Every retaining wall, basement wall, and sheet pile lives or dies by one question: how hard is the soil behind it pushing? The answer isn't a fixed number — it depends on which way the wall moves. That single idea is this whole chapter.
Water pushes on a dam with one predictable pressure — hydrostatic, straight from depth. Soil doesn't. Soil is a pile of grains that can lock together and support themselves, so how hard it pushes on a wall depends entirely on what the wall does.
Soil behaves the same way. A wall that doesn't move at all holds the soil in its natural, undisturbed state — at-rest pressure. A wall that yields (tips or slides away, even slightly) lets the soil relax and mobilize its own shear strength to hold itself up — pressure falls to a minimum called active pressure. A wall that gets pushed into the soil compresses it, forcing it toward failure in the other direction — pressure rises to a maximum called passive pressure.
A tiny outward movement (~0.1–0.5% of wall height) is enough to crash the pressure down to Ka. Getting the full passive resistance Kp takes a movement 10–50× bigger, in the opposite direction. This asymmetry is why designers can trust active pressure calculations after almost no movement, but can't fully trust passive resistance unless the wall has actually shifted a lot.
Basement walls braced by a floor slab on both ends, or a wall between two buildings that literally can't move — these hold soil at rest. Nothing has relaxed and nothing has been compressed; the soil is exactly as confined as when it was deposited.
No shear strength is mobilized at all — the soil isn't anywhere near failure. Horizontal stress is just some fraction of vertical stress, set by how the soil was confined as it formed. Loose, normally-consolidated soil settles into a fairly predictable fraction.
For normally consolidated soil. (Overconsolidated soil has higher K₀ — it "remembers" a bigger past confinement.)
K₀ is not a strength calculation — it's a snapshot of however the soil happens to sit right now. It's always between Ka and Kp, closer to the middle.
Tip a cantilever retaining wall forward, even by a millimeter per meter of height, and a wedge of soil behind it slides down and pushes it — but only with the minimum force needed to keep that wedge from falling further. The soil is doing as little work on the wall as physically possible.
The soil is at the brink of shear failure along a plane tilted at 45°+φ'/2 from horizontal. Rankine's theory assumes a frictionless, vertical wall and a horizontal backfill — simple, but it's the backbone every real design builds on.
Active pressure is the minimum the soil will ever push with. It's what happens once the wall has already yielded enough to let the soil find its easiest, most relaxed equilibrium.
Push a wall into the soil — this is what happens at the toe of a footing, or the embedded tip of a sheet pile — and the soil fights back at its maximum possible resistance. This resistance is what keeps footings and sheet piles from sliding or kicking out.
Same theory, opposite direction: the failure plane flattens to 45°−φ'/2, and the wedge that resists is much bigger and much stronger. That's why Kp is always far larger than Ka.
Clay has cohesion (c') — grains stick to each other even under zero confinement. That stickiness fights the active pressure, subtracting from it. But cohesion can't be squeezed, only pulled apart — near the top of the wall, where confinement is lowest, the math predicts negative pressure. Soil can't actually pull on a wall, so instead it just cracks open.
Below zc, pressure builds normally. Design practice ignores the cracked zone's pressure entirely — but that crack can fill with rainwater and push with full hydrostatic force, which is often the more dangerous case in real walls.
One tool, three pressure states. Groundwater matters because below the water table the soil's effective weight drops (buoyancy), but full hydrostatic pressure gets added back on top — so the total pressure diagram kinks at the water table instead of staying a straight triangle.
Rankine's theory needs a frictionless, vertical wall and a flat backfill — clean for learning the concept, but most real walls have batter, wall friction, and sloped fill. Two extensions handle that:
Pressure now acts parallel to the sloped ground surface, not horizontally.
Coulomb drops the frictionless-wall assumption and lets the wall drag on the sliding wedge, which lowers Ka and (for rough walls) meaningfully raises Kp. The trade-off: the failure surface is no longer a flat plane, so the closed-form expression is heavier. In practice, engineers pull Ka/Kp straight from published charts for the given δ, α, and wall batter β rather than deriving it by hand.
Problem: A 5 m tall basement wall retains dry, normally consolidated sand with γ = 17 kN/m³ and φ' = 32°. The wall is fully braced (no movement). Find the at-rest force per meter of wall and its location.
Problem: A frictionless 6 m wall retains a clay backfill: γ = 18 kN/m³, φ' = 26°, c' = 12 kPa. Find the tension crack depth and the active force after the crack forms.
1. A cantilever wall tips forward by 2 mm at the top. Which pressure state is now acting on it?
2. Why is Kp always much bigger than Ka for the same soil?
3. A tension crack forms in clay backfill because: