A plane strain model for a fault is presented that takes into account the inelastic deformation involved in fault growth. The model requires that the stresses at the tip of the fault never exceed the shear strength of the surrounding rock. This is achieved by taking into account a zone, around the perimeter of the fault surface, where the fault is not well developed, and in which sliding involves frictional work in excess of that required for sliding on the fully developed fault. The displacement profiles predicted by the fault model taper out gradually towards the tip of the fault and compare well with observed displacement profiles on faults. Using this model it is found that both (1) the shape of the displacement profile, and (2) the ratio of maximum displacement to fault length are a function of the shear strength of the rock in which the fault forms. For the case of a fault loaded by a constant remote stress, the displacement is linearly related to the length of the fault and the constant of proportionality depends on the shear strength of the surrounding rock normalized by its shear modulus. Using data from faults in different tectonic regions and rock types, the in situ strength of intact rock surrounding a fault is calculated to be on the order of 100 MPa (or a few kilobars). These estimates exceed, by perhaps a factor of 10, the strength of a well developed fault and thus provide an upper bound for the shear strength of the crust. It is also shown that the work required to propagate a fault scales with fault length. This result can explain the observation that the fracture energy calculated for earthquake ruptures and natural faults are several orders of magnitude greater than that for fractures in laboratory experiments.
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