensive laboratory

process. This fact has lead to a slow implementation of unsaturated soil mechanics into

geotechnical engineering practice. In an effort to encourage practitioners to employ unsaturated

soil mechanics, a study was performed to determine the SWCC based on soil index properties

and one measurement of matric suction. In this study, the matric suction of approximately 82

field soil samples was determined using either suction plate or suction membrane devices. It

was determined that the proposed procedure provides acceptably reliable approximation of the

SWCC.

Introduction

Although a complete theory for the analysis of geotechnical problems involving

unsaturated soils has been developed in the last three decades and despite the well-recognized

importance of suction, unsaturated soil mechanics has not yet been widely implemented by

practicing engineers. “An investigation of practice throughout the Unites States showed that less

than 20% of commercial geotechnical laboratories performed suction measurements on a

regular basis” (Zapata, 1999).

The most important constitutive relations for unsaturated soils (i.e., shear strength,

compressibility, and fluid flow) are directly related to the soil matric suction and hence to the soil-

water characteristic curve (SWCC). For this reason, research was conducted to determine the

complete SWCC based on one measurement of matric suction and soil index properties within

an acceptable uncertainty range. This work is a continuation of the research work done by

Perera (Perera et al. 2005), who defined the SWCC in terms of the soil index properties and the

work done by Zapata (1999) and Zapata et al. (2000) who described the potential variability of

473

the SWCC. The current research effort was aimed at developing a reliable method of predicting

the SWCC, based on one point matric suction measurement and soil index properties.

Background

Fredlund et al. (1993) defined the soil water characteristic curve as “the variation of

water storage capacity within the macro and micro pores of a soil with respect to suction”. This

relationship is generally plotted as the variation of volumetric water content or degree of

saturation against the soil matric suction and is described by Equations (1) and (2).

( )

( )f

f

sv h cb

f

Chln e 1a

θθ =

⎡ ⎤⎛ ⎞⎛ ⎞⎢ ⎥⎜ ⎟+ ⎜ ⎟⎜ ⎟⎢ ⎥⎝ ⎠⎝ ⎠⎣ ⎦

(1)

( )r

h 6

r

hln 1h

C 110ln 1h

⎛ ⎞+⎜ ⎟

⎝= −⎛ ⎞+⎜ ⎟

⎝ ⎠

⎠ (2)

where θv is the volumetric water content; θs is the saturated volumetric water content or porosity

of the soil; e is the exponent; h is the matric suction [kPa]; C(h) is an adjustment factor which

forces the SWCC through zero water content at a suction of 106 kPa; hr, af, bf and cf are fitting

parameters. Note that v

s

θθ

is degree of saturation, S, expressed a decimal.

Family of Soil Water Characteristic Curves (SWCCs)

Figure 1 shows a family of curves developed by Zapata (1999) and Zapata et al. (2000)

who contributed to the quantification of the dependence of SWCC on gradation and plasticity

index. Her findings were followed by research done by Perera et al. (2005) who correlated the

family of curves to equations (1) and (2) by further refining the fitting parameters: hr, af, bf and cf,

based on more data. These fitting parameters are given below for both plastic and non-plastic

474

soils. Equations (3) through (16) are considered to represent a modest improvement over the

family of curves given by Figure 1. The equations are recommended for use when only index

properties are available for estimating a SWCC. Figure 2 shows the updated family of curves for

plastic soils obtained from Equations (3) through (7). For non-plastic soils (wPI = 0) it is no

longer possible to generate a family of curves as was done in Figure 1. The new model, Perera

at al. (2005), utilizes more of the gradation data and thus it is necessary to employ Equations (8)

through (16) to generate a specific SWCC.

0.0

0.2

0.4

0.6

0.8

1.0

0.1 1 10 100 1000 10000 100000 1000000Matric Suction (kPa)

Deg

ree

of S

atur

atio

n

D60=1 mm

wPI= 0.1

wPI = 50

3 510 1

20 30 40D60=0.1 mm

wPI = % Passing #200 x PI

Figure 1. Family of Drying Curves (Zapata, 1999, Zapata et al. 2000)

For plastic soils (wPI >0):

( )fa 32.835ln wPI 32.438= + (3)

( ) 0.3185fb 1.421 wPI −= (4)

( )fc 0.2154ln wPI 0.7145= − + (5)

hr = 500 (6)

475

200PI*PwPI100

= (7)

where PI is the plasticity index [%], and P200 is the percent of soil passing US standard sieve #

200 [%].

wPI = 0.4 0.5 1 2 5 10 20 50

0.0

0.2

0.4

0.6

0.8

1.0

0.1 1 10 100 1000 10000 100000 1000000

Suction [kPa]

Deg

ree

of S

atur

atio

n

Figure 2. Family of Drying Curves for Plastic Soils (Perera et al. 2005)

For non-plastic soils (wPI =0):

fa 1.14a 0.5= − (8)

( ) ( )6 4.3420 200 30 100a 2.79 14.1log D 1.9*10 P 7 log D 0.055D−= − − − + + (9)

( )90 6060

4 log(D ) log(D )log(D )

3100D 10

−+

= (10)

fb 0.936b 3.8= − (11)

0.10.57 1.1990

200 0 20010 90 60

D 30b 5.39 0.29ln P 3D 0.021PD log(D ) log(D )

⎛ ⎞⎛ ⎞ ⎛= − + +⎜ ⎟⎜ ⎟ ⎜⎜ ⎟ −⎝ ⎠ ⎝⎝ ⎠

⎞⎟⎠

(12)

476

( )30 1030

3 log(D ) log(D )log(D )

20D 10

− −+

= (13)

0.758cf 1c 0.26e 1.4D= + 0 (14)

1.15

30 10 f

20 1c log 1log(D ) log(D ) b

⎛ ⎞= −⎜ ⎟−⎝ ⎠

+ (15)

rh 100= (16)

where D% is the soil particle diameter in mm related to the percent of passing.

Testing Procedures for the Current Study

Undisturbed soil samples were obtained from under slabs-on-grade of residential

construction located in the Phoenix metropolitan area, Arizona. The edge moisture variation

distance was roughly estimated and the samples were taken at greater distances from the edge

of the slab. Based on well documented observations made by many researchers, the water

content and therefore the matric suction reaches stability at the edge moisture distance; hence

the collected soil samples were considered to be at an equilibrium condition, given that all slabs

visited had been in places for several years. The suction of the undisturbed samples was

determined with the pressure plate apparatus, by a procedure to be presented subsequently. A

complete SWCC was also determined with the pressure plate (Fredlund SWCC device) and

pressure membrane device. The results of these three sets of measurements were plotted and

compared. An example is given in Figure 3 and 4, which are discussed later.

SWCC - Pressure Plate Method

An undisturbed, moist soil sample was extruded from the Shelby tube into a brass ring of

dimensions 2.54-cm in height and 6.1-cm in diameter. After the initial readings of volume and

mass were collected, the specimen was rested on a porous stone and filter paper. The soil was

477

topped with another layer of filter paper and porous stone. In an effort to maintain in-situ soil

volume, a number of weights sufficient to overcome the soil's swell pressure was placed on top

of the soil specimen. The test specimen was submerged in a distilled water bath for at least 24

hours. After the soil suction in the specimen had been reduced to essentially zero, it was

removed from the water bath, weighed and placed in the pressure cell on a saturated ceramic

stone. After an initial air pressure was applied, weights were placed on top of the pressure cell

to recreate the overburden pressure, and compensate for the applied internal air pressure and

the friction between the bearing and the axial load rod. When the soil volume and water content

of specimen stopped changing, it was removed from the apparatus and weighed. The recorded

mass value was used to obtain the water content of the soil corresponding to the applied

pressure. The specimen was returned to the pressure cell and the test was repeated for higher

value of suction. The degree of saturation was determined for at least three different suction

values. After the test was completed, the soil specimen was oven dried and the results were

plotted as shown in Figure 3. With the Fredlund SWCC device the water content change can be

tracked by reading the volume tubes at each equilibrium suction value without removing the test

specimen. Thus the procedure followed here was not the conventional test procedure. The

samples were removed in part for research purposes, aimed at providing redundant moisture

content change measurements. Very recent modifications to the Fredlund SWCC device, made

after the currently-reported test series was completed, included addition of a small heater on top

of the cell which maintains constant temperature within the cell at slightly above ambient and

thus prevents condensation within the cell.

Pressure Membrane Method

Standard ASTM D 3152-72 was used in the determination of the matric suction with the

pressure membrane method. An undisturbed sample was prepared as for the pressure plate

test. The saturated test specimen was removed from the water bath, weighed and placed in the

pressure membrane apparatus on top of a saturated cellulose membrane. The first desired

478

pressure was applied to the specimen and allowed to equilibrate for one week. After that period

of time the soil specimens were removed from the apparatus, weighed, and the soil volume was

measured. The same specimens were returned to the pressure membrane apparatus and the

test was repeated for a higher value of suction. When the testing was completed, the soil

specimens were oven dried. The collected values of specimen volume, and moist and dry soil

mass were used to determine the specimen degree of saturation corresponding to the applied

pressure. The values were plotted on a semi-log scale and are presented in Figure 4 as an

example. Figure 4 is presented later. Again, even through ASTM D3152-72 was followed

generally, a deviation was employed in that all specimens were removed, volume and mass

determined, and then all specimens returned to the cell. These deviations from the standard

procedure were considered necessary to maximize the accuracy of the degree of saturation

determination.

