In accordance with the collapse characteristic of trench wall during underground diaphragm wall construction, a modified three-dimensional (3D) failure mechanism of trench wall is established. By introducing nonlinear characteristic and the nonhomogeneity of soil into the theoretical calculation, the objective function of the safety factor (F_s) of the trench wall in the limit condition is derived, and the upper bound solution of the F_s of the slurry trench is derived by employing the optimization computation. To prove the validity of the presented approach, the solutions derived from the presented method are compared with those previous solutions and the comparing results show a good agreement. Moreover, the parametric analysis is conducted to study the effect of various parameters on the stability of trench wall. The results of parametric analysis show that nonlinear and the nonhomogeneous parameters have significant influence on the safety factors, and the nonlinear failure characteristic of the nonhomogeneity of soil cannot be ignored in the practical engineering.

Based on the nonlinear failure criterion and modified tangential technique, the upper bound solutions of the critical supporting pressure on the deep tunnel face were obtained under pore water pressure conditions. The influence of parameters on the critical supporting pressure and collapse range was investigated according to the unlimited block failure mechanism. It was found that the upper bound solutions of the critical supporting pressure increase with the growth of the nonlinear coefficient and pore water pressure coefficient. The collapse range of the tunnel face scales out with the increase in the nonlinear coefficient and shrinks with an increasing pore water pressure coefficient. Moreover, with the increase in the nonlinear coefficient, the impact strength on critical supporting pressure and collapse range declines gradually. According to the calculated results, both the pore water pressure and nonlinear criterion factors have negative impacts on the stability of the tunnel face. Thus, more attention should be paid to these parameters to ensure face stability in deep tunnel construction.

Based on the upper bound limit analysis, the multi-log spiral failure mechanism for earth retaining structures under horizontal seismic loads was constructed, which could introduce the nonlinear strength criterion into stability analysis without any linearization technique. By calculating various external work rates and the internal energy dissipation, the energy balance equation was established, and the active earth pressure formula required for the retaining structure to be in a critical stable state was derived. With the application of a genetic algorithm and particle swarm optimization, the optimal upper bound solutions of active earth pressure coefficients were obtained. The validity of the research results was verified through comparative analysis. This paper provided diagrams of the active earth pressure coefficients required for earth retaining structures to maintain a critical stability state under different parameters. The influences of seismic load, slope inclination angle, soil strength tension cutoff (TC), and the δ/ϕ ratio were investigated. By investigating the design charts, the active earth pressures applicable to practical engineering can be obtained, which provide a theoretical basis for the preliminary design of retaining structures in earthquake-prone areas.