13th International Conference on Fracture June 16–21, 2013, Beijing, China -5- denote it by , i.e. (14) where is given by (11). At the end of the breakdown zone, i.e. at y=0, x=-R, the slip of the fault is (15) in which (16) E and v represent Young's modulus and Poisson's ratio of the rock material, respectively. The physical quantity (15) may be taken as a control parameter in checking the fault instability. According to the fracture theory, there is a critical value of denoted by , which should be a material constant, while (17) It can be considered as a criterion for judging the instability. By the criterion one can determine the critical shear stress of the initiation of fault growth. Inserting (11) into (15) and then into (17) yields (18) The initiation will occur as . At H/a →∞, it follows from (10) that (19) Which is identical with the well-known exact solution[12,13]. In this way, as H/a →0, it follows from (10) that (20) This is a completely new result. Ref. [6] shows that one can find a similar result by using J-integral, in which it contains an unknown constant which could not be determined by the method itself. According to formula (10) the constant= . Formulae (19) and (20) give an examination of the correctness of the above derivation.
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