S3-06 TATSUOKA Stress-Strain behaviour of …...Stress – strain properties of soil: (A) actual complicated behaviour vs. (B) simplified model Stress-strain behaviour of compacted
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Session : 3
Stress-strain behaviour of compacted soils
related to seismic earth-fill dam stability
Tatsuoka, F. Tokyo University of Science, Japan
International Symposium
Qualification of dynamic analyses of dams and their equipments
and of probabilistic assessment seismic hazard in Europe
2Stress-strain behaviour of compacted soils related to seismic earth-fill dam stability | 2016
Several important features of the drained & saturat ed-undrained stress-strain properties of soil in monotonic & cyc lic loadings related to the seismic stability of earth-fill dam
●Practical simplified seismic stability analysis needs appropriate balance among the methods chosen in the following items:1) Criterion to evaluate of the stability:
Global safety factor relative to a specified required minimum vs. Residual deformation relative to a specified allowable largest.
2) Design seismic load at a given site:Conventional design load vs. Likely largest load in the future
3) Stress – strain properties of soil:Actual complicated behavior vs. Simplified model
4) Relevant consideration of the effects of other engineering factors:- compacted dry density; soil type; etc.
Several important features of the drained & saturat ed-undrained stress-strain properties of soil in monotonic & cyc lic loadings related to the seismic stability of earth-fill dam
●Practical simplified seismic stability analysis needs appropriate balance among the methods chosen in the following items:1) Criterion to evaluate of the stability:
Global safety factor relative to a specified required minimum vs. Residual deformation relative to a specified allowable largest.
2) Design seismic load at a given site:Conventional design load vs. Likely largest load in the future
3) Stress – strain properties of soil:Actual complicated behavior vs. Simplified model
4) Relevant consideration of the effects of other engineering factors:- compacted dry density; soil type; etc.
SUMMARY-2
3Stress-strain behaviour of compacted soils related to seismic earth-fill dam stability | 2016
Main topic in this presentation
Stress – strain properties of soil:(A) actual complicated behaviour vs. (B) simplified model
4Stress-strain behaviour of compacted soils related to seismic earth-fill dam stability | 2016
(A) actual complicated behavioura) Peak strength corresponding to actual compacted dry densityb) Anisotropic stress – strain properties as a function of δc) Plane strain condition in many casesd) Strain-softening associated with shear banding with the thickness increasing with D50
e) Progressive failure as a result of d)among others.
0
(B)
(A)
Constant strength irrespective of ε
σ
ε
Strain-softening
Peak strength only at a certain ε
Residual strength
Plane strain conditions
1σShear band
δ
(B) simplified model (explained in this presentation)
a) Design strength corresponding to conservatively (but not excessively) determined compacted dry density
b) Isotropic stress – strain propertiesc) Strength by triaxial compression test
at δ= 90o
d) Strain-softening associated with shear banding with the thickness increasing D50 to account for the effects of compaction & particle size
e) No progressive failure in the limit equilibrium-based stability analysis
Good balance is required among simplifications a), b), c) and e)
d) is to encourage good compaction
Stress – strain properties of soil:(A) actual complicated behaviour vs. (B) simplified model
0
(B)
(A)
Constant strength irrespective of ε
σ
ε
Strain-softening
Peak strength only at a certain ε
Residual strength
Plane strain conditions
1σShear band
δ
Discussions on these topics a) - e)
6Stress-strain behaviour of compacted soils related to seismic earth-fill dam stability | 2016
Dry
den
sity
, ρd
Water content, w
ρd (in-situ) in actual construction: averageeach measurement
Laboratory compaction curve by specified compaction energy level (CEL)
(ρd)max
wopt
Zero air voids (Sr= 100 %)
Allowable lower bound of ρd (e.g., Dc= 90 %) in field compaction control
(ρ d)max (laboratory tests)Dc =
ρ d (in-situ)× 100 (%)
The degree of compaction
Conservative determination of design soil shear strength under drained conditions- 1
Average of actual shear strength
Design shear strength- Often employed, but too conservative when well-compacted
7Stress-strain behaviour of compacted soils related to seismic earth-fill dam stability | 2016
Drained TC at σ’3= 50 kPaφpeak= arcsin[(σ’1- σ’3)/[(σ’1+σ’3)]max
Average of actual values
Typical allowable lower bound
The use of the design peak shear strength that is slightly lower than the value that corresponds to the target of Dc set equal to the anticipated average of actual values, together with the residual shear strength, is more realistic and can encourage better compaction (explained later)
Conservative determination of design soil shear strength under drained conditions- 2
9Stress-strain behaviour of compacted soils related to seismic earth-fill dam stability | 2016
Inherently anisotropic stress –strain behaviour under drained conditions- 1
Axial strain, ε1 (%)
Vol
umet
ric s
trai
n, ε
vol(%
)
δ (o) e4.9
σ’3= 392 kPa, loose
σ’3= 392 kPa, dense
δ (o) e4.9
εvol
εvol
σ’1/σ’3
σ’1/σ’3
Prin
cipa
l str
ess
ratio
, σ’
1/σ’
3
Drained PSC, saturated Toyoura sand
Pluviation through air
10Stress-strain behaviour of compacted soils related to seismic earth-fill dam stability | 2016
Inherently anisotropic stress –strain behaviour under drained conditions- 2
Axial strain, ε1 (%)
Vol
umet
ric s
trai
n, ε
vol(%
)
δ (o) e4.9
σ’3= 392 kPa, loose
σ’3= 392 kPa, dense
δ (o) e4.9
εvol
εvol
σ’1/σ’3
σ’1/σ’3
Prin
cipa
l str
ess
ratio
, σ’
1/σ’
3
Drained PSC, saturated Toyoura sand
Angle, δ (in degree)
Densee4.9= 0.685 – 0.714(except a with 0.666)
φ 0(δ
)/φ 0
(δ=
90o )
PS
C
σ1σ1
σ1σ1
Average (D)
Average (D)
Average for loose specimens
Average
σ’3 (kPa)4.9
9.8
49
98
392
Loosee4.9= 0.770 – 0.805except b (0.839) & c (0.836)
Summary
11Stress-strain behaviour of compacted soils related to seismic earth-fill dam stability | 2016
Inherently anisotropic stress –strain behaviour under drained conditions- 3
A similar trend among different
poorly-graded sands collected from different countries,
with and without a minimum
at δ= 20o – 30o, where the shear band direction coincides with
15Stress-strain behaviour of compacted soils related to seismic earth-fill dam stability | 2016
φ0= arcsin[(σ’1- σ’3)/[(σ’1+σ’3)]max
values in the direct shear test and the PSC test (δ= 40o-50o) are nearly the same, because both tests are plane strain tests with similar anisotropy effects.
