2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history...

Critical State Soil Mechanics125 years of history to current use

“No equations…”

Accompanying ‘briefing’ paper and software

Mike Jefferies, P.Eng.

geomek@hotmail.comMarch, 2018

2018 Jennings Lecture

South African Institution of Civil

Engineering: Geotechnical Division

Preamble

Loose sand… f = 31 deg

Dense sand… f = 44 deg

March 9, 2018 2

Why ?

0

50

100

150

200

250

300

350

400

450

500

0 5 10 15 20 25

de

via

tor

str

ess,

q: kP

a

axial strain: %

NorSand

SCIUB

0

50

100

150

200

250

300

350

400

450

500

0 100 200 300 400 500

meaneffec vestress,p':kPa

North American Dam Construction ~ 1900

March 9, 2018 3

100 years ago…

Calaveras Dam 1918

1885: Distortion causes dilation

March 9, 2018 5 Reynolds, 1885

Franklin Falls (NH) 1935

‘sand flow failure'

1939: Fort Peck Dam

March 9, 2018 7

0.75

0.76

0.77

0.78

0.79

0.8

0.81

0.82

0.83

0.84

0.85

10 100

VoidRa

o

s'3: psi

Critical state locus: CLAYS ~1955

March 9, 2018 8

Castro: SANDS - Load controlled tests (1969)

March 9, 2018 9

Critical State Locus: SANDS and SILTS ~ 1990

0.45

0.50

0.55

0.60

0.65

0.70

0.75

10 100 1000 10000

Mean effective stress, p ' (kPa)

Vo

id r

atio

GuindonB.xls

Conventional semi-log idealization of CSL

Improved (curved) idealization of CSL

Initial state of samples

Critical state at end of test

l

De < ± 0.02

CSSM steps for a practical engineer

Determine the CSL for soil(s) in question…

Measure the insitu void ratio vs stress profile (CPT)

March 9, 2018 11

Are you dense enough (Liquefaction potential) ?

Theory of soil behavior

✔

IDEA 1: Soil strength components (1948 - 50)

March 9, 2018 12

Bishop (1950)

“Strength” = “Friction” + “Interlocking”

D

“dilation” or “dilatancy”

h = q/p’ = M - D

Soil strength as two components

March 9, 2018 [Taylor-Bishop, 1948-50]

Friction

IDEA 2: Stress-dilatancy at all strains ~1960

March 9, 2018 14

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

-1 -0.5 0 0.5 1 1.5 2

h

Dilatancy: Dp

CamClay

Mod.CamClay

Nova

Rowe

Li&Dafalias

h = q/p’ = M – f(D)

Actual soil behaviour: h = Mf - D

March 9, 2018 15

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

-0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

Stressra

oh

Dilatancy,D

OCCstress-dilatancy

DENSE

Stress-dilatancyfromTaylor-Bishopdissipa onofplas cwork

LOOSE

Mf(thistest)

STATE-DILATANCYdetermineshowfarstress-dilatancycandevelop

IDEA 3: Plasticity

March 9, 2018 16

0

200

400

600

800

1000

1200

0 2 4 6 8 10 12 14 16 18 20

deviatorstress,q

:kPa

axialstrain,e1:%

Elastic

Plastic

e = ep + ee

Development of plasticity theory

March 9, 2018 17

Plasticity theory introduced to soil mechanics ~ 1945

• Soils change volume with distortion

• Soil strength and stiffness depends on mean stress

All flavours of plasticity theory…

Yield surface …is the stress state plastic ?

Flowrule …which way are things moving ?

Stress-dilatancy theory Poisson’s Ratio

Hardening Law …how does the yield stress change ?

