Analysis of compressive fracture in rock using statistical techniques: Part II. Effect of microscale heterogeneity on macroscopic deformation

We have performed a parameter-sensitivity analysis to evaluate the relative in importance of different types of grain-scale heterogeneity on fracture processes and compressive strength in simulated compression tests of brittle, heterogeneous materials such as rock. This was done using a non-linear, rule-based model described in a companion paper. Results presented hele indicate that heterogeneity in local stress field (due to grain shape and loading) has a fir st-ol del effect on macroscopic properties and is much more important than heterogeneity in site strength or location. In particular, increasing local stress heterogeneity lowers the mean ultimate strength following an inverse power law. Increasing heterogeneity in the lattice-site locations (i.e. irregular lattice spacing) decreases crack localization and decreases normalized crack strain energy. This result is consistent with the postulate that systems with increasing disorder I require more energy to break. Heterogeneity in site-strength distribution had a relatively minor effect on macroscopic behavior., Peak strength is dependent on the mean site strength, not on the width of the site-strength distributions. This study also revealed that percolation thresholds are much lower than those predicted from stochastic fracture models. Consequently, statistical models for rock fracture must consider, alternative percolation algorithms such as directed-bond percolation, because the standard percolation models may not be appropriate for analyzing systems where a crack interaction dominates behavior at a low fraction of sires broken. Published by Elsevier Science Ltd.