Inherently anisotropic stress –strain behaviour under drained conditions- 7
Air-pluviated Toyoura sand
Void ratio, e (converted to the value measured at σ’3= 4.9 kPa)
16Stress-strain behaviour of compacted soils related to seismic earth-fill dam stability | 2016
φ0= arcsin[(σ’1- σ’3)/[(σ’1+σ’3)]max
values in the direct shear test and the TC test (δ= 90o) happen to be nearly the same due to cancelling out of the effects of anisotropy and (σσσσ’2 - σ’3)/(σ’1 - σ’3).
Inherently anisotropic stress –strain behaviour under drained conditions- 8
Air-pluviated Toyoura sand
Void ratio, e (converted to the value measured at σ’3= 4.9 kPa)
18Stress-strain behaviour of compacted soils related to seismic earth-fill dam stability | 2016
φss= arctan(τat/σ’a)max from the direct shear test is significantly lower than φ0 from TC test (δ= 90o).The use of φss in the slope stability analysis is usually too conservative.
Inherently anisotropic stress –strain behaviour under drained conditions- 10
Air-pluviated Toyoura sand
19Stress-strain behaviour of compacted soils related to seismic earth-fill dam stability | 2016
Inherently anisotropic stress –strain behaviour under drained conditions- 10
Air-pluviated Toyoura sand
Plane strain conditions
1σShear band
δ
0.0 30 60 90
Angle, δ (in degree)
φ 0(δ
)/φ 0
(δ=
90o )
PS
C
Drained PSCVoid ratio, e4.9
σ’3= 98 kPa:OCR= 1.0
e4.9= 0.8e4.9= 0.7
Tatsuoka et al. (1986a)Inferred based on
curve A
1.0
0.95
0.9
0.85
0.8
0.75
0.785 – 0.8010.696 – 0.713
X e= 0.67–0.68(Oda et al., 1978)
Drained TC
φ0(o) when e4.9= 0.7
φ0(o) when e4.9= 0.8
30
35
40
35
40
45
0.0 30 60 90
Angle, δ (in degree)
φ 0(δ
)/φ 0
(δ=
90o )
PS
C
Drained PSCVoid ratio, e4.9
σ’3= 98 kPa:OCR= 1.0
e4.9= 0.8e4.9= 0.7
Tatsuoka et al. (1986a)Inferred based on
curve A
1.0
0.95
0.9
0.85
0.8
0.75
0.785 – 0.8010.696 – 0.713
X e= 0.67–0.68(Oda et al., 1978)
Drained TC
φ0(o) when e4.9= 0.7
φ0(o) when e4.9= 0.8
30
35
40
35
40
45
φss= arctan(τat/σ’a)max from the direct shear test, much lower than the average strength along a circular failure plane under plane strain conditions.
TC strength (δ= 90o)
Particle diameter, D (mm)
20Stress-strain behaviour of compacted soils related to seismic earth-fill dam stability | 2016
Strain-softening associated with shear banding under drained plane strain conditions- 1
Uniform granular materials
The stress is plotted against “strain averaged for the whole specimen”, not representative of the strain in the shear band.
Particle diameter, D (mm)
8 cm
us
21Stress-strain behaviour of compacted soils related to seismic earth-fill dam stability | 2016
Strain-softening associated with shear banding under drained plane strain conditions- 2
us: shear displacement along a shear band(us)peak: values of us at the peak stress
(very small)
Uniform granular materials
Peak
Residual
Larger D50
22Stress-strain behaviour of compacted soils related to seismic earth-fill dam stability | 2016
Strain-softening associated with shear banding under drained plane strain conditions- 3
0.1 1 100
50
100
Chert/CL
Particle size (mm)
Par
cent
pas
sing
in w
eigh
t
Andesite 2 Andesite 1Greenrock/CL
Chert/CH
Isomi*
Hime*
Hasaki*
S.L.B.*
Ticino*
Glass ballotini*
Hostun*
Monterey*
Karlsruhe*
Toyoura*
Wakasa*
Ottawa*
PSC tests on many poorly- & well-graded gravelly soils
57cm
Andesite 2(D50= 2.49 mm & Uc= 4.1),
at ε1 = 4.25 %, σ’3= 314 kPa
Large PSC test
23Stress-strain behaviour of compacted soils related to seismic earth-fill dam stability | 2016
Strain-softening associated with shear banding under drained plane strain conditions- 3
0.1 1 100
50
100
Chert/CL
Particle size (mm)
Par
cent
pas
sing
in w
eigh
t
Andesite 2 Andesite 1Greenrock/CL
Chert/CH
Isomi*
Hime*
Hasaki*
S.L.B.*
Ticino*
Glass ballotini*
Hostun*
Monterey*
Karlsruhe*
Toyoura*
Wakasa*
Ottawa*
0 5 10 15 200.0
0.2
0.4
0.6
0.8
1.0
Poorly graded granular materials(Yoshida and Tatsuoka 1997)
Test name NIU6 NIU7 NIU8 NIU9 an2-1 an2-2 an2-3 an2-4
toku1 toku2 toku3 toku4 NIU1 NIU2 NIU3 NIU4
us*= u
s-(u
s)peak
(mm)
She
ar s
tres
s le
vel,
Rn
(us*) res
0.05
Larger shear deformation of shearband for larger D50 why ?