Depends on plastic distortional strain Young’s Modulus

March 9, 2018 18

Soil Constitutive-Model Flavours

Curve fitting Obsessive attention to measured soil behaviour

Convoluted functions whose physical meaning is unclear

May violate basic principles (e.g. stress-dilatancy)

Different properties with different soil density

Postulatory “who cares about test data”…

Introduce simple, understandable idealizations

(e.g. soil as spherical particles)

Simple, clear physics

Can derive new insights through consistency arguments

Justified by how well the model simulates what is measured

March 9, 2018 19

Cam Clay Ideas

Taylor-Bishop strength as combination of friction and dilation

Friction = strength increases linearly with confining stress

Plastic work only dissipated by deviatoric strain

Stress-dilatancy Law… Dp = M - h

Generalization of Taylor-Bishop

Unique critical state locus

Derived for semi-log but does not have to be

Normality (associated flow rule)

THEOREM derived for metals

Controversial in some eyes

March 9, 2018 20

IDEA 4: ‘Normality’ (associated flow rule)

Soil Liquefaction Fig 3-1 9/29/2014

March 9, 2018 21

P2 > P1

22

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0.0 0.5 1.0 1.5 2.0 2.5 3.0

mean effective stress, p

sh

ea

r str

ess, q

“Normality” = Associated Flow Rule

Devp

De q

p

Dp

Dq DevpD

e qp Dp = M – q/p’

- Dq/Dp = Dp

- Dq/Dp = M – q/p

CSSM: Cam Clay

March 9, 2018 23

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.5 1 1.5 2 2.5 3

s q , eq

s m , ev

M (fcv)

“Coulomb line” log(s m )

Dp = M – q/p’

Original Cam Clay works…

March 9, 2018 24

0"

100"

200"

300"

400"

500"

600"

700"

800"

900"

1000"

0.0" 5.0" 10.0" 15.0"

deviator)stress,)q

:)kP

a)

axial)strain:)%)

-1"

0"

1"

2"

3"

0.0" 5.0" 10.0" 15.0"

volumetric)strain:)%)

axial)strain:)%)

Erksak CID-682

Original Cam Clay

…but not in general (~1975)

0.5

0.6

0.7

0.8

10 100 1000

void

ra

tio

mean effective stress, p': kPa

CSL

March 9, 2018 25

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

0 5 10 15

de

via

tor

str

ess,

q: kP

a

axial strain: %

In nearly all situations Cam Clay is much too stiff,

much too strong and dilates unlike real soils…

March 9, 2018 26

100 year history of mechanics…

can “the math” be that wrong ?

28

Berms details

Constructing the berm…

CPT resistance in hydraulically placed sand

0

5

10

15

20

25

30

35

40

45

0 5 10 15 20 25 30 35

dep

th b

elo

w r

efe

ren

ce

ele

va

tio

n (

+2.0

m m

sl)

: m

.

tip resistance, qc: MPa

cpt16

cpt14

cpt01

cpt03

cpt09

Void ratio from the CPT

And now re-plot in familiar form…

0.6

0.65

0.7

0.75

0.8

0.85

0.9

10 100 1000

vo

id r

ati

o

vertical effective stress: kPa

cpt16

cpt14

cpt01

cpt03

cpt09

cpt02

March 9, 2018

Normally

consolidated

hydraulic fill

General pattern of soil behaviour

March 9, 2018 35

Fraction of fill

looser than

the NCL

plotted

AXIOMS (fundamental assumptions)

0.40

0.60

0.80

1.00

1 10 100 1000 10000

p' (kPa)

Vo

id r

atio

, e

State path in

constant p' test

e i

e f

Critical state line, e =e c

March 9, 2018 36

Axiom 1: ec = f(s1,s2, s3) and single valued

Axiom 2: y 0 as eq∞

Mathematical statements that do not depend on soil test data

y

…such that D=0 and DD/De =0

Axiom 2 Dmin = c y-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

-0.20 -0.15 -0.10 -0.05 0.00

Dmin

stateparameteryatDmin

Nerlerk sand

Erksak sand

Brasted Sand

Weald Clay

London Clay

SandDilation_r13.xls

DatafromParry(1958)seetext

March 9, 2018 37

c

AXIOM 2: hmax = M c y

March 9, 2018

38

28

30

32

34

36

38

40

42

44

46

48

-0.3 -0.2 -0.1 0.0

Fri

cti

on

An

gle

, f

: d

eg

State Parameter

Erksak 330/0.7 Erksak 355/3

Erksak 320/1 Isserk 210/2

Isserk 210/10 Isserk 210/5

Nerlerk 270/1 Alaska 240/5

Alaska 240/10 Castro B

Castro C Hilton Mines

Leighton Buzz Monterey #0

Ottawa 530/0 Reid Bedford

Ticino Toyoura

Oil Sands Tail

Effect of fines: Dr does not work

General CSSM: NorSand (1993)

