Upper bound solution of critical heights of reinforced soil slope based on the nonlinear failure criterion and compatibility of deformation

The stability of a reinforced soil slope is conventionally calculated based on the linear Mohr-Coulomb failure criterion. However, experimented data have shown that the strength envelopes of almost all geotechnical materials have the nature of nonlinearity. In view of the problem, in this paper, a nonlinear failure criterion and a tangential technique method are employed to evaluate the critical height of the reinforced soil slope using the upper bound theorem of limit analyses. The characteristics of the deformation compatibility between the reinforced material and soil, and the continuity of speed variation on sliding soil layer are considered according to the engineering properties and deformation mechanism of the reinforced slope. The internal work of soil and the energy dissipation of the reinforced material are calculated separately. New methods for determining the critical height of a reinforced soil slope on the linear fracture surface and logarithmic spiral fracture surface are put forward based on the above research. The objective function of the critical height in the limit state is established. The upper bound solutions of the critical height are obtained by using the sequential quadratic programming optimization algorithm. The feasibility and rationality of the research approach in this paper is shown through comparison and analysis with the centrifuge test results and theoretical research results. It is found that the proposed method is superior. The deformation compatibility and the speed variation continuity on the sliding soil layer are reasonable. It can be seen that the nonlinear failure parameter has a significant effect on the critical height of the reinforced soil slope. Moreover, the critical height decreases with the increasing nonlinear coefficient.