Upper Limit Analysis for the Ultimate Bearing Capacity of a Multilayer Slope with Horizontal Stratification

The ultimate bearing capacity is one of the most important mechanical parameters in the mining and geotechnical fields and has a vital influence on the stability of slopes and the safety of constructions and structures. The determination of the ultimate bearing capacity has become a controversial issue in slope engineering. This study proposes a way to obtain the ultimate bearing capacity of a multilayer slope with horizontal stratification. According to limit analysis theory, three typical multiblock sliding failure modes for a multilayer slope with horizontal stratification are established. The upper limit solution of the ultimate bearing capacity of a multilayer slope, considering the influence of horizontal stratification, is derived. The optimization procedure is carried out to obtain the optimal value of the ultimate bearing capacity by using the sequential quadratic programming algorithm. The accuracy of the present method is proven based on a comparison of calculation results using other analytical methods and the numerical simulation method. The influence analysis of the parameters, involving the slope angle, soil strength, and distance of the foundation from the slope shoulder, is performed. The results indicate that the error between the calculated results of the present method and those of numerical simulation, as well as the error between the calculated results of the present method and those of other existing methods, is less than 10%. The ultimate bearing capacity linearly decreases with increasing slope angle, while it linearly increases with increasing distance of the foundation from the slope shoulder. The analytical method provides a method to analyze the ultimate bearing capacity of a multilayer slope, which effectively solves the problem of heterogeneity of soil layers observed in the natural slope. The results from this study can be used as a guide to estimate the stability of the slope and design of the foundation on a slope considering the load action near the slope.