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 tr/td represents the competition between heat
generation from stress relaxation and heat loss due to thermal diffusion
while the ratio Uel/Uth compares the stored elastic energy to thermal
energy in the system. Thermal runaway occurs if tr/td is small and
Uel/Uth 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.