March 9, 2018

Dmin = c y

Axiom 2:

pi

Mi = f(M,y)

OCR

Equations in paper

pc

Calibration in drained triaxial compression

-6

-4

-2

0

2

volu

metr

ic s

train

: %

0

200

400

600

800

1000

0 2 4 6 8 10axial strain: %

devia

tor

str

ess, q: kP

a

NorSand

Test Data

March 9, 2018 40

Erksak Sand tested at UBC(Sasitharan, 1989)

250dr70-2

Mtc = 1.26

N = 0.2

l10 = 0.046

ctc = 4.5

H = 100 380yGmax = f(e,p)

Calibration

using triaxial

compression

tests

Predict all other soil behaviours…

0

50

100

150

200

250

0 5 10 15

Axial strain (%)

De

via

tor

str

ess,

q (

kP

a)

NorSand

0

50

100

150

200

250

0 200 400 600

Mean stress, p' (kPa)

Test C609 y0 = +0.07

0

100

200

300

400

0 5 10 15

Axial strain (%)

De

via

tor

str

ess, q

(kP

a)

NorSand

0

100

200

300

400

0 200 400 600

Mean stress, p' (kPa)

Test L601 y0 = +0.025

0

200

400

600

800

0 1 2 3 4 5

Axial strain (%)

Devia

tor

str

ess,

q (

kP

a) NorSand

0

200

400

600

800

0 200 400 600 800

Mean stress, p' (kPa)

Test C634 y 0 = -0.08

Cyclic simple shear of Fraser River Sand

0

20

40

60

80

100

120

0 2 4 6 8 10

cycle

PW

P:

kP

aNorSand

Measured

-15

-10

-5

0

5

10

15

0 20 40 60 80 100 120

Mean effective stress: kPa

Tau

_V

H:

kP

a

-15

-10

-5

0

5

10

15

-6 -4 -2 0 2 4 6

Gamma_VH: %

Tau

_V

H:

kP

a

0

20

40

60

80

100

120

-6 -4 -2 0 2 4 6

Gamma_VH: %

PW

P:

kP

a

cycle Gamma_VH: %

Gamma_VH: %mean effective stress: kPa

PW

P:

kP

aTau

_V

H:

kP

a

PW

P:

kP

aTau

_V

H:

kP

a

Contributors and ideas: overview

1885 – dilation is a fundamental soil behaviour Manchester

1935 – critical state as limit of dilation behaviour Harvard

1940 – critical state locus MIT

1950 – work basis of stress-dilatancy Imperial

1951 – THEOREM theromodynamics plasticity Brown

1957 – correct form of associated plasticity for soils Brown + Imperial

1962 – stress-dilatancy applies everywhere Manchester

1968 – first proper model: Original Cam Clay Cambridge

1985 – state parameter Imperial / Gulf Canada

1993 – NorSand Gulf Canada

Generalizing CSSM: The nature of y…

Originally suggested as an obvious “normalizing parameter” in 1985 (inspired by observations of Parry, 1958)

O’Tooles corollary: the CSL is fundamental to any soil

Now ubiquitous in ‘good’ models as it allows enormous simplification

while keeping great detail in the simulations (“The Math” 1993 onwards)

Basically, it has “resurrected” critical state soil mechanics

Fundamental: Appendix 2 of accompanying paper

‘Good’ models include…

NorSand… Stamford, NorthWestern, Cambridge, Imperial

NorSand-like variants… UNSW, UofA, UofC, Bristol/Dundee

Bounding Surface… Davis / NTUA / Belgrade

Simplified MONOT… Delft

March 9, 2018

CSSM steps for a practical engineer

Determine the CSL for soil(s) in question…

Measuring y insitu

March 9, 2018 45

Are you dense enough (Liquefaction potential) ?

Theory of soil behavior

✔

✔

Using state parameter models...

