Soil Liquefaction - Jefferies and Bean

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Soil Liquefaction

A critical state approach

Mike Jefferies & Ken Been

(5)

4RN Simultaneously published in the USA and Canada by Taylor & Francis

270 Madison Ave, New York, NY 10016, USA

Taylor & Francis is an imprint of the Taylor & Francis Group, an informa business

This edition published in the Taylor & Francis e-Library, 2006. “ To purchase your own copy of this or any of Taylor & Francis or Routledge’s

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efforts or omissions that may be made. British Library Cataloguing in Publication Data

A catalogue record for this book is available from the British Library

Library of Congress Cataloging-in-Publication Data Jefferies, Mike, 1952– Soil liquefaction : a critical state approach/Mike Jefferies & Ken Been. p. cm. Includes bibliographical references and index. ISBN 0-419-16170-8 (hardback: alk. paper) 1. Soil mechanics. 2. Soil liquefaction. I. Been,

Ken. II. Title. TA710.J365 2006 624.1′5136–dc22 2006002052 ISBN 0-203-30196-X Master e-book ISBN

ISBN10: 0-419-16170-8 (hbk) ISBN10: 0-203-30196-X (Print Edition) (ebk)

ISBN13: 978-0-419-16170-7 (hbk) ISBN13: 978-0-203-30196-8 (Print Edition) (ebk) 2 Park Square, Milton Park, Abingdon, Oxon OX14

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Contents

LIST OF TABLES vii

LIST OF FIGURES x

SYMBOLS AND NOTATION xxxii

PREFACE xxxix

DISCLAIMER AND CAUTION

xliv

1INTRODUCTION 1

2DILATANCY AND THE STATE PARAMETER 41 3CONSTITUTIVE MODELLING FOR LIQUEFACTION 102 4DETERMINING STATE PARAMETER IN SITU 161 5SOIL VARIABILITY AND CHARACTERISTIC STATES 229 6STATIC LIQUEFACTION AND POST-LIQUEFACTION

STRENGTH

254 7CYCLIC STRESS INDUCED LIQUEFACTION 340

8CONCLUDING REMARKS 405

APPENDIX ASTRESS AND STRAIN MEASURES 412

APPENDIX BLABORATORY TESTING TO DETERMINE THE CRITICAL STATE OF SANDS

419

APPENDIX CTHE CRITICAL FRICION RATIO M 437

APPENDIX DNORSAND DERIVATIONS 445

(7)

FLOW FAILURE

REFERENCES 560

(8)

Tables

2.1 Critical state properties for some soils

54

2.2 Clarification of terminology for describing soils

71

2.3 Laboratory test for design parameters in sands and silts

72

2.4 Summary of proposed relationships for M

i

89

3.1 Summary of NorSand

136

3.2 NorSand parameters and typical values for sands

137

3.3

Triaxial tests on Erksak 330/0.7 sand to determine CSL and

NorSand parameters (Been et al, 1990)

138

3.4

NorSand parameters for Erksak 330/0.7 drained triaxial

calibration

146

3.5 Paired tests on Brasted sand (data from Cornforth, 1961)

156

4.1 Dimensionless parameter groupings for CPT interpretation

162

4.2 Summary of CPT calibration chamber studies

178

4.3 Approximate expressions for general inversion form ψ=f(Q

p

)

198

4.4 Relationship of soil type to soil classification index I

c

206

4.5

Summary of near-undisturbed SBP tests in Tarsiut P-45

hydraulically placed sand fill and adjacent CPT data

(9)

(Rowe and Craig, 1976)

5.2 Cyclic loading stages in caisson models (Rowe and Craig, 1976) 231

5.3

Model time per cycle and time factors for centrifuge models

(Rowe and Craig, 1976)

232

5.4

Resistance factors for characteristic strength percentiles for an

offshore structure example (Been and Jefferies, 1993)

253

6.1

Observed values of the parameters (su/p′)n, and I

B

for

consolidated undrained tests on cohesionless soils (Bishop, 1971)

266

6.2

Summary of steady state strength determinations from laboratory

tests for Lower San Fernando Dam (after Marcuson et al., 1990)

304

6.3

Some important case histories giving insight to full-scale

post-liquefaction strength

314

6.4a

Comparison of post-liquefaction residual strength s

r

(psf) from

back-analysis of failure as reported by various investigators

316

6.4b

Comparison of corresponding characteristic normalized SPT

blowcount (N

1

)

60

suggested by the investigators

316

6.5 Fines content adjustment factors for SPT (after Seed, 1987)

317

6.6

Summary of case history data for mobilized post-liquefaction

strength

323

7.1

Proposed factors for difference between cyclic simple shear and

triaxial testing

362

E.1 Boundary Condition Codes, after Parkin et al. (1980)

499

F.1

Summary of strengths and strength ratios determined by Olson et

al. (2000)

524

F.2 Summary of index and critical state properties for Nerlerk Sands 542

F.3

Summary of shear strengths from back analysis of La Marquesa

Dam

(10)
(11)

1.1 Definition of state parameter ψ

5

1.2

Aerial view of Fort Peck failure (U.S Army Corps of Engineers,

1939)

7

1.3

Nerlerk B-67 berm and foundation cross section (Been et al.,

1987)

8

1.4

Plan of failures that occurred at Nerlerk B-67 and cross section

through Slide3 (Sladen et al., 1985a)

9

1.5

Grain size distribution information for Nerlerk B-67 materials

(Sladen et al., 1985a)

10

1.6

Typical Nerlerk berm CPT (CPTC12 in 1988) including clay

layer between sand fill and the seabed

11

1.7

Summary of CPT distributions in Nerlerk B-67 berm, in Nerlerk

sand and Ukalerk sand

12

1.8

Apartment building at Kawagishi-cho that rotated and settled

because of foundation liquefaction in 1964 Niigata earthquake

(from Karl V Steinbrugge Collection, Earthquake Engineering

Research Center)

14

1.9

Sketch plan of Niigata, showing main area of damage.

