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Draft

Design Procedure for Landslide Stabilization using Sheet

Pile Ribs

Journal: Canadian Geotechnical Journal

Manuscript ID cgj-2018-0082.R1

Manuscript Type: Article

Date Submitted by the Author: 07-May-2018

Complete List of Authors: Bartz, James; University of Manitoba, Civil Engineering Martin, C. Derek; University of Alberta, Hendry, Michael; University of Alberta, Civil and Geological Engineering

Keyword: landslide, slope stabilization, soil-pile interaction, sheet piles, design procedure

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Canadian Geotechnical Journal

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1

Design Procedure for Landslide Stabilization using Sheet Pile Ribs 1

2

James R. Bartz1, C. Derek Martin

2 and Michael T. Hendry

3 3

4

Corresponding Author: 5

James R. Bartz 6

7

8

1 M.Sc. student, Department of Civil and Environmental Engineering, University of Alberta, Edmonton, 9

Canada, T6G 1H9, [email protected] 10

2 Professor, Department of Civil and Environmental Engineering, University of Alberta, Edmonton, 11

Canada, T6G 1H9, [email protected], 1-780-492-2332 12

3 Assistant Professor, Department of Civil and Environmental Engineering, University of Alberta, 13

Edmonton, Canada, T6G 1H9, [email protected], 1-780-492-0200 14

1 Current Affiliation:

Ph.D. student, Department of Civil Engineering, University of Manitoba, Winnipeg, Canada, R3T 5V6,

[email protected]

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ABSTRACT 15

A design procedure was developed for a relatively unknown slope stabilization technique consisting of a 16

series of parallel sheet piles installed parallel to the direction of slope movement. This technique was 17

introduced in Alberta by Dr. R.M. Hardy in the 1970’s and is locally referred to as “Hardy Ribs.” A case 18

study is discussed where CN Rail installed Hardy Ribs to stabilize a landslide affecting its rail line in 19

western Manitoba. A proposed design procedure is discussed that consists of a de-coupled approach 20

with a separate limit equilibrium slope stability analysis and laterally loaded pile analysis using p-y 21

curves to model the soil-pile interaction. Example calculations are provided for the proposed design 22

procedure for the CN case study site to illustrate its use and to estimate the stabilizing effect from the 23

Hardy Ribs at this site. 24

Keywords: landslide, slope stabilization, soil-pile interaction, sheet piles, analysis, design procedure 25

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INTRODUCTION 26

Cast-in-place concrete piles and driven steel piles have been used in many cases to stabilize slow 27

moving landslides in Alberta (Abdelaziz et al. 2011). An alternative pile type that has seen relatively few 28

applications is the use a series of sheet piles installed parallel to each other and parallel to the direction 29

of slope movement. The shear resistance along the sides of the sheet piles prevents soil from squeezing 30

between adjacent rows of sheet piles. The sheet piles are installed below the landslide plane to transmit 31

the landslide load to the stable earth to provide the stabilizing resistance. This passive resistance 32

method was first introduced in Alberta by Dr. R. M. Hardy in the 1970’s and is locally referred to in 33

Alberta as “Hardy Ribs.” CN Rail installed Hardy Ribs near Peace River, Alberta in the 1990s and more 34

recently in 2015 to stabilize a landslide located in western Manitoba. This landslide stabilization 35

technique has seen limited use and therefore there is no generally accepted procedure to analyze the 36

performance of Hardy Ribs to estimate the stabilizing force or the forces acting on the sheet piles. 37

The performance of the Hardy Ribs is expected to differ from that of typical slope stabilizing 38

piles due to the difference in pile geometry. Some design procedures (Cornforth 2012; Vessely, 39

Yamasaki and Strom 2007) for slope stabilizing piles are intended for long piles where the critical failure 40

mechanism is bending failure of the pile below the slide plane. These procedures consist of a laterally 41

loaded pile analysis on only the portion of the pile below the slide plane. Due to the relatively short 42

installation depth below the slide plane for Hardy Ribs, sheet pile ribs may behave as rigid piles and the 43

maximum bending moment may occur above the slide plane. Therefore, these approaches are not 44

applicable for the analysis and design of Hardy Ribs. The construction procedure for installing Hardy Ribs 45

has some advantages over cast-in-place concrete stabilizing piles. A large quantity of spoil material will 46

result from drilling shafts for cast-in-place piles. For remote sites, it may be difficult or costly to deliver 47

concrete. In addition, drilling an open shaft creates the possibility of introducing groundwater or surface 48

water to the slide plane. These issues are less of a concern when driving sheet piles. Hardy Ribs have a 49

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disadvantage however, in that the installation depth can be limited by the ability to drive sheet piles into 50

the soil or rock below the slide plane. A shorter installation depth below the slide plane might result in 51

greater deformation and the achievable installation depth can limit the stabilizing resistance. 52

The proposed design procedure presented in this paper for Hardy Ribs consists of a de-coupled 53

approach with separate limit equilibrium slope stability analysis and a laterally loaded pile analysis of 54

the sheet pile ribs. The soil-pile interaction of a sheet pile rib is numerically modelled based on the 55

beam-column equation by Hetenyi (1946) and utilizing p-y curves. Two extreme scenarios are 56

considered for the behaviour of the joints of the individual sheet pile sections including; 1) there is no 57

displacement along the joints when loaded and the sheet pile rib behaves as a continuous section with a 58

very large moment of inertia; and 2) the joints between sheet pile sections are free to move and the 59

sheet pile rib behaves as a series of independent and in-line piles. These two scenarios will be referred 60

to as Case 1 and Case 2, respectively. 61

The proposed design procedure requires the use of p-y curves to model the soil-pile interaction. 62

