A fracture criterion for brittle anisotropic rock

The McClintock-Walsh modification of Griffith theory is extended to treat brittle fracture of anisotropic rock. It is suggested that anisotropy is due primarily to preferred orientation of cracks in rocks and that a satisfactory mathematical model for fracture analysis is an elastically isotropic medium which contains a nonrandom array of Griffith cracks. The one array considered in detail consists of long cracks having a preferred orientation superimposed on a field of randomly oriented small cracks. Fracture in tension and in compression is considered. The fracture criterion found for compression resembles a similar criterion suggested by Jaeger on a somewhat different basis; it predicts behavior which is in good agreement with observed fracture of a slate reported by Donath. Determination of the effect of anisotropy upon the ratio of compressive strength to tensile strength shows that it can vary widely with sample orientation, with values both above and below that predicted from isotropic analysis.