soil mechanics for unsaturated soils -...
TRANSCRIPT
il l
; ! l
l
Soil Mechanics for Unsaturated Soils
D. G. Fredlund, Ph.D.
Professar of Civil Engineering University of Saskatchewan Saskatoon, Saskatchewan
H. Rahardjo, Ph.D.
Senior Lecturer School of Civil and Structural Engineering
Nanyang Technological University
A Wi1ey-Interscience Pub1ication
JOHN WILEY & SONS, JNC.
New York • Chichester • Brisbane • Toronto • Singapore
CHAPTER l
CHAPTER 2
CONTENTS
Introduction to Unsaturated Soil Mechanics l. l Role of Climate
l . 2 Types of Problems 1.2.1 Construction and Operation of a Dam
1.2.2 Natura! Slopes Subjected to Environmental Changes
1.2.3 Mounding Below Waste Retention Ponds
1.2.4 Stability of Vertical or Near Vertica1 Excavations
1.2.5 Lateral Earth Pressures
1.2.6 Bearing Capacity for Shallow Foundations
1.2.7 Ground Movements Involving Expansive Soils
1.2.8 Collapsing Soils
1.2.9 Summary of Unsaturated Soils Examples
1.3 Typical Profiles of Unsaturated Soils
1.3.1 Typical Tropical Residua! Soil Profile
1.3.2 Typical Expansive Soils Profile
1.4 Need for Unsaturated Soil Mechanics l. 5 Scope of the Book
1.6 Phases of an Unsaturated Soil 1.6.1 Definition of a Phasc
l .6.2 Air- Water Interface or Contractile Skin
l. 7 Terminology and Definitions
1.8 Historical Developments
Phase Properties and Relations 2.1 Properties of the Individuai Phases
2.1.1 Density and Specific Volume
Soil panicles
Water phase
Air phase
2. 1.2 Viscosity
2.1.3 Surface Tension
2.2 Interaction of Air and Water 2.2.1 Solid, Liquid, and Vapor States of Water
2.2.2 Water Vapor
2.2.3 Air Dissolving in Water
Solubility of Air in Water
Di.ffùsion of Gases Through Water
3
3
5
6
6
7 7
8
9
9
9
10
Il
12
13
14
14
14
15
16
20
/ 20
2 1
21
21
21
23
24
25
26
26
27 28
28
xiii
XIV CONTéNTS
2.3 Volume-Mass Relations 29
2.3.1 Porosity 29 2.3.2 Void Ratio 30 2.3.3 Degree of Saturation 30 2.3.4 Water Conteni 31 2.3.5 Soil Densiry 32 2.3.6 Basic Volume- Mass Relationship 32 2.3.7 Changes in Volume-Mass Properties 33 2.3.8 Density of Mixtures Subjected to Compression of 34
the Air Phase
Piston-porous stone analogy 34 Conservation of mass applied to a mixture 36 Soil particles-water-air mixture 37 Air-water mixture 37
CHAPTER 3 Stress State Variables 38 3. 1 History of the Description of the Stress State 38
3. 1.1 Effective Stress Concept for a Saturated Soil 38 3.1.2 Proposed Effective Stress Equation for an 39
Unsaturated Soil
3.2 Stress State Variables for Unsaturated Soils 42 l 3.2.1 Equilibrium Analysis for Unsaturated Soils 42 Normal and shear stresses on a soil element 42 Equilibrium equations 43
1 3.2.2 Stress State Variables 43 Other combinations of stress state variables 44