One Point Method - Pressure Plate Test

Several researchers, including the authors (Zapata et al., 2000, Perera et al. 2005),

have provided models for predicting SWCCs from index properties. These models can be

configured to give unbiased estimates of the SWCC, but some uncertainty is associated with

each estimate. As discussed in above, a band of uncertainty exists even when direct

measurements are made, and somewhat more uncertainty exists when index properties alone

are used to get the SWCC. The uncertainty is reduced somewhat when one direct

measurement of suction and saturation is coupled with index properties to get the SWCC. Thus

the one-point method entails measuring the existing suction and S on either on undisturbed

sample from an in-situ location in the field or on a sample compacted in the laboratory. This pair

of values is than interpreted to represent one point on the SWCC and can be plotted on Figure 2,

for example, if the soil has plasticity. Then an SWCC is sketched through the point as if one

were interpolating within the family of curves. The analytical counterpart of the graphical

procedure just descried is as follows, continuing with the example of a plastic soil. The

479

graphically interpolated curve can be used to estimate an interpolated apparent value of wPI.

This apparent value of wPI, which is different from the actual wPI, is then used with Equations

(3) through (7) to get the fitting parameters. The fitting parameters are then used with Equations

(1) and (2) to compute the suction corresponding to the measured degree of saturation, S. If the

computed suction agrees with the measured suction then the fitting parameters are appropriate.

If not, then the interpolated wPI should be adjusted up or down slightly until a match is obtained.

When the soil is non-plastic, the procedure is only slightly less straightforward. In this case the

measured matric suction and S value are plotted as a point on a standard SWCC graph format.

The gradation parameters are than used to estimate the fitting parameters for a SWCC using

Equations (8) through (16). This SWCC is then plotted on the same graph, together with the

measured point. The graphical procedure then amounts to sketching a SWCC through the

plotted point. The sketched SWCC should be more or less parallel and similar in shape to the

SWCC derived from gradation parameters. The analytical counterpart for this graphical

procedure is a bit more complicated. It is probably best accomplished by sketching in a small

family of gradation curves, similar in shape and more or less parallel to the actual gradation

curve, but either coarser or finer than the actual gradation curve as appropriate. The fitting

parameters for these trial gradation curves are then evaluated one by one, and the

corresponding SWCC is plotted to see if it passes through the measured point. When it does,

the best-estimate set of fitting parameters has been found. When the SWCC through the

measured point has been established, it can be compared with the SWCC derived from index

properties alone. If the user makes numerous such comparisons, it will be possible to develop a

database which could serve as a basis for future modification (improvement) of the SWCC

predictions from index properties alone. A complicating factor, however, is the fact that all the

SWCCs in Figure 1 and 2 are drying curves and the measured point from the field sample, does

not necessarily lie on the drying curve. This issue is discussed in the paragraphs that follow.

480

The SWCCs determined as described above can be interpreted as either drying curves

or wetting curves, depending on the perceived recent wetting/drying history of the corresponding

element of soil in the field. Or, the measured One-point could lie between the wetting curve and

drying curve, in which case the SWCC constructed by the preceding procedure would simply be

a SWCC similar in shape to the drying curve, but intermediate between the drying and wetting

curves. Obviously some knowledge of the wetting/drying history would be quite helpful. In the

absence of any knowledge of the wetting/drying history, however, the following procedure can be

adopted. Although it begs the question somewhat as to the accuracy of the index- property

estimated SWCC, it can be assumed that when the measured point plots near or above the

SWCC based on index properties then the measured point probably lies on a drying curve. If,

however, the measured point falls far below the SWCC based on index properties then it can be

assumed that the point lies on a wetting curve. Note that if it is believed that the point lies on a

scanning curve intermediate between the drying and wetting curve, then the task of accurately

predicting the change in suction, which accompanies a small change in degree of saturation is

much more difficult. If, in this last case wherein the plotted point is believed to lie on a scanning

curve, the user elects to simply construct and use a SWCC though the plotted point that is more

or less parallel to and similar in shape to the index property drying curve, than it must be

recognized that predictions of changes in suction due to small changes in S will have more than

normal uncertainty. If, however, the projected change in S is very large, then the added error

due to starting from a scanning curve is lessened. In section presented subsequently an

approximation which involves adoption of the one-point SWCC as an average curve for both

wetting and drying, thus neglecting hysteresis is proposed for some practical applications.

The Fredlund SWCC device and the procedure for using it to measure the suction of a

sample extracted from an in-situ field location are described elsewhere (Perera et al., 2005).

However, for completeness this procedure is outlined herein in a series of steps as follows: (1)

Transfer the undisturbed sample from the field to the Fredlund SWCC device ring without loss or

gain of water content. (2) Determine the mass of the test ring plus moist soil with a precision

481

adequate to detect a water content change in the test specimen at least as small as 0.05%. (3)

Assembly the specimen and test ring in the device, noting the initial height of the specimen and

the initial volume readings, and apply the first trial value of ua. This trial value can be selected by

using the best available data to estimate the initial S value and the best available index

properties to estimate the position of the SWCC. Then the S value is used to enter the SWCC to

get the first trial value of suction (ua), which is applied in step (3). Alternatively, the first trial

value of ua can be selected from experience and intuition. (4) Open the cell drainage valves to

expose the ceramic stone on which the specimen rests to the water in the volume change tubes,

thus driving uw to essentially zero. (5) Monitor the volume tubes immediately to detect any

tendency for water to be expelled or absorbed and adjust ua so as to prevent volume change.

(6) Repeat observations and adjustments to ua on a more or less logarithmic time scale; i.e., the

elapsed time, at which reading are taken and ua adjusted, from the test beginning, can be

doubled or tripled. When no further tendency for water to be expelled or absorbed is exhibited,

the value of ua is the first approximation of the matric suction, because uw ≈ 0. If ua is very small,

then it might be necessary to use the height of the water columns in the volume change tubes to

evaluate uw, which is typically slightly above zero. In special cases where the suction is

exceptionally low it may be desirable to maintain ua = 0 and lower the water columns so that uw

is modestly negative (Padilla et al., 2005). (7) Close the cell drainage valves and remove the

specimen as quickly as possible, taking care to remove all of the specimen and to prevent

moisture loss or gain and specimen mass loss or gain. (8) Determine the mass of the ring plus

moist specimen. If this value is the same as the pre-test value, no change in moisture content

occurred. If not, compute the change in moisture content and the corresponding change in

degree of saturation, Δ S. (9) Use the oven-dry mass of the specimen, a measured specific

gravity, and the final moisture content to compute the end-of-test S value. (10) Plot the

measured matric suction with the final S value on a SWCC plot, such as Figure 2 for plastic

soils. (11) Using the family of SWCC curves, eg. Figure 2, sketch a SWCC through the point,

and apply ΔS to obtain a corresponding Δ(matric suction), by following along the SWCC curve in

482

the appropriate direction. The new matric suction is the corrected suction, which has been

corrected for the unintended moisture content change that occurred during the test.

The preceding procedure has been used successfully by the authors to complete

numerous measurement of suction. When the measured suction is below the air-entry value of

the ceramic stone the unintended moisture content change is typically 0.2% or less and is rarely

more than 0.3%. However, if the actual suction for the field sample exceeds the air entry value

of the ceramic stone, then substantial water absorption is inevitable. In this case the procedure

used to estimate the in-situ suction is more or less the same, except that a maximum practical

value of ua is simply applied and held constant and this value of ua is treated as the first

approximation of the measured suction. The final S value is plotted with the last applied suction

and a SWCC is constructed through the point as described above. In this case the moisture

content change and �S will probably not be small and it will thus be necessary to move down

the SWCC a substantial distance to find the corrected suction. To the extent that the family of

curves used portrays essentially correct slopes, this represents a fairly reliable technique for

estimating in-situ suctions in excess of the air-entry value of the stone.

Results

After all testing was completed, there were sets of curves where four SWCCs had been

obtained: 1) The pressure membrane SWCC, 2) The pressure plate SWCC, 3) The one-point

SWCC, wherein one of a family of SWCCs is fitted through the one-point measurement of matric

suction and S, and 4) The index properties-based (IPB) SWCC, wherein only index properties

are used to estimate the SWCC as per Equations (3) through (16). Thus numerous comparisons

were possible.

Figures 3 and 4 show some typical results for Phoenix clay. In Figure 3 the

experimental values are plotted with differing symbols as labeled. The form of the equations for

the SWCCs are given by Equations (1) and (2) and trial and error was used to find the fitting

parameters af, bf, cf, and hr which produced a curve that best matched the experimental data. In

483

addition to the experimental points the pressure membrane curve was assumed to pass through

S = 100% at very low suction and suction equal to 106 kPa at S = 0%.

LL = 38PL = 20P200 = 64.9 %%-2mm = 28.8 %Gs = 2.726

ksat = 9.8e-8 cm/s

0102030405060708090

100110

1 10 100 1000 10000 100000 1000000Matric Suction [kPa]

Satu

ratio

n [%

]

Pressure MembranePressure PlateOne Point

Figure 3. Suction measurement; Phoenix clay

IPB SWCCwPI = 11.3af = 112

bf = 0.66

cf = 0.19

hr = 500

One Point SWCCwPI = 7.24af = 97.4

bf = 0.76

cf = 0.29

hr = 500

0102030405060708090

100110

1 10 100 1000 10000 100000 1000000


Satu

ratio

n [%

]

Pressure MembranePressure PlateOne PointIPB SWCCOne-point SWCC

Figure 4: Suction measurement and SWCC prediction; Phoenix clay

Figure 3 shows both the drying curve and the wetting curve for the pressure plate

results. In this case the one-point measurement fell between the wetting and the drying curves.

