Question

When the surcharge angle β is reduced to zero, then the coefficient of passive earth pressure is ______

(a) 1

(b) \(\frac{1-sinφ}{1+sinφ} \)

(c) \(\frac{1+sinφ}{1-sinφ} \)

(d) 0

I got this question in exam.

My question is based upon Passive Earth Pressure: Rankine’s Theory in division Failure Envelopes & Earth Pressure of Geotechnical Engineering II

Answer 1

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

Explanation: For backfill with sloping surface, the coefficient of passive earth pressure is given by,

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

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

substituting this in the equation, we get,

Ka=\(\frac{1+sinφ}{1-sinφ}.\)