S3-06 TATSUOKA Stress-Strain behaviour of compacted soilscnpgb.apambiente.pt/IcoldClub/documents/EWGDamsEarthquakes... · Stress-strain behaviour of compacted soils related to seismic

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

31th August – 2nd September 2016 – Saint-Malo

Saint-Malo © Yannick LE GAL

SUMMARY-1

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.







SUMMARY-2


Main topic in this presentation

Stress – strain properties of soil:(A) actual complicated behaviour vs. (B) simplified model


(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


1σShear band

δ

Discussions on these topics a) - e)


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


1E-4 1E-3 0.01 0.1 1 10 100

0

20

40

60

80

100

DG

YG

NS, IS-I, IS -IV & IS-II

TS

RGSZ

RGYY

CGR

CCA

CBG2

CBG1

CBG1) Chiba gravel (1) CBG2) Chiba gravel (2) CCA) Crushed concrete aggregate CGR) Crushed gravel (for full-scale

GRS integral bridge model) RGYY)Round gravel for rock-fill dam

(Shin Yamamoto dam) RGSZ) Round gravel

(Mt. Fuji Shizuoka Airport) NS) Narita sand IS-I) Inagi sand I IS-II) Inagi sand II IS-IV) Inagi sand IV TS) Toyoura sand YG) Yoshinogawa gravel (cut grading) DG) Dokigawa gravel (cut grading)

Per

cent

age

pass

ing

by w

eigh

t

Particle diameter, d (mm)

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

Design shear strength is often determined to correspond to the allowable lower bound of Dc

used in field compaction control⇒ conservative with better compacted soil



1E-4 1E-3 0.01 0.1 1 10 100

0

20

40

60

80

100

DG

YG

NS, IS-I, IS -IV & IS-II

TS

RGSZ

RGYY

CGR

CCA

CBG2

CBG1

CBG1) Chiba gravel (1) CBG2) Chiba gravel (2) CCA) Crushed concrete aggregate CGR) Crushed gravel (for full-scale

GRS integral bridge model) RGYY)Round gravel for rock-fill dam

(Shin Yamamoto dam) RGSZ) Round gravel

(Mt. Fuji Shizuoka Airport) NS) Narita sand IS-I) Inagi sand I IS-II) Inagi sand II IS-IV) Inagi sand IV TS) Toyoura sand YG) Yoshinogawa gravel (cut grading) DG) Dokigawa gravel (cut grading)

Per

cent

age

pass

ing

by w

eigh

t

Particle diameter, d (mm)

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)



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



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



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

the bedding plane direction.


Drained PSCσ’3= 78.4 kPaOCR=1.0

1.0

0.95

0.9

0.85

0.8φ0

(δ)/

φ0(δ

= 9

0o )P

SC

0.0 30 60 90

σ1σ1

σ1

●

●

●

●

○

○

○

○

◇

◇

◇

■

■ △

△

△

▲

▲

□

□

□

●

▲

◆

◆

□

▲

●

● Toyoura sand○ S.L.B.□ Silica■ Karlsruhe△ Monterey▲ Ticino◇ Hostun◆ Glass beads



Hime

Koushu

Isomi

Particle diameter (mm)

Per

cen

tpas

sin

gby

wei

ght

Hime

Koushu*


1.0

0.9

0.8

φ 0(δ

)/φ 0

(δ=

90o )

PS

C

0.0 30 60 90

Air-dried gravel (* vibro-compacted)

Isomi*(σ’3=78.5 kPa)

Drained TC

Drained PSC

Koushu

Isomi

Drained TC


1σShear band

δ

A similar trend among different

poorly-graded gravelly soils produced by vertical vibratory

compaction



Hime

Koushu

Isomi

Particle diameter (mm)

Per

cen

tpas

sin

gby

wei

ght

Hime

Koushu*


1.0

0.9

0.8

φ 0(δ

)/φ 0

(δ=

90o )

PS

C

0.0 30 60 90

Air-dried gravel (* vibro-compacted)

Isomi*(σ’3=78.5 kPa)

Drained TC

Drained PSC

Koushu

Isomi

Drained TC


1σShear band

δ

The TC strength (δ= 90o) is

similar to, or smaller than, the average strength along a

circular failure plane under

plane strain conditions.



0.0 30 60 90


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


φ 0(δ

)/φ 0

(δ=

90o )

PS

C


σ’3= 98 kPa:OCR= 1.0

e4.9= 0.8e4.9= 0.7


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


1σShear band

δ

Air-pluviated Toyoura sand

The TC strength (δ= 90o)

is noticeably smaller than the average strength

along a circular failure

plane under plane strain conditions.