i 3.2.3 Saturated Soils as a Special Case of Unsaturated 45 Soils
3.2.4 Dry Soils 45 t 3.3 Limit ing Stress State Conditions 46 .
3.4 Experimental Testing of the Stress State Variables 47
3.4.1 The Concept of Axis Translation 47 3.4.2 Null Tests to Test Stress State Variables 48 3.4.3 Other Experimental Evidence in Support of the 48
Proposed Stress State Variables
3.5 Stress Analysis 49
3.5.1 In Situ Stress State Component Profiles 49 Coefficient of latera l eanh pressure 52 Matric suction profile 53
Ground surface condition 53 .l Environmental conditions 53
. Vegetation 53 Water table 54 Permeability of the soil projìle 54
3.5.2 Extended Mohr Diagram 54
Equation of Mohr circles 55 Constructìon of Mohr circles 56
3.5.3 Stress Invariants 58
3.5.4 Stress Points 59
3.5.5 Stress Paths 59
3.6 Role of Osmotic Suction 63
CO]';TENTS xv
CHAPTER 4 Measurements of Soil Suction 64 4.1 Theory of Soil Suction 64
4.1.1 Componcnts of So il Suction 64 4. 1.2 Typical Suction Valucs and Thcir Mcasuring 66
Deviccs
4.2 Capillari ty 67 4.2.1 Capillary Height 67 4.2.2 Capillary Pressure 68 4.2.3 Height of Capillary Rise and Radius Effects 69
4 .3 Measurements of Total Suction 70 4.3.1 Psychrometers 70
Seebeck effecrs 70 Peltier effects 70 Peltier psychrometer 71 Psychrometer calibration 73 Psychrometer performance 74
4.3.2 Filter paper 77 Principle of measurement (filter paper method) 77 Measurement and calibration techniques (jilter 77
paper method)
l The use of the filter paper merhod in practice 79 4.4 Measurements of Matric Suction 80
., 4.4.1 High Air Entcy Disks 81 4.4.2 Direct measurements 82
Tensiometers 83
i Servicing the tensiometer prior to installation 84 Servicing the tensiometer after insrallarion 86 Jet fili tensiometers 86 Small tip tensiometer 86 Quick Draw tensiometers 88 Tensiometer performance for field 88
measurements
Osmotic tensiometers 90 Axis-translation rechnique 91
4.4.3 Indirect Measurements 93 Thermal conductiviry sensors 95 Theory of operation 97 Calibrarion of sensors / 97 Typical results of matric suction measurements 99 The MCS 6000 sensors 99 The AGWA-11 sensors 100
4.5 Measurements of Osmotic Suction 104 4.5. 1 Squeezing technique 105
CHAPTER 5 Flow Laws 107 5.1 Flow of Water 107
5.1.1 Driving Potential for Water Phase 108 5.1.2 Darcy's Law for Unsaturated Soils 110 5.1.3 Coefficient of Permeability with Respect to the 110
Water Phase
Fluid .a1ul porous medium components IlO
xvi CONTENTS
Relationship between permeabìlity {md volume- I l i mass propenies
Ejfect of variatiom in degree of sarurarion 0 11 I l i permeabiliry
Relationship between coejjicient of permeability I l i
l and degree of saturarion
Relationship between water coejjicient of 113 permeability and matric suction
l Relationship between water coejjiciem of 113 permeability and volumetric water conteni
Hysteresis of the permeability function 116
Il )l( 5.2 Flow o f Air 117
5.2.1 Driving PotentiaJ for Air Phase 117 5.2.2 Fick's Law for Air Phase 117 Il 5.2.3 Coefficient of Penneability with Respect to Air 119
Phase
Relationship between air coejjicient of 120 11 permeabiliry and degree of saturation
Relationship between air coejjicient of 120 permeability and matric suction ~ 5.3 Diffusion 121
5.3. 1 Air Ditfusion Through Water 121
~ 5.3.2 Chemical Ditfusion Through Water 123
5.4 Summary of F low Laws 123
CHAPTER 6 Measurement of Permeability 124
6. 1 Measurement of Water Coefficient of Permeability 124 ~ 6.1.1 Direct Methods to Measure Water Coefficient of 124 Penneability
~ Laboratory test methods 124 Steady-state method 124 Apparatus for steady-state method 125
Il Computations using steady-state method 126 Presentation ofwater coejjiciems of 126
permeability
Il Dijficulties with the steady-state method 127 Instantaneous profile method 127 Instantaneous profile method proposed by 128 l Hamilton et al.
