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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
Computational Geotechnics Mohr-Coulomb Model
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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 )
Computational Geotechnics Mohr-Coulomb Model
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Mohr-Coulomb Soil Modelin(
Computational Geotechnics Mohr-Coulomb Model
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Mohr-Coulomb Soil Modelin(
)lo. rule 'or plastic strain1
his means1 , , etc
ip
=g
i
xp
= g
xy
p
= g
y
Computational Geotechnics Mohr-Coulomb Model
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Mohr-Coulomb Soil Modelin(
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
Computational Geotechnics Mohr-Coulomb Model
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Mohr-Coulomb Soil Modelin(
Nonlinear Failure Envelope RepresentationComputational Geotechnics Mohr-Coulomb Model
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Mohr-Coulomb Soil Modelin(
Friction Angle DefinitionsComputational Geotechnics Mohr-Coulomb Model
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Mohr-Coulomb Soil Modelin(
Strength Envelopes for a Range of Soil TypesComputational Geotechnics Mohr-Coulomb Model
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Mohr-Coulomb Soil Modelin(
Versus Relative Density and Unit WeighttcComputational Geotechnics Mohr-Coulomb Model
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)riction *n(le
Dilatancy Angle Relationships
Computational Geotechnics Mohr-Coulomb Model
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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
Computational Geotechnics Mohr-Coulomb Model
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#n'luence o' #ntermediate rincipal Stress on
)riction *n(le
Computational Geotechnics Mohr-Coulomb Model
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#n'luence o' #ntermediate rincipal Stress on
)riction *n(le
Computational Geotechnics Mohr-Coulomb Model
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Drained Simple Shear est
Computational Geotechnics Mohr-Coulomb Model
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o. to /nderstand
= + i or = - i
i= inter particle angle of friction
quartz sand: 30o
Computational Geotechnics Mohr-Coulomb Model
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Drained ria0ial est
v = x + y + z = 2x + y
tan= 2sin
1 sin(identical to biaxial test)
Computational Geotechnics Mohr-Coulomb Model