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International Symposium on Deformation Characteristics of Geomaterials, September 1~3, 2011, Seoul, Korea Bishop Lecture Laboratory stress-strain tests for developments in geotechnical engineering research and practice TATSUOKA, Fumio Department of Civil Engineering, Tokyo University of Science, Japan Professor Alan Bishop (1920-88)

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International Symposium on Deformation Characteristics of Geomaterials, September 1~3, 2011, Seoul, Korea

Bishop Lecture

Laboratory stress-strain tests

for developments in geotechnical

engineering research and practice

TATSUOKA, FumioDepartment of Civil Engineering,

Tokyo University of Science, Japan

Professor Alan Bishop (1920-88)

Topics:

To illustrate significant roles of laboratory stress-strain

tests of geomaterial for developments in geotechnical

engineering research and practice,

several recent advances in our understanding of:

1) quasi-elastic stress-strain behaviour;

2) rate-dependent stress-strain behaviour; and

3) strength and stiffness of compacted soil related to

field fill compaction control and design

are presented.

Shear stress, τ

0 Shear strain, γ (averaged for a specimen)

Behaviour at small strains

Rate effects

Strain softening

Peak strength

Non-linear pre-peak stress-strain behaviour

(Hypo) ElasticityPlasticity Viscosity

Shear banding with particle size effects

Inherent anisotropy

Ageing effect

Pressure-dependency

Dilatancy

1) quasi-elastic stress-strain behaviour; 2) rate-dependent stress-strain behaviour; and 3) strength and stiffness of compacted soil related to field fill compaction control and design;

among other many important topics.

Shear stress, τ

0 Shear strain, γ (averaged for a specimen)

Behaviour at small strains

Rate effects

Strain softening

Peak strength

Non-linear pre-peak stress-strain behaviour

(Hypo) ElasticityPlasticity Viscosity

Shear banding with particle size effects

Inherent anisotropy

Ageing effect

Pressure-dependency

Dilatancy

1) quasi-elastic stress-strain behaviour;

2) rate-dependent stress-strain behaviour; and 3) strength and stiffness of compacted soil related to field fill compaction control and design;

among other many important topics.

(Tatsuoka & Shibuya, 1991)

G0

Elastic ?

Elastic-slightly visco-plastic

Elastic-highly visco-plastic

Esec

Eeq

Gsec: monotonic loading (drained)

Monotonic loadingCyclic loading

Peak

Residual state

Geq: cyclic loading- drained-undrained (saturated

dense materials)

Geq: cyclic loading - undrained (saturated loose materials)

Limit of elastic response

Gsec, Geq

Geq

Gsec

(γ)SA γ

logγ, log(γ)SA

ττττ ττττ

Shear banding

Can we observe “rate-independent and reversible (i.e., elastic) behaviour” at very small strains?

Triaxial test:

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

Proximitytransducer

Local deformation transducer (L.D.T.)

Local axial strain

Axial strain including B.E.

Bedding errorPressure cell

Specimen

Well-compacted air-dried Chiba gravel (crushed well-graded angular sandstone from a quarry); Dmax= 38 mm, D50= 3.5 mm & Uc= 12.75

a b c

d e f

1mm

38.1 – 25.4 mm 25.4 -19.1 mm 19.1-9.52 mm

9.52-4.75 mm 4.75-2.0 mm < 2.0 mm

0.0000 0.0005 0.0010 0.00150

1

2

3

4

5

6

7

Start of loading

Chiba gravel

5th cycleσh=19.6 kPa

dεv/dt (%/min)

3.6x10-1

1.8x10-1

3.6x10-2

7.2x10-3

3.6x10-3

7.2x10-4

3.6x10-4

7.2x10-5

Deviator stress increment, q (kPa)

Axial strain increment, ∆εv (%)

Nearly no rate effects for largely different loading frequencies (by a factor up to 5,000 times)

- Cyclic triaxial tests; a very small axial strain amplitude (about 0.001 %)

-0.0010 -0.0005 0.0000 0.0005 0.0010-4

-2

0

2

4

f (Hz) Ev(s)(MPa)

10 477.9 5 479.0 1 484.8 0.2 476.0 0.1 469.0 0.02 470.3 0.01 458.3 0.002 455.3

Chiba gravel

5th cycleσh=19.6 kPa

Deviator stress, q (kPa)

Axial strain, εv (%)

10-510

-410

-310

-210

-110

010

110

210

310

4

103

104

105

106

Sandy gravel (D)

sand (U)

Hostun sand (D)

Resonant-column

Hard rock core

Ultrasonic waveConcreteMortar

Sagamihara soft rock (U)

OAP clay (U)

Air-dried

Wet Chiba gravel (D)

Metramo silty sand (U)

102

103

104

Vallericca clay (U)

.