Cornputations for the instantaneous profile 129 method l In situ field methods 130
In situ instantaneous profile method 130 Computations f or the in si tu insrantaneous 131
profile method
6.1.2 Indirect Methods to Compute Water Coefficient of 133
li Penneability
Tempe pressure cell apparatus and test 133 procedure
lf Volumetric pressure p/ate extractor apparatus 134
and test procedure
Test procedure f or the volumetric pressure 135
tl plate extractor
Drying portion of soil- water characteristic 136 curve
l l l Il q
Il
~
~
[
\
Il
Il
CHAPTER 7
CHAPTER 8
COI':TENTS xvii
Wetting ponion of rh e .wil- warer characrerisric 136 curve
Cornpuration of k.,, using rhe soil- water characteristic curve
6.2 Mcasurement of Air Coefficient of Penneability
Triaxial permeamerer ce/l for the measurement of air permeability
Triaxial penneameter celi for air and water penneabi/iry measurements
6.3 Measurement of Diffusion
6.3. 1 Mechanism of Air Diffusion Through High Air Entry Disks
6.3.2 Measurements of the Cocfficient of Diffusion
Procedure for computing diffusion properties
6.3.3 Diffused Air Volume Indicators
Bubble pump to measure diffused air volume
Diffused air volume indicator (DAVI)
Procedure for measuring diffused air volume
Compuration of diffused air volume
Accuracy of the diffused air volume indicator
Steady-State Flow 7 .l Steady-State Water Flow
7. 1. 1 Variation of Coefficient of Permeability with Space for an Unsaturated Soil
Heterogeneous, isotropic steady-state seepage
Heterogeneous, anisotropie sready-state seepage
7.1.2 One-Dimensional Flow
Formulation for one-dimensional ftow
Solution far one-dimensional flow
Finite difference method
Head boundary condition
Flux boundary condition
7.1.3 Two-Dimensional Flow
Formulation for two-dimensional flow
Solutions far two-dimensional jfow
Seepage analysis IISing the finite element method ~
Examples of two-dimensional problems
Infinite slope
7. 1.4 Three-Dimensional Flow
7.2 Steady-State Air Flow
7 .2.1 One-Dimensional Flow
7.2.2 Two-Dimensional Flow
7.3 Steady-State Air Diffusion Through Water
Pore Pressure Parameters 8.1 Compressibility of Pore Fluids
8.1 . l Air Compressibiliry
8.1 .2 Water Compressibility
8.1.3 Compressibility of Air- Watcr Mixtures
The use of pore pressure parameters in the compressibili/)' equation
136
138
140
140
143
144
144 145 146
146 146
148 148
149
150 150 151
151 151
152 153 154 155 155 156
159 159 160
161
164
171 173
175
175 176
177
178 178
179 179 179 181
XVIII CONTI:::NTS
CHAPTER 9
8.1.4 Components of Compressibi1ity of an Air- Watcr Mixture
Effects of free air on the compressibility of the mixture
Effec:ts of dissolved air 011 t h e compressibility of the mixture
8.1.5 Other Re1ations for Compressibi1ity of Air- Water Mixrure
Limitation of Kelvin 's equation in formulatin.g the compressibility equation
8.2 Derivations of Pore Pressure Parameters
8.2.1 Tangent and Secant Pore Pressure Paramcters
8.2.2 Summary of Necessary Constitutivc Relations
8.2.3 Drained and Undrained Loading
8.2.4 Tota1 Stress and Soil Anisotropy
8.2.5 Ko-Loading
8.2.6 Hilf's Analysis
8.2.7 Isotropic Loading
8.2.8 Uniaxial Loading
8.2.9 Triaxial Loading
8.2.10 Three-Dimensional Loading
8.2.11 ex Parameters
8.3 Solutions of the Pore Pressure Equations and Comparisons with Experimental Results
8.3.1 Secant B;, Pore Pressure Parameter Derived from Hilf's Analysis
8.3.2 Graphica1 Procedure for Hi1f's Ana1ysis
8.3.3 Experimental Results of Tangent B Pore Pressure Parameters for Isotropic Loading
8.3.4 Theoretical Prediction of B Pore Pressure Parameters for Isotropic Loading
8.3.5 Experimental Results of Tangent Band A Parameters for Triaxia1 Loading
