Uniform seismic accelerations and are assumed in the horizontal and vertical directions respectively in the domain under consideration. As a first step, only planar rupture surfaces have been considered and to keep this assumption valid, wall friction angle has been restricted to less than or equal to as shown by Terzaghi (1943). In Fig.2.39b, the free body diagram of an elemental slice shows the action of different forces. The thickness of the slice is dy, at a depth of y from the top ground surface. The vertical pressure is acting on the top of the element and ( + d ) on the bottom of the element. The reaction normal to the wall and the shear force tan are acting on the interface between the retaining wall and the backfill material. The normal force r and the shear force for tan act on the sliding surface. The other forces are, the weight dW of the element, the seismic forces dW in the horizontal direction and dW in the vertical direction. The critical directions of these seismic forces are as shown in Fig.4.9b. The horizontal slip planes are assumed as principal planes.

Unit earth pressure on the retaining wall

Considering the equilibrium condition of the vertical forces on the element, the basic equation for the unit earth pressure on the retaining wall is given by,