lecture 2 extant theories of clays and sandsprusv/ncmm/workshops/wog/... · 2007. 10. 3. · de...
TRANSCRIPT
![Page 1: LECTURE 2 EXTANT THEORIES OF CLAYS AND SANDSprusv/ncmm/workshops/wog/... · 2007. 10. 3. · de jong, mehrabadi, cowin, harris attempts to overcome the non- coincidence of stress](https://reader036.vdocuments.mx/reader036/viewer/2022081623/61454adb34130627ed50e263/html5/thumbnails/1.jpg)
LECTURE 2
EXTANT THEORIES OF CLAYS AND SANDSEXTANT THEORIES OF CLAYS AND SANDS
Ian F CollinsDepartment of Engineering Science, University of Auckland,
New Zealand.
AUCKLAND BY NIGHT
![Page 2: LECTURE 2 EXTANT THEORIES OF CLAYS AND SANDSprusv/ncmm/workshops/wog/... · 2007. 10. 3. · de jong, mehrabadi, cowin, harris attempts to overcome the non- coincidence of stress](https://reader036.vdocuments.mx/reader036/viewer/2022081623/61454adb34130627ed50e263/html5/thumbnails/2.jpg)
““COULOMB” MODELSCOULOMB” MODELS
![Page 3: LECTURE 2 EXTANT THEORIES OF CLAYS AND SANDSprusv/ncmm/workshops/wog/... · 2007. 10. 3. · de jong, mehrabadi, cowin, harris attempts to overcome the non- coincidence of stress](https://reader036.vdocuments.mx/reader036/viewer/2022081623/61454adb34130627ed50e263/html5/thumbnails/3.jpg)
TWO-DIMENSIONAL COULOMB MODEL
τ
σ
φc
dilation angle
![Page 4: LECTURE 2 EXTANT THEORIES OF CLAYS AND SANDSprusv/ncmm/workshops/wog/... · 2007. 10. 3. · de jong, mehrabadi, cowin, harris attempts to overcome the non- coincidence of stress](https://reader036.vdocuments.mx/reader036/viewer/2022081623/61454adb34130627ed50e263/html5/thumbnails/4.jpg)
WHAT IS COHESION?WHAT IS COHESION?
![Page 5: LECTURE 2 EXTANT THEORIES OF CLAYS AND SANDSprusv/ncmm/workshops/wog/... · 2007. 10. 3. · de jong, mehrabadi, cowin, harris attempts to overcome the non- coincidence of stress](https://reader036.vdocuments.mx/reader036/viewer/2022081623/61454adb34130627ed50e263/html5/thumbnails/5.jpg)
ONE SOURCE of COHESION
r/T2)uu(u ae =−−≡
Gauge water suction at which air enters
For sand r=1mm suction is 1.4kPa
For clays r=1 micron, suction is 140kPa
![Page 6: LECTURE 2 EXTANT THEORIES OF CLAYS AND SANDSprusv/ncmm/workshops/wog/... · 2007. 10. 3. · de jong, mehrabadi, cowin, harris attempts to overcome the non- coincidence of stress](https://reader036.vdocuments.mx/reader036/viewer/2022081623/61454adb34130627ed50e263/html5/thumbnails/6.jpg)
CLAY CLIFFS
![Page 7: LECTURE 2 EXTANT THEORIES OF CLAYS AND SANDSprusv/ncmm/workshops/wog/... · 2007. 10. 3. · de jong, mehrabadi, cowin, harris attempts to overcome the non- coincidence of stress](https://reader036.vdocuments.mx/reader036/viewer/2022081623/61454adb34130627ed50e263/html5/thumbnails/7.jpg)
RICE PADDIES
![Page 8: LECTURE 2 EXTANT THEORIES OF CLAYS AND SANDSprusv/ncmm/workshops/wog/... · 2007. 10. 3. · de jong, mehrabadi, cowin, harris attempts to overcome the non- coincidence of stress](https://reader036.vdocuments.mx/reader036/viewer/2022081623/61454adb34130627ed50e263/html5/thumbnails/8.jpg)
0
20
40
60
80
100
20 40 60 80 100
normal effective stress
shearstress
Quartz
Kaolinite
Illite
Montmorillonite
(psi)
(psi)
Effective failure envelopes for clays (Olson (1974))
![Page 9: LECTURE 2 EXTANT THEORIES OF CLAYS AND SANDSprusv/ncmm/workshops/wog/... · 2007. 10. 3. · de jong, mehrabadi, cowin, harris attempts to overcome the non- coincidence of stress](https://reader036.vdocuments.mx/reader036/viewer/2022081623/61454adb34130627ed50e263/html5/thumbnails/9.jpg)
PROBLEMS WITH COULOMB• WHAT IS THE COHESION?