Larger D50
PSC tests on many poorly- & well-graded gravelly soils
24
Strain-softening associated with shear banding under drained plane strain conditions- 5
(us*)res
tr
At the start ofresidual state
0 5 10 15 200
5
10
15
: Poorly graded (Yoshida and Tatsuoka 1997)
Res
idua
l she
ar d
efor
mat
ion,
(u s* ) re
s (m
m)
Thickness of shear band, tr (mm)
: Well-graded (Okuyama et al. 2003)
Linear fitting:y = 0.7989 xR2 = 0.7288
Non-linear fittingy=1.44*X0.760
(R2 = 0.803)
(us*) res increases with shear band thickness, tr, for a similar shear strain in the shear band
0.1 1 100.5
1
10
1:51:101:20
She
ar b
and
thic
knes
s, t r (
mm
)
Particle size, D50
(mm)
Poorly graded (Yoshida and Tatsuoka, 1997)
An2 (well-graded) Chert (NIU: well-graded) Green rock (Tokuyama; well-graded)
(Desrues and Viggiani, 2004)
50
Hostun sand
tr= c(D
50)0.66
tr increases with D50
0 1 2 30
5
10
15
Res
idua
l she
ar d
ispl
acem
ent,
(us*
) res
Particle mean diameter, D50
(mm)
Regression curve
y = ax0.66
R2=0.89
Yoshida & Tatsuoka (1997) Okuyama et al. (2003) Average
So, (us*) res increases with D50
Slightly non-linear relation
25
Strain-softening associated with shear banding under drained plane strain conditions- 6
0.1 1 100
50
100
Chert/CL
Particle size (mm)
Par
cent
pas
sing
in w
eig
ht
Andesite 2 Andesite 1Greenrock/CL
Chert/CH
Isomi*
Hime*
Hasaki*
S.L.B.*
Ticino*
Glass ballotini*
Hostun*
Monterey*
Karlsruhe*
Toyoura*
Wakasa*
Ottawa*
Poorly- & well-graded gravelly soil
Normalization as us/(D50)0.66 : still a noticeable scatter, but no systematic effects of Uc, σ3, density, strain rate, …..
Useful to infer the Rn – us relation for a given D50
to be used in the slip displacement analysis by the Newmark method.
0 5 10 15 200.0
0.2
0.4
0.6
0.8
1.0
Poorly graded sands & gravels (Yoshida and Tatsuoka 1997)Curves with symbols: Well graded gravels (Okuyama et al., 2003)
She
ar s
tres
s le
vel,
Rn
(us-u
s.peak)/D
50
0.66 (us and D
50 in mm)
26Stress-strain behaviour of compacted soils related to seismic earth-fill dam stability | 2016
Strain-softening associated with shear banding under drained plane strain conditions- 7
On the other hand, the friction angle decreases with an increase in theparticle size in drained TC keeping the Dmax/specimen size constant!
This trend is inconsistent with our intuition that the slope becomes morestable with an increase in the particle size.
University of California, Berkeley (Marachi et al., 1969)
Ang
le o
f int
erna
l fric
tion
to th
e or
igin
,φ
0(in
deg
ree)
Crushed Basalt (Uc= 10)
σ3= 2.1 kgf/cm2
σ3= 10.0 kgf/cm2
σ3= 30.0 kgf/cm2
σ3= 46.4 kgf/cm2
Maximum particle size (inch)
Specimen size; 7.1 cm d x 17.8 cm h
30.5 cm d x 76 cm h
91.5 cm d x 228 cm h
27Stress-strain behaviour of compacted soils related to seismic earth-fill dam stability | 2016
Strain-softening associated with shear banding under drained plane strain conditions- 8
University of California, Berkeley (Marachi et al., 1969)
Pyramid dam material (Uc= 8)
σ3= 2.1 kgf/cm2
σ3= 10.0 kgf/cm2
σ3= 46.4 kgf/cm2
Ang
le o
f int
erna
l fric
tion
to th
e or
igin
,φ
0(in
deg
ree)
Maximum particle size (inch)
σ3= 30.0 kgf/cm2
Oroville dam material (Uc= 40)
σ3= 2.1 kgf/cm2
σ3= 10.0 kgf/cm2
σ3= 30.0 kgf/cm2
σ3= 46.4 kgf/cm2
Ang
le o
f int
erna
l fric
tion
to th
e o
rigin
, φ
0(in
deg
ree)
Maximum particle size (inch)
On the other hand, the friction angle decreases with an increase in theparticle size in drained TC keeping the Dmax/specimen size constant!
This trend is inconsistent with our intuition that the slope becomes morestable with an increase in the particle size.
28Stress-strain behaviour of compacted soils related to seismic earth-fill dam stability | 2016
Strain-softening associated with shear banding under drained plane strain conditions- 9
One method to alleviate this contradiction in the seismic design, at least partly, is the evaluation of slip displacement by the Newmark method taking into account the effects of D50 on the Rn – us relation.
0 5 10 15 200.0
0.2
0.4
0.6
0.8
1.0
Poorly graded granular materials(Yoshida and Tatsuoka 1997)
Test name NIU6 NIU7 NIU8 NIU9 an2-1 an2-2 an2-3 an2-4
toku1 toku2 toku3 toku4 NIU1 NIU2 NIU3 NIU4
us*= u
s-(u
s)
peak (mm)
She
ar s
tres
s le
vel,
Rn
(us*) res
0.05
Larger D50
On the other hand, the friction angle decreases with an increase in theparticle size in drained TC keeping the Dmax/specimen size constant!
This trend is inconsistent with our intuition that the slope becomes morestable with an increase in the particle size.
29Stress-strain behaviour of compacted soils related to seismic earth-fill dam stability | 2016
Undrained stress- strain behaviour of saturated soil
1. Effects of dry density:- much larger than those on drained strength; and- become more significant by effects of preceding cyclic
undrained loading.
