Numerical experiments of crack closure and its influence on elastic and electrical properties

Elastic and electrical properties of a fluid-bearing rock are strongly affected by cracks. Effective elastic compliance of a rock is determined by number density and compliance of cracks. When cracks form an interconnected network, effective electrical conductance is determined by number density and conductance of cracks. Cracks have rough surfaces and asperities on them come into contact under pressure. Elastic compliance and electrical conductance of a crack decrease with its closure to govern changes in elastic and electrical properties with pressure. Though surface topography of cracks is a key to understanding physical properties under pressure, it is still difficult to investigate. We thus conduct numerical experiments of crack closure to understand changes in elastic and electrical properties with pressure. For simplicity, a 2D 50×50 square lattice is used to model a fluid-filled crack. The initial aperture of cells has a Gaussian distribution and is randomly given. For a closure of aperture, the required stress is calculated through Hertzian contact theory and electrical conductance of the lattice is calculated with the finite difference method. The lattice is electrically conductive when more than 50% of cells are open. When more than 70% of cells are open, the conductance is insensitive to the distribution of apertures. The elastic compliance is also calculated as a function of aperture closure. Both elastic and electrical properties are thus obtained as a function of confining pressure and compared with measured elastic wave velocity and electrical conductivity reported in Watanabe et al. (2019, 2024).