A crack model of creep processes on deep sections of faults

A crack model in antiplane shear configuration is shown representing creep processes interpreted in terms of 'viscous' deformation of a narrow plastic layer, characterized by inhomogeneous rheological properties, embedded within a homogeneous elastic medium. The evolution in time of slip and stress over the crack plane is studied through a truncated expansion in Chebyshev polynomials, and convergence is proved to be fast in the simple examples considered. Finite-stress solutions are found which are compatible with constitutive relations of elasto-plastic materials and furthermore these allow us to simulate creep propagation and stress transfer between locked and unlocked fault segments. This model provides a simple interpretation of the shallow depth of the seismogenic layer observed in several areas of the world and lends itself to modelling creep processes during either post-seismic rebound or pre-seismic stress buildup. Stress transfer is accomplished mostly by the slow extension of the creeping section. During a seismic cycle it is envisaged that different regimes dominate over deep, intermediate and shallow sections of faults: (i) slow pre-seismic stress build-up accompanied by creep and stress migration toward intermediate depths; (ii) brittle fracture over shallow and intermediate sections of faults; (iii) post-seismic rebound over intermediate and deep sections of faults. The present crack model, while providing finite-stress solutions, allows a better understanding of how stress may accommodate at different depths over a fault plane during a seismic cycle.