Ev (MN/m

2)

Axial strain rate, dεv/dt (%/min)

N.C. Kaolin (CU TC)

105

Saturated Toyoura

Cement-mixed gravel (D)

- Relationships between Ev at strain of 0.001 % or less and axial strain rate of hardrock cores; mortar & concrete; sedimentary softrock; cement-mixed gravel; gravel; sand; & clay by static tests (mostly) & dynamic tests (partly)

→→→→Generally very small rate-dependency, but some details HH.

-0.0010 -0.0005 0.0000 0.0005 0.0010-4

-3

-2

-1

0

1

2

3

4

Chiba gravel

5th cycle

σh=19.6 kPa

f(Hz) d εv/dt (%/min)

10 3.6x10-1

5 1.8x10-1

1 3.6x10-2

0.2 7.2x10-3

0.1 3.6x10-3

0.02 7.2x10-4

0.01 3.6x10-4

0.002 7.2x10-5

Deviator stress, q (kPa)

Axial strain, εv (%)

Ev

Ev= “E0 in the vertical direction”

A very low rate-dependency in cyclic triaxial tests on moist Chiba gravel→ nearly elastic behaviour

A large number of data sets show that “the shear modulus at very small strain, G0, of high-quality undisturbed samples by triaxial tests” is essentially the same with “Gf from field Vs” evaluated under otherwise the same conditions.

(Tatsuoka et al., 1999a&b)10 100 1000 5000

10

100

1000

5000

RCTBS+DC

(1:2)(1:1)

Range for Soft rocks andCement-treated soils(BS+DC) and clays

RCTBS+DC

Kazusa

Sedimentary soft rock

Local axial strain measurements

G0=E0/{2(1+ν)} (MPa)

( ν=0.5 for clays and 0.42 for softrocks)

Gf=ρ(V

s)vh

2 (MPa)

Kobe

Sagara

Miura

Uraga-A

Slurry

Dry

Pleistocene clay site

Cement-treated soilDMM

TSBS

Tokyo bay

Osaka bay

OAP

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

Suginami

Uraga-B

Tokoname

Relative low G0 of RCT samples due to sample disturbance

Sandy gravel (D)

sand (U)

Hostun sand (D)

OAP clay (U)

Air-dried

Wet Chiba gravel (D)

Metramo silty sand (U)

10-510

-410

-310

-210

-110

010

110

210

310

4

103

104

Vallericca clay

.

Ev (kgf/cm

Axial strain rate, dεv/dt (%/min)

N.C. Kaolin (CU TC)

Saturated Toyoura

10Ev (kgf/cm

2 )With soft soils, a noticeable rate-dependency even at a strain of 0.001 %

CU Cyclic triaxial tests on Metramo silty sand

“More linear stress-strain relations” at higher strain rates

(Santucci de Magistris et al., 1999)

0.0000 0.0005 0.0010 0.00150

2

4

6

8

10

12

14

16

18

20

22

larger strain rate

start of loading

Metramo silty sand

MO03UT

3rd cycle

σ'c= 392.4 kPa

(a)

Axial strain rate εv

3.52x10-5 %/min

1.55x10-4 %/min

4.11x10-4 %/min

8.08x10-4 %/min

2.44x10-3 %/min

8.00x10-3 %/min

2.44x10-2 %/min

Deviator stress increment, ∆q (kPa)

Axial strain increment, ∆εv (%)

Different by a factor of more than 1000 times

Undrained cyclic triaxial test on Metramo silty clay

Axial strain rate:

Higher strain rate

Essentially rate-independent & reversible (i.e., elastic) stress-strain behaviour at strains about 0.0001 % ! More rate-dependent behaviour at larger strains !

(Santucci de Magistris et al., 1999)

0.00001 0.00010 0.00100 0.01000 0.10000800

900

1000

1100

1200

1300

1400

Axial strain, 2(∆εv)sa

1.05x10-6

2.02x10-6

5.00x10-6

1.47x10-5

Metramo silty sand

MO03UT

3rd cycle

σ'c= 392.4 kPa

.

