Lateral Earth Pressure

Lateral earth pressure is the horizontal pressure exerted by soil on a retaining structure. Three principal states are defined: (a) Active pressure (Pa) — the soil tends to move forward (towards the wall) — minimum pressure, occurring when the wall yields slightly; (b) At-rest pressure (P0) — neutral state when the wall does not yield; (c) Passive pressure (Pp) — the soil tends to be pushed back into the ground — maximum pressure, occurring when the wall pushes into the soil. Coulomb's theory and Rankine's theory provide standard methods for computing these pressures; Coulomb accounts for wall friction (typical Indian use) while Rankine assumes a smooth vertical wall.

For a vertical wall retaining horizontal granular soil with friction angle φ (no cohesion, no surcharge): Active pressure coefficient Ka = (1 − sin φ) / (1 + sin φ) (Rankine). For φ = 30°: Ka = 1/3. So at depth z below the top of soil: Pa(z) = Ka × γ × z, where γ is soil unit weight. For 5 m of dry sand at γ = 18 kN/m³ and φ = 30°: total active force per metre length = (1/2) × Ka × γ × H² = 0.5 × 0.333 × 18 × 25 = 75 kN/m. Coefficient Kp for passive = 1/Ka = 3.0; passive force = 675 kN/m for the same wall — much larger than active.

Design considerations: (a) include water pressure if drainage is inadequate (combined active + hydrostatic can double the lateral force); (b) include surcharge from any load on top of retained soil — buildings, vehicles, fill; (c) account for cohesive soil terms — Rankine modified equation gives Pa = Ka × γ × z − 2c√Ka, where c is cohesion. For clay with c = 50 kPa and φ = 0: Pa(z = 0) = −100 kPa (negative — net tension at the surface, often ignored); (d) for seismic loading, IS 1893 + Mononobe-Okabe equation gives dynamic earth pressure increase typically 30-60% above static for design earthquakes. Indian practice for routine retaining walls: use Rankine for granular fill, Coulomb for cohesive fill or non-vertical walls, with hydrostatic if water cannot be properly drained.