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Keywords:

  • fault constitutive law;
  • fault dynamics;
  • fault mechanics;
  • friction;
  • rate- and state-dependent friction;
  • rock experiment

The rate at which one rock slab slides past another, such as along a fault or fracture, depends on the strengths of the applied forces and the friction between the blocks. Though simple in concept, accurately modeling the interactions—especially the extreme cases of prolonged stress accumulation or the sudden rupture of an earthquake—is difficult. Researchers rely on the rate- and state-dependent friction law (RSF) to estimate the slip velocity in a fracture from the imposed stresses. The empirical RSF is itself broken down into two component parts: the constitutive law, which describes how the rock reacts to external forces and pressures, and the evolution law, which attempts to explain how the friction at the fracture interface changes under varying amounts of stress. Embedded within the constitutive law are two empirical parameterizations: the direct effect coefficient, which accounts for stresses perpendicular to the direction of motion, and the state variable, which is derived from the evolution law and describes changes in the physical state of the rock at the friction interface.