Static and seismic earth pressures from Boussinesq’s equations

The calculation of the active and passive earth pressure coefficients is still a major issue for the design of gravity or embedded retaining walls both for static and seismic conditions. For static conditions, one of the conventional approaches to determine these coefficients in weighted ground conditions is to use the tables from Caquot, Kerisel and Absi which are based on the Boussinesq’s theory that can be considered as a lower bound static approach. In order to illustrate in practice the procedure to solve these differential equations, this paper includes an example dealing with their numerical integration by considering the different steps that have been followed. The results are compared to those obtained by Caquot, Kerisel and Absi on the one hand and Sokolowski on the other hand. For seismic conditions, an extension of the Boussinesq’s equations is presented with its solving process and the results are compared to the solutions obtained by applying the rotations principle. For both static and seismic conditions, failure mechanisms are determined and compared to the solutions obtained through the kinematical approach of the yield analysis considering log-spirals and rotational mechanisms.