Akashi strait bridge - Saitama University strait bridge.pdffor Akashi Strait Bridge 10 1.5 Pier 2P of Akashi Strait Bridge a t (MPa) 0.5 1.0 End of tower construction d pressure b

Design and construction of theDesign and construction of the foundations for Akashi Strait Bridgeg

Tatsuoka, F.Department of Civil Engineering

Tokyo University of Sciencey y

Location of Akashi Kaikyo (Strait) Bridge

Akashi Strait Bridge

Akashi Strait Bridge

**

(*about 4 million years)

The longest suspension bridge, but the worst ground condition ever for long suspension bridges in Japan

Anchorages 1A and 4AAnchorages 1A and 4A

1A 4A

Piers 2P and 3P

2P & 3P

(Unit: m; and the figures in the parentheses are for 3P)

Design and construction of the foundations for Akashi gStrait Bridge

A geotechnical engineering case history showing the importance of p- triaxial compression tests over unconfined compression tests to estimate the strength of gravelly g g ysoil and sedimentary soft rock for limit equilibrium stability analysis; and

- the stress-strain behaviour at very small strains and its accurate measurement to estimate the displacements of the foundations.


A geotechnical engineering case history showing the importance of p- triaxial compression tests over unconfined compression tests to estimate the strength of ggravelly soil and sedimentary soft rock for limit equilibrium stability analysis; and


Gravel (Akashi 100

wei

ght

(Formation)

50

assi

ng in

w0

erce

ntag

e p

Diameter (mm)0.1 1.0 10 50 Pe

Platform under operation for geological survey and di t b d liundisturbed sampling

A sample retrieved by large triple-tube core sampling (year 1986) 30 cm in diameter and 60 cm in height gravelly soil1986), 30 cm in diameter and 60 cm in height, gravelly soil from Akashi Formation; and a specimen after a cyclic undrained triaxial test

Large triaxial apparatus;30 cm in dia. x 60 cm h

Grading curves of the samples of Akashi gravelly soil used i d i d li t i i l t tin undrained cyclic triaxial tests

100100ei

ght Gravelly soil

(Akashi

g in

we formation) used

in cyclic triaxial tests (series 2)

50

assi

ng

tests (series 2)

cent

pa

0

Perc

Grain size (mm)0.1 1.0 10 50

A typical set of CU TC tests on Akashi gravelly soil(Yamagata et al 1995)(Yamagata et al., 1995)

4σ3 (kPa)= 1,400

3–σ 3

2

wat

er

MPa

)

ss, q

= σ 1

Pa)

2

ess

pore

es

sure

(M

ator

stre

s(M

P

1 Exce pre

0.8Dev

ia

00.4

0ε1 (%)

-0.4

Design shear strength under drained and undrained condition for limit equilibrium stability analysiscondition for limit equilibrium stability analysis

Undrained for seismic design

M h ’ i l f t t f il f i t i llMohr’s circles of stress at failure of isotropically consolidated samples and failure envelops (CD TC)

(MP

a) 2.5a) CD

ess,

σ( a) CD

ear s

tre

0 2.5 5

She 0

Normal stress, σ (MPa)

Mohr’s circles of stress at failure of isotropically consolidated samples and failure envelops (CU); and definition of shear and

l l h f il l f CU TC ( &normal stresses along the failure plane for CU TC tests (τf & σm: shear & normal stresses along the failure plane)

)σ

(MP

a) 2.5b) CU

far

stre

ss,

f

Normal stress, σ (MPa)

She

a

00 2.5 5

, ( )

τ Mohr’s circle for CU TC tests by the total

stress method

c)

τf

stress method

f

σ, σ’σmσ’nc

Stress-strain relations from CU TC tests before and after cyclic undrained loading; and a decrease ratio of undrained TC strength by cyclic undrained loading (a small decrease)

3

Pa) (4) Irregular cyclic loading

from point A;

2–σ 3

(MP from point A;

(σ1 – σ3)d.max - ε1+ relation (2) ML from point A

max

bef

ore

ding

tes

t

Undrained TC

2

s, q

= σ 1

–

(σ1

–σ 3

)mer

CXT

load

Undrained TC (σ‘mc = 0.65 MPa)

1

ator

stre

s

(3) ML after sinusoidal cyclic loading

Rat

ion

of

and

aft e σ1c’= 1.18 MPa

σ3c’= 0.39 MPa

0

Dev

ia (3) ML after sinusoidal cyclic loading from point A

(1) ML after isotropic consolidation ε1+ (%) at Nc= 500 in cyclic

undrained triaxial (CTX) loading

ε1, ε1+ (%)

Sedimentary soft rock (KobeSedimentary soft rock (Kobe Formation)

Unconfined compression test on sedimentary soft rock, reliable ?

Kobe formation（Sedimentary soft

m2 )

（Sedimentary soft sandstone), Matsuho site：(depth: 20.6 – 20. 9 m)

2 3 / 3

(kgf

/cm

E ≒EAxial stress

ρt= 2.3 g/cm3

stre

ss ( Ei ≒E50

Axi

al s

Specimen Axial displacement

Axial strain (%)Strains in the ground

First stage of investigation:

- A great amount of unconfined compression tests, following the common practice at that time

→ An extremely large scatter in the nconfinedin the unconfined compressive strength

→ Statics analysis ?

Distributions of q of rotary core

→ Statics analysis ?

Distributions of qu of rotary core tube samples of sedimentary soft rock, classified according to the soft rock type (complied in 1985; Tatsuoka & Kohata, 1995).

First stage of investigation:

- Unconfined compressive tests

→ A very large scatter due to ff flarge effects of sample

disturbance (large under nconfined condition) andunconfined condition) and

confining pressure

Distributions of q of rotary coreDistributions of qu of rotary core tube samples of sedimentary soft rock, classified according to the soft rock type (complied in 1985; Tatsuoka & Kohata, 1995).

Second stage of investigation:A typical geotechnical profile of Kobe Formation, Matsuhoyp g p ,site, near Anchorage 4A

A h l tt i fi d i t th→ A much larger scatter in unconfined compressive strength than in CU TC strength (by a geotechnical consultant)

EＰＭＴ (GPa)

0 0.2 0.4

Einitial (GPa)

0 0.2 0.4 0.6 0.8

qu and qmax (MPa)

0 1 2 3 4 5

c (MPa)

0 0.1 0.2 0.3

Kobe group (sedi-mentary soft rock: 0.16

2

MPa

)Unconfined compressive strength: depth= 11 – 30 m)

0.16

0.110.3

1

0 5th, q

u(Mstrength:

- A very large scatter; and

0.3

0.5

0 2e st

reng

ty g ;- A much lower than CU

TC strength0.3

The figures indicated

0.2

0.１pres

sive

→ Utterly unreliable→ Switch to CU and CD The figures indicated

next to data points show σ’c (MPa). Two data of qu for a single data of

0.0５ed

com

p→ Switch to CU and CD TC tests to obtain design strength

0.3

0 21

qu gqmax in two cases.

○ Mudstone● Coarse sandstone

0.0２ncon

fine

Comparison of compressive

g g

0.21 ● Coarse-sandstone▲ Fine-sandstone0.01

U

0.2 0.5 1 2 5 10

Comparison of compressive strength between U and CUTC tests of sedimentary soft rock, Matsuho site near A4 (by

CU TC compressive strength, qmax= (σ’1 - σ’3 ) max (MPa)

0.2 0.5 1 2 5 10Matsuho site, near A4 (by Yamada, S. and Tatsuoka,F.)

Typical sets of CU TC tests on Kobe sedimentary soft rock: a) sandstone; and b) mudstone (Yamagata et al 1995)a) sandstone; and b) mudstone (Yamagata et al., 1995)

30

(kP ) 2 00020

σ3 (kPa)=20

ator

stre

ss,

–σ 3

(MP

a)

σ3 (kPa)= 2,000

or s

tress

,–σ 3

(MP

a)

10

Dev

iaq=

σ1 10

Dev

iato

q= σ

1–

er

ε1 (%)00

pore

wat

er

re (M

Pa)

ε1 (%)00

2

ess

pore

wat

ees

sure

(MPa

)

1 ( )1

2Exce

ss p

pres

su

Exce pre

→ A much more serious problem with unconfined compression→ A much more serious problem with unconfined compression test in the evaluation of stiffness at small strains


A geotechnical engineering case history showing the importance of p- triaxial compression tests over unconfined compression tests to estimate the strength of gravelly g g ysoil and sedimentary soft rock for limit equilibrium stability analysis; and


To predict ground deformations at working loads, p g gthe elastic property is important;

bbecause:1) strains in the ground are relatively small; and

2) deformation properties at these small strainsb li k d t th l ti tcan be linked to the elastic property,

d th l ti t i th fi ld b bt i dand the elastic property in the field can be obtained by field shear wave velocity measurements.