2. Degradation of the undrained stress-strain properties and strength in the course of cyclic undrained loading:
- more when more cyclically sheared undrained; and - how to model this trend for numerical analysis ?Simplified model for simplified numerical analysis* vs.Full model for rigorous numerical analysis
(* explained in this presentation)
30Stress-strain behaviour of compacted soils related to seismic earth-fill dam stability | 2016
Undrained stress- strain behaviour of saturated soil:1. Effects of dry density - 1
Effective stress ratio, σ’v/σ’ vc
She
ar s
tres
s ra
tio, τ v
h/σ’ v
c
Torsional simple shearToyoura sandConsolidated at σ’vc= σ’vc= 98 kPa
Range of drained peak strength state for Dr= 33.6 % -94.4 %
The figures indicate Dr (%).
Drained
Undrained
31
Drained
Undrained
Drained
Shear strain, γvh (%)
Vol
umet
ric s
trai
n (%
)
The figures indicate Dr (%).
Exp
ansi
on
Shear strain, γvh (%)
She
ar s
tres
s ra
tio, τ
vh/σ
’ vc
Torsional shear, Toyoura sandIsotropically consolidated to σ’vc= σ’vc= 98 kPa
In drained tests, the peak strength is noticeably different with largely different volume changes for different dry densities (or different Dr
values) !
Undrained stress- strain behaviour of saturated soil:1. Effects of dry density - 2
32
Effective stress ratio, ' / 'v vcσ σS
hear
str
ess
ratio
,
Torsional simple shearToyoura sandConsolidated at
Effective stress paths
Range of drained peak strength state for Dr= 33.6 % -94.4 %
The figures indicate Dr (%).
Drained
Undrained
She
ar s
tres
s ra
tio,
She
ar s
tres
s ra
tio,
Torsional simple shearToyoura sandConsolidated at
Shear strain, γvh (%)
The figures indicate Dr (%).
Undrained
Drained
σv’ changes at a constant volume !
In undrained tests, the effective stress path is largely different with largely different peak strengths for different densities !
Undrained stress- strain behaviour of saturated soil:1. Effects of dry density - 3
33Stress-strain behaviour of compacted soils related to seismic earth-fill dam stability | 2016
B: undrained peak stress ratio necessary to develop 15 % shear strain
Number of loading cycle, Nc= 5
34Stress-strain behaviour of compacted soils related to seismic earth-fill dam stability | 2016
1) ML drained shear strength increases with Dr, but the increase is not very large: e.g., only about 10 % when Dr= 70 % → 90 %.
2) In the stability analysis based on the drained shear strength, the benefit of compaction is large, but not as large as the one when based on undrained shear strength.
Undrained stress- strain behaviour of saturated soil:1. Effects of dry density - 5
B: undrained peak stress ratio necessary to develop 15 % shear strain
Number of loading cycle, Nc= 5
36Stress-strain behaviour of compacted soils related to seismic earth-fill dam stability | 2016
1) Undrained cyclic shear strength increases with Dr, significantly when Drbecomes larger than a certain value: e.g., by a factor of three when Dr= 70 % → 90 %.
2) Significant benefits can be obtained by compaction to Dr higher than a certain value.
Undrained stress- strain behaviour of saturated soil:1. Effects of dry density - 7
B: undrained peak stress ratio necessary to develop 15 % shear strain
Number of loading cycle, Nc= 5
37Stress-strain behaviour of compacted soils related to seismic earth-fill dam stability | 2016
These undrained shear strengths, B & C, are necessary, but not sufficient, to evaluate the residual deformation by: a) slip displacement analysis
by Newmark-D method; and
b) residual deformation analysis by pseudo-static non-linear FEM.
Undrained stress- strain behaviour of saturated soil:1. Effects of dry density - 8
38
Undrained stress- strain behaviour of saturated soil to evaluate the residual displacement/deformation-1
Minimum safety factor by LE analysis, Fs
Res
idua
l dis
plac
emen
t/def
orm
atio
n
Allowable value
1.0
2. Slip displacement obtained by the Newmark method
1. Residual deformation obtained by pseudo-static non-linear FEM not including slip displacement
3. Total residual displacement/deformation:1. Residual deformation not including slip
displacement; plus2. Slip displacement
Fs against Level 2 design seismic load
Estimated total ultimate residual displacement/deformation
Perfect-plastic behavior without degradation during seismic loading is assumed
0
τ
τinitial
ssss eeee
Shear strain, γ
Undrained τ~γ relation
In pulse n
Initial
Continuous degradation by undrained CL
γ+
γDA
“Increments of slip displacement” in all pulses where slip takes place (such as s→e) are integrated to obtain the ultimate residual slip displacement
0
τw
τi
Apparent working shear stress, τw
ssss eeee
Time
Time history of apparent irregular working stress τw obtained by total stress seismic response analysis not taking into account both strength degradation by undrained CL and slip failure
Pulse n
Three consecutive zero-crossing points Actual τw (= soil shear strength, τf)
decreasing by cyclic undrained loading
Actual τ~γ behavior of soil
Undrained stress- strain behaviour of saturated soil to evaluate the residual displacement/deformation - 2
40
Undrained stress- strain behaviour of saturated soil- Undrained strength during cyclic undrained loading for slip
displacement analysis by Newmark-D method - 1:
地震
動
によ
る荷
重
時間
損傷
ひず
み
土の
強度
すべ
り
変位
繰返
し
応力
振幅
損傷ひずみ=1%, 2%, 5%など
土の
強度
損傷ひずみ
繰返し載荷回数
時間
時間
時間
通常のニューマーク法と同様の
手順ですべり変位を計算
(a)
(b)
(c)
(d)
(e)
(f)
ニューマーク法の手順に従って
すべり変位を計算
Sei
smic
lo
adD
amag
e st
rain
Soi
l st
reng
thS
eism
ic
load
Dam
age
stra
inS
lipdi
spla
cem
ent
Time
Time
Time
Time
Damage strain=1%、2%、5%….
