Simulation of crack propagation in rock in plasma blasting technology

Plasma Blasting Technology (PBT) involves the production of a pulsed electrical discharge by inserting a blasting probe in a water-filled cavity drilled in a rock, which produces shocks or pressure waves in the water. These pulses then propagate into the rock, leading to fracture. In this paper, we present the results of two-dimensional hydrodynamic simulations using the SHALE code to study crack propagation in rock. Three separate issues have been examined. Firstly, assuming that a constant pressure P is maintained in the cavity for a time \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\tau$\end{document}, we have determined the P-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\tau$\end{document} curve that just cracks a given rock into at least two large-sized parts. This study shows that there exists an optimal pressure level for cracking a given rock-type and geometry. Secondly, we have varied the volume of water in which the initial energy E is deposited, which corresponds to different initial peak pressures \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $P_{peak}$\end{document}. We have determined the E-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $P_{peak}$\end{document} curve that just breaks the rock into four large-sized parts. It is found that there must be an optimal \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $P_{peak}$\end{document} that lowers the energy consumption, but with acceptable probe damage. Thirdly, we have attempted to identify the dominant mechanism of rock fracture. We also highlight some numerical errors that must be kept in mind in such simulations.