A note on fault reactivation

Reactivation of existing faults whose normal lies in the σ₁^′σ₃^′ plane of a stress field with effective principal compressive stresses σ₁^′ >σ₂^′ >σ₃^′ is considered for the simplest frictional failure criterion, τ = μσ_n^′ = μ(σ_n − P), where τ and σ_n are respectively the shear and normal stresses to the existing fault, P is the fluid pressure and μ is the static friction. For a plane oriented at θ to σ₁^′, the stress ratio for reactivation is (σ₁^′/σ₃^′) = (1 + μ cot θ)/(1 − μ tan θ). This ratio has a minimum positive value at the optimum angle for reactivation given by (1/μ) but reaches infinity when θ = 2θ^*, beyond which σ₃^′ < 0 is a necessary condition for reactivation. An important consequence is that for typical rock friction coefficients, it is unlikely that normal faults will be reactivated as high-angle reverse faults or thrusts as low-angle normal faults, unless the effective least principal stress is tensile.