Analytical solutions for passive earth pressure considering different failure mechanisms with nonlinear failure criterion

The analytical solutions to passive earth pressure, using Rankine's theory and upper bound theorem, are often based on a linear Mohr-Coulomb failure criterion. However, numerous experimental evidences show that the strength envelopes of almost all geomaterials have the nature of nonlinearity. In this paper, the backfill failure follows a nonlinear failure condition. Analytical solutions for passive earth pressure are derived with the nonlinear failure criterion using two different methods. One is based on kinematical approach of limit analysis. An improved method using a generalized tangential technique to approximate the nonlinear failure criterion is employed to estimate the passive earth pressure. One-rigid-body translation and one-rigid-body log-spiral rotation failure mechanisms are considered and the formulation of the passive earth pressure is a classical nonlinear programming problem. A nonlinear sequential quadratic programming algorithm is used to search for the lowest solutions. The other is based on Mohr's circle analysis. Extended Rankine's solution for passive earth pressure is derived with the nonlinear failure criterion. The upper bound solutions using the rigid translation failure mechanism are equal to extended Rankine's theoretical solutions, but are slightly more than those using the rigid rotation failure mechanism. A study is carried out to illustrate the effects of the nonlinear coefficient and material parameters on the passive earth pressure with the nonlinear failure criterion.