A Brittle Constitutive Law for Long-Term Tectonic Modeling Based on Sub-Critical Crack Growth

Adequate representations of brittle deformation (fracturing and faulting) are essential ingredients of long-term tectonic simulations. Such models commonly rely on Mohr-Coulomb plasticity coupled with prescribed softening of cohesion and/or friction with accumulated plastic strain. This approach captures fundamental properties of brittle failure, but is overly sensitive to empirical softening parameters that cannot be determined experimentally. Here we design a brittle constitutive law that captures key processes of brittle deformation, and can be straightforwardly implemented in standard geodynamic models. In our Sub-Critically-Altered Maxwell (SCAM) flow law, brittle failure begins with the accumulation of distributed brittle damage, which represents the sub-critical lengthening of tensile micro-cracks prompted by slip on pre-existing shear defects. Damage progressively and permanently weakens the rock's elastic moduli, until cracks catastrophically interact and coalesce up to macroscopic failure. The model's micromechanical parameters can be fully calibrated against rock deformation experiments, alleviating the need for ad-hoc softening parameters. Upon implementing the SCAM flow law in 2-D plane strain simulations of rock deformation experiments, we find that it can produce Coulomb-oriented shear bands which originate as damage bands. SCAM models can also be used to extrapolate rock strength from laboratory to tectonic strain rates, and nuance the use of Byerlee's law as an upper bound on lithosphere stresses. We further show that SCAM models can be upscaled to simulate tectonic deformation of a 10-km thick brittle plate over millions of years. These features make the SCAM rheology a promising tool to further investigate the complexity of brittle behavior across scales.