2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history...
Transcript of 2018 Jennings Lecture - Geotechnical Division · Critical State Soil Mechanics 125 years of history...
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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
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Preamble
Loose sand… f = 31 deg
Dense sand… f = 44 deg
March 9, 2018 2
Why ?
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0 5 10 15 20 25
de
via
tor
str
ess,
q: kP
a
axial strain: %
NorSand
SCIUB
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0 100 200 300 400 500
meaneffec vestress,p':kPa
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North American Dam Construction ~ 1900
March 9, 2018 3
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100 years ago…
Calaveras Dam 1918
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1885: Distortion causes dilation
March 9, 2018 5 Reynolds, 1885
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Franklin Falls (NH) 1935
‘sand flow failure'
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1939: Fort Peck Dam
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10 100
VoidRa
o
s'3: psi
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Critical state locus: CLAYS ~1955
March 9, 2018 8
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Castro: SANDS - Load controlled tests (1969)
March 9, 2018 9
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Critical State Locus: SANDS and SILTS ~ 1990
0.45
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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
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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
✔
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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
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Soil strength as two components
March 9, 2018 [Taylor-Bishop, 1948-50]
Friction
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IDEA 2: Stress-dilatancy at all strains ~1960
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-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)
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Actual soil behaviour: h = Mf - D
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Stressra
oh
Dilatancy,D
OCCstress-dilatancy
DENSE
Stress-dilatancyfromTaylor-Bishopdissipa onofplas cwork
LOOSE
Mf(thistest)
STATE-DILATANCYdetermineshowfarstress-dilatancycandevelop
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IDEA 3: Plasticity
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deviatorstress,q
:kPa
axialstrain,e1:%
Elastic
Plastic
e = ep + ee
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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
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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
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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
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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
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IDEA 4: ‘Normality’ (associated flow rule)
Soil Liquefaction Fig 3-1 9/29/2014
March 9, 2018 21
P2 > P1
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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
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CSSM: Cam Clay
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s q , eq
s m , ev
M (fcv)
“Coulomb line” log(s m )
Dp = M – q/p’
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Original Cam Clay works…
March 9, 2018 24
0"
100"
200"
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400"
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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
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…but not in general (~1975)
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void
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tio
mean effective stress, p': kPa
CSL
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ess,
q: kP
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axial strain: %
In nearly all situations Cam Clay is much too stiff,
much too strong and dilates unlike real soils…
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March 9, 2018 26
100 year history of mechanics…
can “the math” be that wrong ?
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28
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Berms details
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Constructing the berm…
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CPT resistance in hydraulically placed sand
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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
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Void ratio from the CPT
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And now re-plot in familiar form…
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vo
id r
ati
o
vertical effective stress: kPa
cpt16
cpt14
cpt01
cpt03
cpt09
cpt02
March 9, 2018
Normally
consolidated
hydraulic fill
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General pattern of soil behaviour
March 9, 2018 35
Fraction of fill
looser than
the NCL
plotted
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AXIOMS (fundamental assumptions)
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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
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Axiom 2 Dmin = c y-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
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Dmin
stateparameteryatDmin
Nerlerk sand
Erksak sand
Brasted Sand
Weald Clay
London Clay
SandDilation_r13.xls
DatafromParry(1958)seetext
March 9, 2018 37
c
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AXIOM 2: hmax = M c y
March 9, 2018
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-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
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General CSSM: NorSand (1993)
March 9, 2018
Dmin = c y
Axiom 2:
pi
Mi = f(M,y)
OCR
Equations in paper
pc
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Calibration in drained triaxial compression
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volu
metr
ic s
train
: %
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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
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Predict all other soil behaviours…
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De
via
tor
str
ess,
q (
kP
a)
NorSand
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Mean stress, p' (kPa)
Test C609 y0 = +0.07
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Axial strain (%)
De
via
tor
str
ess, q
(kP
a)
NorSand
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Mean stress, p' (kPa)
Test L601 y0 = +0.025
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Axial strain (%)
Devia
tor
str
ess,
q (
kP
a) NorSand
0
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600
800
0 200 400 600 800
Mean stress, p' (kPa)
Test C634 y 0 = -0.08
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Cyclic simple shear of Fraser River Sand
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cycle
PW
P:
kP
aNorSand
Measured
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-10
-5
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15
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Mean effective stress: kPa
Tau
_V
H:
kP
a
-15
-10
-5
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5
10
15
-6 -4 -2 0 2 4 6
Gamma_VH: %
Tau
_V
H:
kP
a
0
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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
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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
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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
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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
✔
✔
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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
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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
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Minimal triaxial tests on representative soil
March 9, 2018 48
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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
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Measuring void ratio accurately: e = Gs w
March 9, 2018 50
Sladen & Handford (1987)
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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
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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)
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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
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CPT calibrations in sand
March 9, 2018 54
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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)
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Doing the “the math”: cavity expansion
March 9, 2018
qc =CQ Plimit
Cavity displacement
Cavity p
ressure
Bishop, Mott & Hill (1945)
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Scaling factor and data scatter
March 9, 2018 57
I169
E139
CQ
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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)
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Generalization from Ticino to all CC sands
March 9, 2018 59
331 calibration tests
80% ± 0.04
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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
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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
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VSP by seismic CPT
van den berg ‘ICONE’
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Benders
March 9, 2018 63
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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
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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
✔
✔
✔
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Drained to undrained transition…
Calaveras Dam 1918
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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
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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]
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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
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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
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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)
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Laboratory tests not covered in glory...
March 9, 2018 72
80, 000
people
1971 San Fernando Earthquake
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So, post-liquefaction strengths from slides
March 9, 2018 73
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Looking at the mechanisms in case-histories
March 9, 2018 74
Tar Island Dyke Upstream failure (Plewes et al, 1989)
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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
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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
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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
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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
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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
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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
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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
March 9, 2018 81
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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
March 9, 2018 82
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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 !
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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
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Questions ?