Digital image-based numerical modeling method for prediction of inhomogeneous rock failure

Abstract

Abstract This paper presents a two-dimensional digital image-based numerical modeling method for prediction of inhomogeneous rock failure behavior under loadings. Actual inhomogeneities of granitic rocks are extracted from color images of the granite cross-sections. They are represented as the internal spatial distribution of three main granite minerals (quartz, feldspar and biotite). The actual mineral spatial distribution on granite cross-section is then incorporated into conventional numerical software packages to examine the rock failures under loading. Some digital image processing algorithms are presented to isolate and identify the main internal minerals and their distribution from color digital images. A simple method is proposed to transform the actual image data into vector data for generation of finite meshes or grids. The vector data are used directly as uniform square element meshes or grids that can be inputted into the existing software packages. The finite difference software package FLAC is used as an example for the present investigation. The conventional Mohr–Coulomb and tensile stress failure criteria are used to examine the failure behavior of a circular granite cross-section under the conventional Brazilian indirect tensile test loading conditions. The numerical results indicate that the vertical tensile crack initiates in a biotite located near the geometrical center of the granite cross-section and the actual spatial distribution of the three minerals plays an important role in modifying the propagation pattern of the tensile crack from its theoretical position at the central vertical diameter of a homogeneous circular cross-section. The numerically predicted failure load and tensile strength values for inhomogeneous granite are much lower than the expected values.