484

Figure 4 represents the same experimental data points as Figure 3, but with no curves shown for

the experimental (pressure plate and pressure membrane) points. The two curves which are

shown are the one-point method and the index-property based (IPB) SWCC. Figure 4 shows

that in this case the drying curves for pressure plate, pressure membrane, and the IPB are

practically coincident and the one-point measurement falls slightly below these three drying

curves. Further comparisons between SWCCs are made in the paragraphs which follow by

summarizing some relevant statistics. Because all SWCCs essentially match up at very low

suctions (1 kPa or less) and at very high suctions (106 kPa), the comparisons drawn herein are

simplified by quantifying the vertical distance (ΔS) between curves when the pressure plate

curve is at 50 % saturation.

Comparison of pressure plate and pressure membrane SWCCs

Four sets of pressure plate and pressure membrane SWCCs were compared. It was

found that for all the curves the pressure membrane SWCCs plotted above the pressure plate

SWCCs at low suction values. The curves were found to cross at the suction range from 100 to

1000 kPa. The arithmetic average ΔS is equal to the absolute average ΔS, and it is 4.9 %, with

positive ΔS corresponding to the membrane curve falling below the pressure plate curve. A

small arithmetic ΔS thus corresponds to very little bias in the comparison, meaning that on

average the two sets of curves were about the same. The standard deviation was found to be

5.4 %. A relatively large absolute mean ΔS corresponds to considerable scatter in the

comparisons.

Comparison of pressure plate, pressure membrane and one-point method

For this comparison an additional 4 sets of pressure membrane SWCC and one-point

tests were available. The one-point method plotted below both drying curves in 2 cases,

between the curves in 1 case and above both curves in 1 case. The one point method plotted

below pressure membrane in 4 cases and above it in the remaining 4.

485

Comparison of pressure plate and One-Point SWCCs

For this comparison 6 sets of curves were available, where ΔS is the change in suction

between the curves when the one-point pressure place curve is at 50 % saturation. The one

point SWCC typically falls above pressure plate SWCC for small values of suction. In 4 cases

the pressure plate SWCC crossed the one-point SWCC between 200 and 1000 kPa, plotting

above one-point SWCC for the larger values of suction. For the remaining 2 cases, the entire

one-point SWCCs plotted above the pressure plate SWCCs. The arithmetic mean ΔS was equal

to absolute mean and was 4.9 %, with positive corresponding to the one-point SWCC being

lower, with standard deviation of 4.0 %.

Comparison of pressure plate SWCC to Index-Property-Based SWCCs

For this comparison 6 sets of curves were available, where ΔS is the change in suction between

the curves when the one-point pressure place curve is at 50 % saturation. For low values of

suction IPB SWCCs typically plot above pressure plate SWCCs. The inverse is true for high

suction values. The arithmetic mean ΔS was 3.5 %, with positive corresponding to the IPB

SWCC being higher. The absolute mean ΔS was 7.1 %, with a standard deviation of 4.8 %.

Comparison of One-Point SWCCs with IPB SWCCs

For this comparison the database was considerably larger, with 68 pairs of values

available. In 60 cases the one-point SWCC ( when compared at 50 % saturation) fell below the

IPB SWCC and in 8 cases above; the arithmetic mean ΔS was 18.4 %, with positive

corresponding to the one-point being lower. The absolute mean ΔS was 20.1 %, with a standard

deviation of 11.4 %.

Discussion

Modest differences between the pressure plate and pressure membrane SWCCs are

perhaps to be expected because of moderate differences in apparatus and test procedures. The

486

effect of overburden pressure is reflected in the pressure plate test when the Fredlund SWCC

device is used, but not so in the pressure membrane device. The degree of saturation can be

determined throughout the test with the pressure plate, but is much more difficult to ascertain

with the pressure membrane. Although it is difficult to see how the use of a saturated cellulose

membrane as a barrier to air passage is significantly different from the use of a saturated

ceramic stone, there may nevertheless be a difference that thus for escapes the authors. Due at

least in part to those noted differences, on average, pressure membrane SWCCs tended to fall

above pressure plate SWCCs at low undisturbed suction measurement values. At higher values

of suction the opposite is true. These two curves intersect at suction range from 100 to 1000

kPa. The arithmetic average of the vertical distance (ΔS) between these two curves, when the

pressure plate curve is at 50 % saturation, is 4.9 % where a positive value corresponds to

membrane curve falling below the pressure plate curve.

The one-point method tended to fall around 3 % below the pressure membrane average

and about 5 % below the pressure plate average (drying curves). It also fell about 18 % below

the IPB SWCCs, on average. These results support the conclusion that the elements of soil

represented by these sub-slab samples tend usually to fall between the wetting and drying

curves, though not necessarily midway between. In general, a field specimen may exist on the

wetting curve, or the drying curve, or somewhere in between on the scanning curve. For this

reason, SWCCs obtained using the one point method would generally be expected to provide

suction values at or below the drying curve due to hysteretic behavior of the soil. None the less,

the use of the one point measurement is likely to result in less error than approximations

obtained using index properties alone.

Applications to Soil Engineering Practice

The practice of unsaturated soil mechanics necessarily involves the evaluation of the

soil suction (ua – uw) and the net normal stress (� – ua). These stress state variables must be

related to shear strength, compressibility, moduli and fluid flow parameters for the soils at hand.

487

Thus values of the soil suction at various in-situ points in the field are of the utmost interest.

These values of soil suction can be measured directly with sensors installed in-situ or by the

one-point method on undisturbed samples as described by Perera (Perera et al. 2005).

As seen from Figure 4 the corrected SWCC curve produces average saturation values

per given suctions. It can be concluded that the corrected SWCC produces the expected SWCC

curve once the influence of the hysteresis has ceased. The correction of the SWCC to the one-

point undisturbed suction value obtained by pressure plate accounts for variation of SWCC with

dry density. It produces a curve that is correct for the particular soil conditions encountered at

the site in question. Therefore, the adoption of the corrected SWCC curve will be helpful in the

implementation of unsaturated soil mechanics into geotechnical analysis by the practitioners.

References

Chen, F.H. (1988). Foundations on Expansive Soils, Development in Geotechnical Engineering, vol. 54.

Fredlund, D. G., Rahardjo, H. (1993). Soil Mechanics for Unsaturated Soils, New York: John

Wiley and Sons Inc. Perera, Y.Y., Zapata, C.E., Houston, S.L., Houston W.N. (2005). “Prediction of the Soil-Water

Characteristic Curve Based on Grain-Size Distribution and Index Properties”. Proceedings of Geo-Frontiers 2005, Austin, Texas, Jan. 24-26. ASCE.

Perera, Y. Y., Zapata, C. E., Houston, S.L., Houston W.N. (2004). “Moisture Equilibria Beneath

Highway Pavements”. Transportation Research Board 83rd Annual Meeting - Session 410, Washington D.C., January 11-15. Presented.

Perera, Y.Y., Zapata, C.E., Houston, S.L., Houston W.N. (2004). “Long-Term Moisture

Conditions under Highway Pavements”. Proceedings of Geo-Trans 2004, Los Angeles, CA, 1132-1143.

Zapata, C.E. (1999). Uncertainty in Soil-Water Characteristic Curve and Impact on Unsaturated

Shear Strength Predictions, Ph.D. Dissertation, Arizona State University, Tempe, AZ, USA Zapata, C.E., Houston, W.N., Houston, S.L., Walsh, K.D. (2000). “Soil-Water Characteristic

Curve Variability”. Proceedings of Sessions of Geo-Denver 2000, Denver: ASCE Geo-Institute, 84-124.

APPENDIX D

PRESENTATION OF MODELING RESULTS

Table of Contents SM-ML Soil: Desert Landscape..............................................................................................492 1-D SM-ML Soil: Desert Landscape, year 1, hourly flux.......................................................493 1-D SM-ML Soil: Desert Landscape, year 1-6, hourly flux ...................................................496 1-D SM-ML Soil: Desert Landscape, year 1, average flux ...................................................499 1-D SM-ML Soil: Roof Runoff Ponding, year 1, hourly flux ..................................................502 SM-ML Soil: Turf Landscape ..................................................................................................507 1-D SM-ML Soil: Turf Landscape, year 1, average flux, Flux = 2.2PE.................................512 1-D SM-ML Soil: Turf Landscape, year 1, hourly flux, Flux = PE, IC=5th year desert ..........515 CH Soil: Desert Landscape ..................................................................................................519 1-D CH Soil: Desert Landscape, year 1, hourly flux ...............................................................520 1-D CH Soil: Desert Landscape, years 1-6, hourly flux ..........................................................523 1-D CH Soil: Desert Landscape, year 1, average flux ............................................................527 1-D CH Soil: Roof Runoff Ponding, year 1, hourly flux ...........................................................530 CH Soil: Turf Landscape ......................................................................................................534 1-D CH Soil: Turf Landscape, 1st year, hourly flux, Flux = 2.2PE...........................................535 1-D CH Soil: Turf Landscape, years 1-34, hourly flux, Flux = 2.2PE......................................539 1-D CH Soil: Turf Landscape, 1st year, average flux, Flux = 2.2PE........................................543 1-D CH Soil: Turf Landscape, 1st year, hourly flux, Flux = PE, IC=-153 m.............................546 1-D CH Soil: Turf Landscape, 1st year, hourly flux, Flux = 1.3PE, IC=34the year of turf........550

