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断裂最大位移与断裂迹长遵循幂律关系 :D =cLn,但幂指数n的大小有很大的变化范围。为探索幂指数n的大小和断裂机制 ,从已发表的文献中收集了 18组数据 ,这些数据的断裂长度具有 8个数量级的跨度。经相关分析 ,我们得到n值的大小变化于 0 5 5和 1 6 5之间 ,平均值为 1 0 839。由于走滑断裂的最大长度在其倾向方向 ,不宜与倾滑断裂一起统计 ,我们去掉一组走向滑动断裂的数据 ,幂指数平均值为 1 10 6 6。用双回归方法得到的幂指数峰值 (nd)是 1 0～ 1 1。这些结果表明断裂最大位移与断裂迹长应该是非常接近线性关系。这种线性关系可以用Dugdale模型加以解释。该模型认为弹塑性物质拉张裂缝端点的变形是非弹性变形。模型的适用范围是单一岩性 ,一次构造力作用。我们认为n值的大小之所以有很大的变化范围 ,有可能受到断裂迹线长度偏差的影响 ,造成长度偏差的因素包括 :不同的观察平面 ,断裂端点的分辨率 ,断裂连接作用 ,岩石力学性质变化 ,断裂多期活动等。
The maximum displacement and fracture trace follow the power law: D = cLn, but the size of the power index n has a wide variation range. To explore the magnitude and fracture mechanism of the power index n, 18 sets of data have been collected from published literature, the fracture length of these data having a span of 8 orders of magnitude. After correlation analysis, we found that the value of n changes in size between 0 5 5 and 1 6 5 with an average of 1 0 839. Since the maximum length of strike-slip faults in their dip direction should not be combined with dip-slip faults, we removed a set of data for strike-slip faults with an average power index of 1 106.66. The exponential peak (nd) obtained by the double regression method is 10 ~ 11. These results show that the maximum fracture displacement and fracture trace should be very close to the linear relationship. This linear relationship can be explained by the Dugdale model. The model considers the deformation of the elastic-plastic material at the end of the tension crack as inelastic deformation. The scope of the model is a single lithology, a tectonic force. We think that the reason why the value of n has a large variation range may be affected by the variation of the length of the fracture trace. The factors that cause the length variation include: different observation planes, resolution of fracture endpoint, fracture connection, rock mechanics Changes in nature, fracture and more activities.