Modeling three-dimensional topographic stress and its effects on bedrock fractures

Bedrock fractures in the deep critical zone influence the hydraulic characteristics of rocks, the distribution of slope failures, and the rates of weathering and erosion processes that drive landscape evolution. Topography may in turn influence bedrock fractures. Previous studies found that topographic perturbations of ambient tectonic stress fields could be large enough to create different distributions of fractures beneath ridges and valleys. However, these studies considered only two-dimensional topographic profiles in plane strain. We use a boundary element model to calculate three-dimensional elastic stress fields beneath topographic surfaces, accounting for the effects of gravity and ambient tectonic stress. From the modeled stress fields, we calculate failure potential, a normalized measure of differential stress, as a scalar proxy for rock damage. The effects of three-dimensional topography on the stress field are most evident at channel junctions and ridge crests and depend sensitively on the ambient tectonic stress. We apply our stress modeling procedure to Critical Zone Observatory sites, using nearby hydraulic fracturing and overcoring measurements to constrain the ambient stress fields. We then compare the spatial distributions of failure potential with seismic velocity profiles and fractures observed in borehole image logs. Interestingly, the spatial distributions of failure potential and seismic velocity are similar, suggesting that topographic stresses may influence near-surface bedrock fractures, and thus affect weathering, erodibility, and groundwater flow, in predictable ways.