List of Figures SM-ML Soil: Turf Landscape; 1st Year ; Hourly Flux Figure 1: 2-D view of suction variation with depth and time; .................................................493 Figure 2: 2-D view of suction variation with depth and time, zoomed in on surface; ............493 Figure 3: 3-D front view of suction variation with depth and time;.........................................494 Figure 4: Profile before and after rain in October; .................................................................494 Figure 5: Instantaneous Fluxes .............................................................................................495 Figure 6: Cumulative Fluxes..................................................................................................496 Figure 7: 3-D front view of suction variation with depth and time;.........................................496 Figure 8: 2-D view of suction variation with depth and time zoomed in on the surface; .......497 Figure 9: Driest (Jun) and Wettest (Dec.) Profiles;................................................................497 Figure 10: Instantaneous Fluxes .............................................................................................498 Figure 11: Cumulative Fluxes..................................................................................................498 Figure 12: 2-D view of suction variation with depth and time; .................................................499 Figure 13: Profile at selected times, Jun and December;........................................................500 Figure 14: Cumulative Fluxes,.................................................................................................500 Figure 15: Instantaneous Fluxes .............................................................................................501 Figure 16: 3-D front view of suction variation with depth and time;.........................................502 Figure 17: 2-D view of suction variation with depth and time; .................................................503 Figure 18: 2-D view of suction variation with depth and time, zoomed in on surface; ............503 Figure 19: Profile at selected times, March after rain, end of July, end of Dec.......................504 Figure 20: Cumulative Flux......................................................................................................504 Figure 21: Instantaneous Flux .................................................................................................505 Figure 22: 3-D view of suction variation with depth and time; .................................................508 Figure 23: 2-D view of suction variation with depth and time; .................................................508 Figure 24: Profiles of the driest surface conditions (April) and the wettest (Dec.); .................509 Figure 25: Profile before and after 0.5-h irrigation in April;......................................................509 Figure 26: Instantaneous Fluxes .............................................................................................510 Figure 27: Cumulative Fluxes..................................................................................................511 Figure 28: 3-D front view of suction variation with depth and time;.........................................512 Figure 29: 2-D view of suction variation with depth and time; .................................................512 Figure 30: Instantaneous Fluxes .............................................................................................513 Figure 31: Cumulative Fluxes..................................................................................................514 Figure 32: 3-D front view of suction variation with depth and time;.........................................515 Figure 33: 2-D view of suction variation with depth and time; .................................................515 Figure 34: Profiles of the driest surface conditions (April) and the wettest (Dec.); .................516 Figure 35: Cumulative Flux......................................................................................................516 Figure 36: Instantaneous Flux Data ........................................................................................517 Figure 37: 3-D front view of suction variation with depth and time;.........................................520 Figure 38: 2-D view of suction variation with depth and time; .................................................520 Figure 39: Profile before and after 0.5-h irrigation in April;......................................................521 Figure 40: Cumulative Fluxes..................................................................................................521 Figure 41: Instantaneous Fluxes .............................................................................................522 Figure 42: 3-D back view of suction variation with depth and time; ........................................523 Figure 43: 3-D front view of suction variation with depth and time;.........................................523 Figure 44: 2-D view of suction variation with depth and time; .................................................524 Figure 45: Profile before and after 0.5-h irrigation in April;......................................................524 Figure 46: Instantaneous Flux Data ........................................................................................525 Figure 47: Cumulative Flux......................................................................................................525 Figure 48: 2-D view of suction variation with depth and time; .................................................527 Figure 49: Profile before and after 0.5-h irrigation in April;......................................................527 Figure 50: Instantaneous Fluxes .............................................................................................528 Figure 51: Cumulative Fluxes..................................................................................................529 Figure 52: 2-D view of suction variation with depth and time; .................................................530 Figure 53: 2-D view of suction variation with depth and time; .................................................530

Figure 54: Profile at selected times: July before and after rain, end of Dec............................531 Figure 55: Cumulative Fluxes..................................................................................................531 Figure 56: Instantaneous Fluxes .............................................................................................532 Figure 57: 3-D back view of suction variation with depth and time; ........................................535 Figure 58: 3-D front view of suction variation with depth and time;.........................................535 Figure 59: 2-D view of suction variation with depth and time; .................................................536 Figure 60: 2-D view of suction variation with depth and time; .................................................536 Figure 61: Profile at selected times: driest (end of April), and wettest (after all prec. in March);. ................................................................................................................................537 Figure 62: Cumulative Fluxes..................................................................................................537 Figure 63: Instantaneous Flux Data ........................................................................................538 Figure 64: 3-D front view of suction variation with depth and time;.........................................539 Figure 65: 2-D view of suction variation with depth and time; .................................................539 Figure 66: 2-D view of suction variation with depth and time; .................................................540 Figure 67: Profile before and after 0.5-h irrigation in April;......................................................540 Figure 68: Instantaneous Flux Data ........................................................................................541 Figure 69: Cumulative Fluxes..................................................................................................541 Figure 70: Domain Accumulation ............................................................................................542 Figure 71: Cumulative Flux......................................................................................................542 Figure 72: 3-D back view of suction variation with depth and time; ........................................543 Figure 73: 2-D front view of suction variation with depth and time;.........................................543 Figure 74: Profile before and after 0.5-h irrigation in April;......................................................544 Figure 75: Cumulative Fluxes..................................................................................................544 Figure 76: Instantaneous Fluxes .............................................................................................545 Figure 77: 2-D view of suction variation with depth and time; .................................................546 Figure 78: 2-D view of suction variation with depth and time; .................................................547 Figure 79: Profile before and after 0.5-h irrigation in April;......................................................547 Figure 80: Instantaneous Flux Data ........................................................................................548 Figure 81: Cumulative Flux......................................................................................................549 Figure 82: 3-D back view of suction variation with depth and time; ........................................550 Figure 83: 2-D view of suction variation with depth and time; .................................................550 Figure 84: Profile before and after 0.5-h irrigation in April;......................................................551 Figure 85: Cumulative Flux......................................................................................................551 Figure 86: Instantaneous Flux Data ........................................................................................552 List of Tables Table 1: Flux Data (SM-ML; desert landscape, years 1-6, hourly flux)................................499 Table 2: Flux Data (SM-ML; desert landscape, 1st year, average flux)................................502 Table 3: Flux Data (SM-ML; 1st year, hourly flux).................................................................506 Table 4: Flux Data (SM-ML; turf landscape, years 1-2, hourly flux, Flux = 2.2PE)..............511 Table 5: Flux Data (SM-ML; turf landscape,1st year, average flux, Flux = 2.2PE)...............514 Table 6: Flux Data (SM-ML; turf landscape, 1st year, hourly flux, Flux=PE, IC=5th year desert) ................................................................................................................................518 Table 7: Cumulative Flux Data (CH; desert landscape, years 1-6, hourly flux) ...................526 Table 8: Cumulative Flux Data (CH; desert landscape, 1st year, average flux) ...................529 Table 9: Cumulative Flux Data (CH; roof runoff ponding, 1st year, hourly flux)....................533 Table 10: Cumulative Flux Data (CH; turf landscape, 1st year, average flux, Flux = 2.2PE) .546 Table 11: Cumulative Flux Data (SM-ML; 1st year, hourly flux) .............................................549 Table 12: Cumulative Flux Data (SM-ML; 1st year, hourly flux) .............................................553

SM-ML Soil: Desert Landscape

Analysis results of 1-D 10-m deep SM-ML soil profile are presented. Three desert

landscape analyses were performed.

1. In the first analysis, 6-years of hourly discretized flux was considered. It consists of

precipitation (0.27m/year, value modified by 0.07 m/year due to PE) and potential

evaporation, PE, (2.34 m/year). The precipitation is applied everyday from the beginning

of each month for the average number of rainy days in each month as determined from

statistical analysis of 24 years of historical data. The duration and magnitude of each rain

event is also based on the analysis of the same historical data. The PE is averaged over

each month. The constant head of -153m constitutes the initial and bottom boundary

conditions.

2. In the second analysis the precipitation flux was averaged over each month and applied in

terms of m/h. Similarly, PE was also averaged over each month (2.34 m/year). The

constant head of -153 m constitutes the initial and bottom boundary conditions.

3. In the 3rd analysis, the effects of poor drainage near foundation and roof runoff were

considered. The soil profile obtained with 5th year desert landscape analysis was used as

the input profile where the matric suction varies nonlinearly from 84000kPa at the soil

surface to 1500kPa at the profile bottom. The precipitation flux, described above, was

increased by a factor of 6. In this scenario, all the water was allowed to infiltrate the

profile. This was accomplished be removing the runoff function.

The results are presented in terms of matric suction and degree of saturation.

Instantaneous and cumulative fluxes are presented visually and tabularly, where the tables are

provided on the end final year final year analysis.

493

1-D SM-ML Soil: Desert Landscape, year 1, hourly flux

Figure 1: 2-D view of suction variation with depth and time;

SM-ML; desert flux, 1st year, hourly flux.

Figure 2: 2-D view of suction variation with depth and time, zoomed in on surface;


494

Figure 3: 3-D front view of suction variation with depth and time;


101 102 103 104 105


0 10 20 30 40 50 60 70

0

0.05

0.1

0.15

0.2

0.25

0.3

Dis

tanc

e fro

m s

urfa

ce [m

]


Initial ProfileBefore Prec. (Oct.)After First RainAfter all Rain in Oct.

Figure 4: Profile before and after rain in October; SM-ML; desert flux, 1st year, hourly flux

495

-505

101520

x 10-4

Precipitation [m/h]

Applied Prec. = 0.27 [m/year]

-5-4-3-2-10

x 10-4

PE [m/h]

PE = 2.34 [m/year]

-5-4-3-2-10

x 10-4

Instant. AE [m/h]

0 50 100 150 200 250 300 350-1

0

1

2x 10

-3

Instant. Flux [m/h]

Time [day]

Figure 5: Instantaneous Fluxes

SM-ML; desert landscape, 1st year, hourly flux

496

-0.04

-0.02

0

0.02

Var

iabl

e [m

]

Domain AccumulationCum. Runoff

0 50 100 150 200 250 300 350-2.5

-2

-1.5

-1

-0.5

0

0.5

Var

iabl

e [m

]

Time [day]

Cum. Prec.Cum. AECum. PE

Figure 6: Cumulative Fluxes

SM-ML; desert landscape, 1st year, hourly flux 1-D SM-ML Soil: Desert Landscape, year 1-6, hourly flux


SM-ML; desert landscape, years 1-6, hourly flux.

