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 rel ative 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. R esults presented hele indicate that heterogeneity in local stress fiel d (due to grain shape and loading) has a fir st-ol del effect on macro scopic properties and is much more important than heterogeneity in sit e strength or location. In particular, increasing local stress heterog eneity lowers the mean ultimate strength following an inverse power la w. Increasing heterogeneity in the lattice-site locations (i.e. irregu lar lattice spacing) decreases crack localization and decreases normal ized 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 ef fect on macroscopic behavior., Peak strength is dependent on the mean site strength, not on the width of the site-strength distributions. Th is study also revealed that percolation thresholds are much lower than those predicted from stochastic fracture models. Consequently, statis tical models for rock fracture must consider, alternative percolation algorithms such as directed-bond percolation, because the standard per colation models may not be appropriate for analyzing systems where a c rack interaction dominates behavior at a low fraction of sires broken. Published by Elsevier Science Ltd.