FIGURE G.2 The normal and shear stress, σ and τ, acting across the fault depends on the vertical and horizontal stresses, σv and σh, and the fault inclination β. The fault is infiltrated by fluid at pressure ρ.
The normal and shear stress on the fault can actually be expressed in terms of the in situ vertical and horizontal stresses, σv and σh, through a relation that depends on the fault inclination β (Figure G.2). The above Coulomb criterion can then be expressed as a limiting condition in terms of the effective vertical and horizontal stresses σ′v = σv – ρ and σ′h = σh – ρ or equivalently in terms of their half-sum and half-difference, P′ and S. Figure G.3 provides a graphical representation of the Coulomb criterion in terms of these two quantities.
The fault is stable if the point representative of the (effective) in situ stress state is below the slip criterion. A perturbation (ΔP′, ΔS), induced by fluid injection or withdrawal, to an existing state (P′o, So) that moves the point (P′o+ ΔP′, So+ ΔS) to be on the Coulomb line will cause slip and trigger a seismic event. However, only some perturbations are destabilizing in nature (i.e., they move the representative stress point [P′, S] closer to the critical conditions). For example, the destabilizing perturbation shown in Figure G.3 is characterized by a slope m = ΔS/ΔP′ smaller than mo and a “direction” corresponding to both ΔP′ and ΔS being negative. A perturbation characterized by the same slope m, but positive variations ΔP′ and ΔS, would be stabilizing.