Slip on a curved fault loaded by far-field compressive stress induces changes in normal stress along the fault surface. A two-dimensional crack model is developed to quantify these stresses for curved fault geometries. Under plane strain (or plane stress), the curved slipping region is replaced by continuously distributed dislocations, and the corresponding singular integral equation for the dislocation density is derived and solved numerically. Because our solution scheme incorporates the exact asymptotic form of slip near the end of the slipping region, results for the stress intensity factors are accurate. To determine the effects of fault curvature on faulting, the changes in fault-normal stress accompanying dip-slip are calculated for typical faulting events. The changes in normal stress accompanying normal faulting increase the frictional resistance to slip advance near the free surface, and those accompanying reverse faulting reduce the frictional resistance to slip advance near the free surface.
Under compressional tectonic loading, slip is retarded on the planar slip zones of higher dips, but enhanced if the dip decreases with depth. On the other hand, under extensional tectonic loading, slip is retarded on the planar slip zones of smaller dips, but enhanced if the dip increases with depth. Curvature of a concave-downward slip zone enhances compressive normal stress at the shallow end of the slip zone under compressional tectonic loading, tending to prevent propagation of the slip zones to the free surface. On the other hand, the curvature of a concave-upward slip zone reduces the compressive normal stress at the shallow end under the uniform extensional tectonic loading, thus assisting propagation of slip zones to the free surface. By contrast, for deep slip zones, the changes in normal stress are practically not affected by the fault curvature. To illustrate the local stress field near a sharp bend, we examine a sharply curved slip zone subjected to frictional sliding. Slip on such a fault induces significant compressional fault-normal stress near the bend. These changes add compression across the slip zone, thus increasing the frictional resistance to slip over the curved bend. Our results show that the magnitude of induced normal stresses is sharply localized near the bend.