摘要
分形特征与分形维数广泛应用于岩石裂隙网络的量化,及与工程参数的关系模型建立.然而,严格的分形维数的极限定义形式难以直接应用,工程应用中多用近似分形维数值代替,近似的结果在建立量化关系模型时会产生蝴蝶效应,在量化及预测过程中产生巨大偏差.本文回顾了分形研究一系列的发展过程,并基于最新的分形定义提出了一种新的分形维数计算方法.通过对于十个岩石裂隙网络分形维数的计算,证明该方法能够准确有效的计算出图形的复杂度,避免了以往计算分形维数所产生的问题.
Fractal features and fractal dimension are widely used in the quantification of rock fracture networks and the relationship model construction of engineering parameters.However,the strict limitation definition form of fractal dimension is difficult to be applied directly.In engineering applications,approximate fractal dimension values are often used as a substitute.The approximate results will produce a butterfly effect in the establishment of quantitative relationship model,and generate a huge deviation in the process of quantization and prediction.To solve these problems,this paper reviews a series of development processes of fractal research and proposes a new method for fractal dimension calculation based on the latest fractal definition.By calculating the fractal dimension of ten rock fracture networks,it is proved that this method can calculate the complexity of the graph accurately and effectively,and can avoid the problems caused by the previous fractal dimension calculation.
作者
隋丽丽
王鹤远
张基伟
张桂民
孙启冀
SUI Li-li;WANG He-yuan;ZHANG Ji-wei;ZHANG Gui-min;SUN Qi-ji(School of Science,North China Institute of Science and Technology,Langfang 065201,China;Shaft Construction Branch,Coal Science Research Institute,Beijing 100013,China;School of Mechanics and Civil Engineering,China University of Mining and Technology,Xuzhou 221116,China;School of Petroleum Engineering,Northeast Petroleum University,Daqing 163318,China)
出处
《数学的实践与认识》
2021年第4期109-116,共8页
Mathematics in Practice and Theory
基金
中央高校科研基础经费(3142018059,HKJYGH201817,3142020048)
国家自然基金(11702094,51804157,41877277)
煤炭工业协会科研项目(MTKY2017-310)
河北省科技厅科研项目(162776449)
天地科技股份有限公司科技创新创业资金专项项目(2018-TD-QN008)
黑龙江省自然科学基金(LH2019E017)。
关键词
分形维数
头尾分割
岩石裂隙网络
HT指数
fractal dimension
head/tail breaking
rock fracture networks
HT index
