Abstract

Analysis of the energy required for slip on faults at varying angles (θ) to the greatest principal stress in a fixed stress field yields an upper bound on the effective coefficient of friction μ*d(θ) for slip on faults misoriented with respect to the optimum angle for slip, θ0, given by the Coulomb criteria. Here the effective coefficient of friction is μ*d = μd(1 − Pf / σn), where Pf is the pore pressure confined to the fault zone and σn is the stress normal to the fault. The two-dimensional analysis applies to a pervasively fractured crust with heterogenous fault strength, and the results show that (1) slip will be energetically favored on faults at 45° to 50° to the greatest principal stress if the coefficient of friction along these faults is just 20% to 25% lower than along faults at the optimum Coulomb angle (θ0 = 25° to 30° for commonly accepted values of friction, μd = 0.70 to 0.75, in the upper crust); (2) in the extreme case of vanishingly small frictional strength and low ambient shear stress, the 45° angle for optimum fault slip (parallel with the direction of maximum shear stress) is only weakly favored over a wide range of fault orientations on either side of 45°; and (3) slip will be energetically feasible on strongly misoriented faults (θ > 80°) with an intrinsic coefficient of friction of μd ≈ 0.7 (θ ≈ 28°) if μ*d(θ) ≦ 0.2 along the misoriented fault. The latter implies a lower bound on the fault-confined pore pressure of Pf ≧ 0.8 σn, where σn is the normal stress across the fault. The basic form of this contraint applies to both displacement-averaged dynamic friction and static friction.

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