Rapid Ductile Strain Localization Due To Thermal Runaway

Thermal runaway is a ductile localization mechanism that has been linked to deep-focus earthquakes and pseudotachylyte formation. In this study, we investigate the dynamics of this process using one-dimensional, numerical models of simple shear deformation. The models employ a visco-elastic rheology where viscous creep is accommodated with a composite rheology encompassing diffusion and dislocation creep as well as low-temperature plasticity. To solve the nonlinear system of differential equations governing this rheology, we utilize the pseudo-transient iterative method in combination with a viscosity regularization to avoid resolution dependencies. To determine the impact of different model parameters on the occurrence of thermal runaway, we perform a parameter sensitivity study consisting of 6,000 numerical experiments. We observe two distinct behaviors, namely a stable regime, characterized by transient shear zone formation accompanied by a moderate (100–300 K) temperature increase, and a thermal runaway regime, characterized by strong localization, rapid slip and a temperature surge of thousands of Kelvin. Nondimensional scaling analysis allows us to determine two dimensionless groups that predict the model behavior. The ratio $t_r/t_d$ represents the competition between heat generation from stress relaxation and heat loss due to thermal diffusion while the ratio $U_{\text{el}}/U_{\text{th}}$ compares the stored elastic energy to thermal energy in the system. Thermal runaway occurs if $t_r/t_d$ is small and $U_{\text{el}}/U_{\text{th}}$ is large. Our results demonstrate that thermal runaway is a viable mechanism driving fast slip events that are in line with deep-focus earthquakes and pseudotachylyte formation at conditions resembling cores of subducting slabs.