Effects of variable normal stress on rock friction: Observations and constitutive equations

<jats:p>We investigate the effects of variable normal stress on frictional resistance by performing quasi‐static sliding experiments with 5 × 5 cm blocks of Westerly granite in a double‐direct shear apparatus under servo‐control. The observed response to a change in normal stress mimics that which occurs in response to a change in slip velocity. In particular, a sudden change in normal stress results in a sudden change followed by a transient change in the resistance to sliding. We interpret these changes within the previously established constitutive framework in which frictional resistance is determined by the current slip speed <jats:italic>V</jats:italic>, the current normal stress, and the state of the sliding surface (Dieterich, 1979a, 1981; Ruina, 1980, 1983). Earlier work demonstrated that the state of the sliding surface depends on prior slip speed. Our observations indicate that the state of the sliding surface also depends on prior normal stress. In our model the functional dependence of state on normal stress is expressed in terms of the same state variable, θ, used previously to represent slip rate history effects. We assume that the steady state value of θ is independent of normal stress and that θ<jats:sup><jats:italic>SS</jats:italic></jats:sup> = <jats:italic>D<jats:sub>c</jats:sub></jats:italic>/<jats:italic>V</jats:italic>, where <jats:italic>D<jats:sub>c</jats:sub></jats:italic> is a characteristic slip distance. We interpret the variable θ as a measure of effective contact time. At constant slip speed and from an initial steady state, a sudden change in normal stress results in a sudden change in θ followed by a gradual change in θ back toward the initial θ<jats:sup><jats:italic>SS</jats:italic></jats:sup>, as sliding proceeds. The magnitude of the sudden change in θ is determined by a newly identified parameter that we call α. Earlier workers have established that stability is influenced by stiffness, <jats:italic>d</jats:italic>τ<jats:sup><jats:italic>SS</jats:italic></jats:sup>/<jats:italic>dV</jats:italic>, <jats:italic>D<jats:sub>c</jats:sub></jats:italic>, and slip rate history (Rice and Ruina, 1983). We conclude that stability will also be influenced by normal stress history and by α.</jats:p>