Question

The Rankine’s lateral pressure ratio is given by ________

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

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

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

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

I got this question in quiz.

My question is from Active Earth Pressure: Rankine’s Theory in portion Failure Envelopes & Earth Pressure of Geotechnical Engineering II

Answer 1

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

To elaborate: The ratio K is the conjugate ratio or the Rankine’s lateral pressure ratio, which is given by,

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

where, β=surcharge angle

φ=angle of internal friction.