Question

The stress condition during plastic equilibrium can be represented by _____________

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

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

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

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

This question was posed to me in semester exam.

Query is from Earth Pressure Introduction topic in section Failure Envelopes & Earth Pressure of Geotechnical Engineering II

Answer 1

The correct option is (d) \(\frac{σ_1-σ_3}{2}-\frac{σ_1+σ_3}{2} sinφ=c cosφ\)

The best explanation: The stress condition during plastic equilibrium can be represented by the equation of Mohr-Coulomb,

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

Where, σ1=major principal stress

σ3=minor principal stress

φ=angle of internal friction.