Time-history of the settlement of Pier Foundation 2P on a gravel depositPier Foundation 2P on a gravel depositfor Akashi Strait Bridge

1 0

1.5

Pier 2P of Akashi Strait Bridge

at

(MP

a)0.5

1.0

End of tower constructiond

pres

sure

aba

se, (

p)av

e(

0

0.0 App

lied

he fo

otin

g b

-50

0

The 1995 Hygo-ken Nambu Earthquake

, S(m

m)

t

-100 10 years

Set

tlem

ent

14th Oct., 1989

0 500 1000 1500 2000 2500 3000 3500-150

Elasped time (days)(Tatsuoka & Kohata, 1995;Tatsuoka et al., 2001)

-Instantaneous settlement-Residual settlementResidual settlement

Creep settlement Settlement by seismic effects

1 0

1.5

Pier 2P of Akashi Strait Bridge

at

(MP

a)0.5

1.0

End of tower constructiond

pres

sure

aba

se, (

p)av

e(

0

0.0 App

lied

he fo

otin

g b

-50

0

The 1995 Hygo-ken Nambu Earthquake

, S(m

m)

t

-100 10 years

Set

tlem

ent

14th Oct., 1989

0 500 1000 1500 2000 2500 3000 3500-150

Elasped time (days)

Time-history of the settlement of Pier Foundation 3P on a sedimentaryPier Foundation 3P on a sedimentary soft rock for Akashi Strait Bridge

0.8

1.0 Pier 3P of Akashi Strait Bridge

End of to er constr ctionre a

t the

p)

ave (

MP

a)

0 2

0.4

0.6 End of tower construction

lied

pres

sur

tion

base

, (

0

100.0

0.2

App

lfo

unda

t

-30

-20

-10

0

The 1995 Hyogo ken Nambunt, S

(mm

)

-60

-50

-40

30 The 1995 Hyogo-ken Nambu earthquake

Set

tlem

en

26th Jan. 1990

(Tatsuoka & Kohata, 1995;Tatsuoka et al., 2001)

0 250 500 750 1000 1250 1500 1750 2000-70

Elasped time (days)

- Elastic component is large part of the total settlement- An increase in the tangent modulus d(p)ave/dS with (p)ave,

fl i i i h l di “d( ) /dS ” i h ( )

Se(elastic component, based on (Vs)field

reflecting an increase in the loading rate “d(p)ave/dSe” with (p)ave.

1 0

1.2 & its pressure-dependency from laboratory stress-strain tests)

Sir (=St - Se)Se

(MP

a)

0.8

1.0

Settlement rate

S

mm/day0 1=irS&Fitted to (mm/day)irS&

0 10re, (

p)av

e (

0.6

mm/day0.1=S 0.10 0.0-0.05 0.05-0.10 0.10-0.150 15 0 20

ct p

ress

ur

0.2

0.4

St (total settlment as measured)

0.15-0.20 0.20-0.25 > 0.25

ge c

onta

c


Aver

ag

0 20 40 60 80 100 120Settlement, S (mm)

(Tatsuoka et al., 2001)

-Lower stiffness at slower construction rates-Noticeable creep settlement during the cease of construction

1.2

Se(elastic component, based on (Vs)field & its pressure-dependency from laboratory stress-strain tests)

)

1.0Sir (=St - Se)Se

ave (M

Pa)

0.8Settlement rate

mm/day 0.1=irS&Fitted to (mm/day)irS&

0.100 0 0 05su

re, (

p)a

0 4

0.6 0.0-0.05 0.05-0.10 0.10-0.15 0.15-0.20

act p

ress

0.2

0.4

St (total settlment as measured)

0.20-0.25 > 0.25

ge c

onta


Aver

ag

0 20 40 60 80 100 120Settlement, S (mm)

Decomposition of settlement to elastic and irreversiblecomponents Pier 3P (Tatsuoka et al 2001)components, Pier 3P (Tatsuoka et al., 2001)

1 0 Pi 3P

0 8

1.0 Pier 3P Sir

Se

(MPa

)

0.6

0.8

(mm/day)irS&re, (

p)av

e

0.4

0.05

0.00-0.050 05 0 10ct

pre

ssur

0.2Measured settlement, S

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

age

cont

ac

0.0 >0.25

Ave

ra

0 10 20 30 40 50 60 70

Settlement, S (mm)

-Lower stiffness at slower construction rates-Noticeable creep settlement during the cease of construction

1 0 Pi 3P

0 8

1.0 Pier 3P Sir

Se

(MPa

)

0.6

0.8

(mm/day)irS&re, (

p)av

e

0.4

0.05

0.00-0.050 05 0 10ct

pre

ssur

0.2Measured settlement, S

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

age

cont

ac

0.0 >0.25

Ave

ra

0 10 20 30 40 50 60 70

Settlement, S (mm)

6010-6 10-5 10-4 10-3 10-2

Vertical strain　εvVertical strain, εv

80

60

Pier 2PPier 3P

Strains until the average contact pressure became

100

80

m)

Pier 3Ppressure became 520 kPa (2P) and 390 kPa (3P)

120

100

on　TP-(m

Pier 3P Pier 2PP

(-m

)

140

120

Elevatio Pier 2P

atio

n, T

P

140

Ele

vaCentreline vertical strains in th l d di t 160the gravel and sedimentary softrock below the piers:

180Strains less than about 0.5 %


**

Sampling

(*about 4 million years)

Sampling

A series of field and laboratory tests at the site of A1

A series of field and laboratory tests at the site of A1

-50Kobe group softrock

EmaxEmax Average (from CD TC tests;

axial strains measured with LDTs)

○●

E0average of E0

(from CD TC tests (σc’= 0.51 MPa = σv’(in-situ), axial strains measured with LDTs

-55E50 unconfined compression tests(from external axial strains)

□

axial strains measured with LDTs)Einitial (or E50) from unconfined

compression tests

σv (in situ), axial strains measured with LDTs

m) EPLT; tangent modulus

i i l di▲＋▼

EBHLT; primary loading△

(from external axial strains)

Pressuremeter tests (primary loading)EPMT;

-60

Dep

th (

E (from shear wave velocity)▼＋ 40∼6020∼40,0∼20,▲

range of plate pressure(kgf/cm2) in primary loading Plate loading

testsPressure ranges (MPa)0 - 2 2 - 4 4 - 6

-651A-11A-21A-3

Ef (from shear wave velocity)

-70

Emax from CU and CD TC tests

σc' = σv' (in situ)= 5.2 (kgf/cm2)

1A-41A-51A-60.51 MPa

100 1000 10000 100000-70

Young's modulus E (kgf/cm2)

Young’s modulus, E (GPa)0.01 0.1 1 10

Unconfined compression test on sedimentary soft rock, reliable ?

Kobe formation（Sedimentary soft

m2 )

（Sedimentary soft sandstone), Matsuho site：(depth: 20.6 – 20. 9 m)

2 3 / 3

(kgf

/cm

E ≒EAxial stress

ρt= 2.3 g/cm3

stre

ss ( Ei ≒E50

Axi

al s

Specimen Axial displacement

Axial strain (%)Strains in the ground

Pressure-meter tests:most popular field loading test to

zBorehole

most popular field loading test toevaluate the stress-strain behaviourat small strains

∆p: ressure applied to the bore hole

robore hole wall*

ru: lateral displacement

i th d

θ

in the ground

u0: lateral displacement at the wall face*

Balloon

pΔ If soil is linear material….

12G

0 0

0

ur

1

0

0

ur

Suspension methodp(local up-hole method)

(V )Borehole

(Vs)VH.local

Velocity

z

L= 1 m

Velocitymeasuring

Velocity

Shear wavegeneration

Velocitygeneration

zLocal:V =L/∆t zVs=L/∆t

-50Kobe group softrock

EmaxEmax Average (from CD TC tests;

i l t i d ith LDT )

○●

-55E50 unconfined compression tests(from external axial strains)

□

axial strains measured with LDTs)

60(m) EPLT; tangent modulus

in primary loading▲＋▼


(from external axial strains)

(Anchor 1A)-60

Dep

th

Ef (from shear wave velocity)▼＋ 40∼6020∼40,0∼20,▲

range of plate pressure(kgf/cm2) in primary loading

-65

E f CU d CD TC t t

1A-11A-21A-31A 4

100 1000 10000 100000-70



1A-41A-51A-6 (Tatsuoka

& Kohata 1995)

A t l l i ti i th E l bt i d f

100 1000 10000 100000

Young's modulus E (kgf/cm2)& Kohata, 1995)

An extremely large variation in the E values obtained from different field and laboratory tests; Why ?

