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

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
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
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
Geotechnical modelling and critical state soil mechanics Naples, May 2007
13. Designer models: addition of extra features
(GM 2, 3, EM, GeoF)
David Muir Wood University of Bristol
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
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?
kinematic hardening centre as indicator of current fabric q
50
-1arge
σy
150
σx
comparison of 0.05% strain response envelopes for histories A, AB, ABC
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
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
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
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)
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
Designer models: addition of extra features 1.Kinematic yielding
2. Cam clay 3. Mohr-Coulomb
shear stress elastic - stiff
plastic – less stiff
shear stress
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
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%
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
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
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
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
collected by Graham et al (1988)
typical experimental observation: stiffness falls steadily with monotonic straining: is there an elastic region?