Numerical modelling of cracking in granite due to Joule heating and piezoelectric actuation

Summary

Abstract

Traditional comminution and drilling of hard rock, being based on mechanical breakage, suffers from severe tool wear. This has spurred intensive search for advanced preconditioning methods to facilitate mechanical breakage. One of these method uses high voltage electric pulses to fracture rock. This can happen directly, via Joule heating, whereby a rapid rise of the pressure and temperature in the electric breakdown channel between electrodes break the rock. Alternatively, the quartz phase in quartz-bearing rocks can be actuated by the converse piezoelectric effect. In the present study, a numerical model to simulate both techniques, the Joule heating and the piezoelectric actuation of the quartz phase, is developed. This task involves developing a rock fracture model and a solution scheme for the underlying coupled piezoelectro-thermo-mechanical problem. As to the rock fracture model, the embedded discontinuity finite elements approach is chosen. In this approach, a crack with the normal parallel to the first principal direction is introduced into a finite element upon violation of the Rankine criterion. Moreover, random clusters of finite elements representing the constituent minerals with their respective mechanical, thermal and electrical properties describe the rock heterogeneity. A staggered approach, with explicit time marching for the mechanical equation of motion, is applied in solving the coupled system of equations at the global level. In the numerical examples, cracking of a heterogeneous granitic rock specimen under high voltage pulse boundary condition is simulated in axisymmetric conditions. The results demonstrate that at lower voltages cracking is mainly due to Joule heating while at higher level, say 500 kV, cracks are induced also by the piezoelectric effect. Such a modelling technique is an asset that facilitates geotechnical project risk management by allowing numerical investigation of different physical and operational factors influencing the electropulse based preconditioning of rock mass.