A method for assessing the stability of slurry-supported trenches considering anisotropy and nonhomogeneity using the upper-bound theorem of limit analysis is presented. Only anisotropy and the nonhomogeneity of the cohesion were taken into account in this study. The influence of anisotropy and nonhomogeneity on trench stability was investigated via parametric studies. A series of stability charts was obtained for slurry-supported trenches. It is shown that the results obtained from the upper-bound solutions agree well with those obtained through the variational limit-equilibrium closed-form solutions in isotropic and homogeneous trenches. This article first describes the influences of anisotropy and nonhomogeneity on the required unit weight of slurry, and then the procedures for getting the factor of safety are presented. In addition, the influence of anisotropy and nonhomogeneity on the shape of the trench critical failure surface and on the location of the slip surface of the sliding mass is decribed. The article also gives examples to illustrate the variation in the safety factor with trench depth under different anisotropy and nonhomogeneity conditions.

Simplified 3D Spencer’s method is proposed to evaluate the stability of slopes under earthquake force and a random search algorithm is used to determine the critical slip surface. A computer code was written in Matlab to determine the critical slip surface and calculate its safety factor and direction of sliding (DOS). The applicability of the presented code is verified by reanalyzing three slope stability problems. Then, a comparison is made to investigate the effects of the direction of earthquake force on the factor of safety and the DOS of the critical slip surface. Accounting for the effects of the direction of earthquake force, the difference in safety factors, and the DOS can be up to 40% and 40°, respectively. Finally, a parametric study is also conducted to determine the effects of the soil strength parameters (c′, φ′). It is found that the effective cohesion c′ and friction angle φ′ of the soil have nearly no influence on the unique DOS of the critical surface. Application of the presented approach into 3D slopes under quasistatic load is straightforward.