13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- Fig.2 Breakdown zone and the stress distribution in the neighborhood of the fault tip Reference [6] used this model, but the analysis there is preliminary only for the static case. The present analysis develops the study of Ref [6] in a quite wide range, i.e. it not only studies the static problem, but also the dynamic problem. 2.1 Fault extension initiation The initiation of fault extension is a static problem. Assume that the fault body is anisotropic homogeneous elastic body. We define Airy stress function as U(x, y) , and then the strike slip process of the fault is governed by equation (1) where denotes the two-dimensional Laplace operator, and the stress component, , can be written as ! xx = !2 U !2 y 2 ! yy = !2 U !2 x 2 ! xy = !2 U !2 xy (2) The problem of inverse fault is governed by (3) The problem of the fault extension initiation induced by stress drop ( - ) (the tectonic stress) is described by the following boundary condition: (4) The most effective tool for solving boundary value problem (1), (4) is complex analysis, i.e., take the solution (5) where ! 1 (z) and ! 1 (z)represents any analytic functions of complex variable . The author suggested a conformal mapping approach to solve the boundary value problem (4) of eq. (1),
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