MOHR COULOMB FAILURE CRITERION

MOHR COULOMB
FAILURE CRITERION
Definition:
The variation of peak stress σ1 with confining pressure σ3 is known as
criterion of failure. The simplest and best known criterion of failure is
Mohr coulomb criterion.

 Many geotechnical analysis method require use of this strength model.
 Many geotechnical analysis method require use of this strength model.
 The Mohr coulomb criterion describe a linear relationship b/w normal and
shear stresses at failure.
 It represents the linear envelope that is obtained from a plot of the shear
strength of the material versus applied normal stress

Equation:
𝑇p = 𝑆𝑖 + 𝜎𝑡𝑎𝑛∅
𝑇p = Confinement
Si = Shear stress intercept
𝜎 = Normal stress
∅ = Angle of internal friction

 The angle of friction(Ø) depends upon the grain
size
 If Ø = 0, the Mohr coulomb criterion reduces to
the tresca criterion
 If Ø = 90, then Mohr coulomb model is equivalent
to the rankine model
 Higher values of Ø are not allowed

 Mohr circle is plotted b/w principle stresses
and residual stress.
 The value of 𝜎1 and 𝜎3 are obtained from
the instrument.
 Shear intercept line indicates the peak
shear strength
 The radius of the circle describe the
strength of rock

 Small radius of circle indicate the low strength of
rock
Large radius indicate high strength of rock
 Each circle is the combination of maximum load
and confined pressure.
 The point of tangency of circle with shear
intercept line is the maximum strength of that
rock.
 ∅ is the angle of friction of the peak load on the
plane of normal stresses

When the load increases to its
maximum point the cracks are
produced and residual stresses
released
Rocks having minimum cracks will
have maximum residual stresses

Rock having fine grain particles
will show greater strength.
When there will be coarser grains
then less stress will be apply to
create the failure as compare to
fine grains.

Mohr Coulomb Criterian
Limitations
Mohr coulomb criterion is not particularly satisfactory criterian for rock
 It implies that a major shear fracture occurs at peak
strength.
 The criterion is likely to give incorrect result if the
failure mechanism is not shear.
 It implies direction of shear failure which does not
agree with observation particularly in brittle rock
 It is linear and peak strength envelope determine
experimentally are usually non-linear
 It will be noticed that only 𝜎1 and 𝜎3 are used and 𝜎2 is
ignore in case of rock sample

MOHR COULOMB FAILURE CRITERION

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MOHR COULOMB FAILURE CRITERION