85
Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software Mike Jefferies, P.Eng. [email protected] March, 2018 2018 Jennings Lecture South African Institution of Civil Engineering: Geotechnical Division

2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

  • Upload
    others

  • View
    8

  • Download
    0

Embed Size (px)

Citation preview

Page 1: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

Critical State Soil Mechanics125 years of history to current use

“No equations…”

Accompanying ‘briefing’ paper and software

Mike Jefferies, P.Eng.

[email protected], 2018

2018 Jennings Lecture

South African Institution of Civil

Engineering: Geotechnical Division

Page 2: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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

Page 3: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

North American Dam Construction ~ 1900

March 9, 2018 3

Page 4: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

100 years ago…

Calaveras Dam 1918

Page 5: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

1885: Distortion causes dilation

March 9, 2018 5 Reynolds, 1885

Page 6: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

Franklin Falls (NH) 1935

‘sand flow failure'

Page 7: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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

Page 8: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

Critical state locus: CLAYS ~1955

March 9, 2018 8

Page 9: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

Castro: SANDS - Load controlled tests (1969)

March 9, 2018 9

Page 10: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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

Page 11: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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

Page 12: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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

Page 13: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

Soil strength as two components

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

Friction

Page 14: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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)

Page 15: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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

Page 16: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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

Page 17: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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

Page 18: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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

Page 19: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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

Page 20: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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

Page 21: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

IDEA 4: ‘Normality’ (associated flow rule)

Soil Liquefaction Fig 3-1 9/29/2014

March 9, 2018 21

P2 > P1

Page 22: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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

Page 23: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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’

Page 24: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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

Page 25: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

…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…

Page 26: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

March 9, 2018 26

100 year history of mechanics…

can “the math” be that wrong ?

Page 27: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software
Page 28: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

28

Page 29: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software
Page 30: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

Berms details

Page 31: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

Constructing the berm…

Page 32: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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

Page 33: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

Void ratio from the CPT

Page 34: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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

Page 35: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

General pattern of soil behaviour

March 9, 2018 35

Fraction of fill

looser than

the NCL

plotted

Page 36: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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

Page 37: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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

Page 38: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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

Page 39: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

General CSSM: NorSand (1993)

March 9, 2018

Dmin = c y

Axiom 2:

pi

Mi = f(M,y)

OCR

Equations in paper

pc

Page 40: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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

Page 41: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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

Page 42: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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

Page 43: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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

Page 44: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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

Page 45: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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

Page 46: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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

Page 47: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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

Page 48: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

Minimal triaxial tests on representative soil

March 9, 2018 48

Page 49: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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

Page 50: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

Measuring void ratio accurately: e = Gs w

March 9, 2018 50

Sladen & Handford (1987)

Page 51: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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

Page 52: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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)

Page 53: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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

Page 54: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

CPT calibrations in sand

March 9, 2018 54

Page 55: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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)

Page 56: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

Doing the “the math”: cavity expansion

March 9, 2018

qc =CQ Plimit

Cavity displacement

Cavity p

ressure

Bishop, Mott & Hill (1945)

Page 57: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

Scaling factor and data scatter

March 9, 2018 57

I169

E139

CQ

Page 58: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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)

Page 59: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

Generalization from Ticino to all CC sands

March 9, 2018 59

331 calibration tests

80% ± 0.04

Page 60: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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

Page 61: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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

Page 62: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

VSP by seismic CPT

van den berg ‘ICONE’

Page 63: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

Benders

March 9, 2018 63

Page 64: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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

Page 65: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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

Page 66: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

Drained to undrained transition…

Calaveras Dam 1918

Page 67: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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

Page 68: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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]

Page 69: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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

Page 70: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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

Page 71: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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)

Page 72: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

Laboratory tests not covered in glory...

March 9, 2018 72

80, 000

people

1971 San Fernando Earthquake

Page 73: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

So, post-liquefaction strengths from slides

March 9, 2018 73

Page 74: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

Looking at the mechanisms in case-histories

March 9, 2018 74

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

Page 75: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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

Page 76: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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

Page 77: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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

Page 78: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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

Page 79: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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

Page 80: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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

March 9, 2018 80

Page 81: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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

March 9, 2018 81

Page 82: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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

March 9, 2018 82

Page 83: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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 !

Page 84: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

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.

March 9, 2018 84

Page 85: 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history to current use “No equations…” Accompanying ‘briefing’ paper and software

Questions ?