On the transient behavior of frictional melt during seismic slip

Abstract

In a recent work on the problem of sliding surfaces under the presence of frictional melt (applying in particular to earthquake fault dynamics), we derived from first principles an expression for the steady state friction compatible with experimental observations. Building on the expressions of heat and mass balance obtained in the above study for this particular case of Stefan problem (phase transition with a migrating boundary), we propose here an extension providing a full time‐dependent solution (including the weakening transient after pervasive melting has started, the effect of eventual steps in velocity, and the final decelerating phase). A system of coupled equations is derived and solved numerically. The resulting transient friction and wear evolution yield a satisfactory fit (1) with experiments performed under variable sliding velocities (0.9–2 m s −1 ) and different normal stresses (0.5–20 MPa) for various rock types and (2) with estimates of slip weakening obtained from observations on ancient seismogenic faults that host pseudotachylite (solidified melt). The model allows us to extrapolate the experimentally observed frictional behavior to large normal stresses representative of the seismogenic Earth crust (up to 200 MPa), high slip rates (up to 9 m s −1 ), and cases where melt extrusion is negligible. Though weakening distance and peak stress vary widely, the net breakdown energy appears to be essentially independent of either slip velocity or normal stress. In addition, the response to earthquakelike slip can be simulated, showing a rapid friction recovery when slip rate drops. We discuss the properties of energy dissipation, transient duration, velocity weakening, restrengthening in the decelerating final slip phase, and the implications for earthquake source dynamics.