Kawagishi-cho and South Bank sites marked with X (Ishihara,

1993)

15

1.10

Soil profile and CPT resistance at Kawagisho-cho site (Ishihara

and Koga, 1981)

15

1.11

Soil profile and CPT resistance at South Bank site (Ishihara and

Koga, 1981)

16

1.12 Seed Liquefaction Assessment Chart (Seed et al, 1983)

17

1.13 Liquefaction failure of Lower San Fernando Dam after the 1971

(12)

top photograph)

1.14 Possible failure mechanism for Aberfan Tip No 7 (Bishop, 1973) 19

1.15

Aberfan flow slide shortly after the failure. Flowslide distance

added by authors

20

1.16

Aerial view of the Merriespruit tailings dam failure showing the

path of the mudflow that occurred (Fourie et al., 2001)

22

1.17

Sequence of retrogressive failures of Merriespruit containment

postulated by Wagener et al, 1998 (Fourie et al, 2001)

23

1.18

Grain size distribution and Critical State Line of Merriespruit

tailings materials (Fourie and Papageorgiou, 2001)

24

1.19

Distrubution of in situ void ratios obtained during post failure

investigation of Merriespruit tailings dam (Fourie et al., 2001)

25

1.20 Gulf Canada’s Molikpaq structure in the Beaufort Sea

26

1.21

Details of cyclic ice loading and excess pore pressure 12 April

1986

27

1.22

Piezometric response showing accumulating excess pore

pressure to liquefaction (piezometer E1, mid depth in centre of

loaded side)

28

1.23

Failure of embankment on Ackermann Lake triggered by

vibroseis trucks (Hryciw et al., 1990)

31

1.24

Plan and cross section of the Wildlife instrumentation array

(from Youd and Holtzer, 1994 based on Bennett et al., 1984)

32

1.25

Surface accelerometer (N-S) and piezometer P5 (2.9 m) at

Wildlife site during Superstition Hills 1987 Earthquake (from

Youd and Holtzer, 1994)

34

1.26

Shear stress and shear strain history at depth of piezometer P5 at

Wildlife Site, interpreted from accelerometers by Zeghal and

Elgemal (1994)

(13)

increments interpreted from NS accelerometers at Wildlife site

(after Youd and Holtzer, 1994)

2.1 Difference between rate and absolute definitions of dilatancy

42

2.2

Early hypothesis of critical void ratio from direct shear tests

(Casagrande, 1975)

44

2.3

Comparison of behaviour of sand as a function of relative

density and state parameter for Kogyuk 350/2 and Kogyuk

350/10 sands

50

2.4

Idealized state path to illustrate relationship of dilatancy to state

parameter

52

2.5

Peak dilatancy of twenty soils in standard drained triaxial

compression

58

2.6

Stress-dilatancy component of peak strength of twenty soils in

standard drained triaxial compression

58

2.7

Volumetric strain at peak stress for drained triaxial compression

tests on 20 sands

59

2.8

Friction angle versus state parameter normalized by range of

accessible void ratios (e

max

− e

min

). Note the lack of improvement

over Figure 2.6

60

2.9

Maximum dilatancy as a function of ψ/λ. There is no

improvement to the correlation compared to y alone (See Figure

2.5)

60

2.10

Maximum dilation as a function of state parameter normalized

by (1+e). There is a small improvement compared to state

parameter alone (compare with Figure 2.5)

61

2.11

Effect of sample preparation on the behaviour of Kogyuk sand

(Been and Jefferies, 1985)

62

(14)

Toyoura sand (after Tatsuoka, 1987)

2.13

Effect of fabric on friction angle of sands reported by Tatsuoka

and by Oda and compared to general correlation of friction angle

to state parameter

64

2.14

Comparison of the effect of void ratio and sample preparation

method on the cyclic strength of two sands in simple shear

(Nemat-Nasser and Tobita, 1982)

65

2.15

Influence of overconsolidation ratio on the friction angle of

Erksak 330/0.7 sand

65

2.16 Effect of sample size on the behaviour of dense Ticino sand

67

2.17

Multiple shear bands evident through membrane in large

(300mm diameter) sample after drained shearing

68

2.18

Schematic illustration of relationship between parameters and

testing methods

70

2.19

Stress controlled CIU triaxial test during which a critical (steady)

state is clearly reached

75

2.20

CIU triaxial test showing dilation at large strains and the “quasi

steady state”. Incorrectly treating the quasi-steady state as the

critical state leads to “non-unique critical states” and other errors

76

2.21

Selection of undrained tests to used to give critical state line in

Figure 2.22

77

2.22

Critical state line for Erksak 330/0.7 sand from undrained tests

that reached a distinct critical (steady) state

78

2.23

Examples of drained triaxial tests on loose samples reaching

critical state

79

2.24

Critical state line for Guindon Tailings B (67% fines) showing

use of drained tests on loose samples to define critical state at

higher stresses.

80

(15)

dilatancy for Erksak and Brasted sands under different loading

conditions (Jefferies and Shuttle, 2002)

2.27

Drained triaxial data for Erksak sand reduced to stress dilatancy

form (Been Jefferies, 2004)

87

2.28

Relationship of mobilized friction ratio M

f

to ψ for Erksak data.

Dense sand data at initial D

p

= 0 shown as filled squares; loose

sand data shown as traces for complete strain path. Also shown

are several proposed constitutive model relationships (Been and

Jefferies, 2004)

88

2.29

Effect of sample preparation on undrained behaviour of Erksak

330/0.7 sand

91

2.30

Comparison of critical states from pluviated and moist

compacted samples of Erksak 330/0.7 sand (data from Been et

al, 1991). Note that pluviated samples cannot be prepared at high

void ratios

92

2.31

Peak dilation rate in drained triaxial compression tests as a

function of distance from critical state line determined from

undrained tests. The trend line passes close to zero, indicating

that drained and undrained behaviour relate to the same CSL

92

2.32 Stress conditions in the simple shear test

94

2.33

Undrained simple shear tests on Fraser River sand (Vaid and

Sivathayalan, 1996)

95

2.34

Comparison of triaxial compression, extension and simple shear

behaviour of Fraser River Sand (Vaid and Sivathayalan, 1996)

96

2.35

Critical state loci for several sands whose properties are given in

Table 2.1

98

2.36

Relationship between slope of the critical state line and fines

content; uniformly graded soils

99

(16)

1

) and maximum void ratio (e

max

); uniformly graded soils

2.38

Comparison of critical state lines for uniformly graded and well

graded silty sands

100

3.1 Illustration of normality through hockey puck analogy

106

3.2 Definition of normality (associated plastic flow)

106

3.3 Dilation implied by normality to Mohr Coulomb surface

107

3.4

Correct association of yield surface with soil strength, from

Drucker, Gibson and Henkel (1957)