Secant Young's modulus, Esec (MPa)

Axial strain rate, Év (%/min)

Essentially elastic property

Quasi-elastic property

vε&

Axial strain:Yet, the stiffness becomes rate-independent when the strain rate becomes higher than some limit.

q Elastic limiting line Increasing the strain rate Creep ; Limit of liner elastic behaviour at each strain rate 0 ε

0.001 %

General trends of behaviour:1. The stress-strain relation approaches the elastic limiting line as the strain rate increases. 2. The elastic zone becomes larger as the strain rate increases.3. The elastic zone disappears at very low strain rates.

These trends can be described by the non-linear three-component model.

The test results are interpreted and simulated by:the non-linear three-component model (Di Benedetto

& Tatsuoka, 1997; Di Benedetto et al., 2002; Tatsuoka et al., 2002, 2008)

EP

V

ε&

eε& irε&

Hypo-elastic

Plastic

Viscous

σ

ε&

(stress)

(strain rate)

0.0 0.5 1.0 1.5 2.0 2.5

1.0

1.5

2.0

2.5

Drained TC test at σ'h= 400 kPa

Silica No. 8 sand

Reference stress-strain relation

ML at εv =

0.125 %/min

Experiment

Simulation

Effective principal stress ratio, R= σ

v'/σh'

Irreversible shear strain, γir (%)

.

Sustained loading at q= 300 kPa for 24 hours

(Kiyota & Tatsuoka, 2006, S&F; Tatsuoka et al., 2008a, S&F)

0. 3 mm

Drained TC test (σ’h= 400 kPa) on loose silica No. 8 sand

A large quasi-elastic zone develops upon the restart of ML at a constant strain rate after creep deformation.■The size becomes larger with an increase in the creep strain and the strain rate during ML.

(Tatsuoka et al. 2008b, S&F)

Multiple large quasi-elastic zones develop by ageing effects (i.e., bonding) in addition to creep deformation;drained TC tests on compacted moist cement-mixed well-graded gravelly soil (model Chiba gravel)

0.0 0.1 0.2 0.3 0.40.0

0.5

1.0

1.5

2.0

2.5

}

CD TC (σh'= 19.8 kPa)

J016 (ML;tini= 14.0 days)

JA016(ML; t

ini= 7.5 days)

JA004 (multiple SL stages; t

ini= 6.8 days; t

c= 9.5 days)

8.2 hours13.5 hours

SL for 21.7 hours

Simulation q: Experiment q:

Deviator stress, q (MPa)

Axial strain, εv (%)

Respective basic reference curves

0 7 14Elapsed time (day)

Loading histories Ageing effects by initial curing at q= 0

0.04 0.06 0.08 0.10 0.12 0.141.2

1.4

1.6

1.8

2.0

2.2

2.4

q (experiment)

JA004 (tini= 6.8 days;

tc= 9.5 days)

SL(8.2 hours)

SL(13.5 hours) qf (simulation)

Deviator stress, q (MPa)

Axial strain, εv (%)

q (simulation)

(Tatsuoka et al. 2008b, S&F)

Kinematic development of quasi-elastic zone by ageing effects in addition to creep deformation at multiple stress states

Yield point forlarge-scale yielding

Kinematic development of yield locus by ageing and creep:- initial curing for 9 days at stress point O; and - initial curing for 7 days at O + re-curing for 2 days at stress points B, C, D & E (cement-mixed model Chiba gravel)

(Ezaoui et al. 2010, S&F)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

0.0

2.0

4.0

Cement mixed Chiba gravel 2 days re-curing points

YL expanded from initial curingpoint O (9 days)

E

D

Deviator stress, q (MPa)

Effective mean principal stress, p'(kPa)

YL expanded from point E

Peak States

From point D

From point C

From point B

C

B

Different shapes and locations of YL by different combined effects of bonding & friction mechanisms !

o

Peak stress states (some difference by different loading histories)

1) The elastic deformation characteristics can be evaluated by not only dynamic tests but also static tests.

Rate-independent behaviour: summary-1

‘Static’ & ‘dynamic’: terminologies for systems, not for material properties

Static Young’s modulus & dynamic Young’s modulus:should not be used.

Static and dynamic measurements of Young’s modulus: OK !

2) Statically and dynamically measured elastic deformation properties are essentially the same with fine-grainedgeomaterials.

With heterogeneous materials (e.g., concrete, very coarse-grained geomaterials and hard rocks having dominant discontinuities), the elastic modulus from wave velocity with a short wave length could be significantly larger than the statically determined average value of a given mass.

3) The size of quasi-elastic zone increases with an increase in:

i) the strain rate and the creep strain (due to the viscousproperties); and

ii) ageing effect.