497


SM-ML; desert landscape, year 6, hourly flux.

101 102 103 104 105


0 20 40 60 80

0

0.5

1

1.5

2

2.5

3

Dis

tanc

e fro

m s

urfa

ce [m

]


Initial ProfileYear1-JunYear2-Jun.Year3-Jun.Year4-Jun.Year5-Jun.Year6-Jun.Year6-Wettest Cond. (Jan.)

Figure 9: Driest (Jun) and Wettest (Dec.) Profiles;


498

-5

-4

-3

-2

-1

x 10-4

Inst

ant.

AE

[m/h

]

0 1 2 3 4 5 6-0.5

0

0.5

1

1.5

2

2.5x 10-3

Inst

ant.

Flux

[m/h

]

Time [year] Figure 10: Instantaneous Fluxes


-0.15

-0.1

-0.05

0

Var

iabl

e [m

]

Cum. RunoffDomain Accum.

0 1 2 3 4 5 6-15

-10

-5

0

5

Var

iabl

e [m

]

Time [year]

Cum. Prec.Cum. PECum. AE



499

Table 1: Flux Data (SM-ML; desert landscape, years 1-6, hourly flux)

Cumulative Applied Flux Cumulative Actual Flux

Time Prec. PE AE Flux Runoff

Profile Water

Volume

[Year] [Month] [Day] [m] [m] [m] [m] [m] [m] 0 0 0 0.000 0 0 0.0 1.278 1 31 0.029639 -0.086 -0.0351 -0.005 0.0 1.272 2 59 0.059399 -0.184 -0.0682 -0.009 0.0 1.268 3 90 0.099719 -0.352 -0.1125 -0.014 0.0 1.264 4 120 0.114 -0.573 -0.1344 -0.022 0.0 1.256 5 151 0.11901 -0.871 -0.1476 -0.029 0.0 1.248 6 181 0.12141 -1.173 -0.1568 -0.036 0.0 1.242 7 212 0.16461 -1.497 -0.2036 -0.039 0.0 1.238 8 243 0.19197 -1.766 -0.2326 -0.042 0.0 1.236 9 273 0.21432 -1.987 -0.2573 -0.045 0.0 1.233

10 304 0.23272 -2.159 -0.2763 -0.046 0.0 1.232 11 334 0.25384 -2.267 -0.2971 -0.046 0.0 1.232

1

12 365 0.27208 -2.340 -0.3149 -0.046 0.0 1.232 2 12 365 0.544 -4.680 -0.6040 -0.066 0.0 1.212 3 12 365 0.816 -7.021 -0.8884 -0.081 0.0 1.196 4 12 365 1.088 -9.361 -1.1703 -0.094 0.0 1.183 5 12 365 1.360 -11.701 -1.4506 -0.106 0.0 1.172 6 12 365 1.632 -14.041 -1.7297 -0.116 0.0 1.162

1-D SM-ML Soil: Desert Landscape, year 1, average flux


SM-ML; desert landscape, 1st year, average flux.

500

102 103 104 105


0 10 20 30 40

0

0.25

0.5

0.75

1

1.25

1.5

1.75

2

Dis

tanc

e fro

m s

urfa

ce [m

]


Initial ProfileEnd of JunEnd of Dec.

Figure 13: Profile at selected times, Jun and December;


-0.06

-0.04

-0.02

0

0.02

Var

iabl

e [m

]

Domain Accum.Cum. Runoff

0 50 100 150 200 250 300 350-3

-2

-1

0

1

Var

iabl

e [m

]

Time [day]


PE = 2.34 [m/year]

Cum. Prec.Cum. AECum. PE

Figure 14: Cumulative Fluxes,


501

0

2

4

6x 10

-5

Precipitation [m/h]


-4

-2

0x 10

-4

PE [m/h]

PE = 2.34 [m/year]

-9

-6

-3

0x 10

-5

Instant. AE [m/h]

0 50 100 150 200 250 300 350

-4

-2

0

2

4x 10

-5

Instant. Flux [m/h]

Time [day]

Figure 15: Instantaneous Fluxes SM-ML; desert landscape, 1st year, average flux.

502

Table 2: Flux Data (SM-ML; desert landscape, 1st year, average flux).


Time Irrig.+Prec. PE Flux AE

Flux from water

volume

Cum. Runoff

Profile Water

Volume

[Year] [Month] [Day] [m] [m] [m] [m] [m] [m] [m] 0 0 0 0 0 0 0 0 1.2778 1 31 0.03 -0.0861 -0.056 -0.0392 -0.0094 0.00 1.2682 2 59 0.06 -0.184 -0.124 -0.0739 -0.0141 0.00 1.2636 3 90 0.1 -0.352 -0.252 -0.1193 -0.0190 0.00 1.2586 4 120 0.114 -0.5734 -0.459 -0.1404 -0.0258 0.00 1.2518 5 151 0.119 -0.8711 -0.752 -0.1526 -0.0330 0.00 1.2447 6 181 0.121 -1.1736 -1.053 -0.1603 -0.0391 0.00 1.2385 7 212 0.164 -1.4969 -1.333 -0.2066 -0.0422 0.00 1.2355 8 243 0.192 -1.766 -1.574 -0.2364 -0.0447 0.00 1.2330 9 273 0.214 -1.9859 -1.772 -0.2618 -0.0476 0.00 1.2301 10 304 0.233 -2.1585 -1.926 -0.2811 -0.0485 0.00 1.2291 11 334 0.254 -2.2664 -2.013 -0.3030 -0.0492 0.00 1.2284

1

12 365 0.276 -2.3396 -2.063 -0.3256 -0.0493 0.00 1.2283

1-D SM-ML Soil: Roof Runoff Ponding, year 1, hourly flux


SM-ML; roof runoff ponding, 1st year, hourly flux.

503





504

100 101 102 103 104 105


0 20 40 60 80 100

0

1

2

3

4

5

Dis

tanc

e fro

m s

urfa

ce [m

]


IC-End of Year 5, Desert FluxDriest Cond. - JunWettest Cond. - Dec.

Figure 19: Profile at selected times, March after rain, end of Jun, end of Dec.


0 50 100 150 200 250 300 350-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Var

iabl

e [m

]

Time [day]

Cum. Prec.Cum. AECum. PEDomain Accum.

Figure 20: Cumulative Flux


505

-5

0

5

10

15x 10-3

Precipitation [m/h]

-4

-2

0x 10-4

PE [m/h]

-4

-2

0x 10-4

Instant. AE [m/h]

0 50 100 150 200 250 300 350-5

0

5

10

15x 10-3

Instant. Flux [m/h]

Time [day]

Figure 21: Instantaneous Flux


506

Table 3: Flux Data (SM-ML; 1st year, hourly flux)

Input Output Time

Prec. PE Flux AE Domain Accum.

Profile Water

Volume [Year] [Month] [Day] [m] [m] [m] [m] [m] [m]

0 0 0 0 0 -9E-05 0 1.172 1 31 0.178 -0.0861 0.092 -0.0492 0.084 1.256 2 59 0.356 -0.1842 0.172 -0.1054 0.177 1.349 3 90 0.598 -0.3524 0.246 -0.1827 0.306 1.478 4 120 0.684 -0.5734 0.111 -0.2513 0.315 1.487 5 151 0.714 -0.871 -0.157 -0.2804 0.294 1.466 6 181 0.728 -1.1734 -0.445 -0.3073 0.279 1.451 7 212 0.988 -1.4971 -0.509 -0.4286 0.391 1.563 8 243 1.152 -1.7664 -0.615 -0.5379 0.428 1.600 9 273 1.286 -1.9867 -0.701 -0.6152 0.470 1.642

10 304 1.396 -2.1593 -0.763 -0.6778 0.509 1.681 11 334 1.523 -2.2672 -0.744 -0.7305 0.573 1.744

1

12 365 1.632 -2.3402 -0.708 -0.7759 0.630 1.801

507

SM-ML Soil: Turf Landscape

Analysis results of 1-D 10-m deep SM-ML soil profile are presented. Three turf



irrigation (2.36m/year), precipitation (0.27m/year) and potential evaporation (1.18m/year).

The precipitation is applied as in the desert landscape. The irrigation is applied daily and

lasts up to 1 hour. The PE is averaged over each month. Constant head of -153m

constitutes the initial and bottom boundary conditions.

2. In the second analysis the applied flux consists of precipitation and irrigation averaged

over each month (2.58 m/year) and PE also averaged over each month (1.18 m/year).

Constant head of -153m constitutes the initial and bottom boundary conditions.

3. In the 3rd analysis, irrigation equal to PE was analyzed. The flux was applied on hourly

bases with irrigation and precipitation schedule of scenario 1. The PE is averaged over

each month. Two initial conditions were considered. The first one consisted of constant -

153m head with depth, while the second one varied from 84000 kPa matric suction at the

soil surface to 1500kPa at the base of the soil profile.



provided on the end of analysis for the final year.

508

1-D SM-ML Soil: Turf Landscape, 1st year, hourly flux, Flux = 2.2PE


SM-ML; turf landscape, 1st year, hourly flux, Flux = 2.2PE.



