Question

When the surcharge angle reduces to zero, the coefficient of active earth pressure is given by

(a) Ka=1

(b) \(K_a=\frac{1-sinφ}{1+sinφ}\)

(c) \(K_a=\frac{1+sinφ}{1-sinφ}\)

(d) Ka=0

I got this question in class test.

This interesting question is from Active Earth Pressure: Rankine’s Theory in chapter Failure Envelopes & Earth Pressure of Geotechnical Engineering II

Answer 1

The correct choice is (b) \(K_a=\frac{1-sinφ}{1+sinφ}\)

For explanation I would say: For backfill with sloping surface, the coefficient of active earth pressure is given by,

\(K_a=cosβ\frac{cosβ-\sqrt{cos^2 β-cos^2 φ}}{cosβ+\sqrt{cos^2 β-cos^2 φ}}, \)

When the surcharge angle reduces to zero, β=0,

substituting this in the equation, we get,

\(K_a=\frac{1-sinφ}{1+sinφ}.\)