Rate-independent behaviour: summary-2

Shear stress, τ

0 Shear strain, γ (averaged for a specimen)

Behaviour at small strains

Rate effects

Strain softening

Peak strength

Non-linear pre-peak stress-strain behaviour

(Hypo) ElasticityPlasticity Viscosity

Shear banding with particle size effects

Inherent anisotropy

Ageing effect

Pressure-dependency

Dilatancy

1) quasi-elastic stress-strain behaviour; 2) rate-dependent stress-strain behaviour; and 3) strength and stiffness of compacted soil related to field fill compaction control and design;

among other many important topics.

Rate-dependent stress-strain behaviour

■■■■ Isotach and non-Isotach types in drained TC

■ Viscous behaviour of sand in direct shear

■ Viscous behaviour of clay in 1D compression

■ Mechanism of non-Isotach viscous behaviour

■ Rate-sensitivity and viscosity type parameter

■ Creep and stress relaxation

■ Summary

.Continuous ML at a constant strain rate ε0,assumed to be the same for the four different viscous property types

1 3

ir ir irγ ε ε= −

1 3'/ 'R σ σ=

Isotach type: the strength during ML at constant strain rate increases with an increase in the strain rate; andH...

Isotach

relationsby continuous ML at a constant strain rate 10ε0

.Continuous ML at a constant strain rate ε0

.

1 3

ir ir irγ ε ε= −

1 3'/ 'R σ σ=

irR γ−

The current stress is a unique function of instantaneous strain and its rate. Most classical & popular in modelling

Isotach

relationby continuous ML at a constant strain rate 10ε0

.Continuous ML at a constant strain rate ε0

.Step increase in the strain rate by a factor of 10

irR γ−

1 3

ir ir irγ ε ε= −

1 3'/ 'R σ σ=

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.61.0

1.2

1.4

1.6

1.8

2.0

2.2

(3)

(2)

(1)

.

..

.

.

..

.

.

..

.

.

Experiment

SimulationCreep (12 hours)

Reference relation

.

Elastic relation Creep (24 hours)

Kitan clay No. 20 (undisturbed)Depth= 65.02-65.34 mCD TC: σ'

h= 335 kPa

ε0= 0.00078 %/min

Effective principal stress ratio, R= σ' v/σ' h

Axial strain, εv (%)

2ε0

50ε0

5ε0

ε0/2

20ε0

ε0

ε0/2

2ε0

ε0/2

ε0

10ε0

Isotach behaviour in drained TC on undisturbed Pleistocene clay (e0= 0.81; PI= 41.1) and simulation

σ’h

σ’v

(Tatsuoka et al., 2008a, S&F)

Creep deformation

55 60 65 70 75 80

1.30

1.35

1.40

1.45

1.50

1.55

28 30 32 34 36 38 40 42 440.65

0.70

0.75

0.80

10 12 14 16 18 20 22 24

0.25

0.30

0.35

0.40

Experiment

Simulation

(3) Creep for 24 hours

Times (h)

Simulation

Experiment

Creep for 12 hours(2)

Simulation

Experiment

(1)

Kitan clay No.20Undisturbed

Creep for 12 hours

Axial strain, ε

v (%)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.61.0

1.2

1.4

1.6

1.8

2.0

2.2

(3)

(2)

(1)

.

..

.

.

..

.

.

..

.

.

Experiment

SimulationCreep (12 hours)

Reference relation

.

Elastic relation Creep (24 hours)

Kitan clay No. 20 (undisturbed)Depth= 65.02-65.34 mCD TC: σ'

h= 335 kPa

ε0= 0.00078 %/min

Effective principal stress ratio, R= σ' v/σ' h

Axial strain, εv (%)

2ε0

50ε0

5ε0

ε0/2

20ε0

ε0

ε0/2

2ε0

ε0/2

ε0

10ε0

(Tatsuoka et al., 2008a, S&F)

TESRA type: the strength during ML at constant strain rate is independent of strain rate; andH

Isotach

TESRA

relationsby continuous ML at a constant strain rate 10ε0

.Continuous ML at a constant strain rate ε0

.

Very peculiar

irR γ−

1 3

ir ir irγ ε ε= −

1 3'/ 'R σ σ=

A positive stress jump upon a step increase in the strain rate decays with strain towards zero.

