General variational solution for seismic and static active earth pressure on rigid walls considering soil tensile strength cut-off

According to the limit equilibrium state of soils behind rigid walls and the pseudo-static approach, a general closed-form solution to seismic and static active earth pressure on the walls, which considers shear and tension failure of the retained soil, is put forward using a variational calculus method. The application point of the active resultant force specified in the proposed method is explained with a clear physical meaning related to possible movement modes of the walls. In respect of the derived nine dependent equations reflecting the functional characteristics of the earth pressure, the proposed method can be performed easily via an implicit strategy. There are 13 basic factors related to the retained soils, walls, and external loads to be involved in the proposed method. The tension crack segment of the slip surface is obviously influenced by these parameters, apart from vertical seismic coefficient and geometric bounds of the surcharge, but the shear slip segment maintains an approximately planar shape almost uninfluenced by these parameters. Noticeably, the proposed method quantitatively reflects that the resultant of the active earth pressure is always within a limited range under different possible movements of the same wall.