• WHAT IS THE FRICTION ANGLE?
• THESE ARE NOT MATERIAL • CONSTANTS!
• SLIPLINE AND LIMIT ANALYSIS PROCEDURES REQUIRE NORMAL FLOW RULE-TOO MUCH DILATION!
![Page 10: LECTURE 2 EXTANT THEORIES OF CLAYS AND SANDSprusv/ncmm/workshops/wog/... · 2007. 10. 3. · de jong, mehrabadi, cowin, harris attempts to overcome the non- coincidence of stress](https://reader036.vdocuments.mx/reader036/viewer/2022081623/61454adb34130627ed50e263/html5/thumbnails/10.jpg)
τ
σc φ+π 2/
φ
![Page 11: LECTURE 2 EXTANT THEORIES OF CLAYS AND SANDSprusv/ncmm/workshops/wog/... · 2007. 10. 3. · de jong, mehrabadi, cowin, harris attempts to overcome the non- coincidence of stress](https://reader036.vdocuments.mx/reader036/viewer/2022081623/61454adb34130627ed50e263/html5/thumbnails/11.jpg)
FAILURE IN PLANE STRAIN-1
1σ
2/4/ φ−π
FAILURE CONDITION ACHIEVED ON THESE LINES
φσ+=τ tanc
STRESS CHARACTERISTICSARE NOT ORTHOGONAL
![Page 12: LECTURE 2 EXTANT THEORIES OF CLAYS AND SANDSprusv/ncmm/workshops/wog/... · 2007. 10. 3. · de jong, mehrabadi, cowin, harris attempts to overcome the non- coincidence of stress](https://reader036.vdocuments.mx/reader036/viewer/2022081623/61454adb34130627ed50e263/html5/thumbnails/12.jpg)
SOKOLOVSI “SOLUTION” FOR FOOTING
![Page 13: LECTURE 2 EXTANT THEORIES OF CLAYS AND SANDSprusv/ncmm/workshops/wog/... · 2007. 10. 3. · de jong, mehrabadi, cowin, harris attempts to overcome the non- coincidence of stress](https://reader036.vdocuments.mx/reader036/viewer/2022081623/61454adb34130627ed50e263/html5/thumbnails/13.jpg)
FAILURE IN PLANE STRAIN-2
1σ
STRESS CHARACTERISTICS
φσ+=τ tanc
STRESS CHARACTERISTICSARE NOT ORTHOGONAL.
