Crack Band Model for Fracture of Geomaterials

SYNOPSIS Due to their heterogeneity, fracture in rocks as well as the artificial rock- concrete- propa-gates with a dispersed band of microcracks at the front. The progressive formation of the microcracks is described by a triaxial stress-strain relation which exhibits a gradual strain-softening. The stiffness matrix of a material inter-sected by a system of parallel continuously distributed cracks is obtained in the limit. The area under the stress-strain curve, multiplied by the width of the crack band (fracture process zone) represents the fracture energy. The resulting fracture theory is characterized by three independent parameters, the fracture energy. the tensile strength, and the width of the crack band, the latter being empirically found to approximately equal five-times the grain size in rock. The formulation lends itself easily to a finite element analysis, which is employed to calibrate the theory by fitting various test data on rock fracture available in the literature. Excellent agreement is achieved both with the maximum load data and the R-curve data. A linear fracture theory, which is obtained as the limit for very large sizes of the structure and the finite elements, and the effect of the choice of element size are discussed. Moreover, similarity between the fracture of rocks and of concretes is emphasized and the results obtained in a parallel investi-gation of concrete are sununarized. Finally, fracture analysis from the view point of strain-localization instability is given