Three-Dimensional Slope Stability Analysis with Rotational Failure Mechanism

This paper deals with three-dimensional evaluation of the slopes on the basis of limit analysis. An upper-bound technique of limit analysis is used in this paper to determine either the bearing capacity of a shallow foundation near a slope or the safety factor of the slope. The theorems of limit analysis (upper and lower bound) provide a powerful tool for solving problems in which limit loads need to be found. According to the upper-bound theorem, for a kinematically admissible velocity field an upper bound of the collapse load can be obtained by equating the power dissipated internally in an increment of displacement to the power expended by the external loads. Such kinematically admissible velocity fields have to comply with the kinematical boundary conditions and compatibility conditions. A rotational mechanism consisting of three slip surfaces is used to determine the factor of safety for a slope or the ultimate limit load of a foundation with eccentric load near a slope. This mechanism includes two lateral surfaces and a surface at bottom. As the soil is assumed to obey the associated flow rule, the angle between the relative velocity vector and velocity discontinuity has to be equal everywhere with soil's friction angle (?).
The geometries of lateral surfaces are represented by a nonlinear differential equation. A surface with log-spiral section is used for bottom surface of the mechanism. To obtain the minimum upper-bound, an algorithm is proposed to optimize the failure mechanism. Results from this algorithm for typical conditions are comparable to those of other existing methods. Dimensionless diagrams for various conditions are presented which can be used to predict the bearing capacity of a foundation with eccentric load located on a slope.