FRICTIONAL HEATING AND THE STABILITY OF RATE AND STATE-DEPENDENT FRICTIONAL SLIDING

Numerous laboratory experiments have found that the coefficient of fri ction of simulated faults depends both on the instantaneous sliding ve locity and on a state variable that represents the previous sliding hi st. The coefficient of friction is typically given as mu = mu(0) + alp ha 1n(V/V-0) + b 1n(psi/psi(0)) where mu(0), V-0, psi(0), alpha, and b are constants, V is the sliding velocity and psi is the state variabl e. The time derivative of the state variable is often given by an expr ession of the form 1/t(0) - psi V/D-c where t(0) is a constant with di mensions of time and D-c is a critical displacement. The stiffness of a one-dimensional system must be less than the effective normal tracti on times (b-alpha)/D-c for instability to occur. Temperature increase from frictional heating expands pore fluid, increasing its pressure an d decreasing the effective stress on a sealed fault plane. The amount of temperature change depends on heat conduction into the country rock from the planar heat source of the fault zone. The apparent value of the coefficient alpha is decreased by an amount that depends on the sq uare root of elapsed time of an oscillation from steady-state. Systems which are close to the stability limit and/or have large characterist ic times D-c/V-p, where V-p is the long term slip velocity, exhibit sl ow evolution in the absence of frictional heating and thus are signifi cantly affected by frictional heating. In real faults, the effects of frictional heating at slow creep rates may conceivably be overwhelmed by those of compaction, dilation, hydrofracture, and fluid flow.