Analytical method for determining displacement and bending moment of embedded cantilever retaining walls subjected to pseudo-static earthquake accelerations

The performance of embedded cantilever retaining (ECR) walls, such as the diaphragm and sheet-pile walls, is measured by the permanent displacement they experience during an earthquake. In the conventional design methods, the embedment depth is derived by checking the wall's stability against a probable collapse mechanism and applying safety factors. Thereby, these methods are incapable of determining the wall displacement. The present study proposes an analytical method based on the pseudo-static approach for calculating the earthquake -induced permanent displacement of ECR walls in cohesionless soils. A displacement-dependent earth pressure mobilization relationship, where the earth pressure mobilization is a function of the wall displacement, is used to derive the passive resistance on the excavated side of the wall. With increasing earthquake acceleration, active soil pressure on the retained side of the wall increases and drives the wall towards the excavated side, which causes further mobilization of passive earth pressure; thus, the wall stability is maintained. In observations from past experimental studies, the required embedment depth is derived by assuming rigid rotation of the wall about a point near the wall base and balancing the forces and moments acting on the wall. Analytical expressions are provided for determining bending moment distribution along the wall height. The proposed results are compared with those of the available experimental and numerical studies, and they exhibit good agreement, which sub-stantiates the validity of the proposed method. Parametric studies were performed to investigate the influence of soil friction angle, wall roughness, the magnitude of the horizontal and vertical earthquake accelerations on the wall displacement and internal forces of the wall.