Bearing Capacity of Strip Footings near Slopes Using Lower Bound Limit Analysis

Stability of foundations near slopes is one of the important and complicated problems in geotechnical engineering, which has been investigated by various methods such as limit equilibrium, limit analysis, slip-line, finite element and discrete element. The complexity of this problem is resulted from the combination of two probable failures: foundation failure and overall slope failure. The current paper describes a lower bound solution for estimation of bearing capacity of strip footings near slopes. The solution is based on the finite element formulation and linear programming technique, which lead to a collapse load throughout a statically admissible stress field. Three-nodded triangular stress elements are used for meshing the domain of the problem, and stress discontinuities occur at common edges of adjacent elements. The Mohr-Coulomb yield function and an associated flow rule are adopted for the soil behavior. In this paper, the average limit pressure of strip footings, which are adjacent to slopes, is considered as a function of dimensionless parameters affecting the stability of the footing-on-slope system. These parameters, particularly the friction angle of the soil, are investigated separately and relevant charts are presented consequently. The results are compared to some other solutions that are available in the literature in order to verify the suitability of the methodology used in this research.