108

3.5 Comparison of isotropic compression idealizations

109

3.6

Separation of state parameter from overconsolidation ratio

(Jefferies and Shuttle, 2002)

110

3.7

Example of variation of critical friction ratio M with Lode angle

θ (Jefferies and Shuttle, 2002)

114

3.8 Illustration of the consistency condition

122

3.9

Implied overconsolidation for a given state ψ in Cambridge

models

124

3.10 Illustration of the Hvorslev surface idealization

125

3.11

Distribution of fill density in normally consolidated hydraulic

sand fill (Stewart et al., 1983)

126

3.12

Experimental evidence for an infinity of NCL (isotropic

consolidation of Erksak 330/0.7 sand)

128

3.13

Illustration of NorSand yield surface, limiting stress ratios and

image condition

132

3.14 Dilatancy as a function of state parameter at image condition

134

3.15

Measured bulk modulus of Erksak sand in isotropic

unload-reload tests (Jefferies and Been, 2000)

(17)

3.17

Examples of calibrated fit of NorSand to Erksak 330/0.7 sand in

drained triaxial compression

145

3.18

Plastic hardening modulus versus state parameter ψ

0

for Erksak

sand (Ticino and Brasted sand shown for comparison)

147

3.19

Effect of NorSand model parameters on drained triaxial

compression behaviour

148

3.20

Example of experimentally determined yield surfaces in Fuji

River sand (Tatsuoka and Ishihara, 1974)

151

3.21

NorSand yield surfaces for comparison with experimental results

on Fuji River sand

151

3.22 Isotropic plastic compression behaviour of NorSand

154

3.23 Failure of sample in plane strain test carried out by Cornforth

156

3.24

Peak dilatancy of Brasted sand in triaxial compression versus

state (from Jefferies and Shuttle, 2002)

158

3.25 Calibration of NorSand to Brasted sand in triaxial compression 159

3.26

Validation of NorSand in plane strain by comparison of

predictions versus data for Brasted sand (Jefferies and Shuttle,

2002)

159

4.1 Comparison of SPT and CPT repeatability

165

4.2

Illustration of soil type classification chart using CPT data

(Robertson, 1990)

166

4.3

Relation between q

c

/N and soil type (Burland and Burbidge,

1985)

167

4.4

Example stress-strain behaviour of NAMC material in triaxial

compression (properties for medium dense sand)

171

(18)

NAMC material with Bolton’s s approximation of

stress-dilatancy

4.6

Spherical cavity limit pressure ratio versus state parameter

(broken lines indicate linear approximation of equation [4.7])

175

4.7

Comparison of experimental spherical cavity limit pressure with

penetration resistance of blunt indenter (after Ladanyi and Roy,

1987)

175

4.8 Example of CPT calibration chamber (Been et al., 1987b)

176

4.9

Example of CPT chamber test data (Erksak sand, from Been et

al, 1987b)

177

4.10

Grain size distribution curves for sands tested in calibration

chambers

179

4.11

CPT resistance versus relative density for three sands (after

Robertson and Campanella, 1983)

180

4.12

CPT resistance calibration for Monterey N° 0 sand (test data

from Villet, 1981; graph from Been et al, 1986)

181

4.13

Effect of stress on penetration resistance in normally

consolidated sand (a) vertical stress; (b) horizontal stress.

(Clayton et al., 1985)

182

4.14

Experimentally determined C

N

functions for Reid Bedford and

Ottawa sand by Marcuson and Bieganowski (1977) and

recommended C

N

function by Liao and Whitman (1986)

185

4.15

Dimensionless CPT resistance versus state parameter for

Monterey sand (data from Fig 4.12, after Been et al., 1986)

187

4.16

Normalized Qp−ψ relationships from calibration chamber

studies (NC=normally consolidated; OC=over-consolidated)

188

4.17

Normalized CPT resistance of normally consolidated and

overcon-solidated Ticino Sand

190

(19)

4.20

Summary of stress level bias in Q

p

–ψ relationship for Ticino

sand as suggested by Sladen (1989a,b)

193

4.21

Numerical calculation of Q

p

–ψ relationship for Ticino sand,

showing linearity and effect of elastic modulus as cause of stress

level bias (Shuttle and Jefferies, 1998)

194

4.22

Computed effect of I

r

on k,m coefficients for Ticino sand

(Shuttle and Jefferies, 1998)

195

4.23

Shear modulus of Ticino sand versus confining stress: p

r

is a

reference stress level, here taken as 100 kPa (Shuttle and

Jefferies, 1998)

196

4.24

Computed Q

p

–ψ relationship for Ticino sand, shown as

trendlines, compared to individual calibration chamber tests

197

4.25

Effect of soil properties on spherical cavity expansion pressure

ratio (Shuttle and Jefferies, 1998)

199

4.26

Performance of approximate general inversion on 10 sands with

randomly chosen properties (Shuttle and Jefferies, 1998)

200

4.27

Trends in effective inversion parameters k′, m′ with soil

compressibility λ

10

203

4.28

Relationship between λ

10

and F suggested by Plewes, Davies and

Jefferies (1992)

204

4.29

Suggested relationship between λ and I

c

(adapted from Been and

Jefferies, 1992)

205

4.30 Soil type classification chart showing constant I

c

contours

206

4.31

Shear modulus determined from VSP tests in hydraulically

placed sandfill (Molikpaq core at Tarsiut P-45)

213

4.32 Comparison of I

r

between silts and sands

214

4.33 Results of SBP tests in hydraulically placed Erksak sand

217

(20)

4.34

Horizontal geostatic stress in hydraulic fills (Graham and

Jefferies, 1986)

219

4.35

CPT horizontal stress amplification factor versus state (Jefferies

Jönsson and Been, 1987)

221

4.36

Comparison of geostatic stress from SBP and CPT in

hydraulically placed sandfill (Jefferies, Jönsson and Been, 1987)

222

4.37

Effect of uncertainty in horizontal stress on uncertainty in

estimated in situ state parameter from CPT data (Jefferies,

Jönsson and Been, 1987)

224

5.1

Measured response of caissons subject to increasing stages of

cyclic loading in centrifuge test (from Rowe and Craig, 1976)

230

5.2 Layout of loose pockets below caissons (Rowe and Craig, 1976) 233

5.3

Scaled displacements and pore pressures observed in model with

4% loose zones in fill (Rowe and Craig, 1976)

