The Changeable Power Law Singularity and its Application to Prediction of Catastrophic Rupture in Uniaxial Compressive Tests of Geomedia

Abstract

The acceleration precursor of catastrophic rupture in rock-like materials is usually characterized by a power law relationship, but the exponent exhibits a considerable scatter in practice. In this paper, based on experiments of granites and marbles under quasi-static uniaxial and unconfined compression, it is shown that the power law exponent varies between -1 and -1/2. Such a changeable power law singularity can be justified by the energy criterion and a power function approximation. As the power law exponent is close to the lowest value of -1, rocks are prone to a perfect catastrophic rupture. Furthermore, it is found that the fitted reduced power law exponent decreases monotonically in the vicinity of a rupture point and converges to its lower limit. Therefore, the upper bound of catastrophic rupture time is constrained by the lowest value of the exponents and can be estimated in real time. This implies that, with the increase of real-time sampling data, the predicted upper bound of catastrophic rupture time can be unceasingly improved.