Retaining Walls

Purpose and types

A retaining wall holds back soil (or other material) at a slope steeper than it would naturally stand. Used for basements, road cuttings and embankments, bridge abutments, wing walls, and terraced sites.

Earth pressure

(See Earth Pressure Theories in Soil Mechanics for derivations.)

For a wall that yields slightly away from the soil (active case), Rankine's theory with a horizontal backfill, cohesionless soil:

• Uniform surcharge $q$: extra rectangular pressure $K_{a}q$, total $K_{a}qH$ at $H/2$.
• Submerged backfill: use submerged unit weight ${\gamma }^{\prime }$ for soil pressure plus full hydrostatic pressure ${\gamma }_{w}h$ — water pressure can double the thrust, which is why drainage is essential.
• Sloping backfill at angle $\beta$: $K_a=\cos \beta \frac{\cos \beta -\sqrt{{\cos }^2\beta -{\cos }^2\varphi }}{\cos \beta +\sqrt{{\cos }^2\beta -{\cos }^2\varphi }}$, thrust parallel to the slope.
• Passive pressure in front of the toe ($K_p=1/K_a$) is usually ignored or taken only partly, because the soil there may be removed.

Stability requirements

Classical checks (older practice, still asked): factor of safety ≥ 2.0 against overturning and ≥ 1.5 against sliding.

Bearing pressure: with total vertical load $W$, base width $B$ and eccentricity $e$ of the resultant from the base centre:

• Keep $p_{max}$ ≤ SBC.
• Keep $e\le B/6$ (resultant in the middle third) so there is no tension (no loss of contact) at the heel.

Shear key: if sliding resistance is insufficient, a key projecting below the base mobilises passive resistance and increases the sliding path.