235

5.4

Scaled displacement and piezometric data for centrifuge model

with 10% loose zones in fill (Rowe and Craig, 1976)

236

5.5

Schematic cross section of the Molikpaq at Tarsiut P-45 showing

locations of CPTs to determine fill properties (adapted from

Jefferies et al., 1985 by Popescu et al., 1997)

238

5.6

Examples of CPTs in Tarsiut P-45 fill These CPTs are spaced

about 9m apart. (see Figure 5.5) MAC 05 & 32 and MAC 08 &

33 are spaced 1m apart to demonstrate repeatability of

measurements. (adapted from Jefferies et al., 1985 and Popescu

et al, 1997)

239

5.7

Selected Tarsiut P-45 CPTs plotted against depth with average

trends in core and berm fill shown. Inset histograms are

distributions of q

c

values in 1m depth intervals at depths of 5 m,

15 m and 25 m

239

5.8

Statistical profile of normalized penetration resistance Q and

state parameter at Tarsiut P-45

(21)

5.10

Distribution of fines content measured in Tarsiut P-45 fill

(Jefferies et al, 1988)

243

5.11 Liquefaction of variable fill computed by Popescu 1995

244

5.12

Comparison of uniform and variable fill results in Popescu et al.,

1997

245

5.13

Summary of CPT statistics in the area of Slide 3 of Nerlerk

berm. State parameter interpretation using variable shear

modulus methodology of Chapter 4

246

5.14

Distribution of random ψ field mapped onto Nerlerk berm

geometry, computed by Onisiphorou (2000)

248

5.15

Results of Nerlerk Berm analysis with uniform fill states

(Onisiphorou, 2000)

249

5.16

Results of analysis of Nerlerk berm with variable field ψ:

µ=−0.08, σ=0.05 (Onisiphorou, 2000)

250

6.1 Undrained triaxial compression of Erksak 330/0.7 sand

257

6.2 Loose Ticino sand in undrained triaxial compression

258

6.3 Particle size distribution curve for four liquefying soils

259

6.4

Loose silty sand (Bennett Dam) and sandy silt (Guindon

Tailings) in undrained triaxial compression

259

6.5 Triaxial extension test data for Erksak 300/0.7 sand

260

6.6

Comparison of extension and compression tests on Erksak sand

(normalized)

261

6.7 Effect of stress path on the critical state locus (at expanded scale) 262

6.8

Comparison of Bonnie Silt in simple shear, triaxial compression

and triaxial extension (all tests at initial confining stress of

80kPa, 0.683<e

0

<0.753)

(22)

6.9 Normalized undrained strength of loose liquefiable sands

267

6.10

Undrained strength ratio of normally consolidated clay (equation

in Wroth, 1984)

267

6.11 Pore pressure ratio A

f

of loose sands at peak strength

269

6.12 Comparison of normalized peak and residual undrained strengths 270

6.13

Brittleness index of sands with a range of λ (Filled symbols

represent low λ and open symbols higher λ values)

271

6.14

Comparison of collapse surface and instability or flow

liquefaction line representations for onset of liquefaction (after

Yang, 2002)

272

6.15

Erksak sand test G609 illustrating the nature of static

liquefaction and collapse surface at η

I

.

273

6.16

Very loose Erksak drained test D684 showing intersection of

stress path with “collapse surface”

275

6.17

Initial state diagram for the series of triaxial tests on Erksak

330/0.7 sand

279

6.18

Triaxial compression static liquefaction—NorSand compared to

Erksak sand data

280

6.19

NorSand simulations showing effect of elastic modulus on

undrained behaviour

282

6.20

NorSand simulations showing effect of plastic modulus on

undrained behaviour

283

6.21

Peak undrained triaxial compression strength for liquefying

sands with trends from NorSand

284

6.22

S and F lines from NorSand simulations of triaxial compression

tests (Jefferies and Been, 1992)

285

6.23

Simulations showing modeling of sample preparation effects (for

both samples Γ=0.816, λ

10

=0.031, v=0.2)

(23)

Impoundment

6.25 Simulation of triaxial extension, Erksak 330 test CIUE-G642

290

6.26

Failure in declining mean stress at constant shear experiment of

Sasistharan et al., (1993)

291

6.27

NorSand simulation for declining mean stress drained brittle

failure in experiments by Sasitharan et al., (1993)

292

6.28 NorSand simulations of pseudo steady state condition

293

6.29

Comparison of NorSand with measured undrained silt behaviour

in simple shear

295

6.30

Example of effect of initial geostatic stress ratio K

0

on undrained

strength in simple shear

295

6.31

Effect of initial state on peak undrained strength in simple shear

versus triaxial conditions

297

6.32

Computed peak undrained strength in simple shear versus

triaxial conditions when normalized by the initial vertical

effective stress

298

6.33

Peak undrained strength of normally consolidated clay in

different strain conditions (based on Figs 7 and 27 of Wroth,

1984)

299

6.34

Steady State School method to determine steady state strength of

soil at in situ void ratio (after Poulos et al., 1985)

302

6.35

Cross sections of Lower San Fernando dam (from Seed et al.,

1988)

304

6.36

Adjustments of measured undrained steady state strengths to in

situ conditions at Lower San Fernando dam (from Seed et al.,

1988)

305

6.37 Comparison of in situ void ratios and remoulded SSL for Lower

Sand Fernando dam determined by Vasquez-Herrera and Dobry

305

(24)

(1988)

6.38

X-ray images of shear bands in triaxial samples (Oda and

Kazama, 1998)

308

6.39

Proposed but incorrect correlation between steady state

(residual) strength and adjusted SPT penetration resistance (after

Seed and Harder, 1990)

313

6.40

Alternative correlation between steady state (residual) strength

and adjusted SPT penetration resistance proposed by Stark and

Mesri (1992)

318

6.41

Illustration of the importance to practical engineering of the

difference between the two correlations proposed for s

r

from

SPT data

319

6.42

Residual undrained strength ratio versus penetration resistance

from liquefaction case histories

324

6.43

Relationship between initial in situ state parameter and

mobilized steady state strength from case history data

326

6.44

Lower San Fernando dam showing as-constructed section

(above) and section during the 1985 investigation (below) after

Castro et al. (1989)

328

6.45

Plan of Lower San Fernando dam in 1985 and showing location

of investigation borings/soundings (after Castro et al., 1989)

329

6.46

Cross section through Lower San Fenando dam at St. 09+35

(approximately centerline of sliding mass) showing inferred

zonation of dam from 1985 study

330

6.47

Comparison of CPT and SPT resistances at Lower San Fernando

Dam (from Castro et al., 1989)

331

6.48 CPT C103 from Lower San Fernando dam investigation in 1985 331

6.49

Particle size distribution of soils within Zone 5 of Lower San

Fernando Dam (“Batch Mix No 7” was used for steady state

triaxial tests, after Castro et al., 1989)

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different depths because of different collar elevations)

6.51

CPT C104 from Lower San Fernando dam investigation in 1985,

including screening level interpretation of ψ

334

6.52

Computed residual strength ratio S

r

/σ′v

0

in hydraulic fill at

Lower San Fernando Dam

335

6.53

Boundary between satisfactory and unsatisfactory undrained

performance of sands in terms of CPT penetration resistance.

