Question

The ratio between coefficients of passive and active earth pressure is __________

(a) cot^2 \((45°+\frac{φ}{2})\)

(b) cos^2 \((45°+\frac{φ}{2})\)

(c) tan^4 \((45°+\frac{φ}{2})\)

(d) sin^2 \((45°+\frac{φ}{2})\)

I had been asked this question in an interview for internship.

The query is from Passive Earth Pressure: Rankine’s Theory topic in section Failure Envelopes & Earth Pressure of Geotechnical Engineering II

Answer 1

The correct choice is (c) tan^4 \((45°+\frac{φ}{2})\)

To explain: The coefficient of passive earth pressure is Kp= tan^2 α and that of the coefficient of active earth pressure is \(K_a=\frac{1}{tan^2(45°+\frac{φ}{2})},\)

∴ \(\frac{K_p}{K_a}\) = tan^2 α* tan^2 α

\(\frac{K_p}{K_a} =tan^4 (45°+\frac{φ}{2}).\)