If the retaining wall moves away from the backfill, the value of coefficient of Rankine's earth pressure is given by: 

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RRB JE CE 22 Apr 2025 Shift 2 CBT 2 Official Paper
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  1. (1 − sin φ) 
  2. (1 + sin φ)
  3. \(\rm \frac{(1+\sin \phi)}{(1-\sin \phi)}\)
  4. \(\rm \frac{(1-\sin \phi)}{(1+\sin \phi)}\)

Answer (Detailed Solution Below)

Option 4 : \(\rm \frac{(1-\sin \phi)}{(1+\sin \phi)}\)
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Detailed Solution

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Concept:

Coefficient of Active Earth Pressure Coefficient:

\({C_a} = \frac{{1 - \sin \left( \phi \right)}}{{1 + \sin \left( \phi \right)}} = {\tan ^2}\left( {45 - \frac{\phi }{2}} \right)\;\)

Coefficient of Passive Earth Pressure Coefficient:

\({C_p} = \frac{{1 + \sin \left( \phi \right)}}{{1 - \sin \left( \phi \right)}} = {\tan ^2}\left( {45 + \frac{\phi }{2}} \right)\;\)

Point to be remembered:

For any value of shearing angle, the product of active earth pressure coefficient and passive earth pressure coefficient will always equal 1.

\({C_a} \times {C_p} = \frac{{1 - \sin \left( \phi \right)}}{{1 + \sin \left( \phi \right)}} \times \frac{{1 + \sin \left( \phi \right)}}{{1 - \sin \left( \phi \right)}} = 1\)

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