log(Nc)
Damage strain
Soi
l st
reng
thC
yclic
str
ess
ampl
itude
Calculation of slip displacementby the Newmark-D method
Laboratory stress-strain testsTime histories of stress, strain and slip
Stress-strain behaviour of compacted soils related to seismic earth-fill dam stability | 2016
41
0
20
40
60
80
100
0.001 0.01 0.1 1 10
通過
質量
百分
率(%
)
粒径(mm)
‧ 土粒子密度: 2.67g/cm3
‧ 平均粒径 : 0.204mm
‧ 均等係数 : 17.0
‧ 細粒分含有率 : 13.6%
Hokota sandD50= 0.20 mmUc= 17.0Fc= 13.6 %
Per
cent
pas
sing
in w
eigh
t
Particle diameter, D (%)0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.1 1 10 100
繰返
し応
力振
幅比
, τd/
σ’m
i
繰返し載荷回数, N
εdamage=1%, 2%, 5%, 10%τi/σ’mi
緩詰め
中詰め
密詰め
0.50
× ∗ - +× ∗ - +× ∗ - +× ∗ - +
緩詰め
密詰め
中詰め
(Dc)1Ec85%90%95%
Number of loading cycles, Nc
Cyc
lic s
tres
s ra
tio,
95%
90%
85%
Stress-strain behaviour of compacted soils related to seismic earth-fill dam stability | 2016
Typical example of cyclic undrained triaxial tests on isotropically consolidated specimens compacted to (Dc)1Ec= 85 %; 90 % and 95 %
Undrained stress- strain behaviour of saturated soil- Undrained strength during cyclic undrained loading for slip
displacement analysis by Newmark-D method - 2:
42Stress-strain behaviour of compacted soils related to seismic earth-fill dam stability | 2016
地震
動
によ
る荷
重
時間
損傷
ひず
み
土の
強度
すべ
り
変位
繰返
し
応力
振幅
損傷ひずみ=1%, 2%, 5%など
土の
強度
損傷ひずみ
繰返し載荷回数
時間
時間
時間
通常のニューマーク法と同様の
手順ですべり変位を計算
(a)
(b)
(c)
(d)
(e)
(f)
ニューマーク法の手順に従って
すべり変位を計算
Sei
smic
lo
adD
amag
e st
rain
Soi
l st
reng
thS
eis
mic
lo
adD
ama
ge
stra
inS
lipd
isp
lace
me
nt
Time
Time
Time
Time
Damage strain=1%、2%、5%….
log(Nc)
Damage strain
So
il st
ren
gth
Cyc
lic s
tres
s a
mpl
itud
eCalculation of slip displacementby the Newmark-D method
Laboratory stress-strain testsTime histories of stress, strain and slip
Undrained stress- strain behaviour of saturated soil- Undrained strength during cyclic undrained loading for slip
displacement analysis by Newmark-D method - 3:
43Stress-strain behaviour of compacted soils related to seismic earth-fill dam stability | 2016
0.00 0.05 0.10 0.15 0.20 0.25 0.30
-1
0
1
2
3
4
5
6
7
i cycle
2τcyc,i
= τmax,i
-τmin,i
τmin,i
τmax,i
zero-crossing
S(t)=τcyc,i
/σinit
: shear stress ratio
τinit
τ (t)
t
Buffer zone (i.e., zero-crossing is defined only by full crossing of this zone)
Pulse i
Zero-crossing point
Definition of a pulse
Undrained stress- strain behaviour of saturated soil- Undrained strength during cyclic undrained loading for slip
displacement analysis by Newmark-D method - 4:
44Stress-strain behaviour of compacted soils related to seismic earth-fill dam stability | 2016
log(number of loading cyclic, Nc)
Relationship between SR and “Nc
necessary to develop a given damage strain*” obtained by a series of uniform cyclic undrained tests
SR
Ni
Damage for damage strain* by pulse i : Di= (1/Ni)
SRi
SRi= τcyc,i/σ’0: cyclic stress ratio of pulse i τcyc,i: shear stress amplitude; and σ’0: initial effective confining stress
Cumulative damage concept
Undrained stress- strain behaviour of saturated soil- Undrained strength during cyclic undrained loading for slip
displacement analysis by Newmark-D method - 5:
45
log(number of loading cyclic, Nc)
Relationship between SR and “Nc
necessary to develop a given damage strain*” obtained by a series of uniform cyclic undrained tests
SR
Ni
Damage for damage strain* by pulse i : Di= (1/Ni)
SRi
Cumulative damage concept
Total damage for damage strain* caused by a series of irregular pulses until the end of pulse n: If D becomes 1.0 at the end of pulse n, it is assumed that this damage strain * takes place in pulse n.
1 1
1n n
iii i
D DN= =
= =∑ ∑
Undrained stress- strain behaviour of saturated soil- Undrained strength during cyclic undrained loading for slip
displacement analysis by Newmark-D method - 6:
46
log(number of loading cyclic, Nc)
Relationship between SR and “Nc
necessary to develop a given damage strain*” obtained by a series of uniform cyclic undrained tests
SR
Ni
Damage for damage strain* by pulse i : Di= (1/Ni)
SRi
Cumulative damage concept
Then, we can find the damage strain at the end of pulse n at which the
total damage becomes 1.0.1
1n
ii
DN=
=∑
Undrained stress- strain behaviour of saturated soil- Undrained strength during cyclic undrained loading for slip
displacement analysis by Newmark-D method - 7:
47
log(number of loading cyclic, Nc)
Relationship between SR and “Nc
necessary to develop a given damage strain*” obtained by a series of uniform cyclic undrained tests
SR
Ni
Damage for damage strain* by pulse i : Di= (1/Ni)
SRi
Cumulative damage concept
By this procedure, “a given time history of irregular cyclic stresses causing a certain damage strain can be converted to “uniform cyclic stresses with an arbitrary combination of SR & Nc that develops the same damage strain”.
Undrained stress- strain behaviour of saturated soil- Undrained strength during cyclic undrained loading for slip
displacement analysis by Newmark-D method - 8:
0
τw
τi
sssssssseeee
Uniform cyclic stresses equivalent to “irregular working stresses before the start of pulse n” obtained by the cumulative damage concept.
