Limit analysis method of active earth pressure on cantilever retaining wall subjected to earthquake

In order to determine the seismic active earth pressure on cantilever retaining walls, five potential failure modes of the backfill are provided considering the possible locations of the assumed planar back of the walls. Based on the potential failure mechanisms, formulas of the earth pressure on the planar back are derived in light of the quasi-static method and upper bound theory of the kinematical limit analysis, which can reflect various influence factors including properties of the backfill, dip angle of the filling surface, length of base slab with heel, wall height, as well as horizontal and vertical seismic impact factors. Most of the influence factors are nonlinearly linked with the earth pressure except for cohesion of the backfill and vertical seismic impact factor. Analysis results of some examples show that overturning and translating factors of safety of the wall determined via the earth pressure by the proposed method are both slightly higher than those by the Mononobe-Okabe mehtod in most practical cases, and the analysis model of the assumed wallback starting exactly from the bottom of the wall heel is relatively marginally unsafe if there is the second failure surface in the backfill. The seismic active earth pressure obtained by the failure mode with vertically assumed wall back is relatively minimum, but the corresponding two factors of safety are not certainly maximum.