-50

Kobe group softrock

EmaxEmax Average(from CD TC tests;

○●

-55

g p

E50 unconfinedcompression tests

□

(from CD TC tests; axial strains measured with LDTs)

-55

E t t d l▲


compression tests(from external axial strains)

-60

epth

(m)

▼＋ 40∼6020∼400∼20▲

range of plate pressure(kgf/cm2)

EPLT; tangent modulus in primary loading

▲＋▼

-65

D

1A-11A-2

Ef (from shear wave velocity)▼＋ 40 6020 40,0 20,▲


' ' (i i ) 5 2 (k f/ 2)

1A 21A-31A-41A-5

100 1000 10000 100000-70



1A-6

Young s modulus E (kgf/cm )

Totally different so-called static and dynamic Young’s moduli

-50

Kobe group softrock


○●

-55E50 unconfined compression tests

□


) E ; tangent modulus▲＋▼


p(from external axial strains)

-60

Dep

th (m

)

▼＋ 40∼6020∼40,0∼20,▲



▲＋▼

-65

D

1A-11A-2

Ef (from shear wave velocity)▼,,


' = ' (in situ)= 5 2 (kgf/cm2)

1A-31A-41A-5

100 1000 10000 100000-70


σc' = σv' (in situ)= 5.2 (kgf/cm )

1A-6


But, the Emax values from relevant static tests are essentially the same with those from shear wave velocities (dynamic tests)

10

12

hσ '= 0.51 MPa (CD)Sedimentary soft sandstone (Kobe Formation)

a)

0.8

a)

6

8ExternalLDT

or s

tress

, q (M

P

0.4

0.6

LDT

stre

ss, q

(MP

a

0

2

4

0maxq = 9.39 MPa, E = 1520 MPa

Dev

iato

0.2 External

Dev

iato

r s

0 1 2 30

vAxial strain, ε (%)0.00 0.02 0.04 0.06 0.08 0.10

0.0

vAxial strain, ε (%)

0 04

0.03

0.04

MPa

)

0.02

r stre

ss, q

(M

0.010E = 1520 MPa

1

Dev

iato

r

CD TC test on an undisturbed l lid t d t th fi ld

0.0000 0.0005 0.0010 0.0015 0.00200.00

LDTvAxial strain, (ε ) (%)

sample consolidated to the field effective stress with local axial strain measurement

-50

Kobe group softrock


○●

-55E50 unconfined compression tests

□


) E ; tangent modulus▲＋▼


p(from external axial strains)

-60

Dep

th (m

)

▼＋ 40∼6020∼40,0∼20,▲



▲＋▼

-65

D

1A-11A-2

Ef (from shear wave velocity)▼,,


' = ' (in situ)= 5 2 (kgf/cm2)

1A-31A-41A-5

100 1000 10000 100000-70


σc' = σv' (in situ)= 5.2 (kgf/cm )

1A-6


The Emax values from relevant static tests are essentially the same with those from shear wave velocities (dynamic tests)

To predict ground deformations at working loads, the elastic property is important;elastic property is important; because:1) strains in the ground are relatively small; and1) strains in the ground are relatively small; and

2) deformation properties at these small strainscan be linked to the elastic property,

d th l ti t i th fi ld b bt i d b fi ldand the elastic property in the field can be obtained by field shear wave velocity measurements,

but, once the strain level exceeds the quasi-elastic strain limit, the stress-strain behaviour becomes highly non-linear and viscous effects becomes significant, and the entire pre-peak stress-strain-time relation cannot be obtained only from the l ti b h ielastic behaviour.

Relationships between back-calculated Young’s modulus and measured ground strain and Young’s modulus values for PM t t (T t k & K h t 1995)tests (Tatsuoka & Kohata, 1995).

1.5

Ef: from Vs before construction)

2P case1 for (p)ave= 0 ∼ 5.3 kgf/cm2

1 ∼ 5 Gravelly soil (Akashi) 6 ∼ 9 Sedimentary soft rock△

Ef: Young’s modulus from field Vsbefore construction

2P for (p)ave = 0 – 0.52 MPa△ 1 – 5: gravelly soil (Akashi)

○ 6 – 9: sedimentary soft rock (Kobe)

1.0 ( )3

6*

987

y

PM

T/Ef

y ( )

EPMT/Ef

(strais for EPMT unreported)

5

5

6

EM/E

f, E

P

Ef

EFEM

EPMT/Ef (strains for EPMT unreported)

0.5 range forsoft rock 2

47

45


1 ∼ 6 Sedimentary soft rock (P3)

E FE

｛

f

3P for (p)ave = 0 – 0.53 MPa○ 1 6: sedimentary soft rock (Kobe)

0.0

｛1

13 26

1 ∼ 6 Sedimentary soft rock (P3) 7 Granite * Ef was estimated as 5 x EPMT

｛○ 1 – 6: sedimentary soft rock (Kobe) ○ 7: granite

*) Ef was estimated as 5xEPMT

0.0001 0.001 0.01 0.1 10.0

Gravelly soilMeasured ground vertical strain: ε1 (%)

1.52P case1 for (p) = 0 ∼ 5 3 kgf/cm2

2P for (p) = 0 0 52 MPaEf: from Vs before construction)

2P case1 for (p)ave 0 5.3 kgf/cm 1 ∼ 5 Gravelly soil (Akashi) 6 ∼ 9 Sedimentary soft rock△

Ef: Young’s modulus from field Vsbefore construction

2P for (p)ave = 0 – 0.52 MPa△ 1 – 5: gravelly soil (Akashi)


1.0

(strais for

( )3

6*

987

E PMT/E

f

E /E ( t i fEPMT/Ef

(strais for EPMT unreported)

5

5

FEM/E

f, E

Ef

EFEM

EPMT/Ef (strains for EPMT unreported)

0.5 range forsoft rock 2

47

4



E F

｛3P for (p)ave = 0 – 0.53 MPa

○ 1 6: sedimentary soft rock (Kobe)

0 0

｛1

13 26

1 ∼ 6 Sedimentary soft rock (P3) 7 Granite * Ef was estimated as 5 x EPMT

｛○ 1 – 6: sedimentary soft rock (Kobe) ○ 7: granite


0.0001 0.001 0.01 0.1 10.0

Gravelly soilMeasured ground vertical strain: ε1 (%)

Young’ modulus back-calculated by FEM (Tatsuoka& Kohata, 1995)

1.5

E :2P case1 for (p)ave= 0 ∼ 5.3 kgf/cm2

E : Young’s modulus from field V2P for (p)ave = 0 – 0.52 MPaEf:

from Vs before construction) 1 ∼ 5 Gravelly soil (Akashi)

6 ∼ 9 Sedimentary soft rock△

fEf: Young s modulus from field Vs

before construction△ 1 – 5: gravelly soil (Akashi)


1.0

E /E(strais for

E

( )3

6*

987

E PMT/E

f

EPMT/Ef (strains for

0 5

EPMT/Ef EPMT unreported)

5

45

E FEM/E

f,

Ef

EFEM

PMT f (EPMT unreported)

0.5

｛

range forsoft rock 2

1

4

3

72

4



E

｛3P for (p)ave = 0 – 0.53 MPa


0.0

｛1

13 26 7 Granite

* Ef was estimated as 5 x EPMT

｛○ 7: granite


0.0001 0.001 0.01 0.1 1Gravelly soilMeasured ground vertical strain: ε1 (%)

- Obvious non-linearity (mostly due to strain-non-linearity).

1.5








1.0

E /E(strais for

E

( )3

6*

987

E PMT/E

f


0 5


5

45

E FEM/E

f,

Ef

EFEM


0.5

｛


1

4

3

72

4



E

｛3P for (p)ave = 0 – 0.53 MPa


0.0

｛1

13 26 7 Granite


｛○ 7: granite



- EFEM/Ef approaches 1.0 as the strain becomes very small.

1.5








1.0

E /E(strais for

E

( )3

6*

987

E PMT/E

f


0 5


5

45

E FEM/E

f,

Ef

EFEM


0.5

｛


1

4

3

72

4



E

｛3P for (p)ave = 0 – 0.53 MPa


0.0

｛1

13 26 7 Granite


｛○ 7: granite



Very small values of EPMT/Ef

Some lessons:1) Strains operating in the ground supporting

foundations allowing limited displacements; generally small, lower than about 0.5 %.

2) Non-linear behaviour even at strains less than 0.1 %.

3) The E value approaches E0 from Vs as the strain approaches about 0.001 %, indicating the importance of elastic property for the prediction of ground deformation and structural displacemnts.

4) EPMT from conventional pressure-meter tests with linear interpretation could be too small to directly use in the prediction.