59Stress-strain behaviour of compacted soils related to seismic earth-fill dam stability | 2016
Undrained stress- strain behaviour of saturated soil- Undrained strength during cyclic undrained loading for slip
displacement analysis by Newmark-D method - 20:
地震
動
によ
る荷
重
時間
損傷
ひず
み
土の
強度
すべ
り
変位
繰返
し
応力
振幅
損傷ひずみ=1%, 2%, 5%など
土の
強度
損傷ひずみ
繰返し載荷回数
時間
時間
時間
通常のニューマーク法と同様の
手順ですべり変位を計算
(a)
(b)
(c)
(d)
(e)
(f)
ニューマーク法の手順に従って
すべり変位を計算
Sei
smic
lo
adD
amag
e st
rain
Soi
l st
reng
thS
eis
mic
lo
adD
ama
ge
stra
inS
lipd
isp
lace
me
nt
Time
Time
Time
Time
Damage strain=1%、2%、5%….
log(Nc)
Damage strain
So
il st
ren
gth
Cyc
lic s
tres
s a
mpl
itud
eCalculation of slip displacementby the Newmark-D method
Laboratory stress-strain testsTime histories of stress, strain and slip
Contour of soil shear strength
Newmark-D
TimeTime
TimeTime
Slip displacement, δ=R⋅θ Slip displacement, δ=R⋅θ
Yield seismic coefficient
Yield seismic coefficient
Contour of soil shear strength
Newmark-O
Circular slide 2
Damage strain contour
0 20 40 60 80 100 120 140 160-4.0
-2.0
0.0
2.0
4.0
-0.1
0.0
0.1
. θ [r
ad/s
]..
0.00
0.01
0.02
Elapsed time [sec]
0
3
6
9
yield acceleration
Start of slip:
63.39sec.
δ
max
=5.350 m
Acc
[m/s
2 ]θ
[ra
d/s2 ]
δ=R
⋅θ [m
]
Settlement
0 10 20 30 40 50 (m)
Slide 4
Slide 2
SedimentSlide 3
Reservoir Downstream
Masonry wall
Slide 1
Slip displacement by Newmark-D analysis of old Fujinuma dam, which collapsed by the 2011 Great East Japan Earthquake
Very large ultimate slip displacement:-Slip continues after the moment of peak acceleration (t= 97.01 s) due to continuing deterioration in the undrained shear strength.
62Stress-strain behaviour of compacted soils related to seismic earth-fill dam stability | 2016
Undrained stress- strain behaviour of saturated soil- Undrained stress – strain relation in the course of cyclic
undrained loading modelled for residual deformation analysis by pseudo-static non-linear FEM - 1 :
V
h
r
τvh
σv’
σh’
σ1’
σr’
Horizontal bedding plane
εv=0εh=0
γvh
Axial load, W
Torque, T
po’
pi’
α
Cyclic undrained torsional simple shear test on dense Toyoura sand applying ‘seismic’ random stresses at a constant shear strain rate
f Air-pluviated Toyoura sand (e= 0.778)Cyclic undrained simple shear
(a)
-5 -4 -3 - 2 -1 0 1 2 3 4 5Shear strain, γvh (%)
0.5
0.4
0.3
0.2
0.1
0.0
-0.1
-0.2
-0.3
She
ar s
tres
s, τ
vh(x
98 k
Pa)
gi
c
a1, a2
d1, d2
f’’
f’
f
h
j
e
(c)
b1, b2
o
F
y1
y2
A
- 2 -1 0 1 2 3Shear strain, γvh (%)
0.6
0.4
0.2
0.0
-0.2
-0.4
-0.6
She
ar s
tre
ss r
atio
, τvh
/σv’
e
b
c
¥
d
f
f'
f’’
h
g
oF
Complicated τvh – γvh relation, but smooth strain-hardening hysteretic τvh/σ’v –γvh relation:- Yielding starts when τvh/σ’v exceeds the
previous maximum value in each direction.
- The γvh value at the peak τvh/σ’v state after having passed the yielding point (e.g. point h) can be determined only by the peak τvh/σ’vvalue and the ML stress – strain relation starting from the origin (i.e., o→y1→F→h), not referring to previous cyclic loading histories.
68
The γvh value at the peak τvh/σ’v state after having passed the yielding point (e.g. point h) obtained by following the reloading τvh – γvh
relation (e.g. f’→y2→F→h) is the same as the value obtained by following the monotonic loading τvh – γvh relation starting from the origin (e.g. o→y1→F→h) while not referring to previous cyclic loading histories.
f Air-pluviated Toyoura sand (e= 0.778)Cyclic undrained simple shear
(a)
-5 -4 -3 - 2 -1 0 1 2 3 4 5Shear strain, γvh (%)
0.5
0.4
0.3
0.2
0.1
0.0
-0.1
-0.2
-0.3
She
ar s
tres
s, τ
vh(x
98 k
Pa)
gi
c
a1, a2
d1, d2
f’’
f’
f
h
j
e
(c)
b1, b2
o
F
y1
y2
A
- 2 -1 0 1 2 3Shear strain, γvh (%)
0.6
0.4
0.2
0.0
-0.2
-0.4
-0.6
She
ar s
tre
ss r
atio
, τvh
/σv’
e
b
c
¥
d
f
f'
f’’
h
g
oF
69
The time history of the γvh value at the peakτvh/σ’v states after having passed the yielding point (e.g. the values at points f, h & j) can be obtained by following respective ML stress-strain relations starting from the origin, o, that have degraded by respective preceding cyclic undrained loading histories.
f Air-pluviated Toyoura sand (e= 0.778)Cyclic undrained simple shear
(a)
-5 -4 -3 - 2 -1 0 1 2 3 4 5Shear strain, γvh (%)
0.5
0.4
0.3
0.2
0.1
0.0
-0.1
-0.2
-0.3
She
ar s
tres
s, τ
vh(x
98 k
Pa)
gi
c
a1, a2
d1, d2
f’’
f’
f
h
j
e
(c)
b1, b2
o
F
y1
y2
A
- 2 -1 0 1 2 3Shear strain, γvh (%)
0.6
0.4
0.2
0.0
-0.2
-0.4
-0.6
She
ar s
tre
ss r
atio
, τvh
/σv’
e
b
c
¥
d
f
f'
f’’
h
g
oF
→ In a slope in which initial shear stresses are acting, most of the respective peak γvh value remains as the residual value upon unloading.