Void ratio, e (converted to the value measured at σ’3= 4.9 kPa)

50

0.6 0.7 0.8 0.930

φ0(PSC, δ=40o-50o)

φ 0an

d φ s

s(in

deg

ree)

35

40

45

φ0(TSS, σ’a= 98 kPa; σ’3= 35 – 44 kPa)

0 max

0 max

sin cos( )arctan

1 sin sin( )d

ssd

φ νφφ ν⋅=

− ⋅

Theoretical value

Measured φss=arctan(τat/σ’a) (TSS, σ’a= 98kPa)when τat/σ’a=maxwhen σ’1/σ’3=max

φ0(PSC, σ’3= 49 kPa, δ=90o)

φ0(TC, σ’3= 49 kPa, δ=90o)

'aσatτ

atτ−

'tσ

2'σ

0nε =

2 0ε =

1'σ3'σ

Stress condition in TSS test


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.




50

0.6 0.7 0.8 0.930

φ0(PSC, δ=40o-50o)

φ 0an

d φ s

s(in

deg

ree)

35

40

45

φ0(TSS, σ’a= 98 kPa; σ’3= 35 – 44 kPa)

0 max

0 max

sin cos( )arctan

1 sin sin( )d

ssd

φ νφφ ν⋅=

− ⋅

Theoretical value


φ0(PSC, σ’3= 49 kPa, δ=90o)

φ0(TC, σ’3= 49 kPa, δ=90o)

'aσatτ

atτ−

'tσ

2'σ

0nε =

2 0ε =

1'σ3'σ



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).




50

0.6 0.7 0.8 0.930

φ0(PSC, δ=40o-50o)

φ 0an

d φ s

s(in

deg

ree)

35

40

45

φ0(TSS, σ’a= 98 kPa; σ’3= 35 – 44 kPa)

0 max

0 max

sin cos( )arctan

1 sin sin( )d

ssd

φ νφφ ν⋅=

− ⋅

Theoretical value


φ0(PSC, σ’3= 49 kPa, δ=90o)

φ0(TC, σ’3= 49 kPa, δ=90o)

'aσatτ

atτ−

'tσ

2'σ

0nε =

2 0ε =

1'σ3'σ



In ordinary direct shear tests, φ0= arcsin[(σ’1- σ’3)/[(σ’1+σ’3)]max

cannot be measured, but onlyφss= arctan(τat/σ’a)max is measured.




50

0.6 0.7 0.8 0.930

φ0(PSC, δ=40o-50o)

φ 0an

d φ s

s(in

deg

ree)

35

40

45

φ0(TSS, σ’a= 98 kPa; σ’3= 35 – 44 kPa)

0 max

0 max

sin cos( )arctan

1 sin sin( )d

ssd

φ νφφ ν⋅=

− ⋅

Theoretical value


φ0(PSC, σ’3= 49 kPa, δ=90o)

φ0(TC, σ’3= 49 kPa, δ=90o)

'aσatτ

atτ−

'tσ

2'σ

0nε =

2 0ε =

1'σ3'σ



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.







1σShear band

δ

0.0 30 60 90


φ 0(δ

)/φ 0

(δ=

90o )

PS

C


σ’3= 98 kPa:OCR= 1.0

e4.9= 0.8e4.9= 0.7


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


φ 0(δ

)/φ 0

(δ=

90o )

PS

C


σ’3= 98 kPa:OCR= 1.0

e4.9= 0.8e4.9= 0.7


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)


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



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



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



0.1 1 100

50

100

Chert/CL

Particle size (mm)

Par

cent

pas

sing

in w

eigh

t


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


(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


0.1 1 100

50

100

Chert/CL

Particle size (mm)

Par

cent

pas

sing

in w

eig

ht


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)



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



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)


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)






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




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)


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 (%

)


Exp

ansi

on


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) !


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 %


Drained

Undrained

She

ar s

tres

s ra

tio,

She

ar s

tres

s ra

tio,

Torsional simple shearToyoura sandConsolidated at



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 !



C: undrained cyclic loading strength necessary to develop 15 % double amplitude shear strain

Relative density, Dr (%)

She

ar s

tren

gth,τ v

h/σ’ v

Toyoura sand; σ’vc= σ’vc= 98 kPa

A: drained peak stress ratio

B: undrained peak stress ratio necessary to develop 15 % shear strain

Number of loading cycle, Nc= 5

Comparison among (A)drained strength in ML, (B) undrained strength in ML and(C) undrained CL strength of Toyoura sand

Exc

ess

pore

wat

er

pres

sure

, ∆u

(kP

a)S

hear

str

ain,

γ v

h(%

)S

hear

str

ess,

τ v

h(k

Pa)

10 seconds

Undrained cyclic test




She

ar s

tren

gth,τ v

h/σ’ v






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.




