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 6000 numerical
experiments. We observe two distinct behaviors, namely a stable regime,
characterized by transient shear zone formation accompanied by a
moderate (100 - 300 Kelvin) 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
model behavior. The ratio t/t
represents the competition between heat generation from stress
relaxation and heat loss due to thermal diffusion while the ratio
U/U compares the stored elastic
energy to thermal energy in the system. Thermal runaway occurs if
t/t is small and
U/U 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.