A two-dimensional crack model is used to investigate the effect of the free surface on the propagation of kink cracks that develop at the tip of dip-slip shear zones. The slip zones undergo frictional sliding under tectonic loading with the presence of the gravitational force. Because the numerical scheme incorporates the exact asymptotic form of slip near the end of the shear zone, results for the stress intensity factors are accurate. The calculations show that crack opening occurs along a portion of the planar slip zone near the kink as well as at the kink itself. For a typical shallow reverse dip-slip zone, the mode I stress intensity factor at the tip of the kink can be 60% greater than that for a full space. The effect of free surface is negligible if the ratio of the depth of the shallow end to the length of the slip zone is greater than two.

The influence of the free surface makes it possible for the kink crack to grow to much greater length. Under compressive tectonic loading, the kink that develops at the shallow end of a shear zone does not move toward the free surface; instead, the kink curves away from the free surface, extends stably parallel to the free surface, and is then arrested at a finite length. The calculations suggest that rupture termination of a reverse dip-slip earthquake may be due to extensive tensile cracking near the free surface and that the growth of long extensional fractures parallel to the free surface dissipate sufficient energy to stop the fault rupture. In addition, the present calculations demonstrate that the orientation and the length of observed vein sets are consistent with the extensional fractures developed near the tip of the dip-slip zone. ¿ American Geophysical Union 1995