Topographic perturbations of regional stresses and consequent bedrock fracturing

Stresses at Earth's surface are profoundly influenced by topography. Simple models indicate that gravitational and regional stresses are concentrated, attenuated, even reversed within landforms. Such topographically induced stresses are potentially manifest as bedrock fractures. Fractures reduce rock mass strength, decrease erosional resistance, and create conduits for water. By creating fractures, topographically induced stresses can alter processes of mass wasting, bedrock incision, and groundwater flow. We use Savage et al. 's 1985 solution for stresses in symmetric ridges and valleys on an elastic half‐space in plane strain to assess topographic effects on regional and gravity‐induced stresses. We have extended their solution to include lateral loads that vary with depth, which better approximates states of stress found in Earth's crust and allows us to examine a greater range of stress regimes. We examine the calculated stress fields to assess, in a classic Mohr‐Coulomb context, the potential for consequent fracture. This model indicates that topographic relief can cause stresses of sufficient magnitude to break rock, creating fracture sets having a spatial distribution and orientation governed by landform shape and the regional state of stress. We find that in extensional tectonic regimes, topographically induced stresses favor surface‐parallel fractures through ridges and steeply dipping fractures through valleys. Conversely, in compressional regimes, topographically induced stresses favor steeply dipping fractures through ridges and surface‐parallel fractures through valleys. Such topographic interactions with regional stresses pose consequences for interpretations of fracture orientation, for assessments of slope stability, and for processes of landscape development.