A limitation of this method exists that there has been no full scale testing of laterally loaded sheet pile 63

ribs loaded in the appropriate direction. Therefore p-y curves that were developed for circular piles have 64

been modified for the use of Hardy Ribs. Another limitation is the required assumption of the behaviour 65

of the joints between sheet piles. The two extreme cases of a single rigid sheet pile rib or a series of 66

independent in-line piles has a significant impact on the calculated soil-pile interaction. In reality, the 67

true behaviour may be somewhere in between with sliding along the individual sheet pile joints, but 68

with friction along the joints to transfer some of the load. 69

HARDY RIBS CASE STUDY SITE 70

Background Information for Study Site 71

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The landslide study site is located along an outside bend of the Assiniboine River valley between the 72

towns of St. Lazare and Miniota in western Manitoba. This landslide is adjacent to the CN rail line at Mile 73

191.4 of the Rivers Subdivision. Approximately 110 m of track was being affected by this landslide and 74

was causing ongoing maintenance concerns. During site inspections in the fall of 2014, a scarp was 75

observed identifying the southern extents of the landslide. Signs of riverbank erosion at the toe of the 76

slope were also observed as identified from the steep banks along the outside bend of the Assiniboine 77

River. Light detection and ranging (LIDAR) data was collected along this portion of the rail line in 78

November, 2015 to capture the topography of the region. A topographic contour plan based on the 79

LIDAR data is shown in Figure 1. Cross sections of the site are shown in Figure 2. The inferred limits of 80

the landslide shown in Figure 1 are based on the observed landslide scarp and observed deflections in 81

the rail line. 82

The Assiniboine River is an underfit stream within a trench-shaped valley formed as a meltwater 83

channel during deglaciation of the region approximately 12 000 to 15 000 years ago (Klassen, 1975). The 84

bedrock in this region consists of marine clay shale of the Cretaceous Riding Mountain Formation and 85

the valley bottom fill consists of alluvial sediments (Klassen 1975). A geotechnical investigation including 86

a drilling, laboratory testing and instrumentation program was completed in 2014 and 2015. The three 87

boreholes drilled in 2014 are shown on Figure 1, labelled as BH14-1 to BH14-3. Three additional 88

boreholes were drilled in 2015 and are labelled BH15-1 to BH15-3. The stratigraphy was observed to 89

consist of granular fill comprising the rail embankment underlain by high plastic clay and clay shale 90

bedrock. Cross sections with stratigraphic data from the site investigations are shown in Figure 2. The 91

clay shale bedrock was observed to be highly disturbed above the landslide plane. 92

Instrumentation installed during the 2014 geotechnical investigation included five vibrating wire 93

piezometers with two each in BH14-1 and BH14-3 and one in BH14-2. A slope Inclinometer (S.I.) was 94

installed in each of BH14-1, BH14-2 and BH14-3. Groundwater elevations measured from the 95

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piezometers in November, 2014 are shown in Figure 2. Based on the S.I. monitoring data, a distinct 96

landslide plane was observed with the clay shale bedrock indicating a translational slide as shown in 97

Figure 3. The A-direction S.I. data which is oriented downslope is shown. The approximate elevation of 98

the landslide plane based on the S.I. monitoring data is shown in Figure 2. The landslide plane is inclined 99

and sloping downward toward the Assiniboine River with an approximate slope of 14H:1V. Over a 26 100

day monitoring period in November and December of 2014, the displacement rate along the slide plane 101

was approximately 1 mm per day. 102

Hardy Ribs Design and Construction at Study Site 103

The remediation works at the study site were constructed in June and July of 2015 and consisted of 37 104

sheet pile ribs installed parallel to each other at 3.0 m centre-to-centre spacing. The Hardy Ribs spanned 105

approximately 108 m along the valley. Each sheet pile rib consisted of ten PZC-26 steel sheet pile 106

sections. The dimensions and spacing of the sheet pile ribs are shown in Figure 4. The approximate 107

location of the sheet pile ribs is shown in plan in Figure 1. The intended minimum installation depth was 108

1.83 m below the slide plane and into the intact clay shale bedrock. 109

The sheet piles were installed in pairs and were initially advanced to an approximate depth of 110

5.5 m using a vibratory hammer. A diesel hammer was then used to drive the sheet piles to the final 111

installation depth. The sheet piles were driven to refusal and the final installation depth did vary. The 112

majority of the sheet piles were driven greater than 2.0 m below the slide plane and into the intact 113

shale. Installation of the sheet pile ribs is shown in Figure 5. 114

Performance of Hardy Ribs at Study Site 115

A borehole (BH15-3) was drilled in November, 2015 to install an additional slope inclinometer (S.I.) to 116

monitor the performance of the slope following remediation. There was no S.I. monitoring data during 117

construction as the S.I. casings installed in BH14-1, BH14-2 and BH14-3 had deformed beyond their 118

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functional limits. The A-direction S.I. monitoring data which is oriented downslope is shown in Figure 6 119

for BH15-3. Readings were obtained between December, 2015 and December, 2016. Based on the 120

monitoring data, there has been some ongoing slope displacement which is expected for a passive 121

reinforcement system. The most significant displacement was observed to occur in the disturbed shale 122

between elevations 379 m to 382 m. This suggests there may be displacement of shale between the 123

sheet piles at this elevation range. The magnitudes and rate of displacement are minor however. The 124

rate of landslide displacement is shown in Figure 7 before and after remediation with the A-direction S.I. 125

data from BH14-1 and BH15-3. The average rate of displacement at BH15-3 from December, 2015 to 126

December, 2016 is less than 1 mm per month. 127

PROPOSED DESIGN PROCEDURE OF HARDY RIBS 128

Various authors have suggested analyzing slope stabilizing piles using a de-coupled approach with 129

separate slope stability and laterally loaded pile analyses (Viggiani 1981; Poulos 1995; Vessely et al. 130

