A semiempirical constitutive law is presented for the brittle deformation of intact Westerly granite. The law can be extended to larger displacements, dominated by localized deformation, by including a displacement-weakening break-down region terminating in a frictional sliding regime often described by a rate- and state-dependent constitutive law. The intact deformation law, based on an Arrhenius type rate equation, relates inelastic strain rate to confining pressure Pc, differential stress ????, inelastic strain ??i, and temperature T. The basic form of the law for deformation prior to fault nucleation is In ????i = c - (E*/RT) + (????/a??o)sin-??(???? i/2??o) where ??o and ??o are normalization constants (dependent on confining pressure), a is rate sensitivity of stress, and ?? is a shape parameter. At room temperature, eight experimentally determined coefficients are needed to fully describe the stress-strain-strain rate response for Westerly granite from initial loading to failure. Temperature dependence requires apparent activation energy (E* ??? 90 kJ/mol) and one additional experimentally determined coefficient. The similarity between the prefailure constitutive law for intact rock and the rate- and state-dependent friction laws for frictional sliding on fracture surfaces suggests a close connection between these brittle phenomena.
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A generalized law for brittle deformation of Westerly granite