Coulomb active pressure wedge

Coulomb passive pressure wedge

Remarks:
The resultant active thrust P_a is inclined at an angle δ with the normal of the wall face. Accordingly, the horizontal component of the thrust,P_ah, is obtained by multiplying P_a by sinα and cosδ.

Similar adjustment is also required for the passive case.

Governing Equations:

Bowles (1996)

\[ K_a = \frac{\sin^2(\alpha + \phi)} {\sin^2 \alpha \, \sin(\alpha - \delta) \left[ 1 + \sqrt{ \frac{ \sin(\phi + \delta)\sin(\phi - \beta)}{\sin(\alpha - \delta)\sin(\alpha + \beta) } } \right]^2} \] \[ K_p = \frac{\sin^2(\alpha - \phi)}{\sin^2 \alpha \, \sin(\alpha + \delta)\left[ 1 -\sqrt{\frac{\sin(\phi + \delta)\sin(\phi + \beta)}{\sin(\alpha + \delta)\sin(\alpha + \beta)}}\right]^2} \]

$$ \begin{align*} p_a &= \gamma z K_a \\ P_a &= \int_0^H \gamma z K_a \, dz = \frac{1}{2} \gamma H^2 K_a \end{align*} $$

$$ \begin{align*} p_p &= \gamma z K_p \\ P_p &= \int_0^H \gamma z K_p \, dz = \frac{1}{2} \gamma H^2 K_p \end{align*} $$