Earth Pressure and Retaining Walls
A load that depends on how the structure responds to it — millimetres of movement halve the pressure, and water behind the wall doubles it.
Skip to the animationThe pressure soil exerts on a wall depends on how far the wall moves — millimetres of yield roughly halve it, being pushed into the soil triples it — which makes earth pressure a load defined by the structure's own response to it.
A load that depends on movement
| Wall movement | Case | Coefficient | Movement needed |
|---|---|---|---|
| None | At rest, K₀ | ≈ 1 − sin φ′, about 0.45 | — |
| Away from the soil | Active, K_a | ≈ 0.33 | About 0.1% of wall height |
| Into the soil | Passive, K_p | ≈ 3 | 2–5% of wall height |
No other load in structural engineering behaves like this. A basement wall braced by floor slabs cannot yield, so it must be designed for K₀; a free-standing retaining wall moves enough to develop the active case, which roughly halves the load.
Passive resistance is rarely fully available
Passive pressure is ten times the active value, but it needs fifty times the movement to develop — usually far more than the structure can tolerate. Designers therefore discount it heavily, commonly by half.
An overconsolidated clay that has had overburden removed can have K₀ above 1 — pushing harder sideways than downward, which surprises people the first time they meet it.
The distribution
Pressure grows linearly with depth, so the distribution is triangular and the resultant acts at H/3 from the base — the same reasoning as hydrostatic force on a dam. That lever arm, not merely the force, sets the overturning moment about the toe.
Water is the thing that breaks walls
Soil transmits only K_a of its vertical stress sideways; water transmits all of it. A saturated backfill can more than double the load on a wall designed for drained conditions.
That is why every retaining wall has weep holes and a drainage layer, and why blocked ones are a recurring cause of failure. Drainage is not a detail here — it is half the design.
The four checks
- Overturning about the toe — factor of safety typically 2.0.
- Sliding along the base — typically 1.5.
- Bearing failure beneath the toe — typically 3.0.
- Overall slope stability on a deep surface passing beneath the whole wall — the one most often overlooked, and it takes the wall with it.
Reinforced soil
Placing geogrid or steel strips in the backfill makes the soil mass a coherent block, with the facing as cladding. Soil is strong in compression and weak in tension, and the reinforcement supplies exactly what it lacks — so no massive stem or footing is needed, and it tolerates differential settlement that would crack a rigid wall.
The numbers you will be asked for
- At rest
K₀ = 1 − sin φ′
- Rankine active
K_a = (1 − sin φ′)/(1 + sin φ′) = tan²(45 − φ′/2)
- Rankine passive
K_p = (1 + sin φ′)/(1 − sin φ′) = 1/K_a
- Active thrust
P_a = ½ K_a γ H², acting at H/3
- With cohesion
σ_a = K_a σ′_v − 2c′√K_a
- Water thrust
P_w = ½ γ_w H_w², with K = 1
Watch it work
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