Course · lesson 7 of 7

Retaining walls: stability and the stem

A retaining wall holds back soil, and often water and a surcharge too. This lesson finds the earth pressure, checks the wall against overturning, sliding and bearing (by working factors, the SANS 10160-5 GEO set and a slip circle), designs the stem, toe and heel, and covers drainage, with the STATIX retaining wall calculator.

1. Learning outcomes

After this lesson you can:

choose active, at-rest or passive pressure and work out the thrust, including a surcharge and water;
check overturning and sliding, with and without a shear key;
check bearing with the resultant off-centre, and read the GEO and slip circle checks;
place and size the steel in the stem, toe and heel;
detail drainage, and design a wall in the STATIX retaining wall calculator.

2. Before you start

Lesson 1 (soil strength, GEO factors) and lesson 2 (eccentric bearing, overturning, sliding).
The free retaining wall calculator; the retaining wall Learn page as background.
About 55 minutes.

3. The wall

A cantilever retaining wall: a stem fixed into a base, with a toe in front and a heel under the retained soil (whose weight helps hold the wall), sometimes a shear key below the base. Behind the stem a drainage layer and weep holes keep water from building up.

4. Earth pressure

Earth pressure depends on movement. A cantilever wall yields a little away from the soil, so the soil behind it is in the active state with the smallest pressure. A wall that cannot move (a propped basement wall) takes the at-rest pressure. Soil the wall pushes into gives the passive resistance. The page offers active and at-rest, and passive in front of the toe.

Active thrust. The pressure grows linearly with depth, so the thrust on a height H is ½ K_a γ H², acting a third of the way up. The calculator uses Rankine for level fill and a smooth wall, and Coulomb when you give wall friction, a backfill slope or a batter.

Surcharge. A uniform load q on the retained surface (traffic, stacked materials) adds a constant pressure K_a q, a rectangle acting at mid-height. Where it sits on the heel it also helps stability, so the calculator takes the worse of the surcharge on and off the heel.

Water. A water table behind the wall adds the full water pressure (no K factor), makes the soil below it buoyant and pushes up under the base. It is the most common cause of retaining wall failures, which is why drainage (a free-draining layer, a pipe and weep holes) is part of the design. The calculator takes the water height above the base.

K_a = (1 − sin φ)/(1 + sin φ); K₀ = 1 − sin φ; K_p = (1 + sin φ)/(1 − sin φ) thrust: ½ K_a γ H² at H/3; surcharge K_a q H at H/2; water ½ γ_w h_w²

5. Stability

Forces on the wall. The stem, the base and the soil on the heel (and any surcharge on it) are the weights; the earth and water thrusts push the wall over and along. Taking moments about the toe gives the overturning check and the position of the resultant on the base.

Overturning and sliding. The calculator checks the working safety factors you set (2.0 on overturning and 1.5 on sliding by default), with friction under the base and the passive resistance in front of the toe, which you can include or ignore. A shear key under the base pushes into deeper soil and adds passive resistance.

Bearing. The resultant lands off-centre, towards the toe. As in lesson 2, it should stay in the middle third, so the whole base bears, with the largest pressure under the toe checked against q_all.

Three kinds of stability check. Beside the working safety factors, the calculator runs the SANS 10160-5 GEO set (tan φ divided by 1.25, lesson 1) for sliding and bearing, with the inclination of the load reducing the bearing resistance, and a slip circle round the whole wall and the soil.

overturning: ΣM_restoring / ΣM_overturning (about the toe) ≥ 2.0 sliding: (μ W + P_p) / ΣH ≥ 1.5; bearing: e = B/2 − (M_R − M_O)/W ≤ B/6

6. Stem, toe and heel

The concrete. The stem is a cantilever from the base, with tension at the soil face and the largest moment and shear at its base. The toe bends up under the bearing pressure (bottom steel); the heel is pushed down by the soil on it (top steel). The calculator designs all three and the key.

7. In STATIX

In STATIX: the wall's geometry, the retained soil (φ, γ, surcharge, water), the founding conditions (μ, q_all, front cover, key) and the safety factors. The calculator lists every stability check and designs the stem, toe, heel and key, with the bar schedule.