Question

The coefficient of earth pressure for passive state of plastic equilibrium in terms of sine function is _______

(a) \(K_a=1-sinφ\)

(b) \(K_a=\frac{1-sinφ}{1+sinφ} \)

(c) \(K_a=\frac{1+sinφ}{1-sinφ} \)

(d) Ka=1+sinφ

The question was asked in final exam.

This is a very interesting question from Earth Pressure Introduction in chapter Failure Envelopes & Earth Pressure of Geotechnical Engineering II

Answer 1

Right choice is (c) \(K_a=\frac{1+sinφ}{1-sinφ} \)

Easy explanation: The coefficient of earth pressure for active state of plastic equilibrium is,

\(K_p=tan^2 (45°+\frac{φ}{2}), \)

∴ therefore in terms of sine function,

\(K_p=tan^2 (45°+\frac{φ}{2})=\frac{1+sinφ}{1-sinφ}. \)