509

100 101 102 103 104 105


0 20 40 60 80 100

0

1

2

3

4

5

6

Dis

tanc

e fro

m s

urfa

ce [m

]



Figure 24: Profiles of the driest surface conditions (April) and the wettest (Dec.);


101 102 103 104 105


0 20 40 60 80 100

0

0.01

0.02

0.03

0.04

0.05

Dis

tanc

e fro

m s

urfa

ce [m

]


Initial ProfileBefore Irrig. (April)After Irrig. (April)

Figure 25: Profile before and after 0.5-h irrigation in April; SM-ML; turf landscape, 1st year, hourly flux, Flux = 2.2PE.

510

0

0.005

0.01

0.015

Precipitation andIrrigation [m/h]

-2

-1

0x 10-4

PE [m/h]

-2

-1

0x 10-4

Instant. AE [m/h]

0 50 100 150 200 250 300 350-5

0

5

10

15x 10-3

Instant. Flux [m/h]

Time [day]

Figure 26: Instantaneous Fluxes SM-ML; turf landscape, 1st year, hourly flux, Flux = 2.2PE.

511

0 50 100 150 200 250 300 350-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

Var

iabl

e [m

]

Time [day]



SM-ML; turf landscape, 1st year, hourly flux, Flux = 2.2PE. Table 4: Flux Data (SM-ML; turf landscape, years 1-2, hourly flux, Flux = 2.2PE)

Input Output Time Irrig.+Prec

. PE Flux AE Domain Accum.

Profile Water

Volume

[Year] [Month

] [Day] [m] [m] [m] [m] [m] [m] 0 0 0 0 0 0 0 1.278 1 31 0.098 -0.0331 0.065 -0.0330 0.065 1.343 2 59 0.189 -0.0758 0.113 -0.0758 0.113 1.391 3 90 0.299 -0.1471 0.152 -0.1471 0.152 1.429 4 120 0.383 -0.2475 0.136 -0.2330 0.139 1.416 5 151 0.716 -0.3824 0.334 -0.3675 0.259 1.537 6 181 1.037 -0.5342 0.503 -0.5190 0.349 1.627 7 212 1.409 -0.6945 0.715 -0.6795 0.473 1.751 8 243 1.765 -0.8415 0.924 -0.8265 0.596 1.874 9 273 2.105 -0.9656 1.140 -0.9504 0.726 2.004

10 304 2.451 -1.0686 1.382 -1.0534 0.878 2.156 11 334 2.543 -1.1387 1.404 -1.1235 0.889 2.167

1

12 365 2.633 -1.1815 1.451 -1.1658 0.926 2.204

512

1-D SM-ML Soil: Turf Landscape, year 1, average flux, Flux = 2.2PE


SM-ML; turf landscape, 1st year, average flux, Flux = 2.2PE.

Figure 29: 2-D view of suction variation with depth and time; SM-ML; turf landscape, 1st year, average flux, Flux = 2.2PE.

513

0

2

4

6x 10-4



-2

-1

0x 10-4

PE [m/h]

PE = 1.18 [m/year]

-2

-1

0x 10-4

Instant. AE [m/h]

0 50 100 150 200 250 300 350

0

2

4

x 10-4

Instant. Flux [m/h]

Time [day]


SM-ML; turf landscape, 1st year, average flux, Flux = 2.2PE.

514

0 50 100 150 200 250 300 350-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

Var

iabl

e [m

]

Time [day]



SM-ML; turf landscape, 1st year, average flux, Flux = 2.2PE. Table 5: Flux Data (SM-ML; turf landscape,1st year, average flux, Flux = 2.2PE)

Input Output Time

Irrig.+Prec. PE Flux AE Domain Accum.

Profile Water

Volume[Year] [Month] [Day] [m] [m] [m] [m] [m] [m]

0 0 0 0 0 -7E-05 0 1.278 1 31 0.098 -0.0331 0.065 -0.0332 0.065 1.343 2 59 0.189 -0.0758 0.113 -0.0759 0.113 1.391 3 90 0.295 -0.1471 0.148 -0.1473 0.148 1.425 4 120 0.376 -0.2475 0.129 -0.2474 0.129 1.407 5 151 0.704 -0.3824 0.322 -0.3819 0.321 1.599 6 181 1.019 -0.5342 0.485 -0.5336 0.480 1.758 7 212 1.378 -0.6945 0.683 -0.6940 0.671 1.949 8 243 1.726 -0.8415 0.885 -0.8409 0.864 2.141 9 273 2.06 -0.9656 1.094 -0.9651 1.063 2.341 10 304 2.399 -1.0686 1.331 -1.0681 1.285 2.563 11 334 2.489 -1.1387 1.350 -1.1384 1.293 2.570

1

12 365 2.583 -1.1815 1.401 -1.1807 1.341 2.619

515

1-D SM-ML Soil: Turf Landscape, year 1, hourly flux, Flux = PE, IC=5th year desert

Figure 32: 3-D front view of suction variation with depth and time; SM-ML; turf landscape, 1st year, hourly flux, Flux=PE, IC=5th year desert.


SM-ML; turf landscape, 1st year, hourly flux, Flux=PE, IC=5th year desert.

516

100 101 102 103 104 105


0 20 40 60 80 100

0

0.5

1

1.5

2

2.5

3

Dis

tanc

e fro

m s

urfa

ce [m

]



Figure 34: Profiles of the driest surface conditions (April) and the wettest (Dec.); SM-ML; turf landscape, 1st year, hourly flux, Flux=PE, IC=5th year desert.

0 50 100 150 200 250 300 350-1.5

-1

-0.5

0

0.5

1

1.5

2

Var

iabl

e [m

]

Time [day]

Cum. Prec.+Irrig.Cum. AECum. PEDomain Accum.

Figure 35: Cumulative Flux SM-ML; turf landscape, 1st year, hourly flux, Flux=PE, IC=5th year desert.

517

0

2

4

6x 10-3


-2

-1

0x 10-4

PE [m/h]

-2

-1

0x 10-4

Instant. AE [m/h]

0 50 100 150 200 250 300 350

0

2

4

6x 10-3

Instant. Flux [m/h]

Time [day]

Figure 36: Instantaneous Flux Data SM-ML; turf landscape, 1st year, hourly flux, Fl=PE, IC=5th year desert

518

Table 6: Flux Data (SM-ML; turf landscape, 1st year, hourly flux, Flux=PE, IC=5th year desert)

Input Output Time


Profile Water


0 0 0 0 0 -0.0001 0 1.278 1 31 0.075 -0.0331 0.042 -0.0330 0.041 1.213 2 59 0.145 -0.0758 0.069 -0.0758 0.066 1.238 3 90 0.232 -0.1471 0.084 -0.1440 0.083 1.254 4 120 0.293 -0.2475 0.045 -0.2139 0.070 1.242 5 151 0.465 -0.3824 0.083 -0.3347 0.084 1.255 6 181 0.63 -0.5342 0.096 -0.4657 0.085 1.257 7 212 0.842 -0.6945 0.148 -0.6161 0.121 1.293 8 243 1.038 -0.8415 0.197 -0.7734 0.169 1.341 9 273 1.223 -0.9656 0.257 -0.8972 0.230 1.402 10 304 1.408 -1.0686 0.339 -1.0099 0.312 1.483 11 334 1.477 -1.1387 0.338 -1.0779 0.309 1.481

1

12 365 1.544 -1.1815 0.362 -1.1201 0.334 1.506

519

CH Soil: Desert Landscape

Analysis results of 1-D 10-m deep CH soil profile are presented. Three desert landscape

analyses were performed.


precipitation (0.27m/year) and potential evaporation, PE, (2.34 m/year). The precipitation is

applied everyday from the beginning of each month for the average number of rainy days in

each month as determined from statistical analysis of 24 years of historical data. The

duration and magnitude of each rain event is also based on the analysis of the same

historical data. The PE is averaged over each month. The constant head of -153m

constitutes the initial and bottom boundary conditions. The same scenario was repeated

for a 2-D 10m by 5m domain.

2. In the second analysis the precipitation flux was averaged over each month and applied in

terms of m/h. Similarly, PE was also averaged over each month (2.34 m/year). The

constant head of -153 m constitutes the initial and bottom boundary conditions.

3. In the 3rd analysis, the effects of poor drainage near foundation and roof runoff were

considered. The soil profile obtained with 5th year desert landscape analysis was used as

the input profile where the matric suction varies nonlinearly from 84000kPa at the soil

surface to 1500kPa at the profile bottom. The precipitation flux, described above, was

increased by a factor of 6. In this scenario, all the water was allowed to infiltrate the profile.

This was accomplished be removing the runoff function.



provided on the end final year final year analysis.

520

1-D CH Soil: Desert Landscape, year 1, hourly flux


CH; desert landscape, 1st year, hourly flux.



521

101 102 103 104 105


0 10 20 30 40 50 60 70 80 90

0

0.02

0.04

0.06

0.08

0.1

0.12

Dis

tanc

e fro

m s

urfa

ce [m

]


Initial ProfileBefore Prec. in Nov.After first rain in Nov.After all Rain in Nov.

Figure 39: Profile before and after 0.5-h irrigation in April;


-0.06

-0.04

-0.02

0

Var

iabl

e [m

]


Domain Accum.Cum. Runoff

0 50 100 150 200 250 300 350-2.5

-2

-1.5

-1

-0.5

0

0.5

Var

iabl

e [m

]

Time [day]

PE = 2.34 [m/year]

Cum. PECum. Prec.Cum. AE



522

0

0.5

1

1.5

2x 10-3

Precipitation [m/h]


-5

-4

-3

-2

-10

x 10-4

PE [m/h]

PE = 2.34 [m/year]

-5

-4

-3

-2

-10

x 10-4

Instant. AE [m/h]

0 50 100 150 200 250 300 350-5

0

5

10

15x 10-4

Instant. Flux [m/h]

Time [day]



523

1-D CH Soil: Desert Landscape, years 1-6, hourly flux

Figure 42: 3-D back view of suction variation with depth and time;

CH; desert landscape, years 1-6, hourly flux.



