Limit analysis of the stability of slopes reinforced with piles against landslide in nonhomogeneous and anisotropic soils

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 non-homogeneity 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.