INTRODUCTION
Borehole breakout is the process by which portions of a borehole wall fracture or spall when subjected to compressive stresses. In most of these approaches, the rock surrounding the borehole is micromechanically considered as a nonlinear continuumaterial. Experiments and field studies, however, have shown that the heterogeneous and discontinuous nature of rock has a strong impact on the mechanics of borehole breakout [ 1, 2 ]. This technical note describes a numerical model that has been developed to simulate the progression of borehole breakout in heterogeneous and discontinuous rock. The rock surrounding the borehole is simulated as an elastic material containing a random distribution of microcracks (random locations, orientations, and lengths). As compressive load is applied, the initial cracks grow, interact, and coalesce to form macroscopic fractures. The numerical model was developed by making a series of modifications to the displacement discontinuity code of Crouch and Starfield [3]. The most important modifications include modifying the boundary element for the calculation of the stress intensity factors, and adding Coulomb friction for closed portions of the cracks. The numerical model is used to simulate the progression of breakout in Westerly granite, and the results are very realistic.
NUMERICAL MICROCRACK MODEL
This model is a good representation for the heterogeneous behavior of most rocks in the low- temperature and low-confinement regime. The following modifications to the method[3] have been made:
1. A crack tip element is implemented to accurately calculate the modes I and II
stress intensity factors.
2. Coulomb friction is applied along closed portions of cracks.
3. The S criterion is implemented to calculate crack growth.
4. A crack coalescence criteria is implemented.
5. A random crack generator is implemented.
2.1 Stress Intensity Factor Calculation
Consider a two dimensional elastic body under plane strain conditions containing a number of curvilinear cracks. The stress intensity factors can be estimated using the Dn and Ds values for the crack tip elements. As a demonstration of the accuracy of the modified crack tip element, the stress intensity factors are compared with closed-form solutions and normal boundary element solutions (see fig. l)
2,2 Coulomb friction along closed portions of cracks
Since the body containing cracks will be subjected to compressive stresses, portions of the cracks may be closed and subjected to frictional forces. An iterative scheme has been implemented for the calculation of the correct frictional force along closed crack surfaces. ( see manuscript for details).
