Retaining Wall Design: Checking a Wall Against Overturning, Sliding, and Bearing

Drive past any hillside road cut and you will see them: concrete walls holding back a slope that would otherwise slump onto the pavement. Most people never give them a second look. But behind each wall is a quiet, continuous push from the soil — a force that never lets up, never goes on holiday, and grows with the square of the wall height. A retaining wall does not fail because of one dramatic event. It fails because that steady push slowly wins.

This article walks through how a cantilever or gravity retaining wall is checked for stability. We will turn backfill into a measurable thrust, set up the three classic failure modes, and work a full numerical example you can reproduce by hand.

Why this calculation matters

A retaining wall has only one job: to resist lateral earth pressure without moving in a way that endangers what sits behind or in front of it. There is no redundancy. If the wall rotates, slides, or sinks unevenly, the consequences are immediate and visible — cracked pavements, tilted fences, and in the worst cases a full collapse that brings the retained slope down with it.

The reason the calculation deserves care is that earth pressure is not intuitive. The thrust on a 5 m wall is not 25 percent larger than the thrust on a 4 m wall; it is roughly 56 percent larger, because pressure grows linearly with depth and the total force integrates that triangle. Designers who scale a wall by eye tend to be optimistic. A structured stability check — overturning, sliding, bearing — replaces that guesswork with three numbers you can defend in a design review.

The core method

Start with the lateral pressure the backfill exerts. For granular soil with friction angle phi, level ground, and a smooth vertical wall, Rankine's active earth pressure coefficient is:

Ka = (1 - sin(phi)) / (1 + sin(phi))

Equivalently, Ka = tan^2(45 - phi/2). The active pressure at depth z is Ka times gamma times z, where gamma is the soil unit weight. Integrating that triangular distribution over the wall height H gives the total active thrust per metre of wall:

Pa = 0.5 * Ka * gamma * H^2

Because the pressure diagram is a triangle, its resultant acts at one third of the height above the base — at H/3. That lever arm is what turns the thrust into an overturning moment about the toe (the front bottom edge of the wall):

Mo = Pa * (H/3)

Resisting that rotation is the weight of the wall and its base footing. The total weight W acts down through the combined centre of gravity, located some horizontal distance from the toe. That gives the resisting moment:

Mr = W * (lever arm of W from the toe)

The factor of safety against overturning is simply the ratio:

FS_overturning = Mr / Mo

Two more checks complete the picture. Sliding is resisted by friction along the base — the base friction force divided by the horizontal thrust gives FS against sliding, often required to be at least 1.5. Bearing capacity is checked by comparing the peak contact pressure under the toe against the allowable bearing pressure of the foundation soil. A wall must pass all three; a comfortable overturning margin does not excuse a weak base.

A worked example

Consider a cantilever retaining wall of height H = 5 m holding back granular backfill. The soil has a friction angle phi = 30 degrees and a unit weight gamma = 18 kN/m^3.

Step 1 — earth pressure coefficient. For phi = 30 degrees:

Ka = (1 - sin 30) / (1 + sin 30) = (1 - 0.5) / (1 + 0.5) = 0.333

Step 2 — active thrust. Integrate the pressure triangle over the 5 m height:

Pa = 0.5 * Ka * gamma * H^2
Pa = 0.5 * 0.333 * 18 * 25 = 74.9 kN/m

That is the horizontal push per metre run of wall. It acts at H/3 = 1.67 m above the base.

Step 3 — overturning moment about the toe.

Mo = Pa * (H/3) = 74.9 * 1.67 = 124.8 kN.m per metre

Step 4 — resisting moment. The wall stem and base footing together weigh W = 180 kN/m, and their combined centre of gravity sits 1.6 m horizontally from the toe:

Mr = W * 1.6 = 180 * 1.6 = 288 kN.m per metre

Step 5 — factor of safety against overturning.

FS = Mr / Mo = 288 / 124.8 = 2.3

A factor of 2.3 clears the usual minimum of 2.0, so this wall is safe against rotation about its toe. The next steps would repeat the logic for sliding and bearing, but the overturning result already shows the structure of the method: every check is a ratio of what resists to what drives.

Common mistakes

Forgetting surcharge loads. A road, a stockpile, or a parked vehicle on the backfill adds a uniform pressure that does not vanish near the surface. Surcharge raises the resultant and shifts it upward, increasing the overturning moment more than its magnitude alone suggests.

Using active pressure where it cannot develop. Rankine active pressure assumes the wall yields slightly outward, letting the soil relax to its minimum state. A wall braced at the top, or one that genuinely cannot move, sees at-rest pressure instead — noticeably higher. Choosing the wrong coefficient understates the load.

Ignoring water behind the wall. Drainage is structural, not cosmetic. If the backfill saturates, hydrostatic pressure adds to the soil thrust and the effective unit weight changes. A blocked weep hole can quietly double the design load.

Checking overturning and stopping there. The three failure modes are independent. A wall can be generously stable against rotation yet slide on a slick clay foundation, or punch into soft ground. All three factors of safety must be satisfied.

Treating the friction angle as exact. Phi is measured with scatter and can fall if the soil is disturbed or wetted. A small drop in phi raises Ka and the thrust together, so a thin margin on paper can disappear in the field.

Try the interactive NovaSolver calculator

Running the moment balance once by hand is the right way to learn it, but design is iterative — you change the base width, adjust the stem, and want all three checks to update at once. The Retaining Wall Design Calculator on NovaSolver does exactly that: pick a wall type and either Rankine or Coulomb earth pressure theory, set the geometry, soil properties, surcharge, and allowable bearing pressure, and it returns the earth pressure coefficient, the active force, and live factors of safety for overturning, sliding, and bearing — with a Mononobe-Okabe seismic option when you need to add a horizontal acceleration coefficient.

Related calculators

• Earth pressure calculator — focus purely on the lateral pressure side: compare active, at-rest, and passive states for different soils and wall conditions.
• Bearing capacity calculator — size the foundation that carries the wall, so the bearing check has a defensible allowable pressure behind it.
• Slope stability calculator — when the wall sits in or below a slope, check the global failure surface that can pass beneath the whole structure.

You can browse the full set in the geotechnical tools hub.

Closing note

Retaining wall design is one of those topics that looks heavy but rests on a handful of clear ideas. Soil pushes with a thrust that grows as the square of height. That thrust acts at one third of the height and tries to rotate the wall about its toe. Weight resists. Friction resists sliding. The footing resists bearing failure. Each check is a ratio, and a wall is only as safe as its weakest ratio. Compute all three, give yourself an honest margin on the friction angle, keep the drainage working, and the wall will go on doing its quiet job for decades.