Bearing Capacity of Foundations Located on Concave Slopes in Plan View Using Upper Bound Theorem

Bearing Capacity of concave slopes is such a three-dimensional problem that two-dimensional assumptions do not result in satisfactory and acceptable results. Presented in this article is an algorithm to calculate the bearing capacity of foundations located on such slopes based on the upper bound theorem of the limit analysis approach. Limit analysis method is based on the extensions of maximum work principle derived by Hill, and was given in the form of theorems by Drucker, Prager and Greenberg. Using this approach, the true solution from a lower bound to an upper bound would be bracketed. Applicability of this theorem requires that the soil’s behavior be perfectly plastic and the deformation be governed by the normality rule. Considering the theorem of kinematic approach (upper-bound), the rate of work done by traction and body forces would be less than or equal to the energy dissipation rate in any assumed kinematically admissible failure mechanism. In this algorithm, initially the collapse mechanism is assumed as a set of five or six-face rigid blocks slipping on each other with enrgy dissipation taking place along planar velocity discontinuities. and then, during an optimizing process the minimum result would be considered as the ultimate load of the slope. This approach can be considered as an extension of the procedure proposed by Farzaneh and Askari in 1999. The numerical results indicate that the bearing capacity of a shallow foundation on concave slope is more than that of the same foundation on linear slope and also fewer is the ratio of slope radius to its height, more would be the bearing capacity of the foundation located on it. In addition, unloaded slopes are more stable when they are concave comparing with linear slopes. In bearing capacity, the curvature effect in concave slopes is more considerable for frictional soils than cohesive ones. The results are presented in the form of applicable charts to evaluate the bearing capacity of a foundation located on a concave slope.