She

ar s

tren

gth,τ v

h/σ’ v






1) ML undrained shear strength significantly increases with Dr: e.g., by a factor of three when Dr= 40 % → 60 %.

2) In the stability analysis based on the undrained shear strength, the benefit of compaction is significant.




She

ar s

tren

gth,τ v

h/σ’ v






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.




She

ar s

tren

gth,τ v

h/σ’ v






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.


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%


Typical example of cyclic undrained triaxial tests on isotropically consolidated specimens compacted to (Dc)1Ec= 85 %; 90 % and 95 %




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


時間

時間

時間



(a)

(b)

(c)

(d)

(e)

(f)



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


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





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




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



45




SR

Ni


SRi


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= =

= =∑ ∑



46




SR

Ni


SRi


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=

=∑



47




SR

Ni


SRi


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”.



0

τw

τi

sssssssseeee

Uniform cyclic stresses equivalent to “irregular working stresses before the start of pulse n” obtained by the cumulative damage concept.

TimePulse n

Consecutive zero-crossing points τw (= soil shear strength, τf)

decreasing by cyclic undrained loading

Equivalent τ～γ behavior after have been subjected to “equivalent uniform cyclic stresses obtained by the cumulative damage concept”

0

τ

τinitial

ssss

Shear strain, γ

γ+

γDA

eeee

τf

Undrained τ～γ relation

In pulse n

Initial






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


時間

時間

時間



(a)

(b)

(c)

(d)

(e)

(f)



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


log(Nc)

Damage strain

So

il st

ren

gth

Cyc

lic s

tres

s a

mpl

itud



50

主応

力差

【両試験共通】

圧密過程

（排水条件）

【純単調載荷試験】

単調載荷過程

（非排水条件）

【繰返し+単調載荷試験】

繰返し載荷過程


【繰返し+単調載荷試験】

単調載荷過程


繰返し載荷後に

残存する強度

（損傷強度(σa-σr)maxD）

繰返し載荷過程で

生じた最大ひずみ

あるいはひずみ振幅

（損傷ひずみεD）

純単調載荷試験

繰返し+単調載荷試験

繰返し載荷の

影響が無い強度（初期非排水せん断強度）

（非損傷強度(σa-σr)maxM）

強度低下

(DA)Dev

iato

r str

ess

Time

Consoli-dation

Undrained ML Undamaged peak strength

Undrained CL ⇒ Undrained ML

Damaged peak strength

Strength drop due to damage strainby undrained CL

End of undrained CL, where damage strain has taken place

Undrained monotonic loading (ML)

Undrained ML



51

61

Initial undrained shear strength

Strain

主応

力差

Dev

iato

r st

ress

Strain that has developed by undrained CLUnd

rain

ed s

hear

str

engt

h af

ter

undr

ain

ed C

L, τ

dam

age

Strain

主応

力差

Dev

iato

r st

ress

Strain主

応力

差D

evia

tor

stre

ss




-120

-60

0

60

120

180

-40

-20

0

20

40

60

-10 -5 0 5 10 15 20

過剰

間隙

水圧

, ∆u

(kN

/m2 )

主応

力差

, q(k

N/m

2 )

軸ひずみ, εa (%)

ρd=1.44g/cm3(Dc=85%), σ'mi=100kN/m2, τd/σ’mi=0.112, N=23, εdamage=10%, 純単調載荷試験 : q, ∆u

∆uq

繰返し載荷単調載荷

(a)

強度低下

qmaxS

qmaxD

Undrained ML

De

via

tor

stre

ss,

q (k

N/m

2 )

Axial strain, εa (%)

Initial undrained ML

Exc

ess

pore

wat

er p

ress

ure,

∆u

(kN

/m2 )

Strength drop due to undrained CLUndrained

CL

52




Typical example: loose Hokota sand

53




Typical example: dense Hokota sand

-200

0

200

400

600

800

1000

1200

1400

1600

-100

0

100

200

300

400

500

600

700

800

-10 -5 0 5 10 15 20

過剰

間隙

水圧

比, ∆

u(k

N/m

2 )

主応

力差

, q(k

N/m

2 )

軸ひずみ, εa (%)

ρd=1.61g/cm3(Dc=95%), σ'mi=100kN/m2, τd/σ’mi=0.258, N=44, εdamage=10%, 純単調載荷試験 : q, ∆u

