In situ stress control on microcrack generation and macroscopic extensional fracture in exhuming bedrock

Crustal stresses beneath evolving alpine landscapes result from a combination of tectonic strain, bedrock exhumation, and topography. The stress field is regulated by elastic material properties and the brittle strength of critically stressed elements, particularly those within preexisting faults and intact rock. Combining Byerlee's law for crustal stresses with a recently developed trilinear fracture envelope, we propose an extension of the critically stressed crust concept to constrain in situ stresses through microcrack generation and extensional fracture propagation. A compilation of 814 global in situ stress measurements suggests microcrack development will limit long-term rock strength, and maximum differential stresses in the upper similar to 1km of the crust can be controlled by cohesive bedrock behavior. Using an elastoplastic, 2-D finite-difference model, we approximate in situ stress development within landscapes undergoing high rates of exhumation in both normal and reverse tectonic regimes. Critical near-surface stresses in these environments are defined by the microcrack initiation threshold, estimated to be roughly one third of the unconfined compressive strength of intact rock, while stresses deeper in the crust adhere to Byerlee's law. Our models indicate that exhumation-induced stresses limited by long-term rock strength are the primary contributor to the near-surface stress field, while topographic relief reduces stress near valley axes. Simulating glacial erosion then allows us to illustrate a path-dependent relationship between critical stress development, fracture formation, and geomorphic processes. We find that glacial unloading can generate new microcracks in near-surface bedrock, resulting in unstable macroscopic extensional (or exfoliation) fracture propagation during incision of U-shaped alpine valleys.