8.3.6 Experimental Measurements of the a Parameter
Shear Strength Theory 9.1 History of Shear Strength
9.1.1 Data Associated with Incomplete Stress Variab1e Measurements
9.2 Failure Envelope for Unsaturated Soils
9 .2.1 Failure Criteria
9.2.2 Shear Strength Equation
9.2.3 Extended Mohr-Coulomb Failure Enve1ope
9.2.4 Use of (a - u..,) and (u0 - u,.,) to Define Shear Strength
9.2.5 Mohr-Coulomb and Stress Point Envelopes
9.3 Triaxial Tests on Unsaturated Soils
9.3.1 Consolidate<! Drained Test
9.3.2 Constant Water Content Test
9.3.3 Consolidated Undrained Test with Pore Pressure Measurements
9.3.4 Undrained Test
9.3.5 Unconfined Compression Test
k
Il
181
1
11
Ili 182
182
11 182 l
183
184
185
186
188
190
191
192
194
196
196
199
200
201
201
202
204
206
215
216
217 2 17
224
225
225
227
228
230
231
236
238
238
240
243
245
CHAPTER IO
CHAPTER 11
CONTENTS xix
9.4 Direct Shear Tests on Unsaturcd Soils 247
9 .5 Selection of Strain Rate 248
9.5.1 Background on Strain Rates for Triaxial Testing 248
9.5.2 Strain Rates for Triaxial Tests 250
9.5.3 Displacement Rate for Direct Shear Tests
9.6 Multistage Testing 9.7 Nonlinearity of Failure Envelope 9.8 Relationships Between q/> and x
Measurement of Shear Strength Parameters 10. 1 Special Design Considerations
10.1. 1 Axis-Translation Technique
10.1.2 Pore-Water Pressure Contro! or Measurement
Saturation procedure f or a high air entry disk
10.1.3 Pressure Response Below the Ceramic Disk
10.1.4 Pore-Air Pressure Contro! or Measurement
10.1.5 Water Volume Change Measurement
10.1.6 Air Volume Change Measurement
10.1. 7 Overall Volume Change Measurement
10. 1.8 Specimen Preparation
10.1. 9 Backpressuring to Produce Saturation
10.2 Test Procedures for Triaxial Tests
10.2.1 Consolidated Drained Test
10.2.2 Constant Water Content Test
10.3 10.4
10.2 .3 Consolidated Undrained Test with Pore Pressure Measurements
10.2.4 Undrained Test
10.2.5 Unconfined Compression Test
Test Procedures for Direct Shear Tests /
Typical Test Results
10.4. 1 Triaxial Test Results
Consolidated drained triaxial tests
Constant water content triaxial tests
Nonlinear shear strength versus matric sucrion
Undrained and unconjìned compression tests
10.4.2 Direct Shear Test Results
Plastic and Limit Equilibrium I l . l Earth Pressures
11.1. l At Rest Eanh Pressure Conditions
11. 1.2 Estimation of Depth of Cracking
11. 1.3 Extended Rankine Theory of Earth Pressures
Active earth pressure
Coefficient of active earth pressure
Active earth pressure distriburion (constan.t matric suction with depth)
Tension zone deprh
Active earth pressure distriburion (linear decrease in matric suction to the water table)
254
255
255
258
260 260
260 263
266
266
272 273
275
275
276
277
279
280
281
281
282 282
282
284
284
284
286
286
288
289
297 297
298 300 301
303 304
304
304
304
XX CONTENTS
Acri ve earth pressurc distribution whcn rhe soil has tension cracks
Passive earth pressure
Coefficient of passive earth pressure
Passive earth pressure distribution (constanr matric sucrion wirh depth)
Passive earth pressure distribution (linear decrease in marric suction to the warer table)
Deformarions wirh active and passive states
I l . 1.4 Total Latera! Earth Force
Acri ve earth force
Passive earth force
Il. l .5 Effect of Changes in Matric Suction on thc Active and Passive Earth Pressure
Relationship berween swelling pressures and the earth pressures
I l . l. 6 Unsupported Excavations
Ejfect oftension cracks on the unsupported height
Il. 2 Bearing Capacìty ~o.' 11 ·"
11 .2.1 Tenaghi Bearihg Capacity Theory
11.2.2 Assessment of Shear Strength Parameters and a Design Matric Suction
Stress state variable approach
