Microstructural Modeling Approach Applied to Rock Material

Abstract

The importance of the microstructural parameters in rock mechanical behavior has been investigated by several authors. Moreover, the Weibull statistical model has been used to characterize the heterogeneity of several materials on the basis of the concept that the microscopic defects within the material determine their mechanical strength. The modeling of different rocks is a topic that is fundamental for the prediction of rock fragmentation. In this article, the analysis of rock microstructure is performed using the microstructural modeling approach, which consists of the simplification, quantification, and modeling of the main properties of rock microstructure. The grain size, grain shape, and microcracks are modeled by means of statistical density functions, namely, Cauchy, chi-squared, exponential, extreme value, gamma, Laplace, normal, uniform, and Weibull. It is found that the Weibull distribution is the most appropriate statistical model of the grain size and grain shape, when compared with the other eight statistical models. Regarding microcracks, the results show that the gamma distribution is the most appropriate model. The Weibull and gamma distributions are then used to analyze the heterogeneity of the microstructure. This is done by comparison of the statistical models of each microstructural property evaluated in several thin sections of the same rock. It is found that with respect to grain size and grain shape, the rock is homogeneous, while the size distribution of the microcracks shows a clear trend toward less homogeneity. The microstructural modeling approach is important for modeling, characterizing, and analyzing the microstructure of rock material. Among other applications, it can be used to explain differences in the mechanical behavior obtained in testing several specimens.