Isotach

TESRA

relationsby continuous ML at a constant strain rate 10ε0

.Continuous ML at a constant strain rate ε0

.Step increase in the strain rate by a factor of 10

Very peculiar

irR γ−

1 3

ir ir irγ ε ε= −

1 3'/ 'R σ σ=

Isotach

TESRA

relationsby continuous ML at a constant strain rate 10ε0

.Continuous ML at a constant strain rate ε0

.Step increase in the strain rate by a factor of 10

Very peculiar

irR γ−

1 3

ir ir irγ ε ε= −

1 3'/ 'R σ σ=

TESRA= Temporary Effects of Strain Rate and strain Acceleration (i.e., rate of strain rate)

TESRA behaviour in drained TC (σ’h= 400 kPa); saturated loose Silica No. 8 sand

(Kiyota & Tatsuoka, 2006, S&F; Tatsuoka et al., 2008a, S&F)

0 5 10 15 20

1.0

1.5

2.0

2.5

3.0

3.5

4.0

..

..

... .

No. 12: εv= 20ε

0

Effective principal stress ratio, R = σ

v'/σh'

Irreversible shear strain, γir (%)

Drained TC, ε0= 0.0125 %/min

No. 9: εv= ε

0/10

No. 10: εv= ε

0

No. 11: εv= 10ε

0

.

0. 3 mm

Drained TC, ε0= 0.0125 %/min.

0 5 10 15 20

1.0

1.5

2.0

2.5

3.0

3.5

4.0

.

..

..

..

...

.. .

...

..

..

.

.

No.18: εv change from 1/10ε

0 to 20ε

0

ε0

10ε0

ε0

ε0/10ε

0

10ε0

ε0

ε0/10ε

0

10ε0ε

0

ε0/10

10ε0

ε0/10ε

0

20ε0

10ε0

ε0

ε0

20ε0

ε0/10

10ε0

Effective principal stress ratio, R = σ

v'/σh'

Irreversible shear strain, γir (%)

ε0

Drained TC

No.10: εv= ε

0= 0.0125 %/min

.

(Kiyota & Tatsuoka, 2006, S&F; Tatsuoka et al., 2008a, S&F)

2 3 4 5 6 7 8 9

2.0

2.5

3.0

..

..

10ε0

10ε0

ε0

ε0

ε0

ε0/10

ε0/10

ε0/10

10ε0

20ε0

ε0

Effective principal stress ratio, R = σ

v'/σh'

Irreversible shear strain, γir (%)

Drained TC, ε0= 0.0125 %/min

Axial strain rate from 1/10ε0 to 20ε

0

Experiment

Simulation

Reference stress-strain relation

.

.

.

.

.

.

.

.

. .

TESRA behaviour

0.0 0.5 1.0 1.5 2.0 2.5

1.0

1.5

2.0

2.5

Reference stress-strain reration

Drained TC test at σh'= 400 kPa on silica No. 8

with sustained loading at q= 300 kPa for 24 hoursduring otherwise ML at ε

v = 0.125 %/min

Experiment

Simulation

Principal stress ratio, R= σ

v'/σh'

Irreversible shear strain, γir (%)

.

Creep deformation and its simulation by the TESRA model

Kiyota & Tatsuoka (2006), S&F

Isotach

Combined

TESRA

relationsby continuous ML at a constant strain rate 10ε0

.Continuous ML at a constant strain rate ε0

.

Combined type; combining Isotach & TESRA types, the strength at a constant strain rate increases with strain rate, andH

1 3

ir ir irγ ε ε= −

1 3'/ 'R σ σ=

irR γ−

Isotach

Combined

TESRA

relationsby continuous ML at a constant strain rate 10ε0

.Continuous ML at a constant strain rate ε0

.

A positive stress jump upon a step increase in the strain rate decays with strain to a smaller positive non-zero value

Step increase in the strain rate by a factor of 10

1 3

ir ir irγ ε ε= −

1 3'/ 'R σ σ=

irR γ−

Isotach

Combined

TESRA

P & N

Positive & Negative type: the strength decreases with an increase in the constant strain rate, andH..

relationsby continuous ML at a constant strain rate 10ε0

.Continuous ML at a constant strain rate ε0

.

Most peculiar

irR γ−

1 3

ir ir irγ ε ε= −

1 3'/ 'R σ σ=

A positive stress jump upon a step increase in the strain rate decays with strain towards a negative value.

Isotach

Combined

TESRA

P & N

relationsby continuous ML at a constant strain rate 10ε0

.Continuous ML at a constant strain rate ε0

.

