Retaining wall calculator: stability and earth pressure

Enter a concrete wall, the soil it holds back and the soil it stands on. Rischio’s engine works out the earth pressure behind the wall and checks it for overturning, sliding, bearing and the eccentricity of the resultant, as the studio does. It’s free and needs no account.

How it calculates

The calculator checks a one-metre slice of the wall as a rigid body: its own weight and the soil’s against the push of the backfill.

The backfill pushes with Rankine’s active pressure on the virtual back, the vertical plane through the end of the heel. The soil between the stem and that plane counts as part of the wall’s weight. With the backfill’s surface sloping at $\beta$, the active coefficient is

and the pressure at each depth is $\sigma_a = (\sigma'_v + q)\,K_a - 2c'\sqrt{K_a}$, parallel to the surface. Its horizontal part pushes the wall over; its vertical part bears down on the heel and helps hold it. In a cohesive backfill the soil can’t pull on the wall, so a tension crack opens near the top instead. The engine takes the crack as full of water and says so in a warning.

Below the water table, the backfill pushes with its submerged weight and the water adds its own thrust, $P_w = \tfrac{1}{2}\gamma_w h_w^2$, plus an uplift on the base. In front of the toe, the soil down to the base resists with Rankine’s passive pressure, $K_p = \tan^2(45° + \phi'/2)$.

With those forces, the four checks:

The base friction is $\delta = \tfrac{2}{3}\phi'$ and its adhesion $c_a = \tfrac{2}{3}c'$, both of the foundation soil. The passive thrust doesn’t enter the overturning check, and when sliding depends on it, the engine gives the factor of safety without it. The base bears $q_{max,min} = \frac{\Sigma V}{B}\left(1 \pm \frac{6e}{B}\right)$, and $q_u$ is the general bearing capacity equation on the effective width $B' = B - 2e$, with the load’s inclination (the bearing capacity calculator shows that equation on its own). The minimums are the engine’s defaults, the usual ones for retaining walls in US practice (FHWA).

Each step, with its equations, is in the docs: earth pressure, stability and bearing capacity.

How to use it

1. Pick the wall: a cantilever wall (a stem on a footing) or a gravity wall (one block of concrete).
2. Give its dimensions. For a cantilever, the height from the bottom of the footing to the crest, the base width, the toe’s length, the footing’s thickness and the stem’s width at the top and at the base. For a gravity wall, its height, its base and crest widths and how much its back leans.
3. Give how deep the base sits below the ground in front of the toe. That soil gives the passive thrust.
4. Describe the backfill: its unit weight, cohesion, friction angle, the slope of its surface and any surcharge on it. Turn on the water table if the backfill isn’t drained.
5. Describe the foundation soil the wall stands on.

The results show the four checks, the wall drawn with the earth pressure behind it and the pressure under its base, and a table with every force and moment. Restore the example brings back the studio’s template, a 6 m cantilever wall. To keep the wall, add strata, try a gabion wall or get a calculation report with every step, design it in Rischio’s retaining wall tool.

Frequently asked questions

How do you calculate the stability of a retaining wall?

Work out the forces on a one-metre slice: the weights of the wall and of the soil over its heel, the earth and water pressure behind it and the passive resistance in front. Then check that it doesn’t overturn about its toe, slide on its base or overload the soil under it, and that the resultant crosses the base within its middle third.

What factor of safety does a retaining wall need?

The usual minimums are 2 against overturning, 1.5 against sliding and 3 against bearing capacity failure, the defaults this calculator uses. Some codes and owners ask for other values, so the ones that apply to a project come from its specifications.

What is the middle third rule for retaining walls?

The resultant of all the forces on the wall should cross the base within its middle third, which means an eccentricity of at most $B/6$. Then the whole base presses on the soil. Past that point, $q_{min}$ turns negative and the heel side of the base starts to lift off.

How thick does a retaining wall need to be?

The checks decide it, but there are usual first sizes. For a cantilever wall, a base about 0.5 to 0.7 times the height, a footing about a tenth of the height thick, and a stem at least 0.3 m (12 in) wide at the top, wider at its base. A gravity wall needs more width, because its own weight is what holds it.

What doesn’t this calculator check?

It checks the wall’s external stability. The structural design of the stem and the footing (their bending, shear and reinforcement), the global stability of the slope around the wall and its settlement are separate checks.