∆u

q

繰返し載荷単調載荷

(b) 強度低下

qmaxS

qmaxD

Undrained CL Undrained ML

Dev

iato

r st

ress

, q (

kN/m

2 )

Axial strain, εa (%)

Strength drop

Exc

ess

pore

wat

er p

ress

ure,

∆u

(kN

/m2 )

Initial undrained ML

54



0

0.5

1

1.5

2

2.5

3

3.5

0 2 4 6 8 10 12損傷ひずみ, εdamage(%)

非排

水繰

返し

載荷

後に

残存

する

強度

, τ d

am

ag

e/σ’ m

i

密詰め

中詰め

緩詰め

: 初期非排水せん断

強度比τmaxS/σ’mi

0

0.2

0.4

0.6

0.8

1

1.2

0 2 4 6 8 10 12損傷ひずみ, εdamage(%)

密詰め

中詰め

緩詰め

初期

強度

に対

する

比, τ

dam

age/τ m

axM

τ dam

age/σ

’ mi

τdamage: undrained shear strength after undrained CLσ’mi: initial mean effective stress”

τ dam

age/τ

max

S

τmaxS: initial undrained shear strength

Damage strain, DA (%)

Damage strain, DA (%)

(Dc)1Ec= 95 %

(Dc)1Ec= 95 %

90 %

90 %

85 %

85 %

Undrained shear strength after cyclic

undrained loading becomes

significantly smaller as sand

becomes looser, due to:

1) lower initial undrained shear

strength;

2) larger damage strain by undrained

CL; and

3) a larger drop rate for the same

damage strain.

55



80 85 90 95 100 1050.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0非排水試験、初期平均有効主応力 σ'

mi

= 100 kPa

排水試験、 σ'

mi

=ピーク応力時平均有効主応力 σ'

mf

　供試体作成時飽和度

▲: 50 %

▼: (S

r

)

opt

= 71 %

排水せん断強度

τmaxD

/σ'

mf

N=3

N=10

○,● 軸ひずみ両振幅が

10%になる繰返し応力

振幅比 τd

/σ'

mi

+ 初期非排水

せん断強度,

τmaxS

/σ'

mi

× 非排水繰返し載荷

(τd

/σ'

mi

= 0.19; N=2)

後の残存強度

τdamage

/σ'

mi

各種

せん

強度

比, τ/

σ'm

i

締固め度(1Ec), D

c

(%)

Undrained tests: σ’mi= 100 kPaDrained tests: “σ’m at peak stress”= σ’ mi:

Str

engt

h ra

tio, τ

/σ’ m

i

(Dc)1Ec (%)

Initial undrained strength

Undrained strength after undrained CL*

Drained strength

Sr when compacted

Cyclic undrained strength for DA= 10 %

* τd/ σ’mi= 0.19; Nc= 2


Undrained shear strength

after cyclic undrained

loading becomes

significantly smaller as

sand becomes looser, due

to:

1) lower initial undrained

shear strength;

2) larger damage strain by

undrained CL; and

3) a larger drop rate for the

same damage strain.

56



Undrained shear strength

after cyclic undrained

loading becomes

significantly smaller as

sand becomes looser, due

to:

1) lower initial undrained

shear strength;

2) larger damage strain by

undrained CL; and

3) a larger drop rate for the

same damage strain. * τd/ σ’mi= 0.19; Nc= 2

80 85 90 95 100 1050.0

0.2

0.4

0.6

0.8

1.0

▲, ▼ τmaxD

/σ'

mf

N=3

N=10

○,● τd

/σ'

mi

+ τmaxS

/σ'

mi

×τdamage

/σ'

mi

各種

せん

強度

比, τ/

σ'm

i

締固め度(1Ec), D

c

(%)

Str

engt

h ra

tio, τ

/σ’ m

i

(Dc)1Ec (%)

Initial undrained strength

Undrained strength after undrained CL*

Drained strength

Cyclic undrained strength for DA= 10 %





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


時間

時間

時間



(a)

(b)

(c)

(d)

(e)

(f)



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


log(Nc)

Damage strain

So

il st

ren

gth

Cyc

lic s

tres

s a

mpl

itud



Different soil models for different Newmark methods

時間t

せん

断強

度, τ

f

ピークせん断強度τp

時間t

非排水繰返し載荷

によるＤＡ*

すべり変位δ*これら*は、τfの低下の設

定法によって異なる

非排水繰返し載荷

排水繰返し載荷

初期非排水せん断強度(τf)0

S法（ひずみ軟化を考慮）

O法：τf=残留強度τr（固定）

D法（ τfは非排水繰返し載

荷により低下）(τD)