Most peculiar

irR γ−

1 3

ir ir irγ ε ε= −

1 3'/ 'R σ σ=

Step increase in the strain rate by a factor of 10

P&N behaviour in drained TC (σ’h= 400 kPa); air-dried dense Albany sand (poorly-graded & round; D50= 0.30 mm, Uc= 2.22, Gs= 2.67, emax= 1.335 & emin= 0.73)

Tatsuoka et al. (2008a, S&F)

0 5 10 15 20 25

1

2

3

4

5

Effective principal stress ratio, R= σ' v/σ' h

0.05 %/min ( 86.4 %)

0.005 %/min ( 85.4 %)

0.5 %/min ( 87.6 %)

εv= 5.0 %/min (D

rc= 85.3 %)

Albany sand (air-dried) Dense Drained TC (σ'

h= 400 kPa)

Irreversible shear strain, γir(%)

.

Consistently negative effects of strain rate

0.5 mm

0 5 10 15 20 250.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

Effective principal stress ratio, R= σ' v/σ' h

Drc = 85.1 %

Drained TC, σ'h = 400kPa

SimulationExperiment

Irreversible shear strain, γir (%)

Albany sand (air-dried)

Reference curveStrain rate=

10ε0

. .ε0

5ε0

.ε0/10.20ε

0

.

ε0= 0.0625 %/min.

12 16 20 243.2

3.6

4.0

4.4

Effective principal stress ratio, R= σ' v/σ' h

Simulation

Experiment

Irreversible shear strain, γir (%)

ε0= 0.0625 %/min.

.ε0/10

20ε0

.

5ε0

.

A higher strength at a lower strain rate

Note: nearly the same trend of rate effect when air-dried and saturated

irε

σ

f irσ ε− relation

Interpretation of the peculiar test result

irε

σ

.

.

0.1ε0

Continuous ML at different constant strain rates

ε0

10ε0.

0

f irσ ε− relation

Negative Isotach viscosity: ( )v Isotachσ−

irε

σ

A

B

D

- The behaviour if the viscous property comprises only negative Isotach component - But, no such materials exist !

Step increase in the strain rate

Negative Isotach viscosity: ( )v Isotachσ−

f irσ ε− relation .

.

0.1ε0

Continuous ML at different constant strain rates

ε0

10ε0.

0

irε

A

B

C D

( )v Isotachσ−

Actual behaviour

σ

f irσ ε− relation

Step increase in the strain rate

.

.

0.1ε0

Continuous ML at different constant strain rates

ε0

10ε0.

0Negative Isotach viscosity: ( )v Isotachσ−

irε

A

B

C D

The behaviour solely by the negative isotach component

( )v Isotachσ−

TESRA viscosity (positive viscosity); ( )v TESRAσ

Actual behaviour

σ

f irσ ε− relation

Step increase in the strain rate

.

.

0.1ε0

Continuous ML at different constant strain rates

ε0

10ε0.

0Negative Isotach viscosity: ( )v Isotachσ−

irε

A

B

C D

( )v Isotachσ−

TESRA viscosity (positive viscosity); ( )v TESRAσ

Actual behaviour

σ

f irσ ε− relation

Step increase in the strain rate

0

.ε0

Positive & Negative type:

{ ( }( ) )v isotach

v

TESR

v

A σσ σ −= +

.

.

0.1ε0

Continuous ML at different constant strain rates

ε0

10ε0.

0Negative Isotach viscosity: ( )v Isotachσ−

irε

σ

A

B

- The creep behaviour if the viscous property comprises solely negative Isotach component - But, no such materials exist !

f irσ ε− relation

Actual creep behaviour

Start of creep

.

.

0.1ε0

Continuous ML at different constant strain rates

ε0

10ε0.

0Negative Isotach viscosity: ( )v Isotachσ−

2 3 4 53.8

4.0

4.2

4.4Effective principal stress ratio, R= σ' v/σ' h

Drained creep for two hours

Simulation

Experiment

Irreversible shear strain, γir (%)

ε0= 0.0625 %/min.

ε0

. 10ε0

.

20ε0

.

ε0

. Significant positive creep deformation

10000 12000 14000 16000 18000

3.0

3.2

3.4

3.6

Experiment

Simulation

Start of creep for two hours

Irreversible shear strain, γir (%)

Elapsed time, t (sec)

0.5 mm

Albany sand

Summary: At least, four different viscous property types by a wide variety of geomaterials in TC and PSC tests

Isotach

Combined

TESRA

P & N

Broken curves:relations

by continuous ML at a constant strain rate equal to 10ε0Step increase in the strain

rate by a factor of 10

Isotach

P & N

.

