Question

For a surcharge angle β the coefficient of passive earth pressure is _______

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

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

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

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

I have been asked this question during an online interview.

My doubt stems from Passive Earth Pressure: Rankine’s Theory topic in division Failure Envelopes & Earth Pressure of Geotechnical Engineering II

Answer 1

The correct choice is (b) Kp=\(cosβ \frac{cosβ+\sqrt{cos^2 β-cos^2 φ}}{cosβ-\sqrt{cos^2 β-cos^2 φ}}\)

Explanation: The vertical pressure in case of backfill with surcharge,

σ= γzcosβ,

Therefore, from the assumption of stresses being conjugate,

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