Stability checks of retaining walls

A retaining wall is checked for the following modes; $\sum V$ = total vertical load, $\sum H$ = total horizontal thrust.

1. Overturning about the toe

$$FS_{ot} = \frac{\sum M_R}{\sum M_O} \ge 2 \ (1.5 \text{ minimum in some codes})$$

$M_R$ = resisting moment of wall weight, soil above heel, and passive pressure (if reliable); $M_O$ = overturning moment of lateral thrust about the toe.

2. Sliding along the base

$$FS_{s} = \frac{\sum V\tan\delta_b + c_a B + P_p}{\sum H} \ge 1.5$$

$\delta_b$ = friction angle between base and soil (about $\tfrac23\phi$), $c_a$ = adhesion. A shear key is added if $FS$ is low.

3. Bearing capacity and base pressure

Eccentricity $e = B/2 - \bar{x}$, with $\bar{x} = (\sum M_R - \sum M_O)/\sum V$; need $e \le B/6$ (no tension).

$$q_{max,min} = \frac{\sum V}{B}\left(1 \pm \frac{6e}{B}\right)$$

Check $q_{max} \le q_a$ (i.e. $FS = q_u/q_{max} \ge 3$) and $q_{min} \ge 0$.

4. Overall (deep-seated) slope stability

Check circular slip surfaces below and around the wall (Fellenius or Bishop method), $FS \ge 1.5$.

5. Settlement and structural checks

Estimate settlement of the base and check bending and shear of stem, heel and toe in RC walls.