What is the ideal laboratory stress-strain test ?

What is the difference between the ideal and actual laboratory stress-strain tests?actual laboratory stress-strain tests?

Wh t i th f i thWhat is the consequence from errors in the laboratory stress-strain test ?

LoadBasic postulate:

If we can predict accurately the stress-strain-time behaviours of all the concerned soil elements in the

Stress Settlement ground, we can predict accurately the load-displacement-time behaviours of the ground and

Soil elementB h i i th fi ld

behaviours of the ground and foundation.

vσBehaviour in the field

(with creep deformation)

Start of loading

0 StrainStress path in the soil element However, the actual

hσHowever, the actual situation is different ……

Ideal laboratory stress-strain test (e.g., TC test) *

l l t i tLoad

- local strain measurement

- high-quality core sample

- anisotropic re-consolidation- anisotropic re-consolidation

as in the field

- sustained loadingStress Settlement

g

Behaviour in the fieldSoil element * Very difficult to perform

Behaviour in the field(with creep deformation)

vσTC test

0 Strain

Start of loadingTC test

0 StrainStress path in the field soil element Nearly elastic behaviour

i di t l ft th t t fhσ immediately after the start of loading

TC test (non-ideal)Load- local strain measurement

- high-quality core sample

- Isotropic reconsolidation

- monotonic loading to failureStress Settlement

Soil element

Difference between thefield behaviour and the

0 Strain

Behaviour in the field


field behaviour and thelaboratory test result

0 Strain(with creep deformation)

TC test (non-ideal)Load ( )

- external strain measurement

- high-quality core sample- high-quality core sample- isotropic reconsolidation- monotonic loading to failureStress Settlement

Soil element

Effects of bedding error

0 Strain

Effects of bedding errorBehaviour in the field

(with creep deformation) 0 Strain(with creep deformation)

LoadLoad TC test (non-ideal)- local strain measurement- more-or-less disturbed sample

Stress Settlement

- more-or-less disturbed sample- isotropically reconsolidated- monotonic loading to failure

Soil elementSoil element

Effects of sample disturbance



Load TC test (most conventional)- external axial strain measurementexternal axial strain measurement - more-or-less disturbed specimen- isotropic reconsolidation

i l di f ilStress Settlement

- monotonic loading to failure

Soil element

0 Strain


(with creep deformation) 0 Strain(with creep deformation)

Load

Unconfined compression test

0σ =

Unconfined compression test

-external strain measurement

noticeably disturbed sample

Stress Settlement

- noticeably disturbed sample

Soil element

0 Strain


(with creep deformation) 0 Strain

Significant underestimation of the stiffness in the field due to inadequate stress path and history effects of bedding error


inadequate stress path and history, effects of bedding error and sample disturbance

Load In design based on an allowable footing settlementfooting settlement

Stress Settlement

Soil element

0 StrainBehaviour in the field


T ti d iSignificant


Too conservative designunderestimation of strength and stiffness

LoadElastic stiffness fromfield Vs value

Conventional PLTStress Settlement

Conventional PMT

Soil element

Conventional PMT

0 Strain



Another problem: the link among results from laboratory


p g yand field tests and field full-scale behaviour could be missed.

Non-linear elasto-plastic FEM

Plate loadingtest(D=60cm)

S-1

Pressure – settlement relations from four PLT tests

6

of 3

P)

Pa

S 1 S-3 S-4

relations from four PLT tests using a 60 cm dia.-rigid plate at the excavation .0

GPa

)d

beha

viou

r o

E PMT=

306 M

P

a)plate at the excavation bottom of Anchorage 1A and relations predicted by linear

4

theo

ry (E

=1.

ll-sc

ale

field

tests)

(p) av

e.(M

Pa

theories and FEM analysis (Tatsuoka et al., 1999)

2

Line

ar t

(from

fu

=174 MPa (fr

om U te(

2

Unloading (S-3)

E 50=1

Es

0 3 6 90

Linear theory1

0 3 6 9Settlement, S (mm)

12

Full scale behaviour10

Full-scale behaviour of pier 3P on sedimentary soft sandstone

8

m2)

E=10000kgf/cm2

y

6

(kgf/cm

4(p)ave.

measured EPMT(from 3P site)

=2890kgf/cm2

2FEM

0

2

E50(from 1A site)

=1777kgf/cm2

0

0 20 40 60 80 100Settlement, S (mm)

12

Full scale behaviourEquivalent linear relation

10


8

m2)

E=10000kgf/cm2

y

6

(kgf/cm

4(p)ave.


=2890kgf/cm2

2FEM

0

2

E50(from 1A site)

=1777kgf/cm2

0

0 20 40 60 80 100Settlement, S (mm)

12


10


8

m2)

E=10000kgf/cm2

y

Why very linear?

6

(kgf/cm

The effects of the following two factors are balanced;

4(p)ave.


=2890kgf/cm2

two factors are balanced;1)An increase in the elastic

Young’s modulus Ev with

2FEM

g van increase in σv; &

2)A decrease in Esec with an i i th t i

0

2

E50(from 1A site)

=1777kgf/cm2

increase in the strain.

0

0 20 40 60 80 100Settlement, S (mm)

12


10


8

m2)

E=10000kgf/cm2

y

6

(kgf/cm

4(p)ave.


=2890kgf/cm2

2FEM

-Over-estimation of the instantaneous settlement

h b d th

0

2

E50(from 1A site)

=1777kgf/cm2

when based on the conventional methods.

0

0 20 40 60 80 100Settlement, S (mm)

12


10


8

m2)

E=10000kgf/cm2

y

6

(kgf/cm

4(p)ave.


=2890kgf/cm2

2FEM

-Over-estimation of the instantaneous settlement

h b d th

0

2

E50(from 1A site)

=1777kgf/cm2

when based on the conventional methods.-Accurate simulation by 0

0 20 40 60 80 100Settlement, S (mm)

-Accurate simulation by FEM based on 2

f sG Vρ= ⋅

12

Full-scale behaviour

10of pier 3P

8

m2)

E=10000kgf/cm2

6

(kgf/cm

- A signficant over-estimation of the i t t ttl t

4(p)ave.


=2890kgf/cm2

instantaneous settlement when based on the conventional methods

2FEM

conventional methods.- Accurate simulation by FEM based on 2

f sG Vρ= ⋅

0

2

E50(from 1A site)

=1777kgf/cm2

f

0

0 20 40 60 80 100Settlement, S (mm)(Tatsuoka & Kohata, 1995)

Some conclusions - 1:

“Deformation of ground and displacements of structures at working loads constructed on and in the ground”at working loads constructed on and in the ground could be reliably predicted;

1) based on field shear wave velocities;2) while taking into account the non linearity by pressure2) while taking into account the non-linearity by pressure

and strain (including viscous property) evaluated by relevant laboratory stress strain tests that;relevant laboratory stress-strain tests that;

a) measure accurately stresses and strains; b) using high quality core samples; andb) using high-quality core samples; andc) simulating the field loading history.

Some questions:

1) The elastic deformation characteristics: can be obtained only by dynamic tests ?y y y

2) Are statically and dynamically determined ) y y yelastic deformation properties different ?

Static tests (monotonic or cyclic); stress-strain properties are obtained from measured stresses and strains !(or loads and displacements)

Dynamic tests (RC tests & wave-propagation tests); t t i ti bt i d f d i !stress-strain properties are obtained from dynamic responses !

Importance of proper understanding of the relationship between static & dynamic tests in the framework of non-linear stress-strain behaviour

Non-linear stress-strain behaviour from “quasi-elastic behaviour at very small strains” toward “shear banding at very large strains”

Quasi-LinearElastic-weak visco-plastic

elastic Eeq

E0 Esec

Shear bandingShear banding

El ti

(Tatsuoka & Shibuya, 1991)

Elastic-strong visco-plastic

Laboratory and field testing methods to evaluate non-linear stress-strain behaviour from “elastic behaviour at very small strains” toward “shear banding at very large strains”➔ difficult by a single test methodbanding at very large strains ➔ difficult by a single test method

Quasi-Linearelastic Shear bandingElastic-plastic-

viscouselastic gviscous

Bender

Smallest reliablyMeasurable strains30 – 40 years ago

Element


What are different between static and dynamic tests ?Influencing

ML or CL Loading rate

Wave length/ particle size

Number of cycles

Strain level

Monotonic Slow Nearly infinitive ¼ cycle Very small

gfactors

Static testsy y y

Fast Medium to very large

Cyclic Slow Nearly infinitive Small Very small

MediumFast LargeFast Large

Large

Dynamic Monotonic Large ¼ cycle Very small to ytests

g y ylarge

Fast Small

Cyclic Large Small Very smallCyclic Large Small Very small

Fast Large MediumSmall

V f t V l LVery fast Very large Large

Popular idea about the different factors between static and dynamic tests, but which factors are important ??



