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Earth Pressure at rest
The earth pressure at rest per unit length at a depth of z from the ground surface is expressed as:
\[{p_0}={K_0}\,\gamma \,z\] (25.1)
where \[\gamma\] is the unit weight of the soil, K_{0 }is the coefficient of earth pressure at rest. Thus, the earth pressure is zero at the top of a retaining wall and at the base of the wall is K_{0}\[\gamma\] H (if H is the height of the wall). The total force per unit length at rest condition acting on a retaining wall of height H is expressed as:
\[{P_0}={1 \over 2}{K_0}\,\gamma \,{H^2}\] (25.2)
The force (P_{0}) will act at a height of H/3 from the base of the wall.
For sand and normally consolidated clays, the value of K_{0} is determined as (Jaky, 1944):
\[{K_0}=1\sin \varphi\] (25.3)
where ø is the angle of friction of the soil. For over consolidated soil the K_{0} is expressed as:
\[{K_0}={K_{0(nc)}}\sqrt {OCR}\] (25.4)
where OCR is the over consolidation ratio.
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