These curves are illustrative and must be computed for any

specific soil

338

7.1 Void ratio reduction induced by cyclic shear (after Youd, 1972) 342

7.2 Schematic illustration of the different forms of cyclic loading

343

7.3

Stress conditions in triaxial, simple shear and hollow cylinder

tests

346

7.4

The hollow cylinder test apparatus at University of British

Columbia (Vaid et al., 1990)

348

7.5

Example of sand behaviour in undrained cyclic triaxial test

(Nevada sand, Arulmoli et al, 1992).

350

7.6

Cyclic strength of Toyoura Sand in triaxial compression (data

from Toki et al 1986)

352

7.7

Cyclic triaxial test data on 13 sands for which CSL is known,

with ranges obtained by Garga and McKay (1984) for sands and

tailings sands shown

353

7.8

Cyclic triaxial test data from 7.7 normalized to cyclic resistance

ratio for 15 cycles, CRR15

354

7.9

Cyclic triaxial data normalized to consolidation stress ratio, K

c

,

illustrating absence of trend as a function of K

c

355

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parameter for 13 sands

7.11

Example of effect of fabric (sample preparation method) on

cyclic strength of sands (Ladd, 1978)

356

7.12

Cyclic simple shear test on Nevada sand (Velacs project data,

Arulmoli et al., 1992)

357

7.13 Cyclic simple shear data from several sands

358

7.14

Cyclic simple shear tests on Ottawa sand, illustrating how the

effect of static bias varies depending on the selected “failure”

criterion (Vaid and Finn, 1979)

360

7.15

Shaking table tests “corrected” for compliance effects (De Alba

et al, 1976)

361

7.16

Comparison between cyclic triaxial and shaking table tests on

Monterey sand, with cyclic simple shear tests on Oosterschelde

sand

361

7.17

Demonstration of the importance of principal stress rotation on

behaviour of dense sand by Arthur et al. (1980)

363

7.18

Cumulative volumetric strain in lightly dilatant Leighton

Buzzard sand caused by principal stress rotation (Wong and

Arthur, 1986)

364

7.19

Result of a pure principal stress rotation test on loose Toyoura

sand (Ishihara and Towhata, 1983)

365

7.20

Behaviour of Erksak sand in hollow cylinder test simulating

principal stress history for Molikpaq piezometer E1 during 12

April 1986 ice loading event

367

7.21

Cyclic triaxial test on Bonnie Silt (Velacs project, Arulmoli et

al., 1992)

368

7.22

Cyclic simple shear test on Bonnie Silt (Velacs project, Arulmoli

et al., 1992)

369

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Molikpaq core (for comparison with measured dissipation on

Figure 1.22)

7.25

Earthquake magnitude scaling factors tabulated and

superimposed on cyclic strength curve in Seed and Idriss (1982),

with power law trend added

377

7.26

Most recent version of Seed 1 iquefaction diagram (Youd et al,

2001) Data points numbers correspond to the case history

reference assigned by Fear (1996) based on Ambraseys (1988)

379

7.27

CPT version of Seed liquefaction diagram (Robertson and

Wride, 1998)

380

7.28

CPT resistance adjustment factor to provide equivalent clean

sand value from that measured in the actual soil at the site

(Robertson and Wride, 1998)

381

7.29

Recommended magnitude scaling factors from NCEER

Workshop (Youd and Noble, 1997)

383

7.30 K

σ

values (after Seed and Harder, 1990)

384

7.31 K

σ

values recommended by Hynes and Olson (1999)

385

7.32

Illustration redrawn from Lee and Seed (1967) showing apparent

effect of consolidation stress ratio K

c

on liquefaction resistance

387

7.33

Summary of recommended values for K

α

(Harder and

Boulanger, 1997)

388

7.34 Illustration of alternative hardening laws

390

7.35

Biaxial compression test on an assembly of photo-elastic discs

(after de Josselin de Jong and Verruijt, 1969)

391

7.36

Schematic of yield surface softening induced by principal stress

rotation (from Been et al. 1993)

392

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Nevada sand, from Velacs project

7.38

Comparison of Seed liquefaction diagram with state parameter

presentation of cyclic triaxial test data. Note that both diagrams

are based on 15 cycles of loading, as M=7.5 corresponds to 15

cycles (Figure 7.23)

396

7.39 Field case history data on liquefaction expressed in terms of ψ

397

7.40

Comparison of K

σ

recommended by NCEER with K

σ

computed

from ψ changing with stress level at constant soil density

398

7.41

Illustration of the critical level of repeated loading (from

Sangrey et al., 1978)

401

7.42 Critical state model for liquefaction of sands, silts and clays

402

B.1

Effect of sample preparation on the cyclic resistance of sand

samples (from Ladd, 1977)

420

B.2

Illustration of sample preparation methods for clean sands

(Ishihara, 1993)

421

B.3

Illustration of vacuum saturation apparatus for triaxial sample

preparation (Shen and Lee, 1995)

427

B.4

Volume changes during triaxial sample lifetime (for a drained

test on a dilatant sample)

428

B.5

Potential error in void ratio if volume changes during saturation

are not considered (from Sladen and Handford, 1987)

429

B.6

Normalized membrane penetration coefficient as a function of

median grain size

431

B.7

Comparison of CSL determined from load controlled and strain

rate controlled triaxial compression tests

433

B.8

Triaxial cell with axial load cell located underneath cell to

minimize dynamic effects. Pore pressure transducer is also close

to cell to reduce system compliance

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C.1

Erksak sand stress dilatancy in triaxial compression and

extension (after Jefferies and Shuttle, 2002)