Combined

TESRA

Continuous ML at a constant strain rate ε0

.

irR γ−

1 3

ir ir irγ ε ε= −

1 3'/ 'R σ σ=

Rate-dependent stress-strain behaviour

■ Isotach and non-Isotach types in drained TC

■■■■ Viscous behaviour of sand in direct shear

■ Viscous behaviour of clay in 1D compression

■ Mechanism of non-Isotach viscous behaviour

■ Rate-sensitivity and viscosity type parameter

■ Creep and stress relaxation

■ Summary

0.0

-0.5

-1.0

-1.5

-2.0

-2.5

-3.0

-2 0 2 4 6 8 10 12 14

0.0

0.2

0.4

0.6

0.8

1.0

Stress ratio corrected for friction R

DS=τ vh/σ

v

Shear displacement, s [mm]

Toyoura sand (batchI)σv=50kPa

s [mm/min]

I-01: 0.609 60.907 I-02: 0.606 61.240 I-03: 0.606 15.389 I-04: 0.605 15.377 I-05: 0.605 15.315 I-06: 0.603 1.0070 I-07: 0.603 1.0090 I-08: 0.606 0.1359 I-09: 0.608 0.1357 I-10: 0.606 0.0162 I-11: 0.608 0.0132 I-12: 0.607 0.0132 I-13: 0.609 0.0016 I-14: 0.607 0.0006

e0

.

Vertica

l compressio

n, d [m

m]

Air-dried dense Toyoura sand13 seconds to

complete

13 days

to complete

A series of ML tests at shear displacement rates different by a factor of up to 105(Duttine et al., 2009a, S&F)

Peak strength: essentially independent of shear displacement rate (i.e., TESRA viscosity)

(Duttine et al., 2009a; S&F)

1E-4 1E-3 0.01 0.1 1 10 1000.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00

batchI batchII

batchI batchII

Stress ratio corrected

for friction, R

DS=τ vh/σ

v

Peak state

Residual state

Shear displacement rate, s [mm/mn]

-0.0075

1 : 100 000

Dense Toyoura sandσv=50kPa (batchesI&II)

.

Stress ratio, τ

vh/σ

v

Shear displacement rate (mm/min)

Residual strength: decreases with an increase in shear displacement rate (i.e., P&N viscosity)

(Duttine et al., 2009a; S&F)

1E-4 1E-3 0.01 0.1 1 10 1000.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00

batchI batchII

batchI batchII

Stress ratio corrected

for friction, R

DS=τ vh/σ

v

Peak state

Residual state

Shear displacement rate, s [mm/mn]

-0.0075

1 : 100 000

Dense Toyoura sandσv=50kPa (batchesI&II)

.

Stress ratio, τ

vh/σ

v

Shear displacement rate (mm/min)

Significant rate effects

0 4 8 12

0.0

0.2

0.4

0.6

0.8

1.0

α=0.25 ; m=0.025 ; sir

ref=5.10

-7 mm/s

θi=0 ; θ

f=-0.54 ; r

i=10

-15 ; r

f=10

-25

sir

o.θ=s

ir

o.r1=3.186 mm ; n

θ=n

r1=1.556

Ge

DS=20 /mm

Parameters for simulation.

Stress ratio corrected for friction, R

DS=τ vh/σ

v

Shear displacement, s [mm]

Toyoura sand (batch I)σv=100kPa; D

r0=95.04%

simulation

reference curve

experiment

.ML s=0.008~0.8mm/mn

0.8 1.2 1.6 2.0 2.4 2.80.78

0.80

0.82

0.84

0.86

0.88

0.90

0.92

100

Stress ratio corrected for friction, RDS=τ vh/σ

v

Shear displacement, s [mm]

simulation

experiment

reference curve

Toyoura sand (batch I)σv=100kPa; D

r0=95.04%

10*

* in ratio to the basic disp. rate=0.008mm/min

1

10

100

α=0.25 ; m=0.025 ; sir

ref=5.10

-7 mm/s

θi=0 ; θ

f=-0.54 ; r

i=10

-15 ; r

f=10

-25

siro.θ=sir

o.r1=3.186 mm ; n

θ=n

r1=1.556

Ge

DS=20 /mm

Parameters for simulation.

TESRA behaviour

The viscous property type changes with strain in a single test.

0 4 8 12

0.0

0.2

0.4

0.6

0.8

1.0

α=0.25 ; m=0.025 ; sir

ref=5.10

-7 mm/s

θi=0 ; θ

f=-0.54 ; r

i=10

-15 ; r

f=10

-25

sir

o.θ=s

ir

o.r1=3.186 mm ; n

θ=n

r1=1.556

Ge

DS=20 /mm

Parameters for simulation.