SD法（ τfはひずみ軟化と非排水繰

返し載荷により低下）(τSD)

0

τi

時間, t

作用

せん

断応

力, τ

w

0

Wor

king

str

ess,

τw

Soi

l she

ar s

tren

gth,

τf

Time, t

Time, t

Time, t

Slip displacement δ These values of δ & damage strain are different among different soil models

Peak drained strength, τp

Initial undrained strength, (τf)0

Newmark-S (with strain-softening: τf= τp ⇒ τr)

Newmark-SD (with degradation by undrained CL & strain-softening)

Newmark-O (τf= drained residual strength τr, fixed)

Newmark-D (with degradation by undrained CL

Damage strain by undrained CL

Undrained

Drained

Significant effects of compaction

No effects of compaction

Large effects of compaction




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


時間

時間

時間



(a)

(b)

(c)

(d)

(e)

(f)



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


log(Nc)

Damage strain

So

il st

ren

gth

Cyc

lic s

tres

s a

mpl

itud



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.


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

She

ar s

tres

s ra

tio,

τ vh

/σm

c’

She

ar s

trai

n,

γvh

(%)

Exc

ess

pore

wat

er

pres

sure

ratio

, ∆

u /σ

mc’

Effe

ctiv

e ve

rtic

al

stre

ss ra

tio,

σ’

v/σ

mc’

Elapsed time (hours)

σ’mc= 98 kPa

1968 Tokachi-oki E.Q. main shock

Hachinohe (NS）

σ’ｒc= 66 kPa

[τvh /σ’mc]max= 0.8

(a)

(b)

(c)

(d)

Title | 2016 63

1/0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

Sh

ear

str

ess,

τvh

(x9

8 kP

a)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Effective vertical stress, σv’ (x 98 kPa)

Air-pluviated Toyoura sand (e= 0.671Cyclic undrained simple shear

(c)

-2/5 -2 -1.5 - 1 -0.5 0 0.5 1 1.5 2 2.5Shear strain, γvh (%)

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

She

ar s

tres

s, τ

vh(x

98 k

Pa)

Complicated τvh – γvh relation !

Title | 2016 64

1/0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

Sh

ear

str

ess,

τvh

(x9

8 kP

a)


Air-pluviated Toyoura sand (e= 0.671Cyclic undrained simple shear

(c)

-2/5 -2 -1.5 - 1 -0.5 0 0.5 1 1.5 2 2.5Shear strain, γvh (%)

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

She

ar s

tres

s, τ

vh(x

98 k

Pa)

- 1 -0.5 0 0.5 1 1.5 -1 0.5 0 0.5 1.5 2Shear strain, γvh (%)

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

She

ar s

tres

s ra

tio, τ

vh/σ

v’

Up to point A Up to point A

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.


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 loose Toyoura sand applying ‘seismic’ random stresses at a constant shear strain rate

Sh

ear s

tress

ratio

, τ v

h/σ

mc’

She

ar s

tra

in,

γvh

(%)

Exc

ess

por

e w

ate

r pr

ess

ure

ratio

, ∆

u /σ

mc’

Effe

ctiv

e v

ert

ical

st

ress

ratio

, σ’

v/σ

mc’

Elapsed time (hours)

σ’mc= 98 kPa

1968 Tokachi-oki E.Q. main shock

Hachinohe (NS）

σ’ｒc= 66 kPa

[τvh /σ’mc]max= 0.4

0.4b

ce

f

a1

d1h

g i

j

c

fd1

h

gi

j

fh

g i j

c

f

d1

hg i j

(a)

(b)

(c)

(d)

66

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 a2 a1

b1

d2 d1

f’

h

j

ef’’

c

b2

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

Complicated τvh – γvh relation !

67

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 a2 a1

b1

d2 d1

f’

h

j

ef’’

c

b2


(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.

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 a2 a1

b1

d2 d1

f’

h

j

ef’’

c

b2


(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


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.

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 a2 a1

b1

d2 d1

f’

h

j

ef’’

c

b2


(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


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.

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 a2 a1

b1

d2 d1

f’

h

j

ef’’

c

b2


(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


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


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


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.








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.)


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.


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



Stable

Collapse

A

B

A (stable)

B(collapsed)


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



Stable

Collapse

B

A (stable)

B(collapsed)


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



Fs=Strength/Load= 1



Stable

Collapse

A

B

A (stable)

B(collapsed)


■ 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




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.



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.



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.



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.



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..

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