Analysis of smooth crack growth in brittle materials

When a fault in the crust extends, earthquake faults appear as a set of displacement discontinuities on the ground surface and cause strong motion and large deformation. For the prediction of such earthquake faults, one needs to analyze the propagation of smoothly growing cracks. This paper develops an analysis method based on a new formulation of growing crack problems. In this method, the change in the stress intensity factors due to a small extension is explicitly related to the curvature and length of the extension, and these geometrical parameters can be determined from assumed fracture criteria, without taking any trial-and-error routes of the extension geometry. The validity of the proposed method is numerically examined; in particular, the predicted stress intensity factor changes coincide with numerically computed ones. The proposed method is applied to reproduce two experimental observations. It is shown that in both cases, the configuration of the simulated crack is in good agreement with the observed one.