Contours of saturated and unsaturated overhanging slopes at limiting equilibrium condition

Abstract

SummaryOverhangs are frequently observed in riverbanks, coastal headlands, and rock formations. The geometry of an overhang is an input into most slope stability analyses and is often idealised or back‐calculated from empirical data. This study investigates the geometries of overhang slopes, which exist while in limiting conditions satisfying static equilibrium with soil strength governed by the Mohr‐Coulomb failure criterion. The overhanging contour is formulated as the unknown in a boundary value problem and solved for using the slip line theory. Analyses consider nonhomogeneous soils, where cohesion and, if unsaturated, the contribution of suction to the effective stress vary linearly with depth. The solutions are presented in general dimensionless charts. Applications of the charts are illustrated via examples. It has been observed that soil with varying amounts of friction and cohesion could develop overhanging arches of different sizes and shapes. This study shows that the curvature of an overhang becomes more pronounced for small values of φ′. It is also demonstrated that changing the contribution of suction to the effective stress has a direct impact on the size of an unsaturated soil overhang. Overhanging slope shapes observed in reality may be different from the idealised subset studied in this paper since real slopes are not necessarily at impending failure. The real shapes may be influenced by various physical processes such as weathering, stress variations caused by cycles of wetting‐drying. Even so, the results presented in the paper indicated how key soil properties influence slope shapes, albeit it while in limiting conditions.