A continuum mechanics approach to quantify brittle strain on weak faults: application to the extensional reactivation of shallow dipping discontinuities

S U M M A R Y A number of field observations suggest that sliding on fault planes may occur at very shallow dip in the brittle field. The existence of active low angle normal faults is much debated because (1) the classical theory of fault mechanics implies that faults are locked when the dip is less than 30 and (2) shallow dipping fault planes do not produce large earthquakes (M > 5.5). To reconcile observations and theory, we propose a newmodel for fault reactivation by introducing an elasto-plastic frictional fault gouge as an alternative to the classical dislocation models with frictional properties. Contrary to the classical model which implies that the dilation angle ψ equals the friction angle φ, our model accounts for ψ < φ and permits ψ < 0 in the fault gouge as deduced from laboratory and field observations. Whilst the predicted locking angles differ in most cases by less than 10 from the classical model, a significant amount of plastic strain (strain occurring in elasto-plastic regime) is predicted to occur on badly oriented faults prior to locking in a strain-hardening regime. We describe four modes of reactivation which include complete/partial reactivation with/without tensile failure in the surrounding medium. This paper presents analytical solutions to separate those four different modes as well as numerically computed estimates of the amount of plastic strain accumulated before locking. We conclude that plastic strain on badly oriented faults is favoured by compaction of the fault gouge and that those faults are probably aseismic because this strain always occurs in a hardening regime.