Mohr Coulomb Modelasd

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Mohr-Coulomb Model

Short Course on Computational Geotechnics + Dynamics

Boulder, Colorado

January 5-8, 2!

Stein Sture

Professor of Civil Engineering

University of Colorado at Boulder


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Contents

" #deali$ed and %eal Stress-Strain Beha&ior o' Soils

" Basic Concepts o' Mohr-Coulomb Model

" Mohr-Coulomb Model Modelin(

" )riction *n(le

" #n'luence o' #ntermediate rincipal Stress on)riction *n(le

" Drained Simple Shear est" o. to /nderstand

" Drained ria0ial est

Computational Geotechnics Mohr-Coulomb Model


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#deali$ed and %eal Stress-Strain

Beha&ior o' Soils



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Basic Concepts o' Mohr-

Coulomb Model

Bilinear appro0imation o' tria0ial test

Basic la.1

for

reversible elastic strain

irreversible plastic strain f= yield function

i = ie + i

p

i = x,y,etc.

i

e =

ip =

ip

= 0

f < 0

f = f(x,y,z,xy,yz,zx )



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Mohr-Coulomb Soil Modelin(



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)lo. rule 'or plastic strain1

his means1 , , etc

ip

=g

i

xp

= g

xy

p

= g

y



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a multiplier that determines thema(nitude o' plastic strains

determines the direction o' plasticstrains

Classical associated plasticity1 g = f

General non-associated plasticity1 g f

M-C model1 fr 3 s sin3 c cos 1 yield 'unction

gr 3 s sin3 c cos 1 plastic potential 'unction

=

g

i



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Nonlinear Failure Envelope RepresentationComputational Geotechnics Mohr-Coulomb Model


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Friction Angle DefinitionsComputational Geotechnics Mohr-Coulomb Model


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Strength Envelopes for a Range of Soil TypesComputational Geotechnics Mohr-Coulomb Model


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Versus Relative Density and Unit WeighttcComputational Geotechnics Mohr-Coulomb Model


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)riction *n(le

Dilatancy Angle Relationships



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1 = Correction for particle shape1= -6

o For high sphericity and subrounded shape

1= +2o For low sphericity and angular shape

2 = Correction for particle size (effective size, d10)

2= -11o For d10 > 2.0 mm (gravel)

2= -9o For 2.0 > d10>0.6 mm (coarse sand)

2= -4o For 0.6 > d10>0.2 mm (medium sand)

2= 0 For 0.2 > d10>0.06 mm (fine sand)3 = Correction for graduation (uniformity coefficient, Cu)

3= -2o For Cu> 2.0 (well-graded)

3= -1o For Cu= 2.0 (medium graded)

3= 0 For Cu< 2.0 (poorly graded)

4 = Correction for relative density (Dr)

4= -1

o For 0 < Dr


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cv

max

= cv + 0.8

for NC Clays vs. PI



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#n'luence o' #ntermediate rincipal Stress on

)riction *n(le



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#n'luence o' #ntermediate rincipal Stress on

)riction *n(le



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Drained Simple Shear est



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o. to /nderstand

= + i or = - i

i= inter particle angle of friction

quartz sand: 30o



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Drained ria0ial est

v = x + y + z = 2x + y

tan= 2sin

1 sin(identical to biaxial test)


Mohr Coulomb Modelasd

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