Correct Answer - Option 4 :
\(\dfrac{wh^2}{2}\dfrac{(1-sin\phi)}{(1+sin\phi)}\)
Concept:
Earth pressure on wall = \({1 \over 2} \times K_{a/p} \times w \times h^2\)
Coefficient of Active Earth Pressure Coefficient:
It is the ratio of horizontal and vertical principal effective stresses when a retaining wall moves away (by a small amount) from the retained soil.
\({K_a} = \frac{{1 - \sin \left( \phi \right)}}{{1 + \sin \left( \phi \right)}} = {\tan ^2}\left( {45 - \frac{\phi }{2}} \right)\;\)
Coefficient of Passive Earth Pressure Coefficient:
It is the ratio of horizontal and vertical principal effective stresses when a retaining wall is forced against a soil mass.
\({K_p} = \frac{{1 + \sin \left( \phi \right)}}{{1 - \sin \left( \phi \right)}} = {\tan ^2}\left( {45 + \frac{\phi }{2}} \right)\;\)
Explanation:
Angle of repose = Φ
density of soil = w
height of retaining wall = h
than, coefficient of active earth pressure (Ka) = \({1 - sinΦ \over 1 + sin Φ}\)
Active earth pressure on wall = \({1 \over 2} \times Ka \times w \times h^2\)
= \({1 \over 2} { (1 - sinΦ) \over (1+ sinΦ)} \times w \times h^2\)