Total stress approach
11.2. 3 Bearing Capacity of Layered Systems
11.3 st'ope StabiJity
11 .3. 1 Location of the Criticai Slip Surface
11.3.2 Generai Limit &juil ibrium (GLE) Method
Shear force mobilized equarion
Normalforce equation
Factor of safery with respect t o moment equilibrium
Factor of safety with respect t o force equilibrium
lnterslice force function
Procedures for solving rhe factors of safety equation
Pore-water pressure designation
11.3.3 Other Limit Equilibrium Methods
11.3 .4 Numerica! Difficultics Associated with the Limit Equilibrium Method of Slices
11 .3.5 Etfects of Negative Pore-Water Pressure on Slope Stability
The " total cohesion " method
Two examples using the ''rotai cohesion · ' method
Example no. l
Example no. 2
The "extended shear strength" method
Genera l /ayout of problems and soil properties
lnitial condirfons for the seepage analysis
Seepage and slope stability resulrs under high-intensity rainfall conditions
305
307
307
307
308
308
309
310
311
312
313
313
314
3 15
315 317
317
318
319
320
320
32 1
323
324
324
325
325
327
328
330
332
l l 333
333 l 334
334 l 338
l 1 340
340
342 l 344
u
CHAPTER 12
CHAPTER 13
CONTENTS xxi
Volume Change Theory 12.1 Literature Rcvicw
12.2 Concepts of Volume Change and Deformation
12.2.1 Continuity Requiremcnts
12.2.2 Ovcrnll Volume Change
12.2.3 Water and Air Volume Changes
12.3 Constitutive Relations
12.3.1 Elasticity Form
Water phase constitutive relation
Change in the volume of air
lsotropic loading
Uniaxial loading
Triaxial loading
K0-loading
Piane strain loading
Piane stress loading
12.3.2 Compressibility Form
12.3.3 Volume- Mass Form (Soil Mechanics Terminology)
12 .3.4 Use of (u - uw) and (ua - uw) to Formulate Constitutive Relations
12.4 Experimental Yerifications fo r Uniqueness of Constitutive Surfaces
12.4.1 Sign Convention for Volumetric Deformation Properties
12.4.2 Verification of Uniqueness of the Constiturive Surfaces Using Small Stress Changes
12.4.3 Verification of the Constitutive Surfaces Using Large Stress State Variable Changes
12.5 Relationship Among Volumetric D eformation Coefficients ~
12.5.1 Relationship of Volumetric Deformation Coefficients fo r the Void Ratio and Water Content Surfaces
12.5.2 Relationship of Volumetric Deformation Coefficients for the Volume-Mass Form of the Constitutive_ Surfaces
12.5.3 Laboratory Tests Used for Obtaining Volumetric Deformation Coefficients
12.5.4 Relationship of Volumetric Deformation Coefficients for Unloading Surfaces
12.5.5 Re1ationship of Volumetric Deformation Coefficients for Loading and Unloading Surfaces
12.5.6 Constitutive Surfaces on a Semi-Logarithmic Plot
Measurements of Volume Change Indices l 3. l Literature Review
13.2 T est Procedures and Equipments
13.2.1 Loading Constitutivc Surfaces
Oedometer tests
Pressure plate drying tests
Shrinkage tesrs
346 346
349
349
350
351
351
351
353
353
354
354
354
356
357
357
357
358
358
360
361
361
363
365
366
367
367
369
370
370
374 374
376
377
378
379 380
XXII CONTGNTS
CHAPTER 14
CHAPTER 15
Determination of volume change indices
Determinati an of volume clumge indice.\· associated with the /ransition piane
Typica/ resu/ts from pressure p/ate tests
Determinarion of in si tu stn•ss state using oedomeler test results
" Constant volume" cest
''Free-swell ' ' test
Correction for the compressibility of the apparatus
Correctionfor samp/ing disturbance
13 .2 .2 Unloading Constitutive Surfaces
Unloading tests after compression
Pressure plate weuing tests
Free-swell tests
Determination of volume change indices
Volume Change Predictions 14.1 Literature Review
14.1.1 Factors Affecting Tota1 Heave
