Frictional heating and the stability of rate and state dependent frictional sliding

Numerous laboratory experiments have found that the coefficient of friction of simulated faults depends both on the instantaneous sliding velocity and on a state variable that represents the previous sliding history. The coefficient of friction is typically given as μ = μ 0 + a 1n( V/V 0 ) + b 1n( ψ/ψ 0 ) where μ 0 , V 0 , ψ 0 , a , and b are constants, V is the sliding velocity and ψ is the state variable. The time derivative of the state variable is often given by an expression of the form 1/ t 0 ‐ψ V/D c where t 0 is a constant with dimensions of time and D c is a critical displacement. The stiffness of a one‐dimensional system must be less than the effective normal traction times ( b‐a )/ D c for instability to occur. Temperature increase from frictional heating expands pore fluid, increasing its pressure and 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 a is decreased by an amount that depends on the square root of elapsed time of an oscillation from steady‐state. Systems which are close to the stability limit and/or have large characteristic times D c /V p , where V p is the long term slip velocity, exhibit slow evolution in the absence of frictional heating and thus are significantly 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.