70
The time history of the residual deformation of a slope may be obtained by a series of pseudo-static non-linear FEM analyses incorporating gravity and seismic loads while using respective ML stress – strain relations starting from the origin.
Approximatedly, the maximum value of this deformation can be considered as the ultimate residual deformation caused by a given seismic loading history.
f Air-pluviated Toyoura sand (e= 0.778)Cyclic undrained simple shear
(a)
-5 -4 -3 - 2 -1 0 1 2 3 4 5Shear strain, γvh (%)
0.5
0.4
0.3
0.2
0.1
0.0
-0.1
-0.2
-0.3
She
ar s
tres
s, τ
vh(x
98 k
Pa)
gi
c
a1, a2
d1, d2
f’’
f’
f
h
j
e
(c)
b1, b2
o
F
y1
y2
A
- 2 -1 0 1 2 3Shear strain, γvh (%)
0.6
0.4
0.2
0.0
-0.2
-0.4
-0.6
She
ar s
tre
ss r
atio
, τvh
/σv’
e
b
c
¥
d
f
f'
f’’
h
g
oF
0 20 40 60 80 100 120 140 160
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Settlem
ent at dam
crest [m
]
Elapsed time [sec.]
Settlement at dam crest max=0.564m
(t=100.14sec.)
Settlement
0 10 20 30 40 50 (m)
Slide 4
Slide 2
SedimentSlide 3
Reservoir Downstream
Masonry wall
Slide 1
0 20 40 60 80 100 120 140 160
-400
-300
-200
-100
0
100
200
300
400
500
Naganuma motion record (FKSH08)
deconvoluted to Vs=450m/s rock bed
and to FEM model base
Acceleration [gal]
Elapsed time [sec]
FEM base input motion
dt=0.01s
data:16300
max=-315.2 gal
(t=97.01s)
A series of pseudo-static FEM analysis of old Fujinuma dam, which collapsed by the 2011 Great East Japan Earthquake
The largest deformation (at t= 100.14 s):-not by the peak acceleration (t= 97.01 s), but later after the stress-strain relation has deteriorated more.
Independent analyses
0 20 40 60 80 100 120 140 160
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Settlem
ent at dam
crest [m
]
Elapsed time [sec.]
Settlement at dam crest max=0.564m
(t=100.14sec.)
Settlement
0 10 20 30 40 50 (m)
Slide 4
Slide 2
SedimentSlide 3
Reservoir Downstream
Masonry wall
Slide 1
0 20 40 60 80 100 120 140 160
-400
-300
-200
-100
0
100
200
300
400
500
Naganuma motion record (FKSH08)
deconvoluted to Vs=450m/s rock bed
and to FEM model base
Acceleration [gal]
Elapsed time [sec]
FEM base input motion
dt=0.01s
data:16300
max=-315.2 gal
(t=97.01s)
A series of pseudo-static FEM analysis of old Fujinuma dam, which collapsed by the 2011 Great East Japan Earthquake
The largest deformation (at t= 100.14 s):-not by the peak acceleration (t= 97.01 s), but later after the stress-strain relation has deteriorated more.-This largest deformation is considered as the ultimate residual deformation.
73Stress-strain behaviour of compacted soils related to seismic earth-fill dam stability | 2016
Several important features of the drained & saturat ed-undrained stress-strain properties of soil in monotonic & cyc lic loadings related to the seismic stability of earth-fill dam
●Practical simplified seismic stability analysis needs appropriate balance among the methods chosen in the following items:1) Criterion to evaluate of the stability:
Global safety factor relative to a specified required minimum vs. Residual deformation relative to a specified allowable largest.
2) Design seismic load at a given site:Conventional design load vs. Likely largest load in the future
3) Stress – strain properties of soil:Actual complicated behavior vs. Simplified model
4) Relevant consideration of the effects of other engineering factors:- compacted dry density; soil type; etc.
Design seismic load at a given site:
Conventional design load:- specified in many old seismic design codes- defined as Level 1 design seismic load in new seismic
design codes (introduced after the 1995 Great Kobe E.-Q.)
Likely largest seismic load during the lifetime of a given structure:- defined as Level 2 design seismic motion in new seismic
design codes (introduced after the 1995 Great Kobe E.-Q.)
74Stress-strain behaviour of compacted soils related to seismic earth-fill dam stability | 2016
Japanese Society for Civil Engineers (1996) :•Level 1 design seismic motion: It is a seismic motion with a high likelihood of occurring during the design lifetime of the concerned structure. It is required that, in principle, all new structures have sufficient seismic resistance to ensure "no damage" when subjected to this seismic motion.•Level 2 design seismic motion: It is the strongest seismic motion thought likely to occur at the location of the concerned structure during its lifetime. It is required that the structure should not collapse, although damage that renders it unusable is acceptable if its functionality can be rapidly restored.
The relationship among “the design seismic load”, “design shear strength of soil” and “stability analysis method (i.e., global Fs vs. residual deformation)” is complicated due to historical reasons.
75Stress-strain behaviour of compacted soils related to seismic earth-fill dam stability | 2016
Fs=Strength/Load= 1
Shear strength of fill, τf
Working stress, τwLevel 1 Level 2
Stable
Collapse
A (stable)
B(collapsed)
Performance during severe E.Q.
Actual behavior during severe earthquakes
■ Well-compacted fill A:Examples: high rock fill damsmodern highway embankmentsmodern railway embankmentsearth-fill dams
■ Poorly-compacted fill B:Examples:old soil structures before
introduction of modern design and construction codes and methods
residential embankments
Fs=Strength/Load= 1
Shear strength of fill, τf
Working stress, τwLevel 1 Level 2
Stable
Collapse
A
B
A (stable)
B(collapsed)
Performance during severe E.Q.
