Numerical Comparison of Different Approaches for the Fractured Medium Simulation

Abstract

This chapter is devoted to the investigation of the dynamic loading of fractured media occurred in many applications like the seismic survey process, non-invasive material quality control, and fatigue failure of samples. Two different approaches were described. The first one is based on the continual model of solid media with a discrete set of slip planes and with nonlinear-type slip conditions at them. The constitutive equations of the resulting system of equations contain a small viscosity parameter in the denominator of nonlinear free terms. For a stable numerical solution of a system of differential equations, an explicit–implicit method is used with an explicit approximation of motion equations and an implicit approximation of constitutive relations containing a small parameter. The second one is based on the explicit crack positioning inside the computational grid. With the help of correct contact conditions, unfilled and fluid-filled fractures are described. To solve numerically the elastic system of equations, the grid-characteristic method on structured grids is used. It allows to set precisely all necessary boundary conditions. Both approaches were successfully applied for the simulation of the seismic survey problem in fractured media. Full-wave numerical solutions were obtained and compared. The striker–target interaction problem was simulated using Lagrange grids. Based on the analysis of the dynamic stress state, the process of the new crack initiation was described. The influence of the material strength on it was investigated. Positions of damages were compared with the delamination region.