The stability of a slope with reinforcing piles in anisotropic and nonhomogeneous soils is analyzed using the kinematic approach of limit analysis combined with a strength reduction technique. A slope without piles is considered first and the limit state equation is obtained to determine both the safety factor and the critical sliding surface for a given anisotropic and nonhomogeneous slope. The solutions are compared with published data to verify the practicality of the approach. A slope stabilized by a row of piles is then analyzed. Next, mathematical optimization is used to derive analytical expressions for determining the lateral force provided by piles (this is required to increase the slope safety factor to an expected value). Numerical examples are then applied. The optimal location of piles within a slope and the effects of nonhomogeneity and anisotropy of the soil strength on the dimensionless limit stabilizing force are also studied. Finally, a simplified procedure is proposed for a structural design that stabilizes the piles against landslide.

The vast majority of slopes, both natural and constructed, exhibit a complex geometric configuration and three-dimensional (3D) state, whereas slopes satisfying the assumption of plane strain (infinite length) are seldom encountered. Existing research mainly emphasizes the 3D dimensions and boundary effect in slope stability analysis; however, the effect of complex geometric ground configuration on 3D slope stability is rarely reported. In this paper, an elastoplastic finite-element method using strength-reduction techniques is used to analyze the stability of special 3D geometric slopes. A typical 3D slope underlain by a weak layer with groundwater is described to validate the numerical modeling, safety factor values, and critical slip surface for the 3D slope. Furthermore, a series of special 3D slopes with various geometric configurations are analyzed numerically, and the effects of turning corners, slope gradient, turning arcs, and convex- and concave-shaped surface geometry on the stability and failure characteristics of slopes under various boundary conditions are discussed in detail.

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