A gravity retaining wall resists soil by its own weight, and it is checked against two failures: sliding along its base and overturning about its toe. In the worked example here, a 1.5 m high, 0.8 m thick wall has a sliding safety factor of 1.69 and an overturning factor of 2.71 behind drained soil, but 0.75 and 1.19 once the backfill is saturated, so it slides, which is why every wall needs drainage behind it.
A retaining wall holds back a bank of soil; checking its sliding and overturning resistance against the thrust from the soil shows whether it is safe.
A Gravity Wall Is A Contest Between Thrust And Weight
The soil pushes the wall sideways with a thrust calculated as in Earth Load Calculations. The wall resists in two ways. Its weight, multiplied by the friction between its base and the ground, resists sliding. Its weight acting at a distance from the toe resists the tendency of the thrust to tip it forward. The ratio of resisting to disturbing effect is the factor of safety (FS). A factor of 1 means the wall is on the point of failing.
Textbooks commonly ask for a sliding factor of at least about 1.5 and an overturning factor of at least about 2 (see for example Das, Principles of Foundation Engineering). These are conventional minimums, not tested thresholds for improvised materials.
What You Need
- Soil data: unit weight and friction angle of the retained soil.
- Wall data: height, thickness, material unit weight.
- A base friction coefficient between the wall and the ground.
- A drained backfill: gravel behind the wall and a drain at the foot; see French Drains and Perimeter Drainage.
Method: Four Numbers
Step 1: Thrust. P = ½ Ka γ H², acting at H/3 above the base.
Step 2: Overturning moment. M₀ = P x H/3, about the toe.
Step 3: Wall weight W = thickness x height x material unit weight, per metre of wall, acting at half the thickness from the toe. Resisting moment Mr = W x t/2.
Step 4: Factors of safety. FS(overturning) = Mr / M₀. FS(sliding) = μ W / P.
Worked Example
Assumed inputs: wall height H = 1.5 m, thickness t = 0.8 m (for example, two bags wide), wall unit weight 18 kN/m³, retained soil γ = 17 kN/m³, friction angle 30° so Ka = 0.333, and a base friction coefficient μ = 0.5. All are examples, not measurements.
Drained backfill
- Thrust: P = ½ x 0.333 x 17 x 1.5² = 6.38 kN per metre.
- Overturning moment: 6.38 x (1.5 / 3) = 6.38 x 0.5 = 3.19 kN·m per metre.
- Wall weight: W = 0.8 x 1.5 x 18 = 21.6 kN per metre. Resisting moment: 21.6 x 0.4 = 8.64 kN·m per metre.
- FS(overturning) = 8.64 / 3.19 = 2.71.
- FS(sliding) = 0.5 x 21.6 / 6.38 = 10.8 / 6.38 = 1.69.
Both exceed the conventional minimums, though sliding only narrowly.
Saturated backfill, no drainage (saturated unit weight 19 kN/m³, so submerged 9.19 kN/m³)
- Thrust: P = ½ x (0.333 x 9.19 + 9.81) x 1.5² = ½ x 12.87 x 2.25 = 14.48 kN per metre, 2.27 times the drained value.
- Overturning moment: 14.48 x 0.5 = 7.24 kN·m per metre.
- FS(overturning) = 8.64 / 7.24 = 1.19.
- FS(sliding) = 10.8 / 14.48 = 0.75, below 1, so the wall slides.
This leaves out water uplift under the base, which would reduce the sliding resistance further, and any resistance from soil in front of the toe, which would add some. The wall’s bearing pressure on the ground and its internal strength also have to be checked; see Soil Bearing Capacity. The formulas and the conventional minimums are textbook ones and were not tested on earthbag, stone or timber walls here.
Common Mistakes
- No drainage behind the wall. In the example it turns a safe wall into a sliding one.
- Clay backfill against the wall. It holds water; use gravel or free-draining soil next to the wall.
- Taking μ from memory. Base friction varies with the ground; wet clay is slippery.
- Using a wall height that ignores the bank above it. A slope above the wall adds load.
Safety
Retaining wall failures kill
A wall that fails releases a heavy bank of soil. Do not build it taller than the checks allow, drain the backfill, keep spoil and vehicles back from the top of the wall, and never stand below a bank during or after heavy rain. Any excavation deeper than about 1.2 m needs sloped or shored sides while the wall is built.
What’s Next
- Learn next: Bermed Walls — walls that retain a berm
- Combine with: Tensile Strength — why masonry walls rely on weight, not tension