Typical conventional seismic design of soil structureDesign seismic load (τw)d : kh= 0.15 (Level 1 seismic coefficient)Design shear strength (τf)d*: Drained shear strength when Dc by Standard
Proctor (1Ec) is equal to the required minimum value (e.g., 90 %)→ Required min. Fs by limit equilibrium stability analysis = 1.2, for example
■ Well-compacted fill A: The use of kh=0.15 as Level 2 seismic
load is on the unsafe side. However, the use of (τf)d* as the drained/ undrained strength of well-compacted fill is on the safe side.
→ These two factors may be balanced.
Conventional design of fill A:
1)Under-estimate of seismic load2)Under-estimate of soil shear strength
Fs=Strength/Load= 1
Shear strength of fill, τf
Working stress, τwLevel 1 Level 2
Stable
Collapse
B
A (stable)
B(collapsed)
Performance during severe E.Q.
A
■ Well-compacted fill A: The use of kh=0.15 as Level 2 seismic
load is on the unsafe side. However, the use of (τf)d* as the drained/ undrained strength of well-compacted fill is on the safe side.
→ These two factors may be balanced.
Conventional design of fill A:
1)Under-estimate of seismic load2)Under-estimate of soil shear strengthIf only kh is increased: i.e., if only (τw)d is
increased⇒Under-estimate of stability by losing balance (i.e., collapse despite actual stable performance against level) 2.Solution: 1) use of level 2 design seismic load; and 2) use of realistic high soil strength (τf)d
corresponding to actual Dc (> 90 %) (using undrained strength when relevant)
A
Realistic seismic design:1) Use of level 2 seismic load2) Use of realistic high soil strength
Typical conventional seismic design of soil structureDesign seismic load (τw)d : kh= 0.15 (Level 1 seismic coefficient)Design shear strength (τf)d*: Drained shear strength when Dc by Standard
Proctor (1Ec) is equal to the required minimum value (e.g., 90 %)→ Required min. Fs by limit equilibrium stability analysis = 1.2, for example
Fs=Strength/Load= 1
Shear strength of fill, τf
Working stress, τwLevel 1 Level 2
Stable
Collapse
A
B
A (stable)
B(collapsed)
Performance during severe E.Q.
■ Poorly-compacted fill B: The use of kh=0.15 as Level 2 seismic
load is on the unsafe side.Besides, the use of (τf)d* as “undrained
strength of saturated poorly-compacted fill subjected to seismic load” is on the unsafe side.
→ These two factors are not balanced.
Conventional design of fill B:
1)Under-estimate of seismic load2)Over-estimate of soil shear strength
Only an increase in kh is not sufficient, but use of realistic low (τw)d is necessary to duly evaluate the stability against level 2 seismic load.
Solution:1) use of level 2 design seismic load and; 2) use of realistic soil strength that is much lower than the conventional value (τf)d* if saturated/undrained during seismic loading
B
Realistic seismic design:1) Use of level 2 seismic load2) Use of realistic low soil strength
Typical conventional seismic design of soil structureDesign seismic load (τw)d : kh= 0.15 (Level 1 seismic coefficient)Design shear strength (τf)d*: Drained shear strength when Dc by Standard
Proctor (1Ec) is equal to the required minimum value (e.g., 90 %)→ Required min. Fs by limit equilibrium stability analysis = 1.2, for example
80Stress-strain behaviour of compacted soils related to seismic earth-fill dam stability | 2016
CONCLUDING REMARKS - 1
Several important factors that influence the drained &saturated-undrained stress-strain properties of soil when subjected to monotonic & cyclic loading histories related to the seismic stability analysis of soil structures, including earth-fill dams, were discussed. The following are the main conclusions:1) Compacted soils exhibit significant strain-softening associated with shear banding, resulting in progressive failure in a slope.2) As the thickness of shear band increases with D50, the rate of strain-softening becomes slower with D50 ,so the failure tends to become less progressive, making the slope more stable. 3) Although the effect of dry density on the drained peak shear strength is large, the effect on the undrained shear strength is much more significant.
81Stress-strain behaviour of compacted soils related to seismic earth-fill dam stability | 2016
CONCLUDING REMARKS - 2
4) The drained strength of compacted soil exhibits strong inherent anisotropy in plane strain compression. 5) The strength obtained by different stress-strain tests (i.e., triaxial and plane strain compression and direct shear) could be largely different due to the effects of different angles between the σ1 direction and the bedding plane direction; different ratios of σ2
to σ1 & σ3; and different definition of friction angle.
82Stress-strain behaviour of compacted soils related to seismic earth-fill dam stability | 2016
CONCLUDING REMARKS - 3
6) For the limit equilibrium-based stability analysis of a slope under plane strain conditions, a practical simplified method that assumes the followings, yet takes into account the effects of compacted dry density and particle size, can be proposed:
a) Isotropic stress-strain properties exhibiting strain-softening of which the rate decreases with an increase in D50.
b) Use of the peak & residual strengths determined by the conventional TC tests at δ= 90o,.
c) Use of the peak strength corresponding to somehow conservatively determined compacted dry density (i.e., slightly lower than the value that corresponds to the anticipated average of the actual values of Dc).
d) Progressive failure is not taken into account.
83Stress-strain behaviour of compacted soils related to seismic earth-fill dam stability | 2016
CONCLUDING REMARKS - 4
7) Under undrained monotonic loading conditions, loose & dense saturated soils exhibit the shear strength that is significantly lower and higher than the respective drained shear strengths. 8) The undrained shear strength decreases by preceding cyclic undrained loading. The effects of dry density on the damaged undrained shear strength are significant due to the following trends with an increase in the dry density:
a) the increase in the initial undrained shear strength; b) the decrease in the damage strain by preceding cyclic
undrained loading; and c) the decrease in the degradation rate by damage strain.
84Stress-strain behaviour of compacted soils related to seismic earth-fill dam stability | 2016
CONCLUDING REMARKS - 5
9) For simplified stability analysesof a slope having saturated zones by “slip deformation by the Newmark method” ad “residual deformation by the pseudo-static non-linear FEM”, the characteristic feature of undrained stress – strain properties described above can be modelled in a unified framework from the same results of a set of monotonic and cyclic loading lundrained stress – strain tests of saturated soil..