Number of cycles

Strain level

Monotonic Slow Nearly infinitive ¼ cycle Very smallStatic tests

y y y


Cyclic Slow Nearly infinitive

Small Very small


Large

Dynamic Monotonic Large ¼ cycle Very small to ytests

g y ylarge

Fast Small

Cyclic Large Small Very smallCyclic Large Small Very small


V f t V LVery fast Very large

Large

A historical review of the comparison between staticand dynamic tests - I



Number of cycles

Strain level

Static tests: Monotonic Slow Nearly

infinitive¼ cycle Very small


Static cyclic loading tests

very large


Small Very small

M ditests starting in 60s’

MediumFast Large

Large

Dynamic tests:

Monotonic Large ¼ cycle Very small to large

Fast Small

Resonant-Column

Cyclic Large Small Very small


Very fast Very large Large

Static torsional tests starting from early 70s’ at the PWRIfrom early 70s at the PWRI and 80’s at the IIS

Hollow cylindrical specimenHollow cylindrical specimen

vhτ : shear stress

Toyoura sand

(Iwasaki et al., 1977; Tatsuoka et al.,1978, 1979a&b)

δ

Pure shear

Initial isotropic stress state:

b

Initial isotropic stress state: σ’2= σ’a= σ’r= σ’t; and δ= 45o, b=0.5

12

WhWπΔ

=

mod

ulus

, m

2 )

Static torsional tests

nt s

hear

mG

eq(k

gf/c

m

Reliably measurable strain :S

ecan GReliably measurable strain :

larger than about 0.01 %

(Iwasaki et al., 1977)

Shear stress, τ

Peak-peak secant modulus: GeqDissipated energyΔW

Stored energy: W

ΔW

Shear strain, γ

Damping ratio:

Non-linear stress-strain

p g

12

WhWπΔ

=

Non-linear stress-strain curve of actual soil

Equivalent linearization taking into account the strain-Equivalent linearization taking into account the strainnonlinearity of shear modulus and damping ratio

Linear spring having Geq

Linear dash pot

Shear stress, τ

having GeqEquivalent shear modulus Geq

Dissipated energyΔW

t & γ

Shear strain, γ

Stored energy Wt & γ

An equivalent linear system having the same G & h as

Stress-strain curve of the equivalent linear system

∆having the same Geq & h as soil (i.e., a Voigt model)

(note a different shape from the one of actual soil)

∆γ

D i iGeq

Damping ratio:

14

WhWπΔ

=

Single amplitude shear strain ∆γshear strain, ∆γ

Geq and h depends on Dg

Linear spring having Geq

Linear dash pot

Shear stress, τ

having GeqEquivalent shear modulus Geq

Dissipated energyΔW

t & γ

Shear strain, γ

Stored energy Wt & γ

An equivalent linear system having the same G & h as

Stress-strain curve of the equivalent linear system

∆having the same Geq & h as soil (i.e., a Voigt model)

(note a different shape from the one of actual soil)

∆γ

Note: This linear system can be equivalent only for a sinusoidal time historyof input strain. If it is assumed that the stress-strain relation of soil were rate-independent (which is not true), the viscosity coefficient of the dash pot,p ( ), y p ,h=t/(dg/dt), is inversely proportional to the frequency, f, of the sinusoidalwave of strain. In this sense, the equivalent linearization method isapproximate in nature in particular when used for an arbitrary time history ofapproximate in nature, in particular when used for an arbitrary time history ofinput strain or stress. A relevant non-linear three-component model is a morerational model (fore details, refer to Di Benedetto & Tatsuoka., 1997).

Dynamic torsional tests:Resonant-column test

Reliably measurable strainReliably measurable strain,smaller than about 0.01 %,is possible, but a uncontrollable large number of loading cycles is applied.

Resonant-column apparatus(Lo Presti D Technical University(Lo Presti, D., Technical Universityof Torino )

Resonant-column testsInvented by the late Prof. IIDA, Kumiji in 1930s’ at the Earthquake Research Institute, the University of Tokyo and then ignored inthe University of Tokyo, and then ignored in Japan. Found in 1960s’ in the USA and developed mainly at the Univ. of Michigan (by the late Prof Richart) and imported to Japan

x

Mass: MA

the late Prof. Richart), and imported to Japan in 1970s’ by Dr Iwasaki.

Homogeneous linear isotropic elastic media

(density: ρ , shear modulus: G) dxxττ ∂

+∂

L x∂

（Cross-section: A, mass M A L ρ= ⋅ ⋅ ） Shear wave velocity: dx

V

A

L

Vs τ dy 0 u (horizontal displacement)

2L⎛ ⎞ M

Fig. 1 0( 0) sinu x a tω= = ⋅ Fig. 2

n LGF

ωρ ⋅⎛ ⎞= ⋅⎜ ⎟⎝ ⎠

tanA

MF FM

⋅ =

where

(Tatsuoka & Silver, 1980)

1) Cyclic torsional shear tests (f= 1/10 Hz at N= 10); and2) Resonant-column tests (fast, f= 100 Hz at N larger 5,000)A good agreement between the two types of testsat shear strains around 0.01 %

ulus

,

2(2 17 )

ar m

odu 2

0.5(2.17 )* 7001

eG pe−

= ⋅+

cant

she

aG

eq/G

* se

d se

c GN

orm

alis

N

Single amplitdu shear strain, g (Iwasaki et al., 1997)

Laboratory and field testing methods to evaluate non-linear stress-strain behaviour from “elastic behaviour at very small strains” toward “shear banding at very large strains”➔ difficult by a single test methodbanding at very large strains ➔ difficult by a single test method

Quasi-Linearelastic Shear bandingElastic-plastic-

viscousviscous

Bender

Development in measurements of very small stressand strain in static tests for the last 30 years

Element

Present reliably measurablePresent reliably measurablesmallest strain in static tests


A historical review of the comparison between staticand dynamic tests - II



Number of cycles

Strain level

Static tests: Monotonic Slow Nearly

infinitive¼ cycle Very small


New series starting in 80s’

very large


Small Very small

M di80s MediumFast Large

Large

Dynamic tests:

Monotonic Large ¼ cycle Very small to large

Fast Small

Resonant-Column

Cyclic Large Small Very small



A new static (monotonic & cyclicloading) torsional shear apparatusdeveloped at the IIS

(Tatsuoka et al., 1986, Tatsuoka, 1988)


A typical test result:shear strain rate= 0.001 %/min

（Teachavorasinskun et al., 1991a&b;Tatsuoka & Shibuya, 1991)




Stiffness at strain less than 0.001 %; G0=1,100 kgf/cm20.001 %; G0 1,100 kgf/cm


Shear modulus at strains less than 0 001 %;than 0.001 %;G0=1,100 kgf/cm2

Resonant-column tests

G/G

0(fast and many cycles) Cyclic (slow & a limited

number of cycles, up to 10)

RC & SC (I ki t

atio、

G RC & SC (Iwasaki et al., 1977)

New static cyclic (slow

Static monotonic (Teachavorasin-du

lus

ra e s a c cyc c (s o& a limited number of cycles, up to 10)（Teachavorasinskun et(Teachavorasin

skun et al., 1991a&b)

ar m

od （Teachavorasinskun et al., 1991a&b)

She 2

0.50

(2.17 )7001

eG pe−

= ⋅+

(p: kgf/cm2) Toyoura sand

Shear strain, g (1.0 %）(0.0001 ％）

Resonant-column tests

Agreement of G between static (slow ML & CL) and dynamic (fast CL) tests

G/G

0(fast and many cycles) Cyclic (slow & a limited

number of cycles, up to 10)

RC & SC (I ki t

atio、

G RC & SC (Iwasaki et al., 1977)

New static cyclic (slow

Static monotonic (Teachavorasin-du

lus

ra e s a c cyc c (s o& a limited number of cycles, up to 10)（Teachavorasinskun et(Teachavorasin

skun et al., 1991a&b)

ar m

od （Teachavorasinskun et al., 1991a&b)

She 2

0.50

(2.17 )7001

eG pe−

= ⋅+

(p: kgf/cm2) Toyoura sand

Shear strain, g (1.0 %）(0.0001 ％）

Another example showing a good agreement between the G values from static (slow ML & CL) and dynamic (fast CL & RC) torsional tests

（Tatsuoka et al., 1999a&b)

A historical review of the comparison between staticand dynamic tests - III



Number of cycles

Strain level

Monotonic Slow Nearly ¼ cycle Very smallStatic tests:

New series

yinfinitive

y y


New series starting in 80s’


Small Very small


Large

Dynamic Monotonic Large ¼ cycle Very small ytests:

Resonant-

g y yto large

Fast Small

Cyclic Large* Small (a half VeryResonant-column*

W

Cyclic Large* Small (a half to one)+

Very small+,*

Fast* Large+ Medium*S ll+Wave

propagation+Small+

Very fast*,+

Very large* Large

Resonant-column tests:measuring the dynamic

Wave velocity measurements:measuring the velocity of wavemeasuring the dynamic

response (i.e., the resonantfrequency) of a systemincluding the whole specimen

measuring the velocity of wavethat travels through part of amedia with a relatively small wavel th ( ll d t ti th fi tincluding the whole specimen

with a relatively large wavelength

length (usually detecting the fistarrived body wave of the samecategory).

