Application of Multifractal to Characterize Microscopic Crack Propagation in Red Sandstone

Abstract

Most of existing studies on rock damage are focused on investigating the macroscopic stress-strain relationship, and only limited research is available on analyzing the microscopic crack propagation due to measurement difficulty, cumbersome data reduction procedures, and complexity of damage in micro-level. In this study, a powerful image-processing program is developed to extract the microscopic crack distribution from the digital image of microscopic crack status of red sandstone, and the microscopic crack propagation of red sandstone under single-axial pressure is then evaluated by the technique of multifractal. It demonstrates that the microscopic crack distribution possesses the multifractal character, and the capacity dimension of multifractal singular spectrum can be used to quantitatively characterize the microscopic crack propagation of red sandstone. By comparing the stress-strain relationship with the one of stress-capacity dimension, the capacity dimension is capable of acting as a physical quantity to effectively reflect the damage of red sandstone by the means of characterizing its microscopic crack propagation.