Question

The stress condition during plastic equilibrium in terms of tangent of angle is _______

(a) \(σ_1=tan⁡(45°+\frac{φ}{2})+σ_3 tan^2 (45°+\frac{φ}{2}) \)

(b) \(σ_1=2c+σ_3 tan^2 (45°+\frac{φ}{2})\)

(c) \(σ_1=2c \,tan⁡(45°+\frac{φ}{2})+σ_3\)

(d) \(σ_1=2c \,tan⁡(45°+\frac{φ}{2})+σ_3 tan^2 (45°+\frac{φ}{2})\)

The question was asked during a job interview.

I'm obligated to ask this question of Earth Pressure Introduction topic in chapter Failure Envelopes & Earth Pressure of Geotechnical Engineering II

Answer 1

Correct answer is (d) \(σ_1=2c \,tan⁡(45°+\frac{φ}{2})+σ_3 tan^2 (45°+\frac{φ}{2})\)

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

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

since tan⁡φ=sinφ/cosφ

∴ \(σ_1=2c \,tan⁡(45°+\frac{φ}{2})+σ_3 tan^2 (45°+\frac{φ}{2}).\)