2007; Cornforth 2012). Viggiani (1981) described three general steps for the de-coupled approach which 131

includes: 132

1. evaluating the shear force needed to increase the factor of safety of the slope to a desired 133

value; 134

2. evaluating the maximum shear force that each pile can provide as resistance against sliding of 135

the unstable soil; 136

3. selecting the most suitable location on the slope as well as the number and type of piles to be 137

installed. 138

For Step 2, various potential failure mechanism of the soil and piles need to be considered. 139

Poulos (1995) summarized the four potential failures modes as: (i) the “flow mode,” where the slide is 140

shallow and the unstable soil fails around the piles; (ii) the “short-pile mode,” where the slide is 141

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relatively deep and the pile length in the stable soil is relatively shallow causing the sliding soil to carry 142

the piles through the stable soil; (iii) the “intermediate mode,” where the soil strength is fully mobilized 143

in both the unstable and stable soil; and (iv) “long-pile failure,” where the pile itself yields due to the 144

maximum bending moment reaching the yield moment of the pile section. 145

These three general steps by Viggiani (1981) were considered in developing a design procedure 146

for the Hardy Ribs. Evaluating the shear force that the sheet piles can provide differs from procedures 147

for typical stabilizing piles due to the difference in pile geometry. This proposed design procedure is 148

suitable for translational landslides with a discrete shear zone. This procedure is based on that 149

developed by Bartz (2017) and discussed by Bartz et al. (2017), but further considers the possibility of 150

sliding between the sheet pile joints. The general steps are outlined in Figure 8. 151

Evaluating Required Resisting Shear Force 152

Step 1 is usually approached by performing two-dimensional limit equilibrium analysis of the 153

slope (Viggiani 1981). Adequate site information is required including topography, stratigraphy with 154

representative shear strength parameters, groundwater conditions, and identification of the slide plane. 155

For an active landslide, a back analysis can be performed to calibrate the model knowing that the actual 156

factor of safety is approximately equal to 1.0. Based on the stability analysis results, the required 157

increase in the resisting force per metre along the slope (∆�) can then be calculated from Poulos (1995) 158

as: 159

(1) ∆� = �� − �� 160

where �� is the sum of the disturbing forces along the critical surface, �� is the target factor of safety 161

and �� is the existing factor of safety. 162

Evaluating the Resisting Force for Sheet Pile Ribs 163

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It has been proposed to evaluate the soil-pile interaction for the laterally loaded sheet pile ribs utilizing 164

p-y curves. This method is suitable for analyzing the potential failure modes for both rigid piles and long 165

piles. One of the potential failure mechanisms of soil failing around the piles can be prevented by 166

selecting a sheet pile rib layout with sufficiently small spacing and sufficiently long sheet pile ribs. A 167

proposed design procedure was developed for Step 2 that utilizes p-y curves and prevents the failure of 168

soil around the sheet pile ribs. This procedure consists of the following steps: 169

a) Develop strength parameters for the laterally loaded pile analysis. 170

b) Select spacing between sheet pile ribs to prevent failure of the landslide mass between the 171

piles. 172

c) Develop suitable p-y curves. 173

d) Determine the yield bending moment of the sheet piles. 174

e) Determine soil-pile interaction using numerical models. 175

Develop strength parameters 176

Step 2a involves developing the parameters to be used in the laterally loaded pile analysis. The 177

undrained shear strength is typically used for generally accepted p-y curves for cohesive soil. This 178

include Matlock’s (1970) curve for soft clay and Welch and Reese’s (1972) curve for stiff clay without 179

access to free water. 180

Select sheet pile rib spacing 181

Step 2b involves selecting an appropriate spacing to prevent the soil from failing between the sheet 182

pile ribs. A limit equilibrium solution was developed by Bartz (2017) to calculate this spacing. A series of 183

closely spaced sheet pile ribs is considered as shown in Figure 9 that undergo lateral displacement. The 184

soil-steel interface between the sheet pile ribs will not fail if the development of continuous active and 185

passive wedges is more critical. The forces for this limit equilibrium condition are shown in Figure 9c. 186

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The series of sheet pile ribs will behave as a continuous wall if the difference of the passive and active 187

earth pressures on a sheet pile rib are less than the shearing force on the sides of the sheet pile ribs. 188

This is expressed as: 189

(2) ��2�� + �� − �−2�� + �� < 2�� 190

where �� is the undrained shear strength, � is the unit weight of the soil, � is the depth below ground 191

surface, � is the spacing between sheet pile ribs, � is an adhesion factor between the steel and soil and 192

� is the length of the sheet pile rib. Different combinations of � and � can be selected that satisfy 193

Equation 2 to provide sufficient shear resistance along the sides of each rib to prevent failure of soil 194

through adjacent ribs. � normally ranges from 0.4 for stiff clay to 1.0 for soft clay (Broms, 1983). 195

Equation 2 can be simplified and rearranged to solve for an acceptable spacing as: 196

(3) � < ��/2 197

With a spacing selected that satisfies Equation 3, the series of sheet piles will behave as a continuous 198

wall. Therefore, the ultimate lateral soil resistance per unit depth (��) will be governed by the forces 199

acting on the piles from the passive and active earth pressures. This is expressed as: 200

(4) �� = ��2�� + �� − �−2�� + �� + �� = 4�� 201

where � is the sheet pile rib width and �� is the centre-to-centre spacing between the sheet pile ribs. 202