Bottom fixed & top excitedp

A good agreement with a fine sand:perhaps because of a large wave shear length relativep p g gto the particle size in the BE tests

R t C lResonant-Column

Triaxial test

100

Bender Element(wave velocitymeasurement)G

0/F(e

)

Hostun sand (RF)

measurement)G

10 100 100010

Tested at ENTPE in Lyon (Di Benedetto)

Mean principal stress, p’ ( kPa)

（Tatsuoka et al., 1999a)

A historical review of the comparison between staticand dynamic tests - IV



Number of cycles

Strain level

Monotoni Slow Nearly ¼ cycle Very smallStatic tests: new

c y

infinitivey y



Small Very small

MediumFast LargeFast LargeLarge

Dynamic Monotoni Large ¼ cycle Very small to ytests:wave propagation

cg y y

largeFast Small

Cyclic Large Small (a half Very smallp p g Cyclic Large Small (a half to one)

Very small

Fast Large MediumS llSmall


Study on the effects of strain rate on the stress-strain behaviourat small strains by means of the triaxial tests:Wh th t i i l t t?Why the triaxial test?1) most relevant to undisturbed samples;2) less sophisticated and so better operational than torsional shear2) less sophisticated and so better operational than torsional shear

tests σv

T i i l i >Triaxial compression: σv >σh

Triaxial Extension: σh >σv

σhσh hσh

But, one serious technical problemto be overcome: bedding error !

Proximitytransducer

Bedding errorPressure cell

A i l t iLocal axial

strain

Axial strainincluding B.E.

Localdeformationtransducer

Triaxial testing system for small specimensTriaxial testing system for small specimens locally measuring axial strains developed at the IIS, the University of Tokyo

LDT; Local deformation transducer (Goto et al 1991)(Goto et al., 1991).

Pseudo-hinge

Membrane

Phosphor bronze LDT

g

Instrumentstrain-gaged strip

Heart of LDT(includes electric resistance strain gages

Instrument leadwire

TerminalGage leadwireActive e.r.s.g.

D'

B'

C

A

No. 2

No. 1

(includes electric resistance strain gages, terminals, wiring, sealant)

Scotch tape used to fix wireon the specimen surface

PB strip

(Front)

Teflon tube protectionFront face (tension side)

Instrument Leadwire

Membrane Surface Back face (compression side)

C'

A'

B

D

No. 4

No. 3

Membrane Surface

(Back)

Back face (compression side)

s’ = 49 kPaLoose Toyoura sand (void ratio, e= 0.798)

Proximitytransducer

Axial strain

Proximitytransducer

Axial strain

s h= 49 kPa

LDT

Proximeter

Local

Local axial strain

Axial strain including B.E.

Local

Local axial strain


Local deformation transducer


s’vTriaxialcompressionv

s’v= s’h

compression

v h

0 s’h(Tatsuoka et al., 1995)


Proximitytransducer

Axial strain

Proximitytransducer

Axial strain

s h= 49 kPa

Proximeter

LDT LDT

Local

Local axial strain


Local

Local axial strain


Proximeter




s’v= s’h

compression

v h

0 s’h


Proximitytransducer

Axial strain

Proximitytransducer

Axial strain

s h= 49 kPa

Proximeter

LDT LDT

Local

Local axial strain


Local

Local axial strain


Proximeter




s’v= s’h

compressionLDT

v h

E0: Initial Young’smodulus= 127 5 MPa

0 s’h

127.5 MPa

Elastic-weak visco plasticQuasi-Linear

elasticweak visco-plastic

Eeq

E0 Esec

Shear banding

How is this pictureElastic-strong visco-plastic

(Tatsuoka & Shibuya, 1991) distorted by BE!

Loose Toyoura sands’h= 49 kPa

Loose Toyoura sand

EsecMP

a)

ProximeterEse

c(M

LDT BE

Monotonic loading(ei= 0.798)

1 f1. Even with a fine sand, serious bedding error.2. Nearly the same Emax from static ML and CL testsEven with a fine sand, serious bedding error.


Loose Toyoura sands’h= 49 kPa

Loose Toyoura sanda) Eeq

Cyclic loading(ei= 0.819)Eseceq

(MP

a Eeq

Proximeter

sec

ecor

Ee

LDT

Ese

Monotonic loading(ei= 0.798)

S i b ddi i b th ML d CL t t- Serious bedding error in both ML and CL tests- Nearly the same Ｅ0 from static ML and CL tests only when the

axial strains are measured locally.

Large triaxial apparatusInstitute of IndustrialInstitute of Industrial Science, University of Tokyo,1986y ,

Dr. Goto,S.; the inventor of LDT (local deformation transducer)transducer)

Specimen (30 cm-dia. & 60 cm-high)

Dense well-graded gravel s’h= 785 kPa

LDT

Monotonic loading(ei= 0.224)Proximeter

Cyclic loading(ei= 0.235 & 0.219) BE( i )

Proximeter BE

(Tatsuoka et al., 1995)Gravel showing a more significant bedding error than sand

Dense well-graded gravel s’h= 785 kPa

LDT

Monotonic loading(ei= 0.224)Proximeter

Cyclic loading(ei= 0.235 & 0.219) BE( i )

Proximeter BE

S i b ddi i b th ML d CL t t- Serious bedding error in both ML and CL tests- Nearly the same Ｅ0 from static ML and CL tests only when the

axial strains are measured locally.

A historical review of the comparison between staticand dynamic tests - IV



Number of cycles

Strain level

Monotoni Slow Nearly ¼ cycle Very smallStatic tests: new

c y

infinitivey y



Small Very small

MediumFast LargeFast LargeLarge

Dynamic Monotoni Large ¼ cycle Very small to ytests:wave propagation

cg y y

largeFast Small

Cyclic Large Small (a half Very smallp p g Cyclic Large Small (a half to one)

Very small

Fast Large MediumS llSmall


Usually;- static: low strain rates

d i hi h t i t- dynamic: high strain ratesThen, the effects of strain rate are significant in static cyclic tests ?

At the number of loading cycle equal to 10 for the same stress amplitudeAt the number of loading cycle equal to 10 for the same stress amplitude

(Tatsuoka & Kohata., 1995;Di Benedetto & Tatsuoka, 1997)

Negligible effects ofloading frequency not

200

loading frequency notonly at strains=0.001 % or less but

150

Ai d i d H t d

f(Hz) 0.005 0.10 0.250 50 (MPa

)

also at lager strainsduring cyclic loading 50

100

cyclic loading under steady state conditions

Air-dried Hostun sandTest HOSTN5Neutral stress state σv= 137 kPa & σh= 78.4 kPa

0.50 1.00 1.50

E eq

Cyclic prestraining1961E-3 0.010

0.050.020.0050.002

y g yafter cyclic prestraininng of 65,000 cyclesof σv = 78.4~196 kPa

(Δε ) (%)0.001

s’v

137Cyclic loading toEvaluate Eeq and h

(Δεv)SA (%)

0 020

0.025f(Hz)

0.005 0.10

s’v= s’h78.40.015

0.020

0.25 0.50 1.00 1.50

ping

ratio

, h

0 s’h

(kPa)

0.005

0.010Dam

p

1E-3 0.010.000

HOSTN5

(Δεv)SA (%)0.005 0.02 0.050.0020.001

(Tatsuoka & Kohata., 1995;Tatsuoka et al., 1999b)

- Cyclic triaxial tests with all i l i

4Chiba gravel5th cyclea) very small axial strain

amplitude (less than0.001 %)

Chib l ( h d0

2 f (Hz) Ev(s)(MPa)

10 477.9 5 479.01 484 8

σh=19.6 kPaes

s, q

(kPa

- Chiba gravel (crushedsub-angular sandstoneDmax= 38 mm, D50= 3.5mm and U = 12 75)

-2

1 484.8 0.2 476.0 0.1 469.0 0.02 470.30.01 458.3ev

iato

r stre

7

Pa)

mm and Uc= 12.75)

-0.0010 -0.0005 0.0000 0.0005 0.0010-4

0.002 455.3De

Axial strain, εv (%)

5

6 Chiba gravel5th cycleσh=19.6 kPa

dεv/dt (%/min)

3.6x10-1

1en

t, q

(kPv

3

4

1.8x10-1

3.6x10-2

7.2x10-3

3.6x10-3

ss in

cremDespite a large difference

among the loadingfrequencies (up to 5,000

1

2

Start of loading

7.2x10-4

3.6x10-4

7.2x10-5

ator

stre

sq ( p ,times), essentially no effectsof loading frequency.

