Example Problems

Example Problem 1: A smooth, vertical retaining wall retains a dry sand backfill with an internal friction angle $\phi = 30^\circ$, unit weight $\gamma = 18 \, kN/m^3$, and a total height $H = 5m$. Calculate the total active force ($P_a$) per meter length of the wall using Rankine's theory.

Example Problem 2: A 6m high vertical retaining wall has a layered backfill profile. A uniform surcharge of $10 \, kPa$ is applied at the surface.

Calculate the total active lateral force acting on the wall per meter length.

Example Problem 3: A retaining wall $4 \, m$ high retains a cohesionless backfill with a unit weight of $19 \, kN/m^3$ and an angle of internal friction of $35^\circ$. The wall is restrained from yielding, meaning the soil remains in an at-rest condition. Calculate the total at-rest lateral earth force per meter length of the wall and determine its point of application.