Estimation of seismic passive earth pressures with nonlinear failure criterion

Most conventional calculation of seismic passive earth pressures is based on a linear Mohr-Coulomb failure criterion. However, a substantial amount of experimental data shows that almost all geomaterials follow a nonlinear failure criterion in practice. In this paper, the influence of a nonlinear strength envelope is considered in the framework of limit analysis of plasticity. The seismic passive earth pressures on the rigid walls in seismic conditions are estimated using the upper bound theorem of limit analysis in conjunction with the nonlinear failure criterion. A generalized tangential technique, one tangential line to the nonlinear failure criterion, is used to develop the external work and internal energy dissipation. The seismic earth passive pressure is obtained from optimization. An extended Rankine's theory is proposed with the same nonlinear failure criterion. In order to evaluate the validity of the numerical results using the generalized tangential technique, the solutions of seismic passive earth pressure are also presented in the framework of the extended Rankine's theory. Numerical results for different seismic coefficients and various nonlinear parameters of the failure criterion are compared with each other. The upper bound solutions using the generalized tangential technique are almost equal to the extended Rankine's theoretical solutions, with the maximum difference being less than 1%. The good agreement shows that the generalized tangential technique is an effective method for evaluating the seismic passive earth pressure with a nonlinear failure criterion. This paper extends the work of the seismic passive earth pressure using a linear Mohr-Coulomb failure criterion in previous literature to that using the nonlinear failure criterion.