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An energy constraint for frictional slip on misoriented faults

U. S. GEOLOGICAL SURVEY, 345 MIDDLEFIELD ROAD, MENLO PARK, CALIFORNIA 94025

Abstract

Analysis of the energy required for slip on faults at varying angles () to the greatest principal stress in a fixed stress field yields an upper bound on the effective coefficient of friction µ*_d() for slip on faults misoriented with respect to the optimum angle for slip, ₀, given by the Coulomb criteria. Here the effective coefficient of friction is µ*_d = µ_d(1 – P_f / _n), where P_f is the pore pressure confined to the fault zone and _n 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 (₀ = 25° to 30° for commonly accepted values of friction, µ_d = 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 ( > 80°) with an intrinsic coefficient of friction of µ_d 0.7 ( 28°) if µ*_d() 0.2 along the misoriented fault. The latter implies a lower bound on the fault-confined pore pressure of P_f 0.8 _n, where _n 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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