Application of Upper Bound Limit Analysis for Calculation of Seismic Lateral Active Earth Pressure in the Conditions of Linear MC Criteria

Most conventional calculations of static and seismic active earth pressures are based on a linear Mohr-Coulomb (MC) failure criterion. In recent years, many efforts have been focused on stability problems of geotechnical structures with the limit analysis method. The limit analysis method includes the upper and lower bound theorems. By using the two theorems, the range, in which the true solution falls, can be found. This range can be narrowed finding the highest possible lower bound solution and the lowest possible upper bound solution. The solutions obtained from the limit analysis method are rigorous in that no assumption regarding forces is required. In this paper, a limit analysis method with a MC linear yield criterion in the framework of upper bound theorem of plasticity for calculating both static and seismic active earth pressures is presented. The method using a linear MC failure criterion to formulate the objective function is developed and the active earth pressure is determined from optimization. In order to evaluate the applicability and validity of the proposed method, numerical results in the framework of some examples are presented and compared with the solutions obtained using other well-known techniques. The comparisons show that the results are in good agreement which indicate that the proposed method is an effective method and can be applied to evaluate the active earth pressures in the analyses of slope stability and retaining walls problems.