Sustainable Slopes: Satisfying Rainfall-Erosion Equilibrium and Mechanical Stability

Abstract. While manmade slopes are traditionally constructed with planar cross-sections, natural stable slopes are usually curvilinear with significant concavity of the profile. This concavity occurs as a result of evolutionary processes in which rain-driven erosion and sediment transport are balanced through slope shape adjustments. At the point of equilibrium, a relatively steady concavity with a uniform erosion rate is observed over time. Nevertheless, a true equilibrium state is possible only if mechanical stability is satisfied. In this study, concave profiles in rainfall erosion equilibrium were found based on the principles of the well-known RUSLE2 model. Results showed the existence of a family of steady shapes satisfying the condition of uniform normalized erosion rate. Those steady concave shapes that also satisfied long-term mechanical stability were then investigated. The overall results suggest that concave slopes can be constructed to achieve both minimal steady-state erosion equilibrium and mechanical stability, leading to more natural and sustainable landforms with minimal sediment delivery during initial slope adjustments.

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