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.