IF MATERIAL IS INCOMPRESSIBLE,VELOCITY CHARACTERISTICS ARE ORTHOGONAL
VELOCITYCHARACTERISTICS
![Page 14: LECTURE 2 EXTANT THEORIES OF CLAYS AND SANDSprusv/ncmm/workshops/wog/... · 2007. 10. 3. · de jong, mehrabadi, cowin, harris attempts to overcome the non- coincidence of stress](https://reader036.vdocuments.mx/reader036/viewer/2022081623/61454adb34130627ed50e263/html5/thumbnails/14.jpg)
DOUBLE SHEARING MODELSDOUBLE SHEARING MODELS
MANDEL, SPENCER, DE JOSSELIN MANDEL, SPENCER, DE JOSSELIN DE JONG, MEHRABADI, COWIN, DE JONG, MEHRABADI, COWIN,
HARRISHARRIS
ATTEMPTS TO OVERCOME THE NON- COINCIDENCE OFSTRESS AND VELOCITY CHARACTERISTICS PROBLEM
![Page 15: LECTURE 2 EXTANT THEORIES OF CLAYS AND SANDSprusv/ncmm/workshops/wog/... · 2007. 10. 3. · de jong, mehrabadi, cowin, harris attempts to overcome the non- coincidence of stress](https://reader036.vdocuments.mx/reader036/viewer/2022081623/61454adb34130627ed50e263/html5/thumbnails/15.jpg)
SPENCER’S MODEL
(a) Material is isotropic, perfectly rigid plastic(b) In plane strain, deformation consists of
superposition of two shears on stress characteristics.
(c) Principal axes of stress and plastic strain rate no longer coincide.
(d) Constitutive law is relation between plastic strain rate,stress and stress rate-”hypoplastic”.
![Page 16: LECTURE 2 EXTANT THEORIES OF CLAYS AND SANDSprusv/ncmm/workshops/wog/... · 2007. 10. 3. · de jong, mehrabadi, cowin, harris attempts to overcome the non- coincidence of stress](https://reader036.vdocuments.mx/reader036/viewer/2022081623/61454adb34130627ed50e263/html5/thumbnails/16.jpg)
NON-ASSOCIATED NON-ASSOCIATED PLASTICITYPLASTICITY
![Page 17: LECTURE 2 EXTANT THEORIES OF CLAYS AND SANDSprusv/ncmm/workshops/wog/... · 2007. 10. 3. · de jong, mehrabadi, cowin, harris attempts to overcome the non- coincidence of stress](https://reader036.vdocuments.mx/reader036/viewer/2022081623/61454adb34130627ed50e263/html5/thumbnails/17.jpg)
BASIC EQUATIONS-1
Ph
)ˆ:Q(Dand,F
P:eF
h:ModulusHardening
,ˆ:)PQh1:C(DDD:equationsRate
PD:RuleFlow
F
F
Q......G
G
P;0)e,(GPotentialPlastic
0D:eFˆ:F0)e,(F:ConditionYield:Plasticity
D:Mˆ,ˆ:CD:Elasticity
PP
PE
P
P
PP
P
EE
σ=
σ∂∂
∂∂−
=
σ+=+=
λ=σ∂
∂σ∂
∂
≡
σ∂∂
σ∂∂
≡=σ
=∂∂+σ
σ∂∂⇒=σ
=σσ=
![Page 18: LECTURE 2 EXTANT THEORIES OF CLAYS AND SANDSprusv/ncmm/workshops/wog/... · 2007. 10. 3. · de jong, mehrabadi, cowin, harris attempts to overcome the non- coincidence of stress](https://reader036.vdocuments.mx/reader036/viewer/2022081623/61454adb34130627ed50e263/html5/thumbnails/18.jpg)
BASIC EQUATIONS - 2
"ulusmodsofteningcritical"isP:E:Qhwhere
hhP:E)D:E:Q(D:Eˆ:EquationsRateInverse
0
0
=
+−=σ
