Actual slope stability problems have three-dimensional(3D) characteristics and the soils of slopes have curved failure envelopes. This incorporates a power-law nonlinear failure criterion into the kinematic approach of limit analysis to conduct the evaluation of the stability of 3D slopes. A tangential technique is adopted to simplify the nonlinear failure criterion in the form of equivalent Mohr-Coulomb strength parameters. A class of 3D admissible rotational failure mechanisms is selected for soil slopes including three types of failure mechanisms: face failure, base failure, and toe failure. The upper-bound solutions and corresponding critical slip surfaces can be obtained by an efficient optimization method. The results indicate that the nonlinear parameters have significant influences on the assessment of slope stability, especially on the type of failure mechanism. The effects of nonlinear parameters appear to be pronounced for gentle slopes constrained to a narrow width. Compared with the solutions derived from plane-strain analysis, the 3D solutions are more sensitive to the values of nonlinear parameters.
Based on the upper bound of limit analysis, the plane-strain analysis of the slopes reinforced with a row of piles to the 3D case was extended. A 3D rotational failure mechanism was adopted to yield the upper bound of the factor of safety. Parametric studies were carried out to explore the end effects of the slope failures and the effects of the pile location and diameter on the safety of the reinforced slopes. The results demonstrate that the end effects nearly have no effects on the most suitable location of the installed piles but have significant influence on the safety of the slopes. For a slope constrained to a narrow width, the slope becomes more stable owing to the contribution of the end effects. When the slope is reinforced with a row of piles in small space between piles, the effects of group piles are significant for evaluating the safety of slopes. The presented method is more appropriate for assessing the stability of slopes reinforced with piles and can be also utilized in the design of plies stabilizing the unstable slopes.
