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If the soil density is 'w', 'Φ' is the angle of repose and height of retaining wall is 'h', then the active earth pressure on the wall will be-


1. \(\dfrac{wh^2}{2}\dfrac{(1+sin\phi)}{(1-sin\phi)}\)
2. \(\dfrac{wh^2}{3}\dfrac{(1-sin\phi)}{(1+sin\phi)}\)
3. \(\dfrac{wh^2}{3}\dfrac{(1+sin\phi)}{(1-sinv)}\)
4. \(\dfrac{wh^2}{2}\dfrac{(1-sin\phi)}{(1+sin\phi)}\)

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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 = \({1 \over 2} \times Ka \times w \times h^2\)

\({1 \over 2} { (1 - sinΦ) \over (1+ sinΦ)} \times w \times h^2\)

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