14.2 Past , Present, and Future States of Stress
14.2.1 Stress State History
14.2.2 In Situ Stress State
14.2.3 Future Stress State and Ground Movements
14.3 Theory of Heave Predictions 14.3.1 Total Heave Formulations
14.3.2 Prediction of Fina! Pore- Water Pressures
14.3.3 Example of Heave Calculations
14.3.4 Case Histories
Slab-on-grade jloor, Regina, Saskatchewan
Esron school, Eston, Saskatchewan
14.4 Control Factors in Heave Prediction and Reduction
14.4. 1 Closed-Form Heave Equation when Swclling Pressure is Constant
14.4.2 Effect of Correcting the Swelling Pressure on the Prediction of Total Heave
14.4.3 Example with Wetting from the Top to a Specified Depth
14.4.4 Example with a Portion of the Profile Removed by Excavation and Backfìlled with a Nonexpansive Soil
14.5 Notes on Collapsible Soils
One-DimensionaJ Consolidation and Swelling 15. l Literature Review
15.2 Physical Relations Required for the Formulation
15.3 Derivation of Consolidation Equations 15.3. 1 Water Phase Partial Differential Equation
Saturaced condition
Dry soil condition
Special case of an unsaturated soil condition
15.3.2 Air Phase Partial Differentia1 Equation
Sacuraced soil condicion
380
382
386
388
388
389
389
390
392
392
393
394
395
397 397
401
403
404
405
406
406
407
408
408
410
410
411
41 1
412
413
414
415
417
419 4 19
420
422
423 424
424
424
l 425
426
l'
l l
CHAPTER 16
CONTENTS XXIJI
Dry soil condition 426 Special case of an unsaturared soi/
15.4 Solution of Consolidation Equations Us ing Finite Difference Technique
15.5 Typical Consolidation Test Results for Unsaturated Soils
15 .5. 1 Tcsts on Compacted Kao1in
Presentation of results
Theoretical ana/yses
15 .5.2 Tests on Silty Sand
Presentarion of results
Theoretical analysis
15.6 Dimensionless Consolidation Parameters
Two- and Three-Dimensional Unsteady-State Flow and Nonisothermal Analyses 16.1 Uncoupled Two-Dimensional Formulations
16.1.1 Unsteady-State Seepage in lsotropic Soil
Water phase panial differential equation
Air phase pania/ differential equation
16.1.2 Unsteady-State Seepage in an Anisotropie Soil
Anisotropy in permeability
Water phase panial differemial equation
.Seepage ana/ysis using the finite element method
Examples of two-dimensional problems and their solutions
Example of water flow rhrough an eanh dam
Example of groundwater seepage below a lagoon
Example of seepage within a layered h ili slope .r-
16.2 Coupled Formulations of Three-Dimensional Consolidation
16.2.1 Constitutive Relations
Soil structure
Water phase
Air phase
16.2.2 Coup1ed Consolidation Equations
Equilibrium equations
Water phase continuiry
Air phase continuiry
16.3 Nonisothermal Flow 16.3.1 Air Phase Partia\ Differential Equation
16.3.2 Fluid and Vapor Flow Equation for the Water P ha se
16.3.3 Heat Flow Equation
16.3.4 Atmospheric Boundary Conditions
Surface boundary conditions for air and fluid water flow
Surface boundary conditions for water vapor fio w
Surface boundary conditions for heat flow
426
427
429
429 429
430 433 433 435
437
440
440
440 441 441 441 442 443
444
447
447 447
449
456
456 461 463
472
472
472
473 473
473
473 474
474
475 475
475
477
xxiv CONTENTS
APPENDIX A
APPENDIX B
Units and Symbols
Theoretical Justification for Stress State Variables B. l Equilibrium Equations for Unsaturated Soils B.2 Total or Overall Equilibrium
B.3 Independent Phase Equilibrium
8.3.1 Water Phase Equilibrium
479
483 483 483
484
485 8 .3.2 Air Phase Equilibrium 485 8.3.3 Contractile Skin Equilibrium 485
B.4 Equilibrium of the Soil Structure (i. e., Arrangement of 488 Soil Particles)
B.5 Other Combinations of Stress State Variables 489
References 490
About the Authors 508
lndex 510