Chapter 10 — Lateral Earth Pressure¶
10.1 The three states of earth pressure¶
The pressure that soil exerts on a retaining structure depends on how much the structure is allowed to move:
- At-rest pressure (\(K_0\)) — the wall does not move; the soil is in its natural state. \(K_0 \approx 1 - \sin\phi'\) for normally consolidated soils.
- Active pressure (\(K_a\)) — the wall moves away from the soil, which expands and relaxes to its minimum pressure. This is the minimum pressure a wall must resist.
- Passive pressure (\(K_p\)) — the wall moves into the soil, which compresses and pushes back with its maximum resistance. \(K_p > K_0 > K_a\).
The three coefficients are related by \(K_a = 1/K_p\) for a simple frictionless case, and both depend on the friction angle \(\phi'\) and wall friction \(\delta\).
10.2 Rankine and Coulomb theories¶
Two classical theories give the pressure coefficients:
- Rankine — assumes a smooth, vertical wall and a horizontal backfill; simple and widely used.
- Coulomb — allows wall friction and inclined backfill, giving more realistic (and often lower active) pressures; solved graphically or analytically.
Both assume the soil reaches a plastic state and neglect the wall–soil interaction stiffness, so they are limits rather than exact values.
10.3 Surcharge, water, and layered backfill¶
Real walls carry more than soil self-weight:
- Surcharge — uniform or point loads behind the wall (traffic, stockpiles, adjacent footings) add lateral pressure.
- Water pressure — groundwater behind a wall adds full hydrostatic pressure, often the dominant load. Drainage is essential; a wall designed for soil pressure alone can fail when it fills with water.
- Layered and sloping backfill — pressures are computed layer by layer.
10.4 Compaction-induced pressure¶
Compacting backfill behind a wall with heavy rollers can lock in high lateral pressures that exceed the active value, especially near the surface. This is a frequent cause of unexpected wall movement, and it must be accounted for in design and in the compaction method.
10.5 Key takeaways¶
- Three states: at-rest, active, passive — active is the minimum, passive the maximum.
- Rankine is simple; Coulomb allows wall friction and inclined backfill.
- Water is often the dominant load — provide drainage.
- Surcharge behind a wall adds pressure; account for it.
- Compaction can lock in pressures above active — control the method.