Theoretical and numerical stress analysis at edges of interacting faults: application to quasi-static fault propagation modelling

Abstract

SUMMARY We study theoretically and numerically the process of fault interactions within a quasi-static faulting model at long, tectonic timescale. The model handles birth, growth and sliding of multiple straight but non-coplanar interacting faults, regardless of any coseismic dynamic slip events. The study is restricted to the 2-D elastic antiplane case, an idealization of the normal faulting process. The model handles a general slip-dependent friction law for faults, to take into account a possible long-term fault weakening process. At fault tips, finite stress and progressive weakening lead to fault tip cohesive zones and ensure stability. We introduce a new numerical method based on a series development of slip profiles using a Chebyshev basis, which provides an accurate computation of large stress gradients at fault tips. Here simulations are limited to two parallel faults, which is enough to investigate many important features such as slip partitioning between faults, variable fault tip velocities and the state of stress in fault relay zones, responsible for the fault linking process. We study both a quasi-static problem and the associated spectral problem and show the link between them. We compare our quasi-static simulations with experimental results concerning the acceleration/deceleration of fault tips submitted to stress interaction and concerning the geometrical parameters that favour the linking of two normal faults. We find that the linking (coalescence) process should most likely occur during the deceleration phase of the faults tips subject to stress shadowing in the fault relay. Furthermore, for large ratios of fault lengths to separation, the linking process should begin for fault overlaps comparable to the values observed by Soliva & Benedicto in small natural fault relays (typically 2.9 times the fault separation).