Properties (independent of density and stress)

State (varies from place to place)

March 9, 2018 46

l (CSL)

Mtc, N

ctc

H

Measure in laboratory

Estimate using judgment

CPTu (seismic)

SBP

VSP

y

OCR

Gmax

Getting samples: Mostap

A variation on fixed-piston sampling that works with CPT equipment

35mm or 65mm diameter

Plastic sample tube and stocking

Not a “Class 1” undisturbed sample – too thick sampler wall

March 9, 2018 47

Minimal triaxial tests on representative soil

March 9, 2018 48

Comments on laboratory testing

“Altitude” of the CSL (=G) of CSL

very dependent on fines content

Slope of the CSL (=l) of the depends on:

fines, and especially the wider distribution of particle sizes in the soil

Particle shape and mineralogy

Frictional strength (M or fc)

Particle shape and mineralogy

March 9, 2018 49

Practical approach: test the

average gradation of the deposit

Measuring void ratio accurately: e = Gs w

March 9, 2018 50

Sladen & Handford (1987)

Using state parameter models...

Properties (independent of density and stress)

State (varies from place to place)

March 9, 2018 51

l (CSL)

Mtc, N

ctc

H

Measure in laboratory

Estimate using judgment

CPTu

SBP

VSP/SeismicCPT/Benders

y

OCR

Gmax

CPT: calibration chambers

Esso Resources Canada, Dome Petroleum, Gulf Canada Resources

Figure 4.9 Example of CPT chamber test data (Erksak sand, after Been et al 1987b)

Getting y from the CPT

q c -p (MPa)

p' (k

Pa

)

Q

ERKSAK SAND

(Been et al. 1987)

Q = 22.8 e-11.8 y

10

100

1000

-0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05

State Parameter, y

Q

Esso Resources Canada, Dome Petroleum, Gulf Canada Resources

State parameter, y

Str

ess-n

orm

aliz

ed C

PT

re

sis

tan

ce

, Q

CPT calibrations in sand

March 9, 2018 54

CPT evaluation: loose or compressible ?

Most soil properties affect CPT response…

k = f(M).f(N).f(H).f(l).f(Gmax/p’)

m = f(M).f(N).f(H).f(l).f(Gmax/p’)

Choices…

1) Measure properties

Drained triaxial compression on reconstituted samples

2) Estimate properties from ‘soil behaviour type’

“Plewes Method”

Judgment

March 9, 2018 55

Equations known from

calibrated numerical

analyses

y = -m ln(Q/k)

Doing the “the math”: cavity expansion

March 9, 2018

qc =CQ Plimit

Cavity displacement

Cavity p

ressure

Bishop, Mott & Hill (1945)

Scaling factor and data scatter

March 9, 2018 57

I169

E139

CQ

Effect of Gmax on CPT coefficients

March 9, 2018 58

0

1

2

3

4

5

6

7

8

9

10

0

5

10

15

20

25

30

35

40

100 1000

elastic shear rigidity, Ir (= G/p'0)

CPT coefficient k(left axis)

CPT coefficientm(right axis)

Generalization from Ticino to all CC sands

March 9, 2018 59

331 calibration tests

80% ± 0.04

Moving from sands to silts: Q(1-Bq) + 1

March 9, 2018

1.0

10.0

-0.08 -0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08 0.10

Qp(1

-Bq)+

1

state parameter, y0

p'=50kPa, H=20, Ir=80

p'=500kPa, H=20, Ir=80

p'=50kPa, H=20, Ir=200

p'=500kPa, H=20, Ir=200

p'=50kPa, H=50, Ir=200

p'=500kPa, H=50, Ir=200

Trend line inferred for CPT including the spherical to CPT correction

Geophysical stiffness measurement (VSP)

4 m

Reference

Vertical

Geophone

Reference

Transverse

Geophone

Orientation

Control Rod

To Tri-axial

Phone in

Borehole

0.4 m

Transverse Radial

Ve

rtic

al

4 m

Reference

Vertical

Geophone

Reference

Transverse

Geophone

4 m

Reference

Vertical

Geophone

Reference

Transverse

Geophone

Orientation

Control Rod

To Tri-axial

Phone in

Borehole

0.4 m

Transverse Radial

Ve

rtic

al

Elastic wave theory: G = r Vs2

Range

Example Tri-axial Data: Not From This Survey

Range

Range

Example Tri-axial Data: Not From This Survey

Vs = Range / Time

VSP by seismic CPT

van den berg ‘ICONE’