438

C.2

Brasted sand stress dilatancy in plane strain and triaxial

conditions (after Jefferies and Shuttle, 2002)

439

C.3

Lode angle at peak strength in plane strain (after Jefferies and

Shuttle, 2002)

440

C.4

Comparison of functions for M(θ) with Brasted sand data (after

Jefferies and Shuttle, 2002)

442

D.1

Schematic illustration of self-consistency requirement for

internal cap to yield surface (Jefferies, 1997)

453

D.2

Yield surface softening induced by principal stress rotation

(Been et al., 1993)

459

D.3

Fit of NorSand to data with modified stiffness and dilatancy for

reloading (R>1, P<1) (from Jefferies, 1997)

467

D.4 Comparison of undrained liquefaction alternative softening rules 479

D.5

Dense sand after failure in Imperial College plane strain

apparatus, tested by Cornforth, 1964

482

D.6 Simple shear conditions (from Potts et al, 1987)

486

E.1 Chamber size standardization factors (Been et al., 1986)

499

F.1

Location of flowslide on the coast of Zeeland from 1881–1946

(Koppejan et al., 1948)

519

F.2 Vlietpolder flowslide geometry (Koppejan et al., 1948)

520

F.3

Typical CPT soundings in flowslide material (Koppejan et al.,

1948)

521

F.4

Longitudinal and transverse sections of North Dyke of

Wachusett Dam (Olson et al., 2000)

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F.5

Cross section of Wachusett dam failure with 1991 investigation

results (Olson et al., 2000)

523

F.6

Typical section of hydraulic fill dam during construction (Hazen,

1918)

525

F.7

Sketch of Calaveras Dam failure showing surface before and

after slip (Hazen, 1918).

252

F.8

Sheffield dam, based on Seed et al., (1969), modified to show

liquefying layer

528

F.9 Aerial photographs of Fort Peck Dam failure

531

F.10

Critical state summary for Fort Peck Dam shell material

(Middlebrooks, 1940)

532

F.

11

Section through Fort Peck Dam failure (Casagrande, 1975)

532

F.12 Plan and section of Hokkaido tailings dam (Ishihara et al, 1990) 534

F.

13

CPTs from Hokkaido tailings dam (Ishihara et al, 1990)

535

F.14

Cross section of Mochikoshi tailings dams (Dam N°1 is top,

Dam N°2 is the bottom) (Ishihara et al, 1990)

536

F.

15

Double-tube cone penetration test at Mochikoshi Tailings Dams

(Ishihara et al 1990)

537

F.16

Nerlerk B-67 berm and foundation cross section (Been et al,

1987)

538

F.

17

Plan of failures that occurred at Nerlerk B-67 as reported by

Sladen et al. (1985a)

539

F.18

Example of bathymetric survey data at Nerlerk showing

interpolation of berm contours

540

F.19

Summary of state and stress paths in triaxial tests of

reconstituted Nerlerk 270/1 samples

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sand and Ukalerk sand

F.21

Reconstructed cross section through failed portion of La

Marquesa Dam (De Alba et al., 1988)

546

F.22

Cross section through failure zone of La Marquesa Embankment

(De Alba et al 1988)

546

F.23

Reconstructed cross section through failed portion of La Palma

Embankment (De Alba et al., 1988)

549

F.24

Cross section through failure zone of La Palma embankment (De

Alba et al., 1988)

549

F.25

Illustration and cross-section through failure zone of Sullivan

Mine tailings dyke slide (Davies, Dawson and Chin, 1998)

551

F.26

CPT soundings through Sullivan Dyke failure (see Figure F.25b

for location)

553

F.27 Estimated in situ state from CP91–29 data by screening method 554

F.28

Example of flowslide geometry at Jamuna (Yoshimine et al.,

1999)

556

F.29

Plan view of west guide bund of Jamuna Bridge showing CPT

locations (Yoshimine et al, 2001)

556

F.30

Statistical summary of Jamuna west bund CPT results (based on

data provided by Prof Yoshimine)

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Subscripts

c Critical state (some workers also use “cv” denoting constant volume) cyc Cyclic

L Limit value i

Image condition (occurs when Dp≡0 for all ) k Characteristic (in the sense of limit state Codes) st Static

tc Triaxial compression condition (θ=π/6) te Triaxial extension condition (θ=−π/6) h Horizontal

v Vertical; volume

0 Initial condition

1 Denotes value at reference stress level of 100 kPa (≈1 tsf) 1, 2, 3 Principal directions of stress or strain

Superscipts

e Elastic p Plastic

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Stress Variables (bar over or ‘denotes effective)

σ1, 2, 3

[FL−2] Principal stresses [FL−2]

Mean effective stress [FL−2] Deviatoric stress invariant

p′ [FL−2]

Mean effective stress q [FL−2]

Triaxial deviator stress η [-]

Dimensionless shear measure as ratio of stress invariants θ [Rad]

Lode angle,

α [Rad] Included angle between direction of major principal stress (the “1” direction) and coordinate frame of reference

u [FL−2] Pore pressure

Strain Variables (dot superscript denotes rate)

ε1, 2, 3 [-] Principal strains (assumed coaxial with principal stresses)

[-]

Volumetric strain rate [-]

Shear strain rate measure work conjugate with

Dp [-]

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e [-] Void ratio K0 [-]

Geostatic stress ratio, γd [FL-3] Dry unit weight

γt [FL−3] Total (and generally saturated) unit weight

γ′ [FL−3

] Submerged unit weight ψ [-] State parameter, ψ= e−ec

R [-]

Overconsolidation ratio

Geometry Variables

H [L] Slope height; layer thickness

θ [deg] Slope angle

Laboratory Testing Parameters and Variables

A [-] Skempton’s triaxial excess pore pressure parameter A=∆u/∆σq

B [-] Skempton’s excess pore pressure parameter B=∆u/∆σ3

Gs [-] Specific gravity

[deg] Mohr Coulomb friction angle (effective implied by context) su [FL−2] Undrained shear strength

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sr [FL−2] Residual (post-liquefaction) undrained shear strength Elasticity E [FL−2] Young’s modulus G [FL−2] Shear modulus K [FL−2] Bulk modulus Ir [-]

Soil shear rigidity κ [-]

Slope of elastic line in space v [-] Poisson’s ratio

Critical State

Γ [-]

Reference void ratio on CSL, conventionally defined at p′=1 kPa λ

[-] Slope of CSL in space for semi-log idealization λ10

[-]

Slope of CSL, but defined on base 10 logarithms M

[-]

Critical friction ratio, equals ηc at the critical state. Varies with Lode angle, value at triaxial compression (Mtc) taken as reference.

