A theoretical approach for estimating the surface area of a rough-walled fracture from well logging data

Abstract

The rate of frictional strengthening (healing) during quasi-stationary contact plays an important role in many aspects of repetitive stick-slip sliding. Observations of frictional healing are also a key feature of a class of slip-rate and state-variable friction constitutive laws widely-used to model earthquake faulting. This paper describes a suite of laboratory experiments to measure healing rate in simulated fault gouge. Modeling is carried out to critically evaluate rate and state friction laws. Experiments consisted of both slide-hold-slide tests, in which surfaces were sheared at a specified velocity and held in quasi-stationary contact for a given time, and velocity stepping tests in which step changes in load point velocity were imposed to evaluate friction constitutive parameters. The study addresses two main issues: 1) variation in healing rate with loading velocity, and 2) consistency of friction parameters and constitutive behavior as observed in slide-hold-slide and velocity-step tests. Experiments were performed in the double-direct shear geometry, at room temperature, and at constant normal stress of 25 MPa. Gouge consisted of quartz sand and was sheared within rough Westerly granite surfaces. Surface contact dimensions were 10 cm × 10 cm, the gouge layers were 2.5 mm thick prior to shear, and load point velocities ranged from 0.5–100 μm/s. Velocity stepping tests indicated velocity weakening (the steady-state coefficient of friction decreased with slip rate). In slide-hold-slide tests, friction decayed during holds and exhibited a peak value (taken as the coefficient of static friction) upon reloading. Static friction increased approximately linearly with log hold time. In addition, static friction and the rate of frictional healing varied with loading velocity. Friction relaxation during holds also varied with hold time and loading velocity. The data indicate that healing is not simply a frictional property, but rather is a system response that varies with loading velocity and properties of the elastic loading system. Constitutive modeling is carried out on three aspects of the data: slide-hold-slide tests, velocity stepping tests, and the rate of fricitional healing. Friction parameters are determined by modeling each data set and these are compared to evaluate internal consistency. Both slip- and time-dependent state evolution laws (Ruina and Dieterich laws, respectively) are evaluated. The modeling indicates that individual tests are fit well by either the Ruina or Dieterich laws. However, slide-hold-slide tests indicate that the friction parameter a is larger than b, whereas velocity step tests indicate the opposite. Velocity step tests predict less friction relaxation and faster healing than observed in slide-hold-slide tests. These discrepancies may indicate variation in constitutive parameters as a function of slip velocity and/or limitations in the rate and state friction laws as presently written.