Lateral Earth Pressure and the Wall That Resists It

Three states, and movement is what chooses between them

A soil pushing sideways on a wall does so at one of three intensities, and the material is the same in all three. What differs is whether the wall has MOVED.

AT REST is a wall that has not moved at all — a basement wall propped by the floors, a bridge abutment locked between decks. ACTIVE is a wall that has yielded away from the soil by a small amount, letting the soil mobilise its own shear strength to hold part of itself up; a free-standing retaining wall reaches this after a movement of roughly a thousandth of its height. PASSIVE is a wall pushed INTO the soil, so the soil resists in compression.

The coefficients for a level cohesionless backfill follow from the friction angle, and the spread is the thing to remember. At a friction angle of thirty degrees, the at-rest coefficient is about 0.50, the active about 0.33, and the passive 3.0. **Passive is nine times active for the same soil.** No other input on any of these pages moves the answer by a factor of nine, which is why the first question about a retaining structure is always which state it is in.

Ground that once carried more load than it does now keeps more of its horizontal stress, and a wall that cannot move feels it. Eurocode 7 multiplies the at-rest coefficient by the square root of the overconsolidation ratio — a ratio of 2 raises it by about 41 per cent — and says the relation is not for very high ratios.

The pressure is triangular, so the moment is what sizes the wall

Earth pressure grows with depth, because it is the weight of the soil above acting sideways through the coefficient. So the pressure diagram on a wall with level backfill and no water is a TRIANGLE with its apex at the surface, and the resultant of a triangle acts at one third of the height from the base — not at the middle.

That is why overturning governs so many retaining walls. The force grows with the square of the height and the lever arm grows with the height, so the overturning MOMENT grows with the cube: doubling a wall's height multiplies its overturning moment by eight. A wall that works at 1.2 m and is built at 2.4 m is not twice as loaded, it is eight times.

It is also why the checks are separate and all of them have to pass. Sliding compares horizontal thrust against friction under the base; overturning compares moments about the toe; bearing compares the resultant's eccentricity and the pressure it produces under the heel and toe. A wall can be comfortable on two of the three and fail the third.

Water is what actually fails retaining walls

Water does two things at once and both are bad. It reduces the soil's effective weight to its submerged value — which helps — and it adds its own hydrostatic pressure, which does not act through any coefficient at all. Water pushes with K equal to one, in every direction, always.

Run the arithmetic and the result is stark. A drained granular backfill at a typical unit weight with an active coefficient of a third exerts a horizontal pressure of roughly a third of its vertical weight. Saturate it and the soil skeleton's contribution falls to the submerged weight times that same third, while the water adds its full weight with no reduction — and the total comes out roughly **twice to three times** the drained case.

That is why drainage is the cheapest structural element on a retaining wall: a granular drainage layer, a weep or a pipe costs a fraction of the extra structure needed to resist a saturated case, and a wall designed drained that is not drained is a wall designed for a third of what it will see. Every retaining page here says whether it assumed drained conditions, because it is the assumption that matters most.

Where it fails: Rankine's assumptions, and compaction

The coefficients above are Rankine's, and they assume a smooth vertical wall back, a level backfill surface, and no friction between wall and soil. Real walls violate all three. Wall friction reduces the active thrust and rotates it downward, which HELPS — so Rankine is conservative for active pressure and that is why it survives in practice. Coulomb's theory takes wall friction and a sloping backfill into account and is the right tool when either is significant.

For PASSIVE pressure the same simplification is not conservative. Rankine's passive coefficient over-estimates the available resistance when wall friction is present, because the failure surface is curved rather than planar, and the error grows with the friction angle. Where passive resistance is being relied on, the log-spiral solutions or a reduced coefficient are the standard corrections.

The second failure is compaction. Backfill placed and compacted in lifts locks in horizontal stresses that can EXCEED the at-rest value near the top of the wall, because the compaction plant pushes the soil sideways and the wall does not let it spring back. A wall designed for active pressure and backfilled with a heavy roller against it is loaded in a way the calculation never saw — which is why specifications restrict plant size within a zone behind the wall.

And passive resistance needs movement to develop — far more than active does, often several percent of the embedded depth. A wall that must not visibly move cannot count on its full passive value, and this is exactly the case where an optimistic friction angle compounds an optimistic assumption about deflection.

Surcharge, and the alternatives

A uniform surcharge on the backfill surface — stored material, a car park, a strip of highway — adds a RECTANGULAR pressure of the coefficient times the surcharge at every depth, so its resultant acts at mid-height rather than at the third point. A wall checked for earth pressure alone and then loaded at the top is checked for the wrong diagram, and the surcharge's higher lever arm makes it disproportionately bad for overturning.

A point or line load is a different problem again: it spreads with depth rather than acting uniformly, and Boussinesq's elastic solution is the usual treatment. Applying a uniform-surcharge formula to a wheel load close to a wall over-states the pressure deep down and under-states it just below the load.

Beyond the closed-form methods, the alternative is numerical: a finite-element or finite-difference model that carries soil stiffness, staged construction and wall flexibility. It is the right answer for a deep basement or an anchored wall where the pressure redistributes as the wall deflects, and it is enormous overkill for a garden wall. The pages here are closed-form and say so.