Limit-state solutions for the active earth pressure behind walls rotating about the base

Determining earth pressure-induced moments in the active limit state is critical for the safety assessment of retaining structures. While traditional design methods assume a Coulomb's resultant force acting at one-third of the wall height, the literature suggests that the earth pressure distribution depends on the failure mode. This paper presents a rigorous kinematic solution for the ultimate moment acting on a wall undergoing rotation about its base (due to bending failure or overturning). In addition, an approximate static solution is considered. These solutions give a good approximation to the ultimate load. While the kinematic solution is closer to the exact numerical solution, the approximate static solution provides a reliable conservative approximation for common geometric and soil parameters. Its advantage is that it has a closed-form formulation. The kinematic solution is successfully validated against experimental data and is further used to investigate the peculiarities of the rotational failure mode and to evaluate traditional methods. It is found that traditional methods are close to the rigorous solutions and, therefore, reasonably safe. A useful by-product of this study: the formulation of the kinematic solution is versatile and can be applied to various geotechnical problems involving rotation.