![Page 19: LECTURE 2 EXTANT THEORIES OF CLAYS AND SANDSprusv/ncmm/workshops/wog/... · 2007. 10. 3. · de jong, mehrabadi, cowin, harris attempts to overcome the non- coincidence of stress](https://reader036.vdocuments.mx/reader036/viewer/2022081623/61454adb34130627ed50e263/html5/thumbnails/19.jpg)
“QUASI-THERMODYNAMIC” RESTRICTIONS-1
0)P:ˆ(0h/)P:ˆ)(ˆ:Q(
0D:ˆ:"POSTULATE"S'DRUCKER
signsamehavehand)ˆ:Q(
0P:POTENTIALSHAPEDSTAR
0h/)P:)(ˆ:Q(D::"NDISSIPATIO"
p
p
≥σ⇒≥σσ⇒
≥σ
σ⇒
>σ⇒
≥σσ≡σ⇒
![Page 20: LECTURE 2 EXTANT THEORIES OF CLAYS AND SANDSprusv/ncmm/workshops/wog/... · 2007. 10. 3. · de jong, mehrabadi, cowin, harris attempts to overcome the non- coincidence of stress](https://reader036.vdocuments.mx/reader036/viewer/2022081623/61454adb34130627ed50e263/html5/thumbnails/20.jpg)
“QUASI-THERMODYNAMIC” RESTRICTIONS-2
NO+VE-VE
OK-VE-VE
NO-VE+VE
OK+VE+VE
Q:σ̂ P:σ̂ DRUCKER
P
Q
1
23
4
DRUCKER’S POSTULATE HAS NO RELEVANCE TO NON-ASSOCIATED PLASTICITY
![Page 21: LECTURE 2 EXTANT THEORIES OF CLAYS AND SANDSprusv/ncmm/workshops/wog/... · 2007. 10. 3. · de jong, mehrabadi, cowin, harris attempts to overcome the non- coincidence of stress](https://reader036.vdocuments.mx/reader036/viewer/2022081623/61454adb34130627ed50e263/html5/thumbnails/21.jpg)
“HILL’S STABILITY” POSTULATE
"DEFINITEPOSITIVEisM........."....................
:UNIQUENESSFOR
CONDITIONSUFFICIENTWORKVIRTUALAPPLY
.solutionspossibletwobetweendifferenceiswhere
,0D:M:Dˆ:DD:MˆALSO
0D:M:D:POSTULATES'HILL
hh)E:Q)(P:E(EMwhere,D:Mˆ:EQUATIONRATE
0D:ˆ:POSTULATES'HILL
O
⇒
∆
≥∆∆=σ∆∆⇒∆=σ∆⇒
≥⇒
+−≡=σ
≥σ
![Page 22: LECTURE 2 EXTANT THEORIES OF CLAYS AND SANDSprusv/ncmm/workshops/wog/... · 2007. 10. 3. · de jong, mehrabadi, cowin, harris attempts to overcome the non- coincidence of stress](https://reader036.vdocuments.mx/reader036/viewer/2022081623/61454adb34130627ed50e263/html5/thumbnails/22.jpg)
THE RANIECKI FORMULA SUFFICIENT FORMULA FOR UNIQUENESS:
0hQP
)}Q:E:P()Q:E:Q()P:E:P{(21hh
C
21
21
C
=⇒=
−=>
strain
stress
P=Q
P ≠ Q
![Page 23: LECTURE 2 EXTANT THEORIES OF CLAYS AND SANDSprusv/ncmm/workshops/wog/... · 2007. 10. 3. · de jong, mehrabadi, cowin, harris attempts to overcome the non- coincidence of stress](https://reader036.vdocuments.mx/reader036/viewer/2022081623/61454adb34130627ed50e263/html5/thumbnails/23.jpg)
LOCALIZATION
)}P:E:n()n:E:n)(n:E:Q{(hh 10
−=+
strain
stress
Loss of Uniqueness
n
0)nMndet()Tdet( =≡ (RICE)
Possible Localization
![Page 24: LECTURE 2 EXTANT THEORIES OF CLAYS AND SANDSprusv/ncmm/workshops/wog/... · 2007. 10. 3. · de jong, mehrabadi, cowin, harris attempts to overcome the non- coincidence of stress](https://reader036.vdocuments.mx/reader036/viewer/2022081623/61454adb34130627ed50e263/html5/thumbnails/24.jpg)
CRITICAL STATE MODELSCRITICAL STATE MODELS
