Coulomb Wedge Pressure

The Coulomb wedge method evaluates the active earth pressure exerted on a retaining wall by considering a planar failure surface that intersects the wall at a friction angle (delta) and the backfill at the slope angle (beta). The soil is assumed to be homogeneous, cohesionless, and characterized by its unit weight (gamma) and internal friction angle (phi). By resolving forces along the failure plane, the method derives a pressure coefficient that reflects the combined effect of wall friction and backfill inclination.

Coulomb’s active earth pressure coefficient (K_a) is expressed as a function of the three angles (beta), (delta), and (phi). The coefficient multiplies the vertical stress at the base of the wall ((gamma H)) to give the resultant horizontal pressure. The inclusion of wall friction (delta) reduces the pressure compared with the Rankine case, while a steeper backfill (beta) generally increases it.

The final pressure is obtained by multiplying the coefficient (K_a) by the height of the wall (H) and the soil unit weight (gamma). This pressure is assumed to act at a height of (H/3) from the base for design purposes, providing a simple yet conservative estimate for most retaining structures.