0.0000 0.0005 0.0010 0.00150

Start of loading

Dev

ia

Axial strain increment, Δεv (%)(Tatsuoka et al., 1999b)

- Cyclic triaxial tests with all i l i

4Chiba gravel5th cyclea) very small axial strain

amplitude (less than0.001 %)

Chib l ( h d0

2 f (Hz) Ev(s)(MPa)

10 477.9 5 479.01 484 8

σh=19.6 kPaes

s, q

(kPa

- Chiba gravel (crushedsub-angular sandstoneDmax= 38 mm, D50= 3.5mm and U = 12 75)

-2

1 484.8 0.2 476.0 0.1 469.0 0.02 470.30.01 458.3ev

iato

r stre

1

0

Chiba gravelStart of (k

Pa)

mm and Uc= 12.75)

-0.0010 -0.0005 0.0000 0.0005 0.0010-4

0.002 455.3De


-3

-2

-1 Chiba gravel5th cycleσh=19.6 kPa

unloading dεv/dt (%/min)

3.6x10-1

1.8x10-1

3 6 10-2emen

t, Δq

v

-5

-4

3

3.6x10 2

7.2x10-3

3.6x10-3

7.2x10-4

3 6 10-4ress

incr

eDespite a large differenceamong the loadingfrequencies (up to 5,000

-0.0015 -0.0010 -0.0005 0.0000-7

-63.6x10 7.2x10-5

Dev

iato

r stq ( p ,

times), essentially no effectsof loading frequency.

0.0015 0.0010 0.0005 0.0000D Axial strain increment, Δεv (%)(Tatsuoka et al., 1999b)

1500

2000Ev for (Δεv)SA= 0.0005 %

1000

1500 σh(kPa) σv/σh

19.6 1.0 49.0 1.0

MP

a)

500

49.0 3.2 49.0 5.3 49.0 7.5

Ev (M

1 11E-3 0.01 0.1 1 100

1.0

1.1

Ev for (Δεv)SA= 0.0005 %f (Hz)

Very small effects of

0.9 σv/σh (Ev)f= 10Hz(MPa)

1.0 476.6v) f=10

Hz

strain rate, or f, on thestiffness at small strains,in particular at more

0.8 1.0 604.5 3.2 1111.0 5.3 1419.27 5 1594 5

Ev/(E

vin particular at moreisotropic stress state

1E-3 0.01 0.1 1 100.7

7.5 1594.5

f (Hz)(Tatsuoka et al., 1999b)

Very small effects of strain rate, or f, also onthe strain path at very small strainsthe strain path at very small strains

0.0003

0.0002 f (Hz)

10 5

%)

0.0000

0.0001 1 0.2 0.10.02n,

εh (%

-0.0001

0.0000

Chiba gravelth

0 0 0.01 0.002

ial s

trai

0 0003

-0.00025th cycleσh= 19.6 kPaR

ad

-0.0008 -0.0004 0.0000 0.0004 0.0008-0.0003


(Tatsuoka et al., 1999b)

Very small effects of strain rate, or f, on thePoisson’s ratio at very small strains

0.6

Poisson s ratio at very small strains

0.5 ν for (Δεv)SA= 0.0005 %

0.3

0.4 σh(kPa) σv/σh

19.6 1.0ε h/dε v

0.2 49.0 1.0 49.0 3.249.0 5.3ν vh

= -d

0 0

0.149.0 5.3 49.0 7.5

1E-3 0.01 0.1 1 100.0

f (Hz)

600

8001000

σv/σh= 7.5e= 0.2496

(Δεv)SA=0.0005 %

f(e)= (2.17 - e)2/(1+e) f (Hz)10

400 σv/σh= 5.3e= 0.2481

σv/σh= 3.2e= 0.2474

σ /σh= 1

10 5 1 0.2) (

MP

a)

200

v h

e= 0.2470

σv/σh= 1

0.1 0.02 0.010.02

Ev/f(

e)

10 100 1000

v h

e= 0.2471

σv (kPa)v

1(Δεv)SA= 0.0005 %

f (Hz) 10 51

Young’s modulus and0.5

1 0.2 0.1 0.02 0.010 02h

Poisson’s ratio when dev= de1;increase with an increase in svand s /s respectively (this 0.02ν vand sv/sh respectively (thisissue is discussed more indetail later in this lecture)

1 1050.2

0.5σv/σh

detail later in this lecture)

- Small but noticeable effects of strain rate, or f, on thedamping ratio h0 (as h0 is more sensitive to inelasticdamping ratio, h0 (as h0 is more sensitive to inelasticbehaviour than E and n.

- More effects due to more inelastic behaviour at more

6σ (kPa) σ /σh f ( ) 0 0005 %

anisotropic stress state

4

σh (kPa) σv/σh

19.6 1.0 49.0 1.049.0 3.2

h0 for (Δεv)SA= 0.0005 %(%

)

4 49.0 5.3 49.0 7.5

ratio

, h0

2

ampi

ng r

1E-3 0.01 0.1 1 100

Da

(Tatsuoka et al., 1999b)f (Hz)

Summary of Ev at strains of 0.001 % or less, obtained mostly by static tests Hard rock core

106

(mostly cyclic triaxial tests, and partly monotonic triaxial tests):hard rock cores (Sato et al 1997) Resonant column

Ultrasonic waveConcrete Mortar- hard rock cores (Sato et al.,1997)- mortar & concrete (Sato et al.,1997)- sedimentary softrock

Resonant-column

105

sedimentary softrock- gravels and sands- clays

Sagamihara soft rock (U)

E v (kg

f/cm

2 )

Sandy gravel (D)

OAP clay (U)Metramo silty sand (U)

104

E

3

4

Chiba gravel

Ev= “E0 in thevertical direction”

sand (U)

Wet Chiba gravel (D)

Saturated Toyoura

0

1

2

3 Chiba gravel

5th cycleσh=19.6 kPa

f(Hz) d εv/dt (%/min)

10 3.6x10-1

5 1.8x10-1

1 3.6x10-2

0 2 7 2x10-3ess,

q (k

Pa)

Hostun sand (D)Air-dried

103

Vallericca clay N.C. Kaolin (CU TC)-3

-2

-1

0.2 7.2x10

0.1 3.6x10-3

0.02 7.2x10-4

0.01 3.6x10-4

0.002 7.2x10-5

Dev

iato

r stre Ev

10-5 10-4 10-3 10-2 10-1 100 101 102 103 104

.Axial strain rate, dεv/dt (%/min)

N.C. Kaolin (CU TC)

-0.0010 -0.0005 0.0000 0.0005 0.0010-4


New data:

106

Hard rock core

105

New data:Cement-mixedwell-graded gravel Ultrasonic waveConcrete Mortar

CTX (σ’h= 20 kPa)Cement= 60 kg/m3

105

Resonant-column

104

Cement-mixed gravel (D)

Cement= 60 kg/m3

Compacted at w= 5 %Cured for 7 days


v (MN

/m2 )

Cured for 7 days

104Sandy gravel (D)

OAP clay (U)Metramo silty sand (U)

103

E v

sand (U)


Saturated Toyoura

103


102

Vallericca clay (U) N C Kaolin (CU TC)

10-5 10-4 10-3 10-2 10-1 100 101 102 103 104


N.C. Kaolin (CU TC)

Omae et al. (2003)

Hard rock core

106

Ev= E0 in thevertical direction Hard rock core

f/cm

2 )

Ultrasonic waveConcreteE v (kg

fResonant-column

Ultrasonic waveConcrete Mortar

105Hard rock core & mortar:1. A very low dependency on the strain rate

Sagamihara soft rock (U)m2 )

2. With homogeneous* materials, nearly the same statically and dynamically evaluated Ev values(* compared with the wave length)m( compared with the wave length)

10-5 10-4 10-3 10-2 10-1 100 101 102 103 104

.Axial strain rate, dεv/dt (%/min)(Tatsuoka et al., 1999a&b)

Hard rock core

106

Hard rock core

/cm

2 )

Ultrasonic waveConcreteE v (kg

f/

Resonant-column


E

105

Concrete

Sagamihara soft rock (U)m2 )

ConcreteEv from body wave velocities (P waves): higher than those

evaluated statically, due likely to a high heterogeneity* ofg ( )m

10-5 10-4 10-3 10-2 10-1 100 101 102 103 104

the specimens (* compared with the wave length)

10 5 10 4 10 3 10 2 10 1 100 101 102 103 104


Hard rock core

106

Effects of heterogeneity;g y

Body waves that propagate faster through

Resonant-column


p opagate aste t ougrelatively stiffer parts are first detected.

