A brittle constitutive law for long-term tectonic modeling based on sub-critical crack growth
arxiv(2024)
摘要
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.
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