Active earth pressure in cohesive soils with an inclined ground surface

An analytical solution is developed to determine the active lateral earth pressure distribution on a retaining structure when it consists of a cohesive backfill (internal friction angle phi > 0, cohesion c > 0) with an inclined ground surface. The solution derived encompasses both Bell's equation (for cohesive or cohesionless backfill with a horizontal ground surface) and Rankine's solution (for cohesionless backfill with an inclined ground surface). The orientation of the failure surface is also determined. Results indicate that, unlike the soil-wall scenarios of Bell and Rankine where the failure planes are parallel with a fixed orientation independent of the overburden pressure, for sloping cohesive backfill (phi > 0, c > 0) the slope of the failure surface is a function of the overburden pressure and becomes shallower with depth, thus forming a curvilinear failure surface. The solution developed can also be used to check the sustainability of a slope. The analytical solution can be programmed conveniently in a computer.