Question

The Mohr Coulomb equation in terms of stress components in x-z plane is ______________

(a) \(\sqrt{((\frac{σ_z-σ_x}{2})^2+τ_{xz}^2))} -\frac{σ_z+σ_x}{2} sinφ=c cosφ\)

(b) \(\sqrt{((\frac{σ_z-σ_x}{2})^2+τ_{xz}^2))} \frac{σ_z+σ_x}{2} sinφ=c cosφ\)

(c) \(\sqrt{((\frac{σ_z-σ_x}{2})^2+τ_{xz}^2))} = c cosφ\)

(d) \(\sqrt{((\frac{σ_z-σ_x}{2})^2+τ_{xz}^2))} -\frac{σ_z+σ_x}{2} sinφ=cosφ\)

The question was asked by my school teacher while I was bunking the class.

Question is taken from Earth Pressure Introduction in portion Failure Envelopes & Earth Pressure of Geotechnical Engineering II

Answer 1

Correct option is (a) \(\sqrt{((\frac{σ_z-σ_x}{2})^2+τ_{xz}^2))} -\frac{σ_z+σ_x}{2} sinφ=c cosφ\)

To explain I would say: The Mohr Coulomb equation is given by,

\(\frac{σ_1-σ_3}{2}-\frac{σ_1+σ_3}{2} sinφ=c cosφ,\)

Where, σ_1=major principal stress and σ3=minor principal stress.

∴ in terms of stress components in x-z plane it is,

\(\sqrt{((\frac{σ_z-σ_x}{2})^2+τ_{xz}^2))} -\frac{σ_z+σ_x}{2} sinφ=c cosφ,\)

where, σz=stress in z-direction

σx= stress in x-direction.