Question

A retaining wall with vertical back retains a mass of cohesion-less soil, surface of which is level with top of the wall. Active lateral earth pressure coefficient (in terms of 'ϕ') i.e. angle of internal friction of backfill is given by: 
1. \(\dfrac{1-\sin \phi}{1 + \sin \phi} \ \text{or} \ \tan^2 \left(45^\circ + \dfrac{\phi}{2}\right)\)
2. \(\dfrac{1-\sin \phi}{1 + \sin \phi} \ \text{or} \ \tan^2 \left(45^\circ - \dfrac{\phi}{2}\right)\)
3. \(\dfrac{1+\sin \phi}{1 - \sin \phi} \ \text{or} \ \tan^2 \left(45^\circ - \dfrac{\phi}{2}\right)\)
4. \(\dfrac{1+\sin \phi}{1 - \sin \phi} \ \text{or} \ \tan^2 \left(45^\circ + \dfrac{\phi}{2}\right)\)

Answer 1

Correct Answer - Option 2 : \(\dfrac{1-\sin \phi}{1 + \sin \phi} \ \text{or} \ \tan^2 \left(45^\circ - \dfrac{\phi}{2}\right)\)

Concept:

The active earth pressure of soil at a depth “H” is given by:

pa = kaγH

where,

ka = Active earth pressure coefficient

γ = unit weight of soil

H = Depth of soil strata

\({k_a} = \frac{{1 - \sin \phi }}{{1 + \sin \phi }} = ta{n^2}\left( {{{45}^\circ } - \phi/2 } \right)\)

ϕ = Angle of internal friction of soil