Stability

Together with the earth pressure, the weights and the uplift decide whether the wall overturns about its toe or slides on its base, and where the resultant crosses the base.

Weights and uplift

The soil between the wall and the virtual back, wedge above the crest included, weighs $\gamma$ above the water table and $\gamma_{sat}$ below. Concrete weighs the same under water; a gabion, whose voids fill with water, weighs $\gamma + n\gamma_w$ there, with $n = 0.40$. Buoyancy enters as uplift on the base: hydrostatic at the heel and at the toe, from the water on each side, and linear in between.

Overturning

About the toe, the weights and $P_a\sin\beta$ resist overturning; the earth and water thrusts behind the wall and the moment of the uplift drive it. Passive resistance doesn’t enter.

Sliding

The base slides on the stratum it rests on. It resists with friction on $\Sigma V$, the vertical force net of uplift, at $\delta = \tfrac{2}{3}\phi$; with adhesion $c_a = \tfrac{2}{3}c$ over $B$; and with $P_p$ if the wall is embedded. The result also gives the factor of safety without $P_p$.

Eccentricity

$e$ is how far from the middle of the base the resultant crosses it. Within the middle third, $e \le B/6$, the whole base is in compression; beyond it, $q_{min}$ turns negative and that edge lifts off.