Simulation of time-dependent crack growth in brittle rocks under constant loading conditions

Highlights

• A lifetime prediction scheme was developed for rock under constant loadings.

• Numerical simulations were performed utilizing the developed modeling scheme.

• The damage process and macroscopic fracture pattern of the models were studied.

• Typical fracture patterns were observed in the numerical models.

• Preliminary studies were performed through numerical modeling.

Abstract

Based on the theory of subcritical crack growth, linear elastic fracture mechanics (LEFM), and Charles equation, a lifetime prediction scheme has been developed for rock specimens containing initial microcracks under constant loadings. Numerical simulations were performed utilizing the developed modeling scheme. Lifetimes were obtained through numerical calculation; the damage process and macroscopic fracture pattern of the models were studied. Typical fracture pattern, like tensile cracks and shear bands, were observed. A few preliminary studies were also performed to compare the results with in situ observations. Conclusions were drawn and possible improvements to future research work are proposed.

Introduction

Experiments and theoretical research on the phenomenon of fracture and damage started centuries ago. But no quantitative results were obtained until the great work of Griffith [1], which had lead to the onset of modern fracture mechanics. Griffith analyzed the stresses of a cracked plate, which was studied before by Inglis [2], and develop a theory for crack initiation and propagation. Orowan [3] modified Griffith’s theory by including the influence of plasticity into the energy balance. Irwin [4] introduced the parameter later known as the stress intensity factor K. After the fundamentals of linear elastic fracture mechanics were well established around 1960 [5], researchers had focused more on the influence of materials’ plasticity on the fracture analysis. One trend in recent fracture and damage mechanical research is related to time-dependent studies (life time prediction or time to failure prediction) for rocks (e.g. Kemeny [6], [7], [8], Mishnaevsky [9], Shao et al. [10], Li et al. [11], Rinne [12], Konietzky et al. [13]).

Based on the linear elastic fracture mechanical theory (LEFM), numerical simulations of time-dependent fracture propagation on Westerly Granite have been performed by Konietzky et al. [13]. The innovations of their research work include the simulation of specific initial cracks with certain distributions at the micro-scale, and the simulation of sub-critical and critical fracture growth to describe the time-dependent damage process until failure. It is assumed, that the damage and finally the failure of a rock specimen is the result of the partially parallel growth and coalescence of many initially existing microcracks at the grain size level rather than the growth of one or only a few single cracks. Other studies, like the experimental investigations on dynamic fracture performed by Ravi-Chandar and Knauss [14], [15], also implied this concept. As a further improvement of the work of Konietzky et al. [13], this study includes the influence of orientation distribution of the initial microcracks on the crack growth, and an adopted wing crack propagation scheme to describe the growth of initial microcracks.