Near ground surface, the active earth pressure should be ignored so that the tensile strength of the 203

cohesive soil is not relied upon. �� can be calculated for this scenario as: 204

(5) �� = �2�� + �� + �� = �2�� + �� 205

An appropriate magnitude of �� can be determined by calculating with depth and selecting as the 206

lesser of Equation 4 and Equation 5. 207

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Develop p-y curves 208

Step 2c involves selecting suitable p-y curves for use in the lateral pile analysis. Two scenarios 209

are considered for developing p-y curves. Case 1 considers each sheet pile rib to behave as a continuous 210

section with no sliding between the sheet pile joints. Case 2 considers each sheet pile rib to behave as a 211

series of in-line piles that are free to slide along the joints. 212

Most well-known p-y curves were developed based on field testing on circular piles. This 213

includes the p-y curves by Matlock (1970) for soft clay and Welch and Reese (1972) for stiff clay without 214

access to free water among others. p-y curves originally developed for circular piles have been applied 215

for continuous walls such as conventional sheet pile walls (Wang et al. 2013). This requires selecting an 216

equivalent pile diameter and applying a reduction factor or group-pile efficiency (β) to p-y curves. 217

Since the Hardy Ribs are designed to act as a continuous wall based on Step 2b, the equivalent 218

circular pile diameter (beq) can be selected equal to ��. This is equivalent to a contiguous row of 219

circular pile and is illustrated as Case 1 in Figure 10. Reese and Van Impe (2011) have suggested using β 220

equal to 0.64 for a contiguous row of piles based on a review of experimental data. Wang et al. (2013) 221

have suggested selecting β between 0.5 to 0.7 for conventional sheet pile walls. By selecting the p-y 222

curves based on an equivalent series of contiguous circular piles, this range of β can similarly be applied 223

to Hardy Ribs. 224

For Case 2, each sheet pile section can be treated as an equivalent circular pile with beq equal to 225

the width of the sheet pile rib. This treats each sheet pile rib as an equivalent series of in-line circular 226

piles as illustrated as Case 2 in Figure 10. Reese and Van Impe (2011) reviewed various studies on 227

laterally loaded in-line piles and suggested applying a β of 0.7 to the lead piles and 0.48 to the trailing 228

piles when there is no spacing between piles. 229

Determine yield bending moment 230

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Step 2d consists of calculating the structural capacity of the sheet piles. The yield bending 231

moment (� ) can be calculated from: 232

(6) � =!"#$% 233

where &' is the moment of inertia about the axis of bending, ( is the yield tensile strength and ) is the 234

distance from the neutral axis to the farthest point on the section. For Case 1, &' and ) should consider 235

the entire sheet pile rib geometry assuming it behaves as a continuous section. For Case 2, &' and ) 236

should consider the geometry of a single sheet pile section about the appropriate axis of bending. The 237

calculated magnitude of � needs to be considered for Step 2e. 238

Determine soil-pile interaction 239

Step 2e involves calculating the soil-pile interaction. Numerical models can be used to 240

determine the deflection, shear force, and bending moment in the pile and the soil reaction for a 241

laterally loaded pile (Vessely et al. 2007; Cornforth 2012). Lateral pile analysis software such as RSPile by 242

Rocscience Inc. (Rocscience Inc. 2017a) or LPile by Ensoft Inc. (Isenhower and Wang 2014) are capable of 243

solving the differential equation of a beam-column using nonlinear p-y curves. Behaviour of the laterally 244

loaded pile can be obtained by solving the differential beam-column equation by Hetenyi (1946): 245

(7) *'&' +,-+., + /. +0-

+.0 − � +1 = 0 246

where *' is the Young’s modulus of the pile, &' is the moment of inertia of the pile, /. is the axial load 247

on the pile, 3 is the pile length coordinate, p is the soil reaction per unit length, 4 is the lateral deflection 248

of the pile at point 3, and 1 is the distributed load along the pile. When the soil is loaded by laterally 249

moving soil, a distribution of horizontal soil displacement with depth is required. Poulos (1995) provided 250

an appropriate assumption of the lateral soil movement and labelled the movement into zones 251

described as the “stable zone”, “slide zone” and “drag zone” as is illustrated in Figure 11. This assumes 252

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there is zero lateral soil displacement in the stable zone and a constant magnitude of displacement in 253

the slide zone. The drag zone is a relatively thin zone undergoing intense shearing (Poulos, 1995). To 254

numerically model this scenario with moving soil, RSPile and LPile calculate the soil reaction from the 255

relative soil and pile movement. 256

Running the analysis until failing the pile by mobilizing transverse resistance along the pile can 257

require a substantial and unrealistic magnitude of soil movement up to 2 metres (Rocscience 2017b). In 258

this case, a certain magnitude of soil displacement in the slide zone can be selected to define landslide 259

failure. 260

When calculating the soil-pile interaction using the p-y curves developed from Case 1, &' of the 261

entire sheet pile rib should be considered. When using Case 2, &' should be equal to that of a single 262

sheet pile section about the appropriate axis of bending. 263

Select Location to Install Hardy Ribs 264

Poulos (1995) suggested that stabilizing piles: (i) must be relatively stiff to generate large stabilizing 265

force without failing in bending; (ii) must extend well below the landslide plane such that the failure 266

surface is not shifted downward with a factor of safety less than the target value, (iii) should be located 267

near the centre of the landslide mass to avoid relocating the failure surface upslope or downslope of the 268

piles. These recommendations for stabilizing piles are similarly applicable for Hardy Ribs. The preferred 269

location of the Hardy Ribs can be determined by analyzing additional potential landslide planes upslope, 270

downslope and extending below potential Hardy Ribs installation locations. 271

APPLICATION OF DESIGN METHOD TO CN STUDY SITE 272

The proposed design procedure was used to analyze the CN case study site to illustrate how to execute 273

the procedure and to estimate the stabilizing force. 274

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Evaluating Required Resisting Shear Force 275

A two-dimensional limit equilibrium slope stability analysis was performed using Slide 7.0 (Rocscience 276

