THE ROLES OF TIME AND DISPLACEMENT IN VELOCITY-DEPENDENT VOLUMETRIC STRAIN OF FAULT ZONES

The relationship between measured friction mu(A) and volumetric strain during frictional sliding was determined using a rate and state varia ble dependent friction constitutive equation, a common work balance re lating friction and volume change, and two types of experimental fault s: initially bare surfaces of Westerly granite and rock surfaces separ ated by a 1 mm layer of < 90 mu m Westerly granite gouge. The constitu tive equation is the sum of a constant term representing the nominal r esistance to sliding and two smaller terms: a rate dependent term repr esenting the shear viscosity of the fault surface (direct effect), and a term which represents variations in the area of contact (evolution effect). The work balance relationship requires that mu(A) differs fro m the frictional resistance that leads to shear heating by the derivat ive of fault normal displacement with respect shear displacement, d de lta(n)/d delta(s). An implication of this relationship is that the rat e dependence of d delta(n)/d delta(s) contributes to the rate dependen ce of mu(A). Experiments show changes in sliding velocity lead to chan ges in both fault strength and volume. Analysis of data with the rate and state equations combined with the work balance relationship preclu de the conventional interpretation of the direct effect in the rate an d state variable constitutive equations. Consideration of a model bare surface fault consisting of an undeformable indentor sliding on a def ormable surface reveals a serious flaw in the work balance relationshi p if volume change is time-dependent. For the model, at zero slip rate indentation creep under the normal load leads to time-dependent Stren gthening of the fault surface but, according to the work balance relat ionship, no work is done because compaction or dilatancy can only be i nduced by shearing. Additional tests on initially bare surfaces and go uges show that fault normal strain in experiments is time-dependent, c onsistent with the model. This time-dependent fault normal strain, whi ch is not accounted for in the work balance relationship, explains the inconsistency between the constitutive equations and the work balance . For initially bare surface faults, all rate dependence of volume cha nge is due to time dependence. Similar results are found for gouge. We conclude that mu(A) reflects the frictional resistance that results i n shear heating, and no correction needs to be made for the volume cha nges. The result that time-dependent volume changes do not contribute to mu(A) is a general result and extends beyond these experiments, the simple indentor model and particular constitutive equations used to i llustrate the principle.