Research On Quantification And Application Of Rock Fracture Network Based On Fractal Geometry

Fractal characteristics and fractal dimension are widely used in the quantification of rock fracture network and the establishment of relationship model with engineering parameters.However,the strict limit definition of fractal dimension is difficult to be directly applied.In engineering applications,approximate fractal dimension values are often used instead.The approximate results will produce butterfly effect in the establishment of quantitative relationship model,resulting in huge deviation in the process of quantification and prediction.Therefore,in order to solve the problems of fractal dimension inaccuracy in engineering application,find a suitable fractal dimension calculation method,and establish an efficient and accurate fractal dimension calculation model of rock fracture network,this paper analyzes the rock fracture network and fractal related theory,explores the fractal characteristics of rock fracture network,and combines the spatial syntax metric with rock fracture network to establish a fractal dimension calculation model The main work of this paper is as follows(1)In this paper,the rock fracture network is described in detail,and the origin and development of fractal and three fractal definitions since the birth of fractal geometry are introduced.Fractal dimension is the core content of fractal geometry.This paper also introduces the mathematical basis of fractal dimension and the calculation model of fractal dimension based on the definition of fractal.According to the analysis of the current commonly used fractal dimension calculation model,we know the cause of the inaccuracy of fractal dimension calculation in the current engineering application.In addition,combined with the latest fractal definition,we put forward a new fractal dimension calculation model to solve the problem of inaccuracy in previous fractal dimension calculation.(2)Based on the self-similarity and heavy tailed distribution of fractal,we propose a new method to calculate fractal dimension,and improve it according to the practical application.The advantages of the new method are as follows: the calculation process does not take the limit operation,which is more stable than the previous fractal dimension calculation method;because it combines HT index and fractal dimension,the new method can better and more effectively capture the fractal characteristics of the fractal set.Ten rock fracture network diagrams are analyzed and discussed.The rock fracture diagram with fracture number less than 100 does not meet the new fractal definition,so it cannot be calculated by this method.For the remaining rock fractures,the calculation results are the same as the complexity of rock fractures,which verifies the effectiveness and accuracy of the new method.(3)Based on the self-similarity,heavy tailed distribution,scale-free and other characteristics of urban street network and rock fracture network,we find that the spatial syntax metric in urban street network can be well applied in rock fracture network;and taking the rock fracture in rock fracture network as the axis will not lead to disputes about the definition of the axis,and can better represent the rock fracture the space of network.Using the head and tail segmentation method to calculate the metric of seven spatial sentences,it is found that only the connection value and the control value meet the requirements of fractal.Compared with the length fractal dimension,the length fractal dimension has the same trend with the control value fractal dimension,but the connection value fractal dimension has the opposite trend.Compared with using the length fractal dimension as the parameter,using the connection value and the control value as the parameter to calculate the fractal dimension can better reflect the spatiality of the rock fracture network,which also verifies the applicability of the spatial syntax metric in the rock fracture network.This paper includes 22 figures,3 tables and 103 references.