2016) and was described by Bartz et al. (2017). The model geometry is shown in Figure 12 and the 277

material properties are shown in Table 1. The factor of safety (��) was estimated using the method of 278

vertical slices. Both the Morgenstern-Price method with a half sine interslice force function and the 279

Janbu simplified method were used. The estimated �� is equal to 1.03 and 1.01 using the Morgenstern-280

Price and Janbu simplified method, respectively. To achieve a Factor of Safety of 1.3, the resisting force 281

needs to be increased by 708 kN/m. This increase was determined using Equation 1 and �� = 2360 kN/m 282

determined from the Janbu analysis with a �� = 1.0. 283

Evaluating the Resisting Force for Sheet Pile Ribs 284

Develop strength parameters 285

To simplify the laterally loaded pile analysis, the soil layers were simplified into two layers with an 286

unstable slide zone overlying a stable zone as shown in Figure 13. The analyzed slide zone extends 9.0 m 287

below ground surface with the sheet pile ribs extending 2.0 m into the stable zone. The soil was 288

considered to be saturated with a piezometric surface at ground surface. Actual groundwater 289

monitoring data near the alignment of the Hardy Ribs at BH14-2 in December, 2014 indicated a 290

piezometric surface approximately 1.3 m below ground surface. The conservative assumption was made 291

that the piezometric surface could rise to the ground surface. The thin layer of sand and gravel fill at 292

ground surface was neglected since it does not extend across the entire alignment of the Hardy Ribs. Lab 293

vane and pocket penetrometer testing was conducted during the geotechnical investigation program to 294

estimate �� of the soil. Based on this testing, �� ranged from approximately 35 kPa to 130 kPa for the 295

high plastic clay and ranged from approximately 135 to 170 kPa for the disturbed shale above the slide 296

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plane. Below the slide plane, �� for the intact shale ranged from approximately 250 kPa to 285 kPa. The 297

material properties used in the lateral pile analysis are shown in Figure 13. 298

Select sheet pile rib spacing 299

Equation 3 was used to estimate the critical spacing to prevent soil failing between the sheet 300

piles. The length of the sheet pile ribs is 7.08 m. The adhesion factor (�) was estimated as 0.75 by 301

considering the corrugated geometry of the sheet piles. � of approximately 0.5 is expected for stiff clay 302

(Broms, 1983) and is equal to 1.0 where the shear surface is entirely through the soil. From Equation 3, 303

the critical spacing was calculated to be 2.66 m. The actual clear spacing between sheet pile ribs at this 304

site is 2.55 m. Therefore, the Hardy Ribs are expected to behave as a continuous wall and failure of soil 305

between sheet pile ribs is prevented. 306

Develop p-y curves 307

The p-y curve developed by Matlock (1970) for soft clay was selected for the slide zone and is 308

defined by: 309

(8) � = 0.5�� 7 --89

:;/<

310

where 4=> is equal to the deflection at one-half the ultimate resistance. 4=> can be estimated as 2.5ε50� 311

where ε50 is the strain corresponding to one-half the maximum principal stress difference. ε50 was 312

estimated as 0.005 as suggested by Peck et al. (1974) for clay with an undrained shear strength between 313

96 and 192 kPa. �� is calculated as the smaller of the following two equations. 314

(9) �?@A = B3 + DEFGH

+ IFJ K �� 315

(10) �� = 9�� 316

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where �′ is the effective unit weight of the soil, � is the depth below ground surface and Nis factor found 317

to be 0.5 by Matlock (1970). 318

The p-y curve developed by Welch and Reese (1972) for stiff clay without access to free water 319

was selected for the stable zone and is defined by: 320

(11) � = 0.5�� 7 --89

:;/P

321

�� is similarly selected as the lesser value from Equations 9 and 10, however the average undrained 322

shear strength over the depth � should be considered for Equation 9. ε50 was estimated for the stable 323

zone as 0.005 as suggested by Reese and Van Impe (2011) for overconsolidated clay when laboratory 324

testing data is not available. 325

For Case 1, the equivalent pile diameter for the lateral pile analysis can be selected as the 326

centre-to-centre sheet pile rib spacing of 3.0 m. A reduction factor of 0.64 was applied to the p-y curves 327

as suggested by Reese and Van Impe (2011). The magnitude of �� with depth as calculated considering 328

the Hardy Ribs to act as a continuous wall from the lesser of Equations 4 and 5 is shown in Figure 14. 329

This is compared to the magnitude of �� from Equations 9 and 10 from Matlock (1970) and Welch and 330

Reese (1972) for the slide zone and stable zone, respectively. The method of Georgiadis (1983) was used 331

to calculate �� for the stable zone due to the transition in soil properties. The magnitude of �� is 332

shown to be approximately equal to Equations 4 and 5 when using p-y curves with beq = �� and an 333

applied reduction factor. 334

For Case 2, beq was selected as the width of the PZC-26 sheet pile which is 0.45 m. A reduction 335

factor of 0.7 was applied to the lead pile and reduction factor of 0.48 was applied to the trailing piles as 336

suggested by Reese and Van Impe (2011). 337

Determine yield bending moment 338

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The structural capacity of the sheet pile ribs was assessed to calculate the yield bending 339

moment of the pile. Assuming the sheet pile rib acts as a continuous section, the yield bending moment 340

is calculated as 41342 kN·m which is considered for Case 1. This was calculated from Equation 6 with &' 341

equal to 0.5854 m4 and ) equal to 3.54 m. For Case 2, the yield bending moment is calculated as 423 342

kN·m for one PZC-26 sheet pile about the axis of bending, with&' equal to 5.996 x 10-4

m4 and ) equal to 343

0.354 m. These magnitudes of the yield bending moment should be considered when calculating the 344

soil-pile interaction to determine if the piles behave as rigid or long piles. 345