Benders

March 9, 2018 63

Benders vs Insitu VSP

March 9, 2018 64

0

100

200

300

0 100 200 300 400 500 600

elascshearm

odulus,G

max:MPa

meaneffec vestress,p':kPa

NCS(B) NCP(B)

CQD(I) EKO(B)

RoC(I)

LooseSilts(e~0.9)

DenseSilts(e~0.7)

Gmax_silts.xlsx

Data&TestMethod:(I)=insituusingSCPT

(B)=laboratory"bender"tests

CSSM steps for a practical engineer

Determine the CSL for soil(s) in question…

Measuring y insitu + Soil Properties

March 9, 2018 65

Are you dense enough (Liquefaction potential) ?

Theory of soil behavior

✔

✔

✔

Drained to undrained transition…

Calaveras Dam 1918

Measured drainage time in clean sand

March 9, 2018 67

-40

-20

0

20

40

60

80

100

120

140

160

0 2 4 6 8 10 12 14 16 18 20

Elapsed time: minutes

Po

re w

ate

r p

res

su

re:

kP

a

PIEZO 947 E1

PIEZO 948 E3

PIEZO 956 W3

PIEZO 957 W2

All data referenced to mean sea level

5 minutes

Drained to undrained transition

March 9, 2018 68

0 5 10 15Major principal strain, e1 (%)

0

100

200

0 100 200

Dev

iato

r st

ress

, q (

kPa)

Mean effective stress, p' (kPa)

Critical friction ratio, M

Drained

loading

Reserve of

undrained strength

Drained

loading

Δu = B[Δσ3 + A(Δσ1 − Δσ3]

What is dense enough ?

March 9, 2018 69

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

-0.3 -0.2 -0.1 0.0 0.1 0.2

h

y@qmax

instability_limit_r1.xls

Limi ngstressra ohL

indrainedtestsEqn[10](averagesandproper es)

Stressra ohILatinstabilityinlooseundrainedtests

instability_limit_r1.xls

Dy = -0.05

Undrained > Drained

1

10

100

1000

0.1 1 10

friction ratio F: %

dim

ensio

nle

ss p

enetr

atio

n r

esis

tance

, Q

(1-

Bq

) +

1

Gravelly

sands

Sands to

sand some silt

Silty sands to

sandy silts

Clayey silts

y = -0.05

Demarcation between strain softening and

strain hardening behaviour following initial

liquefaction (Shuttle & Cunning, 2008)

STEP ONE: Identify potential behaviour

Ground improvement

Induced displacements

Includes

drained

and

undrained

penetration

pwp

measured

by CPT

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

-6 -4 -2 0 2 4 6

Shear strain, evh: %

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0 200 400 600 800

CYC

LIC

STR

ESS

RA

TIO

, th

/ s

' vo

Vertical effective stress, s'v: kPa

Criterion

from both

theory and

experienc

e

Processing CPT data [CPTplot.xlsm]

0

5

10

15

20

25

0 2 4 6 8 10

Dep

th :

m

Tip resistance, qt: MPa

0

5

10

15

20

25

0.00 0.02 0.04 0.06 0.08

Friction, f: MPa

0

5

10

15

20

25

-0.1 0.1 0.3 0.5 0.7

Pore pressure, u2: MPa

hydro

sta

tic p

rofile

show

n a

s lig

ht blu

e lin

e

March 9, 2018 711

10

100

1000

0.1 1 10

dim

en

sio

nle

ss p

en

etr

atio

n r

esis

tan

ce

, Q

(1

- B

q)

+ 1

friction ratio F: %

Gravelly sands

Sands to sand some silt

Silty sands to sandy silts

Clayey silts

y = -0.05

Demarcation between strain softening and strain hardening behaviour following initial liquefaction (Shuttle & Cunning, 2008)

Data from CPT 09 (5 m to 20 m plotted)

Laboratory tests not covered in glory...

