Fracture growth under compressive loading is studied using the maximum strain energy release rate criterion by means of both the finite element and the boundary element methods. Although this approach is computationally intensive, it is indispensable for this type of problem because other criteria cannot account for the friction effect on the fracture faces. We use a repulsion scheme to handle the frictional contact constraints on the fracture faces: the interpenetration is eliminated by adjusting the normal compressive force (repulsion), and the friction law is satisfied by modifying the friction resistance at each iteration.
Our results explain the fact that a natural fracture under uniaxial compression often grows in its own plane, while an artificial cut grows by means of a kink: the reason lies in the lower friction coefficient on an artificial cut than on a natural fracture.
Fracture growth under simple shear and under transtension occurs by a kink and along a smooth, slightly convex trajectory; the computed path is almost identical to the one obtained in the laboratory. Under transpression, fracture also grows by a kink and along a smooth trajectory which is of the opposite convexity than in the previous case, when compression is large. Right-stepping fractures under a left-lateral shearing run away from each other when their centers are more than one fracture length distant; when this is not the case, they turn toward each other. Interaction is thus significant only in this last case.
Geologically, our results imply that essentially planar faults may be due to continuing remote compressional stress at about 30$\sp\circ$ to the fault, while abrupt changes in orientation may indicate that the previous stress has been replaced by a remote shear stress. Finally, a convex fault path may indicate simple shear or transtension, whereas a concave one may indicate transpression.