Determine soil-pile interaction 346

RSPile (Rocscience 2017c) was used to numerically model the soil-pile interaction using the 347

appropriate p-y curves and flexural rigidity of the pile for Cases 1 and 2. The landslide loading was 348

applied by applying a uniform lateral soil displacement from the ground surface to the sliding depth. No 349

drag zone was considered. The calculated magnitude of shear force at the slide plane is shown versus 350

the soil displacement in Figure 15 for Case 1. The maximum shear force that each sheet pile rib can 351

apply to resist landslide loading approaches approximately 2800 kN. A significant and unrealistic amount 352

of soil displacement is required however to achieve transverse failure along the pile. If landslide failure 353

is defined as 0.3 m of soil displacement in the slide zone, then each pile can apply approximately 2008 354

kN to resist landslide loading. The profiles of lateral displacement, soil reaction, bending moment and 355

shear force are shown in Figure 16. Figure 16a shows the profiles with a lateral soil displacement of 300 356

mm above the slide plane and Figure 16b shows the profiles for a lateral soil displacement of 3000 mm. 357

The maximum bending moment developed in the pile is less than � and therefore the sheet pile rib is 358

expected to behave as a rigid pile for the Case 1 analysis. With 3 m of soil displacement, the soil reaction 359

is observed to reach �� in both the stable zone and slide zone indicating intermediate or overturning 360

failure mode. With 0.3 m of soil displacement, the soil reaction does not reach �� at any depth along 361

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the sheet pile rib. The magnitude of the shear force at the slide plane can be divided by the 3.0 m 362

centre-to-centre spacing to obtain the resisting force along the slope. With a soil displacement of 0.3 m, 363

the estimated resisting force is 669 kN/m and the estimated FS is then equal to 1.28. 364

The calculated magnitude of shear force at the slide plane is shown versus the soil displacement 365

in Figure 17 for Case 2. The profiles of lateral displacement, soil reaction, bending moment and shear 366

force are shown in Figure 18 for the Case 2 analysis. The profiles are shown for both the lead and trailing 367

piles. A maximum lateral soil displacement of 43 mm was applied above the slide plane, at which point 368

the maximum bending moment of the lead pile reaches the yield value. Therefore, when considering the 369

sheet pile rib as a series of in-line piles, each sheet pile is expected to behave as a long pile. The soil 370

reaction does not reach �� at any depth along the pile for this case. At the point of bending failure of 371

the lead pile, the shear force at the slide plane is equal to 370 kN from the lead pile and 274 kN from 372

each of the nine trailing piles. Therefore, the total resisting force is equal to 2836 kN for Case 2. This 373

magnitude of the shear force at the slide plane can be divided by the 3.0 m centre-to-centre spacing to 374

obtain the resisting force along the slope of 945 kN/m. This is greater than the required increase to 375

achieve the target FS of 1.3. 376

Select Location to Install Hardy Ribs 377

Additional 2D limit equilibrium slope stability analyses were performed using Slide 7.0 (Rocscience 2016) 378

to assess the stability of potential slide planes upslope and downslope of the Hardy Ribs. The additional 379

slide planes that were analyzed are shown on Figure 19. The material properties were consistent with 380

the back analysis conducted in Step 1. Also, a slide plane extending beneath the Hardy Ribs was 381

analyzed where the disturbed shale geometry was modified to extend below the sheet pile ribs. The 382

Morgenstern-Price method with a half-sine interslice force function was used in all the factor of safety 383

calculations. 384

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The analysis indicated the estimated factor of safety for the potential upper slope slide plane 385

was 2.29, well above the target factor of safety of 1.3. The estimated factor of safety for the potential 386

lower slope slide plane was 1.12. Although this potential slip surface does not directly affect the rail line, 387

the Hardy Ribs rely on the passive resistance from downslope soil. Excessive landslide displacement 388

downslope of the Hardy Ribs would result in a loss of stabilizing resistance. CN is planning on to add 389

riprap along the river bank to prevent against river erosion and loss of stabilizing resistance downslope 390

of the Hardy Ribs. The estimated factor of safety of the potential slide plane extending below the Hardy 391

Ribs is 1.29 which is approximately equal to the target value. 392

CONCLUSIONS 393

A relatively unknown landslide stabilization technique was developed by Dr. R.M. Hardy in the 1970’s 394

that consists of a series of parallel sheet pile ribs. This method, referred to as “Hardy Ribs,” was recently 395

implemented by CN to stabilize a landslide at Mile 191.4 of the Rivers subdivision in the Assiniboine 396

River valley. These Hardy Ribs have significantly decreased the rate of landslide movement resulting in 397

decreased maintenance requirements for the rail line. 398

Although this landslide stabilization technique has proven to be effective, there are no generally 399

accepted design procedures. A design procedure for Hardy Ribs has been proposed that consists of a de-400

coupled approach with separate two dimensional slope stability analysis and a laterally loaded pile 401

analysis using p-y curves. A de-coupled approach is consistent with design procedures for stabilizing 402

shear piles by Viggiani (1981), Poulos (1995) Vessely et al. (2007) and Cornforth (2012) among others. 403

The proposed design procedure for Hardy Ribs is simple to perform and considers the various potential 404

failure mechanisms. Sample calculations for the CN case study were provided to illustrate how the 405

proposed design procedure can be used to consider the various possible failure mechanisms and 406

calculate the stabilizing effect of Hardy Ribs. By designing an appropriate sheet pile rib length and 407

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spacing, the flow mode failure mechanism where soil fails around the sheet pile ribs is prevented. 408

