Thermal localization and rheological control on the steady-state width of 1D ductile shear zones

N. M. Beeler, H.S Shabtian, & Greg Hirth

In Preparation 2026, SCEC Contribution #15047

Over geologic time, the existance and development of upper crustal plate boundary faults that host present Earth's largest earthquakes and tsunamis are controlled by thermally localized deformation in the ductile portion of the crust and upper mantle. The current mechanical properties and the spatial localization of these ductile shear zones (DSZ) influence elastic loading over the earthquake cycle, and the down dip extent of earthquakes M>=7 that rupture into and beyond the brittle ductile transition (BDT). Despite their mechanical importance to crustal deformation, relatively little is known about DSZ properties such as strain rate and strength, in part due to difficulties in reliably estimating them. As first shown by Yuen et al. (1978), properties of DSZs can be estimated by coupling ductile strength to shear heat and heat conduction, as in this simplified study of steady-state 1D shear. Our simulations are over a region of fixed shear zone half-length, L/2, that is the location of a constant temperature boundary condition. The length and boundary temperature are a crude 1D proxy for 2D conduction limited by the Earth's free surface at ~25C. As in numerous prior 1 and 2D studies, localized ductile shear arises spontaneously from weakening due to shear heating. In our simulations, in the presence of self-heating the DSZ characteristic scale of localization, lc, is determined by a balance between the rheology's opposing temperature weakening and rate strengthening. The 1D geometry produces shear zones with a strain rate distribution that is approximately Gaussian in space, apparently largely independent of the choice of rheology. The 1D geometry, boundary conditions, and resulting strain rate distribution allows for novel analysis that is less obvious and more difficult in 2D. For a Gaussian shear zone at steady-state, the characteristic scale of localization is twice the variance of the distribution; the velocity and temperature distributions are analytic as is the rate that internal thermal energy is generated from sheaing, equivalently the rate that energy exits the region at L/2. Perturbation analysis shows there is a favored shear zone width where strength is minimized, and thermally enhanced shear at steady-state is localized at the lowest possible energy release rate. Using power law dislocation creep (quartz) and low temperature plasticity (talc) as examples, we contrast the effects of rheology on shear zone strain rate and width, and establish the control of loading rate and rheological parameters, activation energy, power law exponent and nominal strength on DSZ width.

Citation
Beeler, N. M., Shabtian, H., & Hirth, G. (2026). Thermal localization and rheological control on the steady-state width of 1D ductile shear zones. Earth Surface Processes and Landforms, (in preparation).

Related Projects & Working Groups
Fault and Rupture Mechanics (FARM)