524



102 103 104 105


0 20 40 60 80

0

0.5

1

1.5

2

2.5

Dis

tanc

e fro

m s

urfa

ce [m

]


Initial ProfileYear1-JunYear2-Jun.Year3-Jun.Year4-Jun.Year5-Jun.Year6-Jun.Year6-March



525

-5

-4

-3

-2

-1

x 10-4

Inst

ant.

AE

[m/h

]

0 1 2 3 4 5 6-5

0

5

10

15x 10-4

Inst

ant.

Flux

[m/h

]

Time [year] Figure 46: Instantaneous Flux Data


-0.15

-0.1

-0.05

0

Var

iabl

e [m

]

Net RunoffDomain Accum.

0 1 2 3 4 5 6-15

-10

-5

0

5

Var

iabl

e [m

]

Time [year]

Cum. Prec.Cum. PECum. AE



526

Table 7: Cumulative Flux Data (CH; desert landscape, years 1-6, hourly flux) Input Output

Time Irrig. PE Net

Flux AE Domain Accum.

Profile Water

Volume

[Year] [Month] [Day] [m] [m] [m] [m] [m] [m] 0 0 0 0 0 0 0 2.560 1 31 0.03 -0.086 -0.056 -0.0370 -0.007 2.553 2 59 0.059 -0.184 -0.125 -0.0698 -0.010 2.549 3 90 0.1 -0.352 -0.253 -0.1146 -0.015 2.545 4 120 0.114 -0.573 -0.459 -0.1380 -0.024 2.536 5 151 0.119 -0.871 -0.752 -0.1533 -0.035 2.525 6 181 0.121 -1.173 -1.052 -0.1671 -0.044 2.516 7 212 0.165 -1.497 -1.332 -0.2153 -0.049 2.511 8 243 0.192 -1.766 -1.574 -0.2434 -0.052 2.507 9 273 0.214 -1.987 -1.772 -0.2684 -0.057 2.503

10 304 0.233 -2.159 -1.927 -0.2870 -0.058 2.502 11 334 0.254 -2.267 -2.013 -0.3068 -0.057 2.502

1

12 365 0.272 -2.340 -2.068 -0.3234 -0.056 2.504 2 12 365 0.544 -4.680 -4.136 -0.5979 -0.081 2.479 3 12 365 0.816 -7.021 -6.204 -0.8822 -0.100 2.460 4 12 365 1.088 -9.361 -8.272 -1.1636 -0.116 2.444 5 12 365 1.36 -11.701 -10.341 -1.4274 -0.130 2.430 6 12 365 1.633 -14.041 -12.409 -1.7053 -0.143 2.417

527

1-D CH Soil: Desert Landscape, year 1, average flux


CH; desert landscape, 1st year, average flux.

103 104 105


0 10 20 30 40 50 60

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Dis

tanc

e fro

m s

urfa

ce [m

]


Initial ProfileEnd of JunEnd of Dec.



528

0

1

2

3

x 10-5

Precipitation [m/h]


-5

-4

-3

-2

-1

0x 10-4

PE [m/h]

PE = 2.34 [m/year]

-1

-0.5

0x 10-4

Instant. AE [m/h]

0 50 100 150 200 250 300 350-15

-10

-5

0

x 10-6

Instant. Flux [m/h]

Time [day]



529

-0.3

-0.2

-0.1

0

0.1

0.2

0.3V

aria

ble

[m]


Cum. AECum. Prec.Domain Accum.

0 50 100 150 200 250 300 350-2.5

-2

-1.5

-1

-0.5

0

Var

iabl

e [m

]

Time [day]

PE = 2.34 [m/year]

Cum. PE



Table 8: Cumulative Flux Data (CH; desert landscape, 1st year, average flux) Input Output

Time Irrig.+Prec. PE Flux AE Domain

Accum.

Profile Water


0 0 0 0 0 0 0 2.5597 1 31 0.025 -0.0861 -0.061 -0.0366 -0.0116 2.5495 2 59 0.048 -0.184 -0.136 -0.0647 -0.0169 2.5442 3 90 0.076 -0.352 -0.276 -0.0984 -0.0226 2.5385 4 120 0.084 -0.5734 -0.490 -0.1134 -0.0295 2.5316 5 151 0.088 -0.8711 -0.783 -0.1251 -0.0373 2.5238 6 181 0.088 -1.1736 -1.085 -0.1331 -0.0445 2.5165 7 212 0.114 -1.4969 -1.383 -0.1639 -0.0495 2.5116 8 243 0.135 -1.766 -1.631 -0.1880 -0.0527 2.5084 9 273 0.153 -1.9859 -1.833 -0.2090 -0.0560 2.5051 10 304 0.168 -2.1585 -1.991 -0.2248 -0.0571 2.5040 11 334 0.185 -2.2664 -2.081 -0.2430 -0.0577 2.5034

1

12 365 0.205 -2.3396 -2.135 -0.2627 -0.0578 2.5032

530

1-D CH Soil: Roof Runoff Ponding, year 1, hourly flux


CH; roof runoff ponding, 1st year, hourly flux.



531

10-1 100 101 102 103 104 105


0 50 40 60 80 100

0

0.5

1

1.5

2

2.5

3

Dis

tanc

e fro

m s

urfa

ce [m

]


Initial ProfileBefore Prec. in JulyAfter All Rain in JulyEnd of Dec.

Figure 54: Profile at selected times: July before and after rain, end of Dec.


0

0.2

0.4

Var

iabl

e [m

]

Cum. Prec.Domain Accum.

0 50 100 150 200 250 300 350-2.5

-2

-1.5

-1

-0.5

0

Var

iabl

e [m

]

Time [day]

Cum. AECum. PE



532

0

10

20x 10-3

Precipitation [m/h]Applied Prec. = 1.64 [m/year]

-4

-2

0x 10-4

PE [m/h]PE = 2.3 [m/year]

-4

-2

0x 10-4

Instant. AE [m/h]

0 50 100 150 200 250 300 3500

10

20x 10-3

Instant. Flux [m/h]

Time [day]



533

Table 9: Cumulative Flux Data (CH; roof runoff ponding, 1st year, hourly flux) Input Output

Time Prec. PE Flux AE Flux Domain

Accum.

Profile Water

Volume [Year] [Month] [Day] [m] [m] [m] [m] [m] [m] [m]

0 0 0 0 0 0 0 0 2.560 1 31 0.181 -0.0945 -0.064 -0.0541 0.149 0.087 2.647 2 59 0.366 -0.2020 -0.141 -0.1238 0.281 0.171 2.730 3 90 0.611 -0.3731 -0.271 -0.2245 0.461 0.291 2.851 4 120 0.695 -0.5891 -0.473 -0.3131 0.502 0.284 2.844 5 151 0.725 -0.8718 -0.751 -0.3659 0.523 0.261 2.821 6 181 0.739 -1.1598 -1.037 -0.3998 0.530 0.238 2.798 7 212 0.994 -1.4723 -1.307 -0.5453 0.702 0.333 2.892 8 243 1.15 -1.6955 -1.504 -0.6689 0.784 0.348 2.908 9 273 1.284 -1.9187 -1.705 -0.7733 0.869 0.369 2.929 10 304 1.397 -2.1047 -1.872 -0.8636 0.936 0.384 2.944 11 334 1.526 -2.2271 -1.973 -0.9457 1.016 0.426 2.985

1

12 365 1.637 -2.3063 -2.034 -1.0177 1.066 0.457 3.017

534

CH Soil: Turf Landscape

Analysis results of 1-D 10-m deep SM-ML soil profile are presented. Three turf



irrigation (2.43m/year), precipitation (0.20m/year) and potential evaporation (1.18m/year).

The precipitation is applied as in the desert landscape. The irrigation is applied daily and

lasts up to 1 hour. The PE is averaged over each month. Constant head of -153m

constitutes the initial and bottom boundary conditions.

2. In the second analysis the applied flux consists of precipitation and irrigation averaged over

each month (2.58 m/year) and PE also averaged over each month (1.18 m/year). Constant

head of -153m constitutes the initial and bottom boundary conditions.

3. In the 3rd analysis, irrigation equal to PE was analyzed. The flux was applied on hourly

bases with irrigation and precipitation schedule of scenario 1. The PE is averaged over

each month. Two initial conditions were considered. The first one consisted of constant -

153m head with depth, while the second one varied from 84000 kPa matric suction at the

soil surface to 1500kPa at the base of the soil profile.



provided on the end of analysis for the final year.

535

1-D CH Soil: Turf Landscape, 1st year, hourly flux, Flux = 2.2PE


CH; turf landscape, 1st year, hourly flux, Flux = 2.2PE.



536





537

100 101 102 103 104 105


0 50 40 60 80 100

0

0.2

0.4

0.6

0.8

1

Dis

tanc

e fro

m s

urfa

ce [m

]


Initial ProfileDriest Profile (April)Wettest (March. after Prec.)

Figure 61: Profile at selected times: driest (end of April), and wettest (after all prec. in

March); CH; turf landscape, 1st year, hourly flux, Flux = 2.2PE.

