Expression for the seismic passive earth pressure

Resolving all the forces in the vertical and horizontal directions, from the boundary condition = 0 at y = 0, and ignoring higher order differential terms and upon simplification, the expression for the seismic passive earth pressure at any depth y is obtained as,

where = seismic passive pressure at any depth y from top acting normal to the wall

K = lateral earth pressure coefficient

d = wall friction angle

θ = angle of inclination of the failure plane with horizontal