Stress ratio corrected for friction, R

DS=τ vh/σ

v

Shear displacement, s [mm]

Toyoura sand (batch I)σv=100kPa; D

r0=95.04%

simulation

reference curve

experiment

.ML s=0.008~0.8mm/mn

8.4 8.8 9.2 9.6 10.0 10.40.58

0.60

0.62

0.64

0.66

0.68

0.70

α=0.25 ; m=0.025 ; sirref=5.10-7 mm/s

θi=0 ; θ

f=-0.54 ; r

i=10-15 ; r

f=10-25

siro.θ=sir

o.r1=3.186 mm ; n

θ=n

r1=1.556

Ge

DS=20 /mm

Parameters for simulation.

1

1

Stress ratio corrected for friction, R

DS=τ vh/σ

v

Shear displacement, s [mm]

simulation

experiment

reference curve

Toyoura sand (batch I)σv=100kPa; D

r0=95.04%

* in ratio to the basic disp. rate=0.008mm/min

100*

1

100

P & N behaviour

Rate-dependent stress-strain behaviour

■ Isotach and non-Isotach types in drained TC

■ Viscous behaviour of sand in direct shear

■■■■ Viscous behaviour of clay in 1D compression

■ Mechanism of non-Isotach viscous behaviour

■ Rate-sensitivity and viscosity type parameter

■ Creep and stress relaxation

■ Summary

16

18

20

22

24

500 1000

i

hi

f

Effective axial stress, σa' (kPa)

300

Axial strain, ε a (%)

Experiment Simulation (isotach) Reference curve

Test Name: KLN05 Kaolin w

0= 48.1 (%)

wL= 44.1 (%)

IP= 21.3

Strain rate gh, ij: 0.005 %/minfg; jk: 0.05 %/mkl: 0.0005 %/minhi: creep for one day

l

k

j

h

g

1D compression changing the strain rate, saturated kaolin made from slurry(Isotach type) (Kawabe et al. 2009b).

16

18

20

22

24

500 1000

i

hi

f

Effective axial stress, σa' (kPa)

300

Axial strain, ε a (%)

Experiment Simulation (isotach) Reference curve

Test Name: KLN05 Kaolin w

0= 48.1 (%)

wL= 44.1 (%)

IP= 21.3

Strain rate gh, ij: 0.005 %/minfg; jk: 0.05 %/mkl: 0.0005 %/minhi: creep for one day

l

k

j

h

g

1D compression changing the strain rate, saturated kaolin made from slurry(Isotach type) (Kawabe et al. 2009b).

0 6 12 18 24

0.0

0.2

0.4

0.6

0.8

Simulation

Simulation

Experiment

Experiment

Creep axial strain, ∆ε a (%)

Elapsed time, ∆t (hour)

Test Name: KLN05 Kaolinw0= 48.1 (%)

wL= 44.1 (%)

IP= 21.3

hi: σa' = 500 kPa

de: σa' = 250 kPa

Sustained loading for one day

Non-Isotach behaviour (combined type) in 1D compression, saturated reconstituted Fujinomori clay (Kawabe et al. 2009a)

22

21

20

19

18

17

800 1100 1400 1700 2000

Simulation Isotach Combined Reference curve

Irreversible axial strain, εa

ir (%)

Effective axial stress, σa' (kPa)

Experiment

Test No. 5: Reconstituted Fujinomori clay

0 5 10 15 20 250.0

0.1

0.2

0.3

Sustained loading at σa' = 900 kPa

Creep axial strain, ∆ε a (%)

Elapsed time, ∆t (hour)

ExperimentSimulation

Isotach Combined

Rate-dependent stress-strain behaviour

■ Isotach and non-Isotach types in drained TC

■ Viscous behaviour of sand in direct shear

■ Viscous behaviour of clay in 1D compression

■■■■ Mechanism of non-Isotach viscous behaviour

■ Rate-sensitivity and viscosity type parameter

■ Creep and stress relaxation

■ Summary

Non-Isotach behaviour in DS tests on unbound interfaces between various types of solid (i.e., rocks and others), Dieterich and Kilgore (1994)

Granite#60 surfaceσave= 15 MPa

Granite#60 surface, 1 mm gougeσave= 10 MPa

Soda-lime g lass#60 surfaceσave= 5 MPa

10μm/s 10μm/s

10μm/s 10μm/s

1μm/s 1μm/s

1μm/s 1μm/s

1μm/s 1μm/s0.1μm/s 0.1μm/s

Mobilised friction coefficient

conta ave ct

a contave ct

A

A

τµ

α

σσ

τ

α

⋅ ⋅= =

⋅ ⋅

aveσ

aveτ

Real contact area, α

Real yield shear contact stress, τcontactA