Calculating the soil-pile interaction using p-y curves is a very flexible method that will allow the designer 409

to determine which failure mode is most critical. The bending moment developed in the sheet piles is 410

also calculated to ensure that it does not fail in bending. Using p-y curves also provides the flexibility to 411

input multiple soil layers in the pile analysis and to calculate the soil-pile interaction for varying amounts 412

of soil displacement. Both RSPile (Rocscience Inc. 2017a) and LPile (Isenhower and Wang 2014) can 413

analyze the soil reaction for moving soil by taking into account the relative movement between the pile 414

and the soil. For this de-coupled approach, it is important to understand the slide mechanics to 415

accurately estimate the landslide forces. This is also important for estimating the factor of safety of 416

alternative potential slides planes and ensure that the overall slope has a factor of safety above the 417

target value. 418

The proposed design procedure for Hardy Ribs was developed borrowing concepts from 419

stabilizing shear piles and utilizing p-y curves originally developed for circular piles. Due to a lack of field 420

testing and monitoring data, there are currently limitations to be considered when using this procedure. 421

The lateral pile analysis utilizes undrained shear strength parameters for clay and stiff clay. Due to the 422

sustained loading on the sheet pile ribs, it may be more logical to analyze the soil-pile interaction with 423

drained shear strength parameters. The most common p-y curves for clay and stiff clay were developed 424

based on undrained parameters however. Another limitation in this procedure is the required 425

assumption of the joint behaviour between sheet pile sections. Case 1 assumes that there is no sliding 426

along the joints. This results in a sheet pile rib section with a very large moment of inertia and bending 427

stiffness causing it to behave as a rigid pile. Case 2 assumes that each sheet pile section is free to slide 428

and bend independent of each other. In this scenario, the sheet pile rib may behave as a series of in-line 429

long piles. These two cases consider the extremes, where in reality, the true behaviour is likely 430

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somewhere in between. Further case studies with pile instrumentation is required to determine which 431

behaviour controls the soil-pile interaction. 432

ACKNOWLEDGEMENTS 433

The research was funded by partners of the Railway Ground Hazard Research Program at the University 434

of Alberta which includes CN Rail, CP Rail and Transport Canada. The authors would also like to thank CN 435

for permission to publish the case study results and acknowledge Tom Edwards and Melissa Ruel of CN 436

Rail for providing construction and site monitoring data. 437

Site investigation, slope stability analysis and preliminary design services for the case study site were 438

conducted for CN by Clifton Associates. The material properties used in slope stability analyses by the 439

authors were based on work by Clifton Associates. 440

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REFERENCES

Abdelaziz, T.S., Proudfoot, D.W., and Skirrow, R. (2011). Stabilization of Alberta highway landslides using

pile walls. In Proceedings of the 2011 Pan-am CGS Geotechnical Conferenece, Toronto, ON, 02-06

October 2011. Canadian Geotechnical Society, Richmond, BC.

Bartz, J.R. 2017 Analysis and Design of Sheet Pile Ribs for Slope Stabilization (M.Sc. Thesis). University of

Alberta, Edmonton, AB.

Bartz, J.R., Hendry, M.T., Martin C.D., and Ruel, M. 2017. Case study of landslide stabilization using sheet

pile ribs. In Proceedings of GeoOttawa 2017, Ottawa, ON, 01-04 October 2017. Canadian

Geotechnical Society, in press.

Broms, B.B. 1983. Earth pressures on piles in a row due to lateral soil movements. Discussion, Soil and

Foundations, 23(3): 127-129.

Cornforth, D.H. 2012. Advances in investigation and analysis for landslides: Three selected topics. In

Proceedings of the 11th

International Symposium on Landslides and Engineered Slopes, Banff,

Alberta, 03-08 Jun 2012. CRC Press, Leiden, pp. 59-71.

Isenhower, W.M., and Wang, S.T. 2014. User’s manual for LPile 2013 (Using data format version 7) – A

program to analyze deep foundations under lateral loading. Ensoft, Inc., Austin, Texas.

Georgiadis, M. 1983. Development of p-y curves for layered soils. In Proceedings of the Geotechnical

Practice in Offshore Engineering, Austin, Texas, 27-29 April 1983. ASCE, New York, pp. 536-545.

Hetenyi, M. 1946. Beams on elastic foundation. University of Michigan Press, Ann Arbor, Michigan.

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Klassen, R.W. 1975. Quaternary geology and geomorphology of Assiniboine and Qu’Appelle valley of

Manitoba and Saskatchewan. Geological Survey of Canada, Department of Energy, Mines and

Resources, Ottawa, Ontario.

Matlock, H. 1970. Correlations for design of laterally loaded piles in soft clay. In Proceedings of the 2nd

Annual Offshore Technology Conference, Houston, Texas, 22-24 Apr 1970. IEEE, New York, pp. 577-

594.

Peck, R.B., Hanson, W.E., and Thorburn, T.H. 1974. Foundation Engineering, 2nd

edition. Wiley, New

York.

Poulos, H.G. (1995). Design of reinforcing piles to increase slope stability. Canadian Geotechnical

Journal, 32: 808-818.

Reese, L.C., and Van Impe, W.F. 2011. Single piles and pile groups under lateral loading, 2nd

edition. CRC

Press, Boca Raton, Florida.

Roscience Inc. 2017a. Laterally Loaded Piles Theory Manual [Online]. Available from

https://www.rocscience.com/help/rspile/webhelp/rspile.htm [accessed 20 July 2017].

Rocscience Inc. 2017b. Computing pile resistance from applied soil displacement for slope stability

analysis [online]. Available from https://www.rocscience.com/help/rspile/webhelp/rspile.htm

[accessed 20 July 2017].

Rocscience Inc. 2017c. RSPile 1.0 [Computer Software], v1.005. Toronto, ON.

Rocscience Inc. 2016. Slide 7.0 [Computer Software], v7.017. Toronto, ON.

