Retaining wall stability
A cantilever wall fails in one of three ways: it tips over, it slides, or it pushes the soil past its bearing capacity. This computes the Rankine thrust from the soil, surcharge and water, then checks all three modes and reports the stem moment the reinforcement has to carry.
| Check | Value | Note |
|---|---|---|
| Active coefficient Ka | 0.333 | Rankine, φ = 30° |
| Passive coefficient Kp | 3.00 | 1 / Ka |
| Coulomb Ka (δ = 20°) | 0.297 | Wall friction reduces the thrust further |
| Soil thrust | 48.0 kN/m | Lever arm 1.48 m |
| Surcharge thrust | 13.3 kN/m | 10.0 kPa over 4.0 m |
| Water thrust | 0.0 kN/m | Drained |
| Total horizontal | 61.3 kN/m | The sum of the three |
| Total vertical | 239.2 kN/m | Stem, base and heel soil |
| Overturning moment | 90.7 kN·m | About the toe |
| Resisting moment | 380.7 kN·m | About the toe |
| FS overturning | 4.20 | ≥ 1.50 for a gravity wall |
| Passive resistance | 4.3 kN/m | Often neglected for a buried toe |
| FS sliding | 2.02 | ≥ 1.50 |
| Eccentricity | 0.29 m | Within B/6 = 0.50 m |
| Bearing, max | 126 kPa | Allowable 200 kPa |
| Bearing, min | 34 kPa | Negative means uplift at the heel |
| Stem moment at base | 90.7 kN·m/m | For the stem reinforcement design |
A drained wall is a different structure from a flooded one. If the water height is anything other than zero, a drain and a filter are usually cheaper than the extra concrete the water demands.
Ka = (1 − sin φ)/(1 + sin φ) · Valid for a vertical wall with horizontal backfill.
Pa = ½ Ka γ H² · Acts at H/3 above the base.
FS = ΣMr / ΣMo · Moments taken about the toe.
q = V/B (1 ± 6e/B) · Valid while e ≤ B/6; beyond that the heel lifts.
A clear path from inputs to results.
A cantilever retaining wall fails in one of three ways: it tips over, it slides, or it pushes the soil past its bearing capacity. This computes the lateral thrust from the retained soil, any surcharge and any water, then checks all three modes and reports the stem moment the reinforcement has to carry.
How to use
- Enter the retained height and the base width.
- Set the soil unit weight and the effective angle of internal friction.
- Add any uniform surcharge on the backfill.
- Set the water table height — zero for a drained wall.
- Read the coefficient, the thrust, and the three stability factors.
The formula
Reference: Rankine earth pressure theory; stability factors and the bearing equation follow Das, Principles of Foundation Engineering, and the usual 1.5 working-stress targets.
Worked example
4 m wall, 3 m base, φ = 30°, 10 kPa surcharge
- Retained height 4 m, base width 3 m, drained.
- Soil 18 kN/m³ with φ = 30°, 10 kPa surcharge.
- Base friction 0.5, allowable bearing 200 kPa.
- Stem 0.4 m thick at the base, base slab 0.4 m, concrete 24 kN/m³.
- 1
Ka = (1 − sin 30°)/(1 + sin 30°) = 0.333.
- 2
Soil thrust is ½ × 0.333 × 18 × 4² = 48.0 kN/m, acting 1.33 m above the base.
- 3
Surcharge thrust is 0.333 × 10 × 4 = 13.3 kN/m, acting at mid-height.
- 4
Overturning moment about the toe is 48 × 1.33 + 13.3 × 2 = 90.7 kN·m.
- 5
Resisting weight is 38.4 kN of stem, 28.8 kN of base and 149.0 kN of heel soil, plus 23 kN of surcharge on the heel.
- 6
That gives 239.2 kN and a resisting moment of 380.7 kN·m, so overturning is 4.20 — comfortably above 1.5.
- 7
Sliding is 239.2 × 0.5 / 61.3 = 2.02, also above 1.5.
- 8
The resultant sits 0.29 m off centre, inside B/6 = 0.50 m, so the toe pressure is 126 kPa against an allowable 200 kPa.
Ka 0.333 · thrust 61.3 kN/m · overturning 4.20 · sliding 2.02 · toe 126 kPa.
Interpreting the result
Overturning and bearing almost always pass on a sensibly proportioned wall; sliding is the one that catches people out, because the base friction coefficient is a soil property and not a design choice. Water is the other trap: raising the table to the top of the wall roughly doubles the thrust and adds a pore pressure that the soil weight no longer offsets.
Assumptions & limitations
- Rankine theory, which assumes a vertical wall, horizontal backfill and no wall friction. A Coulomb coefficient is shown alongside so the difference is visible.
- The soil is homogeneous and drained above the water table; below it the effective unit weight is reduced by 9.81 kN/m³.
- The stem is modelled as a rectangle of the base thickness rather than a taper, which is slightly conservative.
- Passive resistance in front of the toe is computed but is often neglected in practice because the ground there may be excavated.
- Seismic earth pressure, global slope stability and the structural design of the reinforcement are not modelled.
- The wall is a cantilever on a spread base; piled and anchored walls need a different analysis.
Frequently asked questions
Why is Ka one third at φ = 30°?
Because (1 − 0.5)/(1 + 0.5) = 0.333. It is a useful number to remember: at a friction angle of 30°, the soil pushes with a third of its vertical stress, and the passive resistance is three times it.
Why does water matter so much?
Because it adds 9.81 kN per cubic metre of height squared, on top of removing the buoyant weight of the soil it displaces. A metre of water at the base of a 4 m wall adds about 5 kN/m of thrust and 1.6 kN·m of moment — small — but at the full height it adds 78 kN/m and dominates everything.
What is the difference between active and passive pressure?
Active pressure is what the soil exerts when the wall moves away from it; passive is the resistance when the wall pushes into it. Passive is several times larger but requires much more movement to mobilise, which is why it is treated cautiously.
What factor of safety should I use?
1.5 against overturning and sliding is the usual working-stress target for a gravity or cantilever wall, and 2.0 for sliding where the friction coefficient is uncertain. LRFD designs use load and resistance factors instead, which give a different but comparable margin.
Why is my sliding factor so low?
Usually the base friction coefficient. A value of 0.5 is typical for silt and fine sand; 0.35 is realistic for clay. Adding a shear key or widening the base helps, and both are cheaper than increasing the wall thickness.
Can I use this for a basement wall?
The pressure calculation is the same, but a basement wall is restrained at the top by the floor diaphragm, which changes the structural model from cantilever to propped. Use this for the earth pressure and design the wall for the propped case separately.
Methodology last reviewed 2026-10-21. Results are informational and not financial or engineering advice — see our disclaimer.