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χ [-] Dilatancy constant H [-] Plastic hardening modulus

Hr [-] Plastic softening modulus under principal stress rotation

Mi [-] Current value of η at Dp=0 (used in the flow rule)

CPT Parameters and Variables

qc [FL−2] CPT tip resistance, as measured

qt [FL−2] CPT tip resistance after correction for unequal area effect

fs [FL−2] CPT friction sleeve stress measurement

uc [FL

−2

] Pore pressure measured by CPT during sounding at shoulder location (sometimes denoted as u2 location in the literature).

Q [-] Dimensionless CPT resistance based on vertical stress.

Corresponds to standard usage within in situ testing community,

Qp [-]

Dimensionless CPT resistance based on mean stress, Bq [-]

CPTu excess pore pressure ratio,

F [-]

Stress normalised CPT friction ratio,

Ic [-] Soil classification index from Been and Jefferies (1992)

(38)

Ic,RW

Nk [-]

CPT undrained strength factor,

(39)
(40)

Preface

Soil liquefaction is a phenomenon in which soil loses much of its strength or stiffness for a generally short time but nevertheless long enough for liquefaction to be the cause of many failures, with both deaths and some very large financial losses. Unsurprisingly, there is a vast literature on liquefaction. Apart from a sustained set of contributions to the usual journals over the past thirty years or so there have been publications by university departments specializing in the subject, specialty conferences, theme sessions at geomechanics conferences, state-of-the-art papers, two Rankine lectures, the Canadian Liquefaction Experiment (Canlex), a book by the National Research Council (USA) and research competitions sponsored by the National Science Foundation to test theories and modeling techniques (VELACS in particular).

So where does this book fit in? This book assumes some background in soil mechanics, and an interest in understanding liquefaction. But, this book is most certainly not an overview of the literature nor does it seek to strike a balanced view of the various theories and experience about liquefaction (if indeed a balanced view is possible). Rather the aim is demystifying liquefaction, both in terms of the physics of soil behaviour and how it can be avoided in practice by good engineering. To achieve these dual goals, a number of viewpoints are adopted:

• Full scale experience of liquefaction, while immensely important as calibration

information, can be erroneously extrapolated without an underlying constitutive model to guide the interpretation of observations. An “understanding” of liquefaction is not enough, and a mere geological classification approach is unacceptable for engineering as such classification approaches are likely to mislead in some circumstances. • Liquefaction is simply another facet of soil behaviour which proper constitutive models

capture, including the effect of density and stress level on that behaviour. There are now several such models, and there is no need to resort to the witchcraft or dogma about liquefaction (e.g. “metastable soil particle arrangements” and similar “explanations” of the phenomenon).

• Constitutive models are idealizations, but idealization is not the sole domain of constitutive models. Both laboratory test data and physical model tests must be used equally cautiously. There are issues of scale.

• A proper appreciation of liquefaction thus requires a mixture of constitutive theory, soil properties and their determination (the in situ state in particular), and detailed

evaluation of the case history record.

In exploring these views, the book does not follow the mainstream US and Japanese research on liquefaction. The reason is that the subject is much broader than earthquake engineering. There is also much valuable experience outside the Pacific Rim. More importantly, there are aspects of the Pacific Rim approach, which is based on a reference stress concept, that are questionable mechanics. In some instances, the usual reference

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proper dimensionless approach based on mechanics.

Mainstream experience around the Pacific Rim has been concerned with earthquake induced liquefaction through cyclic changes of shear stress, which is entirely reasonable given the economic base in California and Japan and the earthquake hazard of both these areas. Earthquakes are by no means necessary for liquefaction, however, and in seeking a full understanding it is important to use full scale experience. There is useful experience to be assimilated from coastal flowslides in The Netherlands which have been triggered quasi-statically. Equally, earthquakes usually last less than twenty or so significant load cycles and there is additional understanding to be gained from the offshore and coastal facilities exposed to several hundreds or thousands of load cycles in storm loading.

This book aims to help, and to do this we have made the files used to create plots downloadable from the internet (including the supporting raw data). Downloads can be found at the Golder Associates website (use the link www.golder.com/liq or search under the “library” menu) and which has a readme file with the latest information. Much of the interesting data on liquefaction is hidden in hard to access files at universities, consultants and research organizations. So we have made available for downloading all sorts of source data that we have found useful, as well as raw and processed data for many of the tests carried out by Golder Associates. The source code for numerical routines is entirely open code, and hope that you might be prepared to load an Excel file and try something. Look for the following on the website:

• Files with actual test data for the various plots in the book, These include triaxial test results, CPTs, and summaries of CPT calibration chamber studies.

• Source code for numerical routines discussed in the book, provided as Visual Basic within Excel spreadsheets. These are readily translated to other languages as needed. We refer to plots or routines with italics in the text and also to the name of the file used to create a particular figure with the figure number. Source code for the numerical routines is in commented open-code, and we hope the commenting is sufficiently detailed that the way the code works is clear. Files can be downloaded and the various routines used within Excel while reading the book so the development of ideas can be seen. We encourage this, as seeing the simulations come alive on a screen makes the effect of changing properties way more interesting than looking at the plots only on paper. Running the simulations also gives a feel for things, Plus, plots scales can be changed and so forth if interested in some detail. Please contact us if you discover any bugs as that will help everyone. You will have guessed by now that we are strong supporters of open software and freely shared data, and we hope for the same from you the reader. Although the downloads are “freeware”, they are copyrighted; but, they can be redistributed and/or modified under the terms of the GNU General Public License Version 2 as published by the Free Software Foundation (see page xxviii). Broadly, we are asking for developments built on this book to be as open as provided here—that will help everyone. Some of the articles on the Free Software Foundation website (http://https://www.fsf.org) show why this will be helpful to the profession in general. If it is desired to incorporate code in a proprietary product, contact us.

We also draw your attention to the Appendices, which contain detailed derivations that you will not find in published papers (and which textbooks do not usually explain either).

