Question

The plastic equilibrium stress equation in terms of flow valve is _____

(a) σ1=2c∛Nφ+σ3 Nφ

(b) σ1=2c√Nφ+σ3 Nφ

(c) σ1=2cNφ-σ3 Nφ

(d) σ1=Nφ+σ3 Nφ

I got this question in an international level competition.

My doubt stems from Earth Pressure Introduction in chapter Failure Envelopes & Earth Pressure of Geotechnical Engineering II

Answer 1

Right answer is (b) σ1=2c√Nφ+σ3 Nφ

The explanation: The stress condition during plastic equilibrium is given by,

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

since, \(N_φ= tan^2 (45°+\frac{φ}{2}),\)

∴ σ1=2c√Nφ+σ3 Nφ.