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 the 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) 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 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) 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

and normal stress. In addition, the response to earthquake-like 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.