Question

The resultant active pressure per unit length of wall for dry backfill with no surcharge is _______

(a) \(P_a=\frac{1}{2}K_aγH^2\)

(b) Pa=γH^2

(c) Pa=Ka γH^2

(d) Pa=Ka H^2

The question was posed to me during an online exam.

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

Answer 1

The correct option is (a) \(P_a=\frac{1}{2}K_aγH^2\)

Best explanation: The pressure intensity p0 is given by,

pa=Ka γz,

The total earth pressure P0 at rest per unit length is,

\(P_a=\int_0^HK_a γz.dz\)

∴  \(P_a=\frac{1}{2}K_aγH^2\)