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 θ ^∗ = {1}/{2}tan^-1 (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.