Mohr Coulomb Failure Criterion

• The Maximum shear stress theory proposed by coulomb postulates that failure will occur in a material when the maximum shear stress at a point in a material reaches a specific value, which is referred to as its shear strength.
• Coulomb suggested that the strength (shear) of rock is made up of two parts, a constant cohesion and a normal stress dependent frictional component.
• Cohesion of a material is its minimum shear strength, and this shear strength increases with increasing normal stress.
• Cohesion also describes the limiting or minimum amount of shear stress needed to get a surface slipping when the normal stress is very tiny or (zero), or in other words in the absence of normal stress, failure will occur only if shear stress component will overcome the cohesion of that material.
• The Mohr Coulomb failure criterion expresses the relation between the shear stress and the normal stress at failure.
• The Mohr Coulomb criterion is developed for compressive stress only.
• The Mohr Coulomb criterion sets up the criterion for predicting weather the stresses are sufficient to overcome the frictional resistance to slip along a surface.
• Mohr Coulomb strength criterion assumes that a shear failure plane is developed in the rock material and when failure occurs the stresses developed on the failure plane are on the strength envelope.
• The normal stress acting across the plane of failure increases the shear resistance of the material.
• The Mohr Coulomb failure criterion represents the linear strength envelope that is obtained from a plot of the shear strength of a material versus the applied normal stress.
• Mohr envelope defines the limiting size for Mohr’s circle.
• σ-τ coordinate below the strength envelope represents stable condition.
• σ-τ coordinate on the strength envelope represents equilibrium condition.
• σ-τ coordinate above the strength envelope represents failure condition.

Discussion about Applicability of Mohr’s Coulomb Failure Criterion

• We estimate that the criterion is most suitable at high confining pressure when the material does in fact fail through developments of shear planes. At lower confining pressure and in the uniaxial case, the failure occurs due to gradual increase in the density of micro-cracks and hence we would not expect such type of frictional criterion to apply directly. However at the higher confining pressures the criterion can be useful.
• Despite the difficulties associated with application of this it does remain in use as a rapidly calculable method for engineering practice.