A Quasi-Static Displacement-Based Approximation of Seismic Earth Pressures on Rigid Walls

A number of linear-elastic solutions have been dedicated to resolve the problem of earth pressures on a rigid wall overlying rigid bedrock, among which, the classic solutions have been provided by Matsuo and Ohara (1960), Wood (1973), and Veletsos and Younan (1994). Wood's solution is mathematically involved (it requires evaluation of a double infinite sum) and the other two involve severe simplifying assumptions. An approximation procedure is presented to develop easy-to-evaluate estimates for the lateral earth thrust on rigid retaining walls under quasi-static loading. The procedure is based on the estimation of soil kinematic variables in the vicinity of the wall, from which strains, stresses, and total thrust are obtained. While the procedure is presented for quasi-static loading of a rigid wall overlaying rigid bedrock, this novel approach could be used to account for other complex effects that have been cumbersome to include in state-of-the art earth pressures procedures, such as dynamic loading, soil non-linear behavior, and wall compliance.