Evolution of Topographic Stress Perturbations Near the Surface of the Earth and Application to Sheeting Joints

Abstract:

Topography perturbs the near-surface stress fields caused by gravity and by regional horizontal stresses. Two-dimensional analytical solutions for elastic stresses in uniform, isotropic rock allow the effects of gravity and a uniform regional horizontal stress P to be distinguished beneath isolated bell-shaped ridges and valleys. The topographic stress perturbations vary depending on the shape of the topography. Gravity, by itself, causes surface-perpendicular and surface-parallel compressive stresses beneath the crest of a bell-shaped ridge. Regional compression contributes a surface-parallel compression atop broad gentle bell-shaped ridges with steepest slopes less than 45°, but a surface-parallel tension atop narrower ridges with steeper slopes. If P is an order of magnitude less compressive than rg|b|, where r is rock density, g is gravitational acceleration, and b is the topographic relief, then effects of gravity dominate effects of the regional compression near the topographic surface. Conversely, if P is an order of magnitude more compressive than rg|b|, then effects of regional compression dominate the effects of gravity, and tensile stresses can develop normal to the surface beneath gentle convex bell-shaped ridges and the convex portions of bell-shaped valleys. The latter conditions promote the widespread development of sheeting joints. The locations of topographic inflection points help define where sheeting joints can develop at a particular time. As erosion progresses and the shape of the topographic surface changes, sheeting joints can form in new areas and be left as relict structures in others. The distribution of sheeting joints thus reflects the dynamic response of geologic systems that evolve through time.