Approximate solution for seismic earth pressures on rigid walls retaining inhomogeneous elastic soil

An approximate elasto-dynamic solution is developed for computing seismic earth pressures acting on rigid walls retaining continuously inhomogeneous elastic material and excited by vertically propagating shear waves. The shear modulus of the soil is represented as a nonlinear function of depth, in a manner that is consistent with established analytical and empirical relationships, while mass density and Poisson's ratio are assumed constant. Solutions are presented for a single wall and for a pair of walls spaced at a finite distance. A shape function characterizing the vertical variation of horizontal displacement of the soil column in the free-field is assigned, and simplifying assumptions regarding the dynamic vertical stresses and the vertical-to-horizontal displacement gradient are made to facilitate closed-form expressions for horizontal displacement and stress fields. These solutions are used to compute the distribution of dynamic horizontal earth pressure acting on the wall. A Winkler stiffness intensity relationship is then derived such that the proposed method can be extended beyond the boundary conditions considered herein. These solutions agree well with exact analytical elasto-dynamic solutions for inhomogeneous soil that are considerably more complicated to implement. Causes of differences between the solutions are discussed.