Retaining Wall Stability | mysimulator.uk

A wall does more than hold itself up

A retaining wall's job is to hold back a slope of soil that would otherwise slump to a shallower, more natural angle. The soil behind the wall is not passive dead weight resting on a shelf — it is a mass under its own internal stress, and the moment the wall gives it anywhere to go, that stress pushes outward against the wall as a real, sustained horizontal force. Getting the wall's geometry and weight right means first working out how large that push actually is, and then checking three separate, quite different ways the wall could fail under it.

Rankine active earth pressure

In 1857 William Rankine showed that when a wall is free to move or rotate slightly away from the soil it retains, the soil mass behind it shears internally and relaxes down to a minimum, stable pressure state called the active state. The horizontal pressure this produces at a given depth z is proportional to the vertical overburden pressure at that depth, scaled by the active earth pressure coefficient Ka = tan²(45° − φ/2), where φ is the soil's angle of internal friction — a measure of how strongly the soil resists shearing against itself. A looser, weaker soil (lower φ) has a larger Ka and pushes harder; a dense, well-compacted granular soil (higher φ) has a smaller Ka and pushes less. Because the vertical stress in the soil grows linearly with depth, so does the horizontal active pressure, producing a triangular pressure distribution over the height of the wall: zero at the top, maximum at the base.

The resultant thrust and its lever arm

A triangular distribution is easy to sum: integrating the pressure over the full wall height H gives a single resultant horizontal force Pₐ = ½·Ka·γ·H², where γ is the soil's unit weight. This resultant does not act at mid-height — like any triangle, its centroid sits one-third of the way up from the wide end, so Pₐ acts at H/3 above the base. That lever arm matters as much as the force itself, because it is what turns a horizontal push into a rotational, overturning effect on the wall.

Ka  = tan²(45° − φ/2)
σₐ(z) = Ka · γ · z            // pressure at depth z
Pₐ  = ½ · Ka · γ · H²          // resultant thrust, acting at H/3 above base

FS(overturning) = M_resisting / M_overturning   // target ≥ 2.0
FS(sliding)      = F_resisting / Pₐ              // target ≥ 1.5

Illustrative example: φ = 30°, γ = 18 kN/m³, H = 4 m
  Ka  = tan²(45° − 15°) = tan²(30°) ≈ 0.333
  Pₐ  = 0.5 × 0.333 × 18 × 4² ≈ 48 kN per metre of wall, acting at 4/3 ≈ 1.33 m above base
  If wall + soil self-weight gives a resisting moment of ≈ 130 kN·m about the toe
  and Pₐ's overturning moment is 48 × 1.33 ≈ 64 kN·m,
  FS(overturning) ≈ 130 / 64 ≈ 2.0  — right at the design target

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Checking overturning and sliding

Two failure mechanisms follow directly from the resultant thrust. Overturning asks whether the wall would rotate forward about its toe — the front bottom edge, the hinge point if the wall were to tip. The wall's own weight, and the weight of any soil sitting on the footing's heel, create a resisting moment about that toe; the active thrust, acting at its H/3 lever arm, creates an overturning moment about the same point. The Factor of Safety against overturning is simply resisting moment divided by overturning moment, and standard practice targets FS ≥ 2. Sliding asks a different question: would the whole wall translate forward along its base? Resistance here comes mainly from friction between the base and the soil beneath it — friction force equals a friction coefficient times the total vertical load pressing the base down — plus, often conservatively ignored, some passive resistance from soil piled against the front of the wall. The Factor of Safety against sliding is that resisting friction force divided by the driving horizontal thrust, with a standard target of FS ≥ 1.5.

Base eccentricity and the middle-third rule

A wall can pass both the overturning and sliding checks and still be poorly proportioned. Summing moments about the centreline of the base locates exactly where the resultant vertical load lands — its eccentricity e from the centre. Because soil can only push, never pull, the bearing pressure under the footing must stay compressive everywhere; that is only guaranteed if the resultant lands within the base's middle third, meaning e ≤ B/6 for a base width B. Push the resultant past that limit and part of the base effectively lifts off the soil, concentrating the full load onto a shrinking area near the toe — a bearing pressure spike that can crush or unevenly settle the soil, slowly tilting the wall even if it never overturns or slides outright.

Frequently asked questions

What does 'active' earth pressure mean as opposed to 'at-rest' or 'passive'?

At-rest pressure is what the soil exerts on a wall that never moves at all. Active pressure is lower: it develops once the wall deflects slightly away from the soil, letting the soil mass relax and shear internally until it reaches its minimum stable pressure state. Passive pressure is the opposite extreme, developing when the wall is pushed into the soil, and it is much larger than active pressure for the same soil.

Why does the factor of safety against overturning need to be at least 2 but sliding only 1.5?

Overturning is a brittle, sudden failure mode with little warning once the resultant leaves the base, so codes demand a larger margin. Sliding tends to show warning signs first, such as small cracks or gradual movement, and friction resistance is itself already a conservative lower-bound estimate, so a smaller safety margin is accepted.

What happens if the resultant force falls outside the middle third of the base?

Soil cannot resist tension, so if the resultant lands outside the middle third the bearing pressure diagram would require negative (tensile) stress at the heel, which is impossible. Instead the base partially lifts off the soil, the contact area shrinks, and the same load concentrates onto a smaller area at the toe, sharply raising the peak bearing pressure there and risking a local bearing failure.

Try it live

Everything above runs in your browser — open Retaining Wall Stability and drag the wall's height, base width and soil friction angle to see the factors of safety update in real time. Nothing is installed, nothing is uploaded, the whole model lives in one tab.

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Retaining Wall Stability: Rankine Pressure and the Factor of Safety