![Page 25: LECTURE 2 EXTANT THEORIES OF CLAYS AND SANDSprusv/ncmm/workshops/wog/... · 2007. 10. 3. · de jong, mehrabadi, cowin, harris attempts to overcome the non- coincidence of stress](https://reader036.vdocuments.mx/reader036/viewer/2022081623/61454adb34130627ed50e263/html5/thumbnails/25.jpg)
A BASIC CRITICAL STATE MODEL
![Page 26: LECTURE 2 EXTANT THEORIES OF CLAYS AND SANDSprusv/ncmm/workshops/wog/... · 2007. 10. 3. · de jong, mehrabadi, cowin, harris attempts to overcome the non- coincidence of stress](https://reader036.vdocuments.mx/reader036/viewer/2022081623/61454adb34130627ed50e263/html5/thumbnails/26.jpg)
VOIDS RATIO-PRESSURE PLOT
e
Ln (p)
O
DENSE
LOOSE
CSL
NB A “DENSE’ SPECIMEN CAN BECOME “LOOSE” IF p IS INCREASED
![Page 27: LECTURE 2 EXTANT THEORIES OF CLAYS AND SANDSprusv/ncmm/workshops/wog/... · 2007. 10. 3. · de jong, mehrabadi, cowin, harris attempts to overcome the non- coincidence of stress](https://reader036.vdocuments.mx/reader036/viewer/2022081623/61454adb34130627ed50e263/html5/thumbnails/27.jpg)
ISOTROPIC COMPRESSION
e
Ln(p)
Elastic loading
Elastic unloading
Plastic loading
![Page 28: LECTURE 2 EXTANT THEORIES OF CLAYS AND SANDSprusv/ncmm/workshops/wog/... · 2007. 10. 3. · de jong, mehrabadi, cowin, harris attempts to overcome the non- coincidence of stress](https://reader036.vdocuments.mx/reader036/viewer/2022081623/61454adb34130627ed50e263/html5/thumbnails/28.jpg)
q
pO
CSLEg CONSTANT PRESSURE DRAINED PATHS
LOOSE-COMPACTS
DENSE-DILATES
BOTH LOOSE AND DENSE SPECIMENS END UP ON CSL
![Page 29: LECTURE 2 EXTANT THEORIES OF CLAYS AND SANDSprusv/ncmm/workshops/wog/... · 2007. 10. 3. · de jong, mehrabadi, cowin, harris attempts to overcome the non- coincidence of stress](https://reader036.vdocuments.mx/reader036/viewer/2022081623/61454adb34130627ed50e263/html5/thumbnails/29.jpg)
CHARACTERISTICS REVISITED
Normal flow rule CSL
A
AT POINT “A” THERE ARE TWO CONSTRAINTS, AND HENCE TWO FAMILIES OF STRESS CHARACTERISTICS
p
q
O
![Page 30: LECTURE 2 EXTANT THEORIES OF CLAYS AND SANDSprusv/ncmm/workshops/wog/... · 2007. 10. 3. · de jong, mehrabadi, cowin, harris attempts to overcome the non- coincidence of stress](https://reader036.vdocuments.mx/reader036/viewer/2022081623/61454adb34130627ed50e263/html5/thumbnails/30.jpg)
FAILURE MECHANISMS
q
p
CSL
Failure by plastic compression
“Peak” failure or Shear Band formation
Tension cut off
OHvorslev Surface
![Page 31: LECTURE 2 EXTANT THEORIES OF CLAYS AND SANDSprusv/ncmm/workshops/wog/... · 2007. 10. 3. · de jong, mehrabadi, cowin, harris attempts to overcome the non- coincidence of stress](https://reader036.vdocuments.mx/reader036/viewer/2022081623/61454adb34130627ed50e263/html5/thumbnails/31.jpg)
STATE BOUNDARY SURFACE
![Page 32: LECTURE 2 EXTANT THEORIES OF CLAYS AND SANDSprusv/ncmm/workshops/wog/... · 2007. 10. 3. · de jong, mehrabadi, cowin, harris attempts to overcome the non- coincidence of stress](https://reader036.vdocuments.mx/reader036/viewer/2022081623/61454adb34130627ed50e263/html5/thumbnails/32.jpg)
