Numerical simulations of frictional melting: Small dependence of shear stress drop on viscosity parameters

Abstract

Frictional melting during coseismic slipping strongly affects dynamic sliding. An idealized numerical simulation of shear stress drop due to lubrication of fault surfaces by frictional melting is performed to investigate dynamical adjustment of melt thickness and its dependence on material properties. We numerically solved one‐dimensional heat conduction equations coupled with hydrodynamic equations of motion of the melt layer. We adopt a simple Arrhenius‐type temperature dependence of melt viscosity with a parametric factor η 0 . After the initial transient stage, the evolution of the melt layer asymptotes to the late stage, where the melt thickness increases as and the generated shear stress drops as 1/ . An analytic self‐similar solution of the temperature profile for the late stage is obtained. The balance between the viscous heat generation and conductive heat loss characterizes the late stage. For small η 0 , the melt thickness is proportional to η 0 , whereas it will saturate for a larger η 0 . This is because the strong temperature dependence of viscosity enables an automatic adjustment of viscosity, which drops through the temperature increase due to the viscous heating even if a large η 0 is chosen. Numerical results and the thickness data of natural pseudotachylyte layers were compared. A maximum ratio X / ( X is thickness, D is sliding distance) exists above which no solution is found. The effective thermal conductivity of the melt layer should be large, probably due to the sliding surface roughness. Comparison with laboratory experimental results showed that the normal stress applied to the sample is an important parameter for stress drop.