Prediction of faulting from the theories of elasticity and plasticity: what are the limits?

Elasticity, rigid-plasticity and elasto-plasticity are the simplest constitutive models used to describe the initiation and evolution of faulting. However, in practice, the limits of their application are not always clear. In this paper, we test the behaviour of these different models using as examples tectonic problems of indentation of a die, compression with basal shear, bending of a plate and normal faulting around a dike. By comparing the results of these tests, we formulate some guidelines that may be useful for the selection of an appropriate constitutive model of faulting. The theory of elasticity reasonably predicts the initiation of the fault pattern but gives erroneous results for large strains. The theory of rigid-plasticity is more appropriate for large deformations, where the geometry of faults can be found by the method of characteristics. This method works well for zones of failure that are not severely constrained by elastic material outside e.g. when faults are connected to the free-surface, a viscous substratum or a zone of weakness. Non-associated elasto-plasticity is the most complete theory among those considered in this paper. It describes the evolution of faults from the initiation of localized deformations to the formation of a complicated fault network.