THREE DIMENSIONAL MODELSLADE
![Page 33: LECTURE 2 EXTANT THEORIES OF CLAYS AND SANDSprusv/ncmm/workshops/wog/... · 2007. 10. 3. · de jong, mehrabadi, cowin, harris attempts to overcome the non- coincidence of stress](https://reader036.vdocuments.mx/reader036/viewer/2022081623/61454adb34130627ed50e263/html5/thumbnails/33.jpg)
THREE DIMENSIONAL MODELS
ttanconsII
SURFACEYIELDDUNCANLADE3
31 =−
ttanconsIII
SURFACEYIELDNAKAIMATSUOKA3
21 =−
![Page 34: LECTURE 2 EXTANT THEORIES OF CLAYS AND SANDSprusv/ncmm/workshops/wog/... · 2007. 10. 3. · de jong, mehrabadi, cowin, harris attempts to overcome the non- coincidence of stress](https://reader036.vdocuments.mx/reader036/viewer/2022081623/61454adb34130627ed50e263/html5/thumbnails/34.jpg)
EXTENSIONS OF CRITICAL EXTENSIONS OF CRITICAL STATE MODELSSTATE MODELS
![Page 35: LECTURE 2 EXTANT THEORIES OF CLAYS AND SANDSprusv/ncmm/workshops/wog/... · 2007. 10. 3. · de jong, mehrabadi, cowin, harris attempts to overcome the non- coincidence of stress](https://reader036.vdocuments.mx/reader036/viewer/2022081623/61454adb34130627ed50e263/html5/thumbnails/35.jpg)
STATE PARAMETER MODELSBEEN&JEFFERIES, DAFALIAS,..
eeCSL −=ψ
CSL
ln(p)
e
dense
loose
)Iln(
ppI
p
cslp =
![Page 36: LECTURE 2 EXTANT THEORIES OF CLAYS AND SANDSprusv/ncmm/workshops/wog/... · 2007. 10. 3. · de jong, mehrabadi, cowin, harris attempts to overcome the non- coincidence of stress](https://reader036.vdocuments.mx/reader036/viewer/2022081623/61454adb34130627ed50e263/html5/thumbnails/36.jpg)
MULTI-SURFACE MODELSHASHIGUCHI, DAFALIAS,WOOD,….
p
q“BUBBLE”
“BOUNDING SURFACE”
O
![Page 37: LECTURE 2 EXTANT THEORIES OF CLAYS AND SANDSprusv/ncmm/workshops/wog/... · 2007. 10. 3. · de jong, mehrabadi, cowin, harris attempts to overcome the non- coincidence of stress](https://reader036.vdocuments.mx/reader036/viewer/2022081623/61454adb34130627ed50e263/html5/thumbnails/37.jpg)
ACHIEVEMENTS OF CSSM• Coulomb condition is
a failure condition, not a yield condition.
• Provides an explanation of non-coincident characteristics.
• Models both loose and dense behaviour.
• Provides a relatively simple elastic/plastic model.
• Provides design criteria
• Is in good agreement with experiments on “lightly” over-consolidated clays.
![Page 38: LECTURE 2 EXTANT THEORIES OF CLAYS AND SANDSprusv/ncmm/workshops/wog/... · 2007. 10. 3. · de jong, mehrabadi, cowin, harris attempts to overcome the non- coincidence of stress](https://reader036.vdocuments.mx/reader036/viewer/2022081623/61454adb34130627ed50e263/html5/thumbnails/38.jpg)
SHORTCOMINGS OF CSSM• Does not well model
behaviour of sands and heavily over-consolidated clays.
