[1] We use a two-dimensional displacement discontinuity method (DDM) for quasi-static boundary value problems to investigate sinusoidal faults of finite length in an otherwise homogeneous and isotropic elastic material. The DDM incorporates a complementarity algorithm to enforce appropriate contact boundary conditions along the model fault. The numerical solution for the model sinusoidal fault converges to the analytical solution for a straight fault of finite length as the ratio amplitude/wavelength goes to zero. It does not converge to the analytical solution for an infinite sinusoidal interface as the ratio distance/wavelength goes to zero. We provide stick, slip, and opening distributions along wavy faults with a range of uniform coefficients of friction, amplitude/wavelength ratios, and wave numbers. As the number of sinusoidal waves or the amplitude/wavelength is increased, mean slip decreases. Additionally, the fault geometry causes slip to deviate significantly from the elliptical distribution of a planar fault. We demonstrate that the displacement discontinuity of wavy faults cannot be prescribed a priori. This necessitates implementation of the complementarity algorithm and precludes an analytical solution. We employ the terms lee and stoss instead of releasing and restraining bends because a local minimum in slip may occur along lee sides, as well as stoss sides. In some cases, lee sides stick while stoss sides slip. Trends in the slip perturbation can be explained by the angular relationship between the local fault trace and the orientation of the remote principal stresses; however, the displacement discontinuity along a wavy model fault cannot be explained by this relationship alone.Citation: Ritz, E., and D. D. Pollard (2012), Stick, slip, and opening of wavy frictional faults: A numerical approach in two dimensions,

Meter-scale subvertical strike-slip fault traces in the central Californian Sierra Nevada exhibit geometric complexities that significantly contribute to their mechanical behavior. Sections of faults that opened at depth channelized fluid flow, as evidenced by hydrothermal mineral infillings and alteration haloes. Thin sections show a variation in the style of ductile deformation of infill along the fault, with greater intensities of deformation along restraining bends. Orthorectified photo-mosaics of outcrops provide model geometries and parameter constraints used in a two-dimensional displacement discontinuity model incorporating a complementarity algorithm. Model results show that fault shape influences the distribution of opening, and consequently the spatial distribution of fluid conduits. Geometric irregularities are present at many scales, and sections of opening occur along both releasing and restraining bends. Model sensitivity tests focus on boundary conditions along the fault: frictional properties on closed sections and fluid pressure within sections of opening. The influence of the remote stress state varies along a non-planar fault, complicating the relationships between remote stresses, frictional properties, slip, and opening. Discontinuous sections of opening along model faults are similar in spatial distribution and aperture to the epidote infill assemblages observed in the field. 1 Introduction Faults have irregularly shaped surfaces, and often are composed of discontinuous segments. Such irregularities cause the mechanical behavior of faults to deviate from that of the idealized planar structure. Understanding opening and slip on faults at depth is crucial to many economic and scientific applications. For example, economic geologists have noted ore deposits along geometrically complex faults for nearly a century (

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The two-dimensional circular arc crack solution of Muskhelishvili (Some basic problems of the mathematical theory of elasticity, P. Noordhoff Ltd, Groningen, Holland, 1953) has been used widely to study curved crack behavior in an infinite, homogeneous and isotropic elastic material. However, for certain orientations and magnitudes of the remotely applied loads, portions of the crack will close. Since the analytical solution is incorrect once the crack walls come into contact, the displacement discontinuity method is combined with a complementarity algorithm to solve this problem. This study uses stress intensity factors (SIFs) and displacement discontinuities along the crack to define when the analytical solution is not applicable and to better understand the mechanism that causes partial closure under various loading conditions, including uniaxial tension and pure shear. Closure is mainly due to material from the concave side of the crack moving toward the outer crack surface. Solutions that allow interpenetration of the crack tips yield nonzero mode I SIFs, while crack tip closure under proper contact boundary conditions produce mode I SIFs that are identically zero. Partial closure of a circular arc crack will alter both mode I and II SIFs at the crack tips, regardless of the positioning or length of the closed

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