Fault stability under conditions of variable normal stress

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Abstract
The stability of fault slip under conditions of varying normal stress is modeled as a spring and slider system with rate‐ and state‐dependent friction. Coupling of normal stress to shear stress is achieved by inclining the spring at an angle, ø, to the sliding surface. Linear analysis yields two conditions for unstable slip. The first, of a type previously identified for constant normal stress systems, results in instability if stiffness is below a critical value. Critical stiffness depends on normal stress, constitutive parameters, characteristic sliding distance and the spring angle. Instability of the first type is possible only for velocity‐weakening friction. The second condition yields instability if spring angle ø < ‐cot −1μss, where μss is steady‐state sliding friction. The second condition can arise under conditions of velocity strengthening or weakening. Stability fields for finite perturbations are investigated by numerical simulation.