March 9, 2018 72

80, 000

people

1971 San Fernando Earthquake

So, post-liquefaction strengths from slides

March 9, 2018 73

Looking at the mechanisms in case-histories

March 9, 2018 74

Tar Island Dyke Upstream failure (Plewes et al, 1989)

Movement vectors from calibrated NorSand

March 9, 2018 75

Effect of drainage versus loading rates (stress path)

Effect of basal yield

Effect of loose layers

Using lab properties seems to match to measured deformation pattern

FLAC UDM in downloads

Results from case-histories

0.00

0.05

0.10

0.15

0.20

0.25

-0.10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25

Residualundrained

strengthra

o,s

r/s' vo

Characteris cstateparameter,yk

Sullivan

Jamuna

Mochikoshi 1

Mochikoshi 2

Hokkaido

Nerlerk

Lower San Fernando

Wachussett

La Marquesa

La Palma

Sheffield

Zeeland

March 9, 2018 76

Large scale post-liquefaction strength

0

100

200

300

0 5 10 15

de

via

tor

str

es

s,

q:

kP

a

axial strain: %

0

100

200

300

0 100 200 300

mean effective stress, p': kPa

Cri calstatestrength

Opera ngstrengthatlargescale

March 9, 2018 77

Case-histories vs CSSM (laboratory calibration)

0.00

0.05

0.10

0.15

0.20

0.25

-0.10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25

Residualundrained

strengthra

o,s

r/s' vo

Characteris cstateparameter,yk

Sullivan

Jamuna

Mochikoshi 1

Mochikoshi 2

Hokkaido

Nerlerk

Lower San Fernando

Wachussett

La Marquesa

La Palma

Sheffield

Zeeland

NorSand (clean sand calibration)

(insitu seismic Gmax)

(pure silt calibration)

(insitu seismic Gmax)

March 9, 2018 78

Best-practice for residual strength

0.00

0.05

0.10

0.15

0.20

0.25

-0.10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25

Residualundrained

strengthra

o,s

r/s' vo

Characteris cstateparameter,yk

Sullivan

Jamuna

Mochikoshi 1

Mochikoshi 2

Hokkaido

Nerlerk

Lower San Fernando

Wachussett

La Marquesa

La Palma

Sheffield

Zeeland

l10 = 0.05

l10 = 0.10

l10 = 0.20

March 9, 2018 79

A caution…

0.55

0.65

0.75

0.85

0.95

1.05

1 10 100 1000 10000

vo

id r

atio

mean effective stress, p': kPa

CSL

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Conclusion

Practical Engineer 😊

CSSM explains/quantifies soil behaviour with density

Not perfect, but calibrated to experience

su / sr (= instability issues, LE analysis); FE rare but doable

Some laboratory txl testing generally needed

Must use freezing

Same standard practice as now: seismic CPTu principal test

Applied Mechanic 😰

Not perfect: perfect in laboratory, but not to field experience

Undrained softening ‘kludge’; options with the theory

Missing aspects: ‘non-coaxiality’; n; possibly scale; creep/aging

Silts: laboratory procedures; CPT calibration chamber

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Software – CSSM is a numerical world

Free Software Foundation

Any user can study the source code, modify it, and share the program

Decent level of internal code documentation

Do run verification checks

NOT free support !

Downloads

Soil properties: NorTxl(r7)_Nerlerk.xlsm

CPT calibration: Widget Geot Res J, S&J 2016 please cite…

CPT processing: CPTplot(r21)_14-03.xlsm

Fancy modelling: FLAC8 NorSand UDM

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Shameless commerce…

Lecture briefing give list of principal peer-reviewed references. BUT…

Text on critical state soil mechanics and its applications

Liquefaction is secondary…

Derivations in painful detail

Lots of associated data files and documentation

Trust is wonderful...

But, distrust is better !

Acknowledgements

Professors Alan Bishop, Peter Wroth, and Ian Smith

Dr Dawn Shuttle & Dr Ken Been

Gulf Canada Resources: Nelson’s ‘Band of Brothers’Howard Goldby, Kathy Griffin, Mike Hardy, Karen McKenzie, Volker

Neth, Brian Rogers, Hugh Stewart, Brian Wright, and Wes Wright.

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Questions ?