An improved model of fracture propagation by gas during rock blasting—some analytical results

Abstract

Over the last few years, a number of research papers have been published which propose the use of mathematical models to describe the rock blasting process. These models consider a large number of physical processes to be important; however, this paper concentrates on the treatment of the stress field within the rock. Previously this has been modelled both by extrapolation of simple situations and by numerical solutions for stresses throughout the rock mass. In this paper, an improved model of the stress field around a cylindrical borehole with radial cracks is introduced. This model takes the form of an analytical expression for the crack height as a functional of the gas pressure and the in situ stress. The model is valid for the physically interesting cases where the rock acts as a linear elastic material, there are a large number of radial fractures and the rock is held together by in situ stresses and fracture toughness. It accounts for cracks opening due to stresses created both by the borehole gas and by the gas in the fractures, as well as determining the change in the borehole size as the stress distribution changes. To illustrate the behaviour of this model some very simple idealized situations are considered which allow analytical expressions to be derived for the crack propagation and the gas motion. These expressions show that the improved model predicts important effects such as the cracks tips starting ahead of the gas front, the gas front catching up with the crack tips, the borehole radius reducing as the stress field relaxes and the rapid reduction in borehole pressure.