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Vessely, D.A., Yamasaki, K., and Strom, R. 2007. Landslide stabilization using piles. In Proceedings of the

First North American Conference on Landslides, Vail, Colorado 3-10 Jun 2007. Omnipress, Madison,

Wisconsin, pp. 1173-1183.

Viggiani, C. 1981. Ultimate lateral load on piles used to stabilize landslides. In Proceedings of the 10th

International Conference on Soil Mechanics and Foundation Engineering, Stockholm, Sweden, 15-19

Jun 1981. A.A. Balkema, Rotterdam, the Netherlands, pp. 555-560.

Wang, R.C., Vasquez, L., and Xu, D. 2013. Application of soil-structure interaction (SSI) in the analysis of

flexible retaining walls. In Proceedings of the IACGE International Conference on Geotechnical and

Earthquake Engineering, Chengdu, China, 25-27 Oct 2013. ASCE, Reston, Virginia, pp. 567-577.

Welch, R.C., and Reese, L.C. 1972. Laterally loaded behaviour of drilled shafts. Research Report 3-5-65-

89, Center for Highway Research, University of Texas at Austin, Austin, Texas.

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Figure Captions

Figure 1. Contour plan of CN case study site in UTM zone 14U (After Bartz 2017).

Figure 2. Cross sections of CN case study site (Bartz 2017): (a) Section A; (b) Section B.

Figure 3. Slope inclinometer monitoring data of CN case study site prior to remediation: (a) BH14-1; (b)

BH14-2; (c) BH14-3.

Figure 4. Hardy Ribs layout at CN case study site.

Figure 5. Hardy Ribs installation at CN case study site (Photo courtesy of CN).

Figure 6. Slope inclinometer monitoring data of CN case study site after landslide remediation.

Figure 7. Landslide displacement before and after slope stabilization works. (Bartz et al. 2017).

Figure 8. Flow chart showing proposed design procedure for Hardy Ribs.

Figure 9. Laterally loaded series of sheet pile ribs: (a) Configuration of sheet pile ribs; (b) Clay block

between two sheet pile ribs; (c) Magnitude of forces acting on the clay block (Bartz 2017).

Figure 10. Equivalent circular pile diameter and layout.

Figure 11. Idealized distribution of lateral soil movement for landslides.

Figure 12. Slope geometry and slide plane for slope stability analysis.

Figure 13. Simplified soil properties for laterally loaded pile analysis (Bartz 2017).

Figure 14. Comparison of calculating �� as a continuous wall or an equivalent circular pile.

Figure 15. Mobilization of landslide resistance for a single rigid sheet pile rib.

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Figure 16. Soil-pile interaction for a rigid sheet pile rib from landslide loading: (a) From 0.3 m of lateral

soil displacement; (b) From 3.0 m of lateral soil displacement.

Figure 17. Mobilization of landslide resistance for in-line series of sheet piles.

Figure 18. Soil-pile interaction for in-line series of sheet piles: (a) For the lead pile from 43 mm of lateral

soil displacement; (b) For a trailing pile from 43 mm of lateral soil displacement.

Figure 19. Slope geometry and additional potential slide planes for slope stability analysis.

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Figure 1. Contour plan of CN case study site in UTM zone 14U (After Bartz, 2017).

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Figure 2. Cross sections of CN case study site (Bartz, 2017): (a) Section A; (b) Section B.

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Figure 3. Slope inclinometer monitoring data of CN case study site prior to remediation: (a) BH14-1; (b)

BH14-2; (c) BH14-3.

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Figure 4. Hardy Ribs layout at CN case study site.

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Figure 5. Hardy Ribs installation at CN case study site (Photo courtesy of CN).

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Figure 6. Slope inclinometer monitoring data of CN case study site after landslide remediation.

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Figure 7. Landslide displacement before and after slope stabilization works. (Bartz et al., 2017).

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Figure 8. Flow chart showing proposed design procedure for Hardy Ribs.

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Figure 9. Laterally loaded series of sheet pile ribs. a) Configuration of sheet pile ribs; b) Clay block between

two sheet pile ribs; c) Magnitude of forces acting on the clay block (Bartz, 2017).

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Figure 10. Equivalent circular pile diameter and layout.

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Figure 11. Idealized distribution of lateral soil movement for landslides.

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Figure 12. Slope geometry and slide plane for slope stability analysis.

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Figure 13. Simplified soil properties for laterally loaded pile analysis (Bartz, 2017).

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Figure 14. Comparison of calculating 𝑝 as a continuous wall or an equivalent circular pile.

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Figure 15. Mobilization of landslide resistance for a single rigid sheet pile rib.

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Figure 16. Soil-pile interaction for a rigid sheet pile rib from landslide loading: (a) From 0.3 m of lateral soil

displacement; (b) From 3.0 m of lateral soil displacement.

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Figure 17. Mobilization of landslide resistance for in-line series of sheet piles.

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Figure 18. Soil-pile interaction for in-line series of sheet piles: a) For the lead pile from 43 mm of lateral

soil displacement; b) For a trailing pile from 43 mm of lateral soil displacement.

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Figure 19. Slope geometry and additional potential slide planes for slope stability analysis.

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Table 1. Material properties used in slope stability analysis.

Material Region γ (kN/m3) Strength Model c’ (kPa) φ’

Sand 18 Mohr-Coulomb 0 32°

Clay 1 20.82 Mohr-Coulomb 8 22

Clay 2 17.92 Mohr-Coulomb 4 20

Disturbed Shale 18.25 Mohr-Coulomb 8 16

Residual Shale 18.25 Mohr-Coulomb 4.5 9.5

Intact Shale 20 Infinite Strength NA NA

Valley Wall 20 Infinite Strength NA NA

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