Hillslopes As Stress-Optimizing Structures

Abstract:

Topographic heights can be viewed as structures that carry the load due to their own weight. Hillslopes evolve over time by gravity-driven processes, either directly, or through the mediator of flowing water. The distribution of gravity-induced surface stresses modulates this evolution, together with substrate properties, and in interaction with external forcing. If the stress vector at the surface of the slope has a surface-normal component, the detachment of material may be eased or made more difficult. Here, we propose that hillslopes evolve to obtain a stress-optimized form wherein at the surface, the vectors of stresses are everywhere parallel to the surface, and total strain is equal along every horizontal and vertical section. These conditions yield an optimal hillslope shape. There are two solutions for this shape, which are self-similar, such that the scale is dependent on a single length parameter, the base width of the structure. We present examples of optimal hillslopes, and discuss the general implications of this paradigm.