Test: Mohr Coulomb's Failure Theory - Civil Engineering (CE) MCQ

If the normal and shear stress corresponding to failure are plotted, then a curve is obtained. The plot or curve is called the strength envelope.

According to Mohr’s strength theory, the critical shear stress causing failure depends upon the properties of the materials as well as on normal stress on the failure plane.

The Mohr-Coulomb failure theory can be expressed algebraically by the equation:τf = s = F (σ)
Where, τf = s=shear stress on failure plane, at failure=shear resistance of material
F (σ) = function of normal stress.

Concept:
Shear strength of soil is the capacity of soil to resist shearing stresses.  It can be defined as the maximum value of shear stress that can be mobilized within a soil mass.

Note:
If this value exceeded by the shear stress on any plane or a surface at a point, failure will occur in soil because of the movement of a portion of the soil mass along that particular plane. The soil is then said to fail in shear. Therefore, shear strength generally represented the strength of the soil.
As per Mohr-Coulomb criteria, Shear strength (s) of soil is given as:
s = c' + σ' tanϕ'
Where,
c' = effective cohesion
σ' = effective normal stress
ϕ' = effective angle of friction

Mohr envelope can be considered straight if the angle of internal friction φ is assumed to be a constant.

The empirical constant φ in coulomb’s equation represents angle of internal friction or shearing resistance respectively.

Coulomb defined the function F (σ) as a linear function of σ and gave the following strength equation:
S = c + σ tan φ.

The theory of failures was first expressed by coulomb in 1776 and later generalized by Mohr.

Coulomb considered that the relationship between shear strength and normal stress could be adequately represented by the straight line.

When a material is subjected to three dimensional stresses, the intermediate principal stress does not have any influence on the strength of material.