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本文应用康托集理论对美国纽约州西部阿巴拉契亚平原地区27个野外点上发育的天然裂缝的空间分布特征进行了研究。主要新发现如下:①天然裂缝间距具有多分维的特点。在相对小尺度范围内,平均分维数为0.15,反映出裂缝在小尺度上的不规则性和丛集性;在相对大尺度范围内,平均分维数为0.52,表明裂缝在大尺度上倾向于规则性和均匀性;②分维数随裂缝优势方向的变化而发生变化,这一现象可解释为是先存裂缝与后期裂缝相互作用的结果,也可解释为裂缝形成时由应力强度不同所致;③本项研究提出的裂缝多分维分析方法可有效地开展构造复杂区(尤其是对野外观察不到多期裂缝交
In this paper, the spatial distribution characteristics of natural fractures developed in 27 wild spots in the Appalachian Plains in the western part of New York State were studied using Cantor set theory. The main new findings are as follows: ① The natural fracture spacing has the characteristics of multi-fractal dimension. In the relatively small scale, the average fractal dimension is 0.15, which reflects the irregularity and clustering of fractures on a small scale. In the relatively large scale, the average fractal dimension is 0.52, indicating that the fractures tend to be large-scale Regularity and evenness; (2) The fractal dimension changes with the direction of the fracture predominance, which can be interpreted as the result of the interaction between the pre-existing fracture and the post-fracture, and also the result of the different stress intensity ; ③ The fractal multifractal analysis method proposed in this study can effectively carry out the complicated structure area (especially the multi-period crack observation in the field can not be observed