According to Rankine's theory, the passive earth pressure coefficient \(K_p\) for a frictionless vertical wall with horizontal cohesionless backfill (friction angle \(\phi\)) is:

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Architecture Engineering QUESTION #2340

Question 1

\(K_p = \dfrac{1 - \sin\phi}{1 + \sin\phi}\)
\(K_p = \tan^2\!\left(45° - \dfrac{\phi}{2}\right)\)
\(K_p = \dfrac{1 + \sin\phi}{1 - \sin\phi}\)✔️
\(K_p = 1 + \sin\phi\)

Correct Answer Explanation

Rankine's passive pressure coefficient: \(K_p = \dfrac{1 + \sin\phi}{1 - \sin\phi} = \tan^2\!\left(45° + \dfrac{\phi}{2}\right)\). Note that \(K_p = 1/K_a\). Passive pressure develops when the wall moves into the retained soil, mobilizing the maximum shear resistance. Options A and B represent the active coefficient \(K_a\).

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