Modeling of crack initiation, propagation and coalescence in rocks

One of the most successful criteria proposed so far to describe the initiation and propagation of cracks under quasi-static loading in rock-like materials is a stress-based criterion developed by Bobet (Fracture coalescence in rock materials: experimental observations and numerical predictions. Sc. D, Thesis, Massachusetts Institute of Technology, 1997) which is embedded in FROCK, a Displacement Discontinuity code that was developed by the rock mechanics group at MIT. Even though the predictions obtained with this criterion generally correspond to the experimental results, there are cases in which the quasi-static crack propagation results obtained with FROCK are not satisfactory. For this reason, a qualitative study using the Finite Element code, ABAQUS, was conducted to analyze stress-, strain- and energy-based criteria used for modeling crack development. Based on the ABAQUS relative quantitative analysis, it was found that the strain- and stress-based criteria may be more appropriate than the energy-based criterion to model quasi-static crack development. Thus, a strain-based and a normal stress-dependent criterion were implemented in FROCK. The cracking patterns obtained with these proposed criteria were compared with those obtained using Bobet’s original stress-based criterion and with experimental observations made in molded gypsum specimens. The proposed strain-based criterion implemented in FROCK appeared to yield better results than Bobet’s stress-based criterion. The influence of the friction angle (φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\upvarphi $$\end{document}) on the cracking patterns was studied with the proposed normal stress-dependent criterion and showed that friction angles closer to 0∘\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0^{\circ }$$\end{document} yielded the best results, which may indicate that, at least for the microscale, the critical shear stress at which rock fails does not depend upon the normal stresses applied.