Resonant column

105

The resonant-frequency of


cm2 )

q ya system consisting of the whole specimen represents

ff f

E v (kg

f/c the average stiffness of the whole specimen.

Sandy gravel (D)OAP clay (U)Metramo silty sand (U)

104

E


Saturated Toyoura

l ( )Metramo silty sand (U)

E v (k


104

Wet Chiba gravel (D)A very low

sand (U)Saturated Toyouradependency on the

strain rate


103

Vallericca clay N C Kaolin (CU TC)

5 4 3 2 1 0 1 2 3 4

y N.C. Kaolin (CU TC)

10-5 10-4 10-3 10-2 10-1 100 101 102 103 104


l ( )Metramo silty sand (U)

E v (k

2 )


104

kgf/c

m2

Wet Chiba gravel (D)E v (k

A noticeablesand (U)Saturated ToyouraA noticeable

dependency on the strain rate


103

Vallericca clay N C Kaolin (CU TC)

5 4 3 2 1 0 1 2 3 4

y N.C. Kaolin (CU TC)

10-5 10-4 10-3 10-2 10-1 100 101 102 103 104


1200

1400(a)

1000

1200

E 0 (

MPa

)Higher dependency on the strainE v

Lower dependency on the strain rate at higher strain rates

800

mod

ulus

, E Higher dependency on the strain rate at lower strain rates

E

400

600

You

ng's

m

200

400 σ'c = 98.1 kPa σ'c =196.2 kPa

' =392 4 kPa

Initi

al Y

0.00001 0.00010 0.00100 0.01000 0.100000

σ'c =392.4 kPa

Axial strain rate É (%/min)ε&Ev (= E0 at strains less than 0.001 %) from cyclic undrained t i i l t t i t i ll lid t d M t ilt d

.Axial strain rate, Év (%/min)vε

triaxial tests on isotropically consolidated Metramo silty sand

(Santucci de Magistris et al., 1999)

1200

1400(a)

MPa

)8

10

Metramo silty sandtest MO03undrained

(b)

%)

800

1000

mod

ulus

, E 0 (

M

6

εa,SA = 0.00075 %e0 = 0.307

σ' = 98.1 kPang ra

tio, h

0 (%

400

600

σ'c = 98.1 kPa' 196 2 kPtia

l You

ng's

m

2

4σ c 98.1 kPa σ'c =196.2 kPa σ'c =392.4 kPa

Initi

al d

ampi

n

0.00001 0.00010 0.00100 0.01000 0.100000

200 σ'c =196.2 kPa σ'c =392.4 kPa

.

Init

Axial strain rate, É (%/min)0.00001 0.00010 0.00100 0.01000 0.1000

0

.Axial strain rate É (%/min)ε& ε&

Ev and h0 at strains less than 0.001 %, respectively, decreases and increases noticeably with a decrease in the

.Axial strain rate, Év (%/min) Axial strain rate, Év (%/min)vε vε

decreases and increases noticeably with a decrease in the loading rate; showing that

1) the stress-strain behaviour at strains less than 0.001 % is not1) the stress strain behaviour at strains less than 0.001 % is not perfectly elastic; and

2) the viscous property is important even at strains less than 0.001 %.

(Santucci de Magistris et al., 1999)

20

22Metramo silty sandMO03UT

(a)

)16

18MO03UT

3rd cycleσ' = 392 4 kPaΔq

(kPa

)

12

14

larger strain rate

σ c= 392.4 kPa

Axial strain rate εvcrem

ent, Δ

8

10v

3.52x10-5 %/min

1.55x10-4 %/min

4 11 10-4 %/ istres

s inc

4

64.11x10 %/min

8.08x10-4 %/min

2.44x10-3 %/min Dev

iato

r s More than1000 times

0 0000 0 0005 0 0010 0 00150

2 start of loading 8.00x10-3 %/min

2.44x10-2 %/min

D

0.0000 0.0005 0.0010 0.0015Axial strain increment, Δεv (%)

Th t t i l ti t t i l th 0 001 %The stress-strain relations at strains less than 0.001 %: not perfectly linear ! - more linear at higher strain rates

Highly linear & rate-independent (i.e., elastic) stress-strainbehaviour appears only at strains of the order of 0 0001 % in

1400 Hi hl l ti t

behaviour appears only at strains of the order of 0.0001 % inthis particular case

1300

1400

Pa)

Highly elastic property

1200

s, E se

c (M

P

Quasi-elasticproperty

1100

Axial strain, 2(Δε )

s m

odul

us

1000

Axial strain, 2(Δεv)sa

1.05x10-6

2.02x10-6Metramo silty sandMO03UTnt

You

ng's

900 5.00x10-6

1.47x10-5

3rd cycleσ'c= 392.4 kPa

Seca

n

0.00001 0.00010 0.00100 0.01000 0.10000800

.Axial strain rate, Év (%/min)vε&

q Elastic limiting line

Slope; Eo at Increasing

strain rate 1 constant strain rate strain rate 1 constant strain rate

Creep

Strain rate 1

p

Strain rate 1 Strain rate 1

; Limit of elastic behaviour at each strain rate

Strain rate 1

; Limit of elastic behaviour at each strain rate

0 0.001 % ε

General trends of behaviour:1. A longer elastic (linear) zone at a higher strain rateg ( ) g2. The elastic zone may disappear at very low strain rates

The shear modulus at very small strain, G0, of RCT

BS+DC

Slurry Dry

Cement-treated soilDMM

RCT=rotary coringDC=direct coringBS=block samplingTS=fixed-piston thin-wall sampling

0high-quality samples is nearly the same with “Gff fi ld V ”

BS+DC

RCT Kazusa

Sedimentary soft rock Kobe Sagara

Miura

Uraga-A

RCT rotary coring

Uraga-B

Tokoname

from field Vs”.5000

BS+DC

Local axial strain measurements

s)

1000Range for Soft rocks andC t t t d il

Pa)

or s

oftro

cks

Cement-treated soils(BS+DC) and clays

{2(1

+ν)}

(Man

d 0.

42 fo

100G

0=E 0/{

5 fo

r cla

ys

Pleistocene clay site

(1:2)(1:

1)(ν=0

.5

TSBS

Tokyo bay

Osaka bay

OAP

Suginami

10 100 1000 500010

Gf=ρ(Vs)vh2 (MPa)(Tatsuoka et al., 1999a&b)

The shear modulus at very small strain, G0, of RCT

BS+DC

Slurry Dry

Cement-treated soilDMM

RCT=rotary coringDC=direct coringBS=block samplingTS=fixed-piston thin-wall sampling

0high-quality samples is nearly the same with “Gff fi ld V ”

BS+DC

RCT Kazusa

Sedimentary soft rock Kobe Sagara

Miura

Uraga-A

RCT rotary coring

Uraga-B

Tokoname

from field Vs”.

G0 values of more

5000BS+DC

Local axial strain measurements

s)

G0 values of moredisturbed samples are noticeably lower than “Gf

1000Range for Soft rocks andC t t t d il

Pa)

or s

oftro

cks

from field Vs”.

Technical problems with

Cement-treated soils(BS+DC) and clays

{2(1

+ν)}

(Man

d 0.

42 fo

Technical problems with conventional rotary core tube (RCT) sampling

100G

0=E 0/{

5 fo

r cla

ys

Pleistocene clay sitetube (RCT) sampling method for soft rocks

(1:2)(1:

1)(ν=0

.5

TSBS

Tokyo bay

Osaka bay

OAP

Suginami

10 100 1000 500010

Gf=ρ(Vs)vh2 (MPa)(Tatsuoka et al., 1999a&b)

Some conclusions - 2: 3) Elastic deformation characteristics can be

obtained by static tests measuring very small y g ystrains.

4) Statically and dynamically measured elastic deformation properties are essentially the samedeformation properties are essentially the same with fine-grained soils(Hardin (1978) & Woods (1991) have already(Hardin (1978) & Woods (1991) have already pointed out this fact).

Documents

Akashi strait bridge - Saitama University strait bridge.pdffor Akashi Strait Bridge 10 1.5 Pier 2P of Akashi Strait Bridge a t (MPa) 0.5 1.0 End of tower construction d pressure b