professor alan bishop (1920-88) laboratory stress-strain ... · undrained cyclic triaxial test on...
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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)
fσ
vσ
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
.
.
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