经典土力学教材David Muir Wood_ Geotechnical modelling and critical state soil mechanics

Cam clay providing inspiration: search for ‘Cam clay like’ yield loci eg kaolin (Al-Tabbaa, 1984)
200 150 100 50 0 0 -50 -100 -150
Fig 3: Anisotropic yield locus for one-dimensional stress history (after Al-Tabbaa, 1984)
Hostun sand Sadek, 2006
ABC120 250
σz
σz
ABC150
distortional probing constant mean stress non-monotonic stress paths stress probe rosettes
-250
ABC90 ABC60 ABC30 C 50 ABC300 150
stress stress
a.
b.
strain
strain
70
yielding of Bothkennar clay: boundaries deduced from inspection of stress:strain response Y1 approximately centred on in situ stress state Y3 reflects natural structure – damaged by any irrecoverable strain - evanescent
ABC180
ABC … probe
ABC210 B qx:kPa A
ABC360 -150
-50 -50
50
150
250 ABC240
σz
σz 250 AB90 AB60 150 AB30
σx
AB120 AB150 AB180 AB210 B AB240 qx:kPa
σx
ABC330
-150 ABC300 -250 qz:kPa ABC270
typical actual response
void ratio strain
geometrical construction for estimation of preconsolidation pressure
preconsolidation pressure
vertical stress (log scale)
200 150 100 50 0 0 -50 50 100 150 200 250 300 350 400 mean effective stress p': kPa deviator stress q: kPa
b.
data from Al-Tabbaa (1987)
q kPa
q kPa
p' kPa
200 150 100 50 0 0 -50 50 100 150 200 250 300 350 400 450 deviator stress q: kPa
a.
mean effective stress p': kPa
data from Al-Tabbaa (1987)
kaolin revisited: one-dimensional consolidation histories
distortional strain 0.05%: history recalled 1%: history ‘forgotten’
Sadek, 2006
σz 150
stress response envelopes small/medium strain stiffness
B b
C
c 50 a
Sadek, 2006
Designer models: addition of extra features
1. Kinematic yielding
2. Cam clay
3. Mohr-Coulomb
Cam clay
elastic-hardening plastic model volumetric hardening associated flow – normality
p' kPa
plastic strain increments: approximate normality to kinematic yield loci
q kPa q kPa
p' kPa
p' kPa
kaolin: Al-Tabbaa, 1987
Deviatoric stress response envelopes
kinematic hardening centre as indicator of current fabric q
50
-150
-50 -50
A
but strain too large
σy
150
σx
comparison of 0.05% strain response envelopes for histories A, AB, ABC
after Smith et al (1992)
q: kPa 60 50 40 30 20 Y1 yield locus 10 0 0 -10 -20 10 20 30 40 p': kPa 50 60 Y2 yield locus
Y3 yield locus
kaolin revisited: isotropic consolidation histories
compare response of soil on nonmonotonic loading with capability of single yield surface model elastic-hardening plastic model expects elastic behaviour on reversal, sudden drop in stiffness at yield soils typically show hysteretic behaviour on unload-reload cycles, steady change in incremental stiffness
σy
σy
AB … probe
-250 AB360 -150 -50
50
A -50
50
150
250
Sadek, 2006
σx
σx
-150 AB330 -250 AB300 qz:kPa
AB270
σy
σy
Stress response envelopes: Hostun sand: small-medium strain radial shearing two corners AB ABC
Designer models: addition of extra features 1.Kinematic yielding
2. Cam clay 3. Mohr-Coulomb
shear stress elastic - stiff
plastic – less stiff
shear stress
C-A120 -150 C-A210 C-A180 C-A150 -250 qz:kPa
σx
σy
σy
σx
σx
-150
σy
σy
εd = 0.05, 0.2, 0.4, 0.6, 0.8, 1, 1.2%
•distortional stress probe rosettes •constant mean stress •cross anisotropy? •Ev > Eh
Cam clay
response in drained triaxial compression tests with constant p' asymptotic approach to critical state effect of overconsolidation ratio sharp division between elastic and plastic response
collected by Graham et al (1988)
typical experimental observation: stiffness falls steadily with monotonic straining: is there an elastic region?
limit of elastic response??
Geotechnical modelling and critical state soil mechanics Naples, May 2007
13. Designer models: addition of extra features
(GM 2, 3, EM, GeoF)
Fra Baidu bibliotek
David Muir Wood University of Bristol
σz
σz
250
250
150
150
C 50
B
B 50
qx: kPa
qx: kPa -150 -50 -50 A 50 150 250
-250
-150
-50 -50
A
50
150
-250 250
σx
σy -150
σx
σy -150
εd = 0.05, 0.2, 0.4, 0.6, 0.8, 1, 1.2%
mean stress
shear strain
classical elastic-plastic modelling of soil
for example, Cam clay (1963, 1968)
stress
yield?
classical identification of yield from stress:strain response
q: kPa
Cam clay?
p': kPa 100 200 300 400
yield loci for natural clays
0.9 0.8 0.7 0.6 q/σ vc 0.5 0.4 0.3 0.2 0.1 0 0 0.1 0.2 0.3 0.4 p/σ v c 0.5 0.6 0.7 0.8 0.9 Rang de Fleuve Belfast Winnipeg St Alban Lyndhurst Mastemyr
shear stiffness degradation data for Quiou sand from resonant column and torsional shear tests (after LoPresti et al, 1997)
how do we objectively identify yielding? occurrence of irrecoverable strain? dissipation of energy in loading/unloading cycles? change in slope of stress:strain response?
compare response of soil on nonmonotonic loading with capability of single yield surface model extension to simple models using kinematic hardening and bounding surface plasticity
kinematic hardening extension yield locus carried around with stress state – 'bubble' – strongly influenced by recent history stiffness falls as yield 'bubble' approaches bounding surface – controlled by distance b when loading with 'bubble' in contact with bounding surface model is identical to Cam clay
250 C-A330 150 C-A300 50 A270 -250 C-A240 σx -150 A -50 -50 50 150 C-A90 250
σz
σz
250
C-A30
σz
σz
C-A0
A: isotropic compression
150
C-A60
50
qx:kPa
A -250 -150 -50 -50 50 150 250