0

0.02

0.04

0.06

0.08

0.1

0.12

Cum

. Cha

nge

in P

rofil

e W

ater

Vol

. [m

]

0 50 100 150 200 250 300 350

-1

0

1

2

3

Var

iabl

e [m

]

Time [day]

Cum. Applied Prec.Cum. AECum. PE



538

-3

0

3

6

9

12x 10-3

Precipitationand Irrigation [m/h]

Applied Prec. and Irrg. = 2.63 [m/year]

-2

-1

0x 10-4

PE [m/h]

PE = 1.18 [m/year]

-2

-1

0x 10-4

Instant. AE [m/h]

0 50 100 150 200 250 300 350-3

0

3

6

9

12x 10-3

Instant. Flux [m/h]

Time [day] Figure 63: Instantaneous Flux Data


539

1-D CH Soil: Turf Landscape, years 1-34, hourly flux, Flux = 2.2PE


CH; turf landscape, Years 1-11, hourly flux, Flux = 2.2PE.



540



101 102 103 104


20 40 60 80 100

0

1

4

3

4

5

6

7

8

9

10

Dis

tanc

e fro

m s

urfa

ce [m

]


Initial ProfileEnd of Year1End of Year3Year6-March(Wettest)Year6-April(Driest)End of Year 10End of Year 20End of Year 34

Figure 67: Profile at selected times;


541

-2

-1

0x 10-4

Inst

ant.

AE

[m/h

]

0 1 2 3 4 5 60

5

10

15x 10-3

Inst

ant.

Flux

[m/h

]

Time [year] Figure 68: Instantaneous Flux Data


0 1 2 3 4 5 6-10

-5

0

5

10

15

20

Var

iabl

e [m

]

Time [year]

Cum. Prec.+ IrrigCum. PECum. AE



542

0 1 2 3 4 5 6 7 8 9 10 110

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5D

omai

n A

ccum

. [m

]

Time [year] Figure 70: Domain Accumulation


-0.02

0

0.02

0.04

Dom

ain

Acc

um.

0 50 100 150 200 250 300 350

-1

0

1

2

3

Var

iabl

e [m

]

Time [day]



CH; turf landscape, Year 11, hourly flux, Flux = 2.2PE

543

1-D CH Soil: Turf Landscape, 1st year, average flux, Flux = 2.2PE


CH; turf landscape, 1st year, average flux, Flux = 2.2PE



544

10-1 100 101 102 103 104


40 60 60 70 80 90 100

0

0.5

1

1.5

2

2.5

3

Dis

tanc

e fro

m s

urfa

ce [m

]


Initial ProfileEnd of AprilEnd of Dec.

Figure 74: Profile before and after 0.5-h irrigation in April; CH; turf landscape, 1st year, average flux, Flux = 2.2PE

0

0.1

0.2

0.3

0.4

Var

iabl

e [m

]


Cum Flux

Cum. Change in Profile Water Volume

0 50 100 150 200 250 300 350-2

-1

0

1

2

Var

iabl

e [m

]

Time [day]

PE = 1.18 [m/year]

Cum. AECum. PECum. Applied Flux



545

0

2

4

6x 10-4

Precipitation [m/h]


-3

-2

-1

0x 10-4

PE [m/h]

PE = 1.18 [m/year]

-3

-2

-1

0x 10-4

Instant. AE [m/h]

0 50 100 150 200 250 300 350-1

0

1

2

3

4x 10-4

Instant. Flux [m/h]

Time [day]

Figure 76: Instantaneous Fluxes CH; turf landscape, 1st year, average flux, Flux = 2.2PE

546

Table 10: Cumulative Flux Data (CH; turf landscape, 1st year, average flux, Flux = 2.2PE)


Time Irrig.+Prec. PE Flux AE Flux

Flux from water

volume

Profile Water

Volume

[Year] [Month] [Day] [m] [m] [m] [m] [m] [m] [m] 0 0 0 0 0 0 0 0 2.5612 1 31 0.098 -0.0331 0.065 -0.0330 0.0656 0.0653 2.6265 2 59 0.189 -0.0758 0.113 -0.0756 0.1121 0.1119 2.6731 3 90 0.295 -0.1471 0.148 -0.1469 0.1490 0.1487 2.7099 4 120 0.376 -0.2475 0.129 -0.2471 0.1306 0.1303 2.6915 5 151 0.704 -0.3824 0.322 -0.3825 0.1871 0.1864 2.7475 6 181 1.019 -0.5342 0.485 -0.5343 0.2146 0.2138 2.7750 7 212 1.378 -0.6945 0.683 -0.6947 0.2392 0.2384 2.7996 8 243 1.726 -0.8415 0.885 -0.8416 0.2613 0.2606 2.8218 9 273 2.06 -0.9656 1.094 -0.9657 0.2813 0.2805 2.8417 10 304 2.399 -1.0686 1.331 -1.0686 0.3007 0.3000 2.8611 11 334 2.489 -1.1387 1.350 -1.1386 0.3157 0.3149 2.8761

1

12 365 2.583 -1.1815 1.401 -1.1809 0.3326 0.3319 2.8930

1-D CH Soil: Turf Landscape, 1st year, hourly flux, Flux = 1.3PE, IC=-153 m.


CH; turf landscape, 1st year, hourly flux, Flux =1.3PE

547

Figure 78: 2-D view of suction variation with depth and time zoomed in on surface;


100 101 102 103 104 105


0 20 40 60 80 100

0

0.2

0.4

0.6

0.8

1

Dis

tanc

e fro

m s

urfa

ce [m

]



Figure 79: Driest and wettest profile;


548

-30369

12x 10

-3



-2

-1

0x 10-4

PE [m/h]

PE = 1.18 [m/year]

-2

-1

0x 10-4

Instant. AE [m/h]

0 50 100 150 200 250 300 350-30369

12x 10-3

Instant. Flux [m/h]

Time [day]

Figure 80: Instantaneous Flux Data CH; turf landscape, 1st year, hourly flux, Flux =1.3PE

549

0

0.02

0.04

0.06

0.08

0.1

0.12

Dom

ain

Acc

um.

0 50 100 150 200 250 300 350

-1

0

1

2

3

Var

iabl

e [m

]

Time [day]



CH; turf landscape, 1st year, hourly flux, Flux =1.3PE Table 11: Cumulative Flux Data (CH; turf landscape, 1st year, hourly flux, Flux =1.3PE)

Input Output Time


Profile Water


0 0 0 0 0 0 0 2.5597 1 31 0.075 -0.0331 0.042 -0.0329 0.0354 2.5966 2 59 0.145 -0.0758 0.069 -0.0755 0.0517 2.6128 3 90 0.232 -0.1471 0.084 -0.1463 0.0527 2.6139 4 120 0.293 -0.2475 0.045 -0.2199 0.0379 2.5991 5 151 0.465 -0.3824 0.082 -0.3433 0.0455 2.6067 6 181 0.63 -0.5342 0.096 -0.4733 0.0436 2.6048 7 212 0.842 -0.6945 0.148 -0.6203 0.0517 2.6129 8 243 1.038 -0.8415 0.197 -0.7580 0.0554 2.6166 9 273 1.223 -0.9656 0.257 -0.8787 0.0611 2.6223

10 304 1.408 -1.0686 0.339 -0.9809 0.0721 2.6332 11 334 1.477 -1.1387 0.338 -1.0493 0.0667 2.6279

1

12 365 1.544 -1.1815 0.362 -1.0919 0.0864 2.6476

550

1-D CH Soil: Turf Landscape, 1st year, hourly flux, Flux = 1.3PE, IC=34the year of turf


CH; turf landscape, 1st year, hourly flux, Flux =1.3PE, IC=turf

Figure 83: 2-D view of suction variation with depth and time zoomed in on surface; CH; turf landscape, 1st year, hourly flux, Flux =1.3PE, IC=turf

551

100 101 102 103 104 105


0 20 40 60 80 100

0

0.2

0.4

0.6

0.8

1

Dis

tanc

e fro

m s

urfa

ce [m

]



Figure 84: Driest and wettest profile;


-0.25

-0.2

-0.15

-0.1

-0.05

0

Dom

ain

Acc

um.

0 50 100 150 200 250 300 350

-1

0

1

2

Var

iabl

e [m

]

Time [day]




552

-3

0

3

6x 10-3



-2

-1

0x 10-4

PE [m/h]

PE = 1.18 [m/year]

-2

-1

0x 10-4

Instant. AE [m/h]

0 50 100 150 200 250 300 350-3

0

3

6x 10-3

Instant. Flux [m/h]

Time [day]

Figure 86: Instantaneous Flux Data


553

Table 12: Cumulative Flux Data (CH; turf landscape, 1st year, hourly flux, Flux =1.3PE, IC=turf)

Input Output Time


Profile Water


0 0 0 0 0 0 0 3.8821 1 31 0.075 -0.0331 0.042 -0.0330 -0.0536 3.8291 2 59 0.145 -0.0758 0.069 -0.0758 -0.0759 3.8071 3 90 0.232 -0.1471 0.084 -0.1471 -0.1054 3.7771 4 120 0.293 -0.2475 0.045 -0.2334 -0.1487 3.7341 5 151 0.465 -0.3824 0.082 -0.3624 -0.1661 3.7161 6 181 0.63 -0.5342 0.096 -0.4978 -0.1883 3.6941 7 212 0.842 -0.6945 0.148 -0.6484 -0.2005 3.6821 8 243 1.038 -0.8415 0.197 -0.7883 -0.2140 3.6691 9 273 1.223 -0.9656 0.257 -0.9103 -0.2240 3.6591

10 304 1.408 -1.0686 0.339 -1.0127 -0.2283 3.6541 11 334 1.477 -1.1387 0.338 -1.0822 -0.2443 3.6381

1

12 365 1.544 -1.1815 0.362 -1.1248 -0.2364 3.6461

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