• Assumes isotropy.• Is limited to normal
flow rules.• Assumes a critical
state actually exists
• Makes no allowance for the “internal structure” of soil.
• The underlying thermomechanics is wrong!!
![Page 39: LECTURE 2 EXTANT THEORIES OF CLAYS AND SANDSprusv/ncmm/workshops/wog/... · 2007. 10. 3. · de jong, mehrabadi, cowin, harris attempts to overcome the non- coincidence of stress](https://reader036.vdocuments.mx/reader036/viewer/2022081623/61454adb34130627ed50e263/html5/thumbnails/39.jpg)
EXTANT THERMOMECHANICAL ARGUMENT(Schofield and Wroth)
• “Plastic work equation”
• Rewrite as a “Dilatancy relation”
• ODE for potential function
• Integrate to give potential and yield locus
assumes a normal flow rule.
pppv depMqdepde γγ =+
Mdede
pq
p
pv =+γ
Mdpdq
pq =−
)p/pln(Mpq c=
(ORIGINAL CAM CLAY)
{Frictional dissipation}
![Page 40: LECTURE 2 EXTANT THEORIES OF CLAYS AND SANDSprusv/ncmm/workshops/wog/... · 2007. 10. 3. · de jong, mehrabadi, cowin, harris attempts to overcome the non- coincidence of stress](https://reader036.vdocuments.mx/reader036/viewer/2022081623/61454adb34130627ed50e263/html5/thumbnails/40.jpg)
Two examples of extant procedure
⇒+=Φ γ
2p22pv eMepˆ
q
p
q
pO
q
p
q
pO
⇒=Φ γpeMpˆ
Schofield and Wroth“Original Cam Clay”
Roscoe and Burland“Modified Cam Clay”
![Page 41: LECTURE 2 EXTANT THEORIES OF CLAYS AND SANDSprusv/ncmm/workshops/wog/... · 2007. 10. 3. · de jong, mehrabadi, cowin, harris attempts to overcome the non- coincidence of stress](https://reader036.vdocuments.mx/reader036/viewer/2022081623/61454adb34130627ed50e263/html5/thumbnails/41.jpg)
CRITIQUE OF EXTANT PROCEDURE-1
• Original Cam Clay violates the Second law of Thermodynamics.
• Confuses plastic work with dissipation.• Fails to recognize that the dissipation function
automatically gives the yield condition.• Has no memory of prior consolidation.• No attempt to model granular nature of
material.
pppv depMqdepde γγ =+
![Page 42: LECTURE 2 EXTANT THEORIES OF CLAYS AND SANDSprusv/ncmm/workshops/wog/... · 2007. 10. 3. · de jong, mehrabadi, cowin, harris attempts to overcome the non- coincidence of stress](https://reader036.vdocuments.mx/reader036/viewer/2022081623/61454adb34130627ed50e263/html5/thumbnails/42.jpg)
MODERN THERMOMECHANICSMODERN THERMOMECHANICS
In next lecture I will show that the In next lecture I will show that the modern procedures of the theory of modern procedures of the theory of thermomechanics of dissipative materials thermomechanics of dissipative materials overcomes many of these problems.overcomes many of these problems.
CSSM will be re-evaluated and aspects of CSSM will be re-evaluated and aspects of the microstructure such as micro-level the microstructure such as micro-level inhomogeneity, and induced dilatancy and inhomogeneity, and induced dilatancy and anisotropy can be modelledanisotropy can be modelled
![Page 43: LECTURE 2 EXTANT THEORIES OF CLAYS AND SANDSprusv/ncmm/workshops/wog/... · 2007. 10. 3. · de jong, mehrabadi, cowin, harris attempts to overcome the non- coincidence of stress](https://reader036.vdocuments.mx/reader036/viewer/2022081623/61454adb34130627ed50e263/html5/thumbnails/43.jpg)
ANY QUESTIONS?
NEW ZEALAND – A GOOD PLACE TO STUDY SAND BEHAVIOUR