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We trust that there is no equation in this book that appears without an appropriate derivation, as having a detailed derivation removes any black-magic aspects. The Appendices also document testing procedures, give the entire database of cone chamber calibration tests, and have details on interesting case histories as well as records of difficult to find information. These appendices are a substantive part of the book.

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Those of you who have read some of our papers will recognize that we owe a great deal to the Canadian offshore oil industry and Golder Associates. Much of what is presented in this book was developed on construction projects for Gulf Canada Resources, Esso Resources Canada, and Dome Petroleum. We thank in particular John Hnatiuk, Bill Livingstone, Brian Wright, Brian Rogers, Chris Graham, David James, and Sanjay Shinde. Without the support from these gentlemen, much of what you will find in this book would not exist.

We also owe an enormous debt to our colleagues in Golder Associates who have both encouraged and humoured us. Our co-authors are acknowledged by reference to the various joint papers, and we thank in particular Jack Crooks, Brian Conlin, John Cunning, Dave Horsfield, Joe Hachey, and Dawn Shuttle. Production of this book has also been supported by Golder Associates. We thank all people in the company for this.

As we pulled the final version for this book together, we realized that we also had worked rather closely with the University of British Columbia. Although we have disagreed with Yogi Vaid over many issues, his testing has been a tremendous stimulus and he directed some of the more interesting testing of Erksak sand. This relationship has continued today in the context of both laboratory (Dharma Wijewickreme) and in situ testing (John Howie). The most recent developments of NorSand, and its implementation in computable models (FLAC and Finite Element codes) have actually been carried out by Dawn Shuttle and her students. Some their routines and programs can be downloaded from the UBC Geotechnical Engineering website (http://www.civil.ubc.ca/).

Many friends and acquaintances not already mentioned also provided useful case history and laboratory data over the years. At the risk of missing a few names we acknowledge data provided by Mike Jamiolkowski (calibration chamber data), Ramon Verdugo (Toyoura sand test data), Mike Hicks and Radu Popescu (probabilistic analyses), Gonazalo Castro (Lower San Fernando data), Scott Olson (various CPT data), Prof Yoshimine (Jamuna Bridge data) and Howard Plewes (Sullivan Dam data).

It is also appropriate that we acknowledge intellectual mentoring over the years, Professor Bob Gibson introduced one of us (MJ) to theoretical soil mechanics. Other guidance and encouragement was provided by Professor Andrew Palmer, and the late Professors Peter Wroth and Dan Drucker. We are very appreciative of their time and interest. Hopefully, this book will do justice to their influence.

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Finally, both of us must thank our parents for providing our initial engineering education and our families for their forbearance subsequently, This book, and the papers that lead to it, have taken many hours of our lives. Our families have humoured us by not complaining as we disappeared into our studies for many nights over the best part of twenty years, Thank you, Hilary and Fiona,

Mike Jefferies, C.Eng. Associate, Golder Associates (mjefferies@golder.com)

Ken Been, P.E. Principal, Golder Associates (kbeen@golder.com)

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As a of the subject, this book and may be hazardous. Substantial and is to work safely. This book not cover work for Appropriate training should be received attempting any of the in this book. Neither the authors nor the publisher any liability for your working

This book provides and equations. Neither the nor the publishers warrant the or suitability for a particular of any of the information or and you must carry out your own quality relying on trends, equations, or numerical routines. This is a normal requirement for a professional engineer, and this book is to be only by professional geotechnical engineers.

Software can be downloaded for use the of this book is provided on the Golder Associates website http://www.golder.com/. Downloaded. is but is copyrighted and provided as “Freeware”; you can redistribute it and/or modify it under the of the GNU General Public License Version 2 as published by the Free Foundation. A copy of this is on the Golder website, and will be automatically included with every download. Programs and are downloadable from Golder in the that they will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for details.

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CHAPTER ONE

Introduction

1.1 WHAT IS THIS BOOK ABOUT?

Soil liquefaction is a phenomenon in which soil loses much of its strength or stiffness for a generally short time but nevertheless long enough for liquefaction to be the cause of many failures, deaths and major financial losses. For example, the 1964 Niigata (Japan) earthquake caused more than $1 billion in damage and most of this damage was related to soil liquefaction. The Aberfan (Wales) colliery spoil slide was caused by liquefaction and killed 144 people (116 of whom were children) when it inundated a school. Liquefaction was involved in the abandonment of the Nerlerk (Canada) artificial island after more than $100 million had been spent on its construction. Liquefaction at Lower San Fernando dam (California) required the immediate evacuation of 80,000 people living downstream of the dam. Liquefaction is an aspect of soil behaviour that occurs worldwide and is of considerable importance from both public safety and financial standpoints.

In terms of age of the subject, Ishihara in his Rankine Lecture (Ishihara, 1993) suggests that the term spontaneous liquefaction was coined by Terzaghi and Peck (1948). The subject is much older than that, however. Dutch engineers have been engineering against liquefaction for centuries in their efforts to protect their country from the sea. Koppejan et al. (1948) brought the problem of coastal flow slides to the soil mechanics fraternity at the 2nd International Conference in Rotterdam. In the last paragraph of their much-cited paper, they mention flow slides in the approach to a railway bridge near Weesp in 1918 triggered by vibrations from a passing train. They claim that this accident, with heavy casualties, was the immediate cause of the start of practical soil mechanics in the Netherlands.

At about the same time, Hazen (1918) reporting on the Calaveras Dam failure clearly recognized the phenomenon of liquefaction and the importance of pore pressures and effective stresses. If the files of the US Corp of Engineers are consulted one finds that Colonel Lyman densified fill for the Franklin Falls dam (part of the Merrimack Valley Flood Control scheme) in the late 1930s specifically to ensure stability of the dam from liquefaction based on the concept of critical void ratio given in Casagrande (1936). Reading these files and reports is an enlightening experience as Casagrande discussed many topics relevant to the subject today, and Lyman’s report (1938) of the Corps’ engineering at Franklin Falls is a delight that historians of the subject will enjoy.

We will not attempt our own definition of liquefaction, or adopt anyone else’s, beyond the first sentence of this book. Once it is accepted that liquefaction is a constitutive behaviour subject to the laws of physics, it becomes necessary to describe the mechanics mathematically and the polemic is irrelevant.

Liquefaction evaluation is only considered worthwhile if it may change an engineering decision. Testing and analysis of liquefaction potential is only undertaken in practice in the context of a particular project. As will be seen later, liquefaction is an intrinsically

Figure

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References