Modelling microcrack kinetics in rocks

Abstract

SUMMARYMathematical concepts of statistical mechanics are used here to formulate the problem of microcrack kinetics. A stochastic distribution function is defined to characterize some modelling parameters of microcracks. This formalism results in an integral-differential equation of the Boltzmann type. A functional form for the microcrack production rate is imposed to model dilatancy and failure under shear-loading histories. This simple model illustrates some concepts of this theoretical approach.