13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- model concerning fault instability has been developing since the 1970s and numerous work has been done since then, e.g. refs. [1-6]. Thus studies may be beneficial for investigating the land strong earthquakes in China. Due to the dependence of the earthquakes with blocks, the complex system consisting of blocks and faults are studied. For this system a characteristic size is needed. For this purpose we consider the model shown in Fig.1. The configuration concerning a strike slip fault is only an example, if the applied shear stress in plane instead by a shear stress out of plane, then it represents an inverse fault. The boundary between blocks is a transitional region with thickness 2H, and the fault with length a, we takes a/H as a characteristic size of the complex system. The tip of the fault is often the earthquake source, it has some intra-structures, one among them is the so-called the slip weakening zone (or breakdown zone), which can be described by a size R, so that have another characteristic size R/H. Fig. 1. The cracked strip model on fault The tectonic shear stress acting at the external boundary of the body is removed, whereas the two faces of the fault are subjected to the stress over the length an extending back from the fault tip; the quantity may simulate a finite fault. The fact that tectonic stress acts at fault plan has been proved by quite a lot of geological and geophysical observations, which comes from the interaction between blocks. Because of the roughness of rock materials, there is the frictional stress at the fault plane, so that the total stress applied at the fault faces should be ( ). There is a breakdown zone with length R near the fault tip mentioned above, whose magnitude is unknown so far, whereas it will be determined in the successive analysis. At the break down zone another stress drop ( - ) acts as well, in which denoting the breakdown limit of the rock material, should be a material constant. The introduction of the breakdown zone is consistent with the slip-weakening model adopted in the above-mentioned references, or say, it is a concrete application of the slip-weakening model. Fig. 2 shows the model schematically. According to the terminology of the fracture theory, ( - ) is also named the cohesive stress.
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