Three-dimensional topographic stress controls on bedrock fractures and landscape evolution

Abstract:

Bedrock fractures in the critical zone influence the rates of surface processes that drive landscape evolution, and are also influenced by topography, which perturbs ambient tectonic and gravitational stress fields. Previous studies examined connections between topographic stress and bedrock fractures using two-dimensional topographic profiles across ridges and valleys in plane strain. In this study, we calculate three-dimensional elastic stress fields beneath topography using a boundary element model and examine how the stress fields vary with topographic shape and horizontal tectonic stress magnitude, orientation, and anisotropy. We illustrate the general effects of these factors using synthetic landforms consisting of elongated ridges with different aspect ratios, and then consider natural landscapes from two critical zone observatories. From the modeled stress fields, we calculate two stress proxies—the least compressive principal stress and the failure potential (a normalized measure of differential stress)—that represent the potential for generating new fractures and dilating or shearing existing fractures. If the ratio of horizontal tectonic compressive stress to gravitational stresses associated with topographic relief is small, the base of a zone where more abundant open fractures are predicted generally parallels the land surface. If the ratio of stresses is large, the base of the fracture-rich zone generally mirrors the land surface. We find that these topographic stress perturbations are most sensitive to the tectonic stress magnitude perpendicular to the long axis of elongated landforms such as ridges and valleys, and are most pronounced beneath landforms with higher mean curvatures, such as channel junctions and ridge crests. We use the three-dimensional distributions of stress proxies to infer spatial patterns of weathering and erodibility in scenarios with different topography and tectonic settings, and examine how topographic stress and landscapes might co-evolve.