Analytical study of displacements along faults with irregular fault-plane geometry

Vita.The growth of slip along a bend in a fault is analyzed using complex variable techniques of plane elasticity and conformal mapping of the fault-plane geometry. The analytical model uses fault-displacements of the form, [(s - a)(s - b)][superscript -3/2], to produce bounded stresses at the end-regions of slip in accordance with the behavior of previous photoelastic models. The analytical model is applied to faults with maximum angles of bend, relative to fault-strike, of 12°, 21°, and 32°. As slip develops along the bend, the orientations of the principal stress axes remain almost parallel to those of the regional field. Because the bend is unfavorably oriented with respect to slip, contact loads on the bend tend to increase the resistance to slip. In contrast, slip on the favorably oriented fault-segments decreases the resistance to slip on the bend by increasing the shear stress but decreasing the normal stress. Although the growth of slip along a bend in a fault is stable (except possibly for small angles of bend where contact-load effects would be negligible), the decrease in resistance caused by slip on the favorably oriented segments permits fault displacements along the entire fault at stress levels much lower than those predicted on the basis of maximum inclination of the fault surface. In previous photoelastic models, slip along the entire fault produced fault-surface separation, which would appear in nature as dilatancy. Therefore, dilatancy created by slip on an irregular fault-surface can occur, at least on shallow faults, at lower stress-levels than those required to initiate significant fracturing of the rock mass