Stability of Hillslopes with Compound Convex-Concave Profile Under Vertically Loaded Strip Footings

Hillslopes can be affected by expansion of infrastructures, roadways, and urbanization. When establishing the bearing capacity of shallow foundations placed on the top of the slopes, slope failure is one of the mechanisms that requires due attention. Unlike man-made slopes with a planar profile, the hillslopes are frequently found in a curved cross section. The current paper studies the global slope stability aspect of a footing-on-slope system using a limit equilibrium-based analytical solution to compute the factor of safety of hillslopes with a combined convex-concave cross section under a strip footing on the top. The convex and concave parts of the profile were represented as circular arcs and assumed to be connected by an inflection point. A geometric parameter namely mid-chord offset (MCO) was used to describe the curvature of circular arcs. Utilizing a log-spiral failure surface, the solution takes footing setback, footing width, and seismic coefficients into account in predicting the factor of safety and critical failure surface. A good agreement in terms of the factor of safety and critical slip surface was observed when comparing the results of the proposed analytical solution with those of finite element. Parametric studies were conducted on a given slope to examine how the stability is influenced by varying footing setback, the MCO of concave and concave segments, and the location of the inflection point. The results also indicate that the allowable load of footing on the top of combined concave-convex slopes can be decreased or increased in comparison to those placed on the planar slopes.