Mechanics of dip‐slip faulting in an elastic half‐space

The mechanics of dip‐slip faulting is examined using a model of a crack in a plane strain elastic half‐space loaded by remote stresses: vertical stresses are equal to the overburden and horizontal stresses are the sum of a constant (c) times the overburden and a depth‐independent term σtect, which may be compressive or tensile. Opening is allowed in response to local tension, and slip on closed regions is governed by Mohr‐Coulomb conditions. Because regions of opening and slip, in general, must be determined as part of the solution, relative displacements and stress intensity factors are calculated by iterative solution of integral equations. If the fault is not too shallow (h/L > 0.3, where h is the depth of the upper end of the slip zone and L is the length along dip) and the Coulomb stress (the shear stress minus the friction coefficient ƒ times the effective normal stress) is of one sign over most of the fault, simple approximations suffice. Use of these approximations and the criterion that the energy release rate equals a critical value demonstrates that updip propagation is unstable if the slip zone length exceeds a minimum value. For typical values of ƒ dip angle, and c, the slip zone will be locked below a certain depth. In general, the depth at which the Coulomb stress changes sign underestimates the locking depth, but the magnitude of the difference decreases as the depth of the sign change approaches the lower end of the slip zone. For shallow slip zones, h/L < 0.3, slip induces changes in both shear and normal stresses on the slip surface. For reverse (normal) slip, this coupling reduces (increases) the compressive normal stress and amplifies (diminishes) slip near the upper end of the slip zone surface. For extensional loading (σtect < 0), opening can occur for shallow embedded zones and, more prominently, for surface breaking zones. Although the shear stress drop is nonuniform in this model, calculations reveal that unless fault opening occurs, the surface displacement is well‐approximated by that due to a uniform shear stress drop equal to the average.