结构面几何特性分形研究现状及实例分析

Current situation and case analysis of fractal research on geometric characteristics of structural surfaces

岩体稳定性的关键在于岩体的结构特征,而岩体结构特征受控于岩体结构面的几何特性,对岩体结构面几何特性的研究一直是岩土工程领域致力于解决的重难点问题之一。20世纪70年代,分形理论的创立为结构面几何特性分析提供了较好的数学工具,在岩体结构面几何特性研究中得到广泛应用,一些研究成果充分展示了分形理论在定量描述结构面几何特性方面的优越性,使得结构面几何特性研究逐步由定性描述转向定量分析。在总结探讨前人研究成果的基础上,以西南某大型水电站工程为实例,采用分形理论,类比不均匀Cantor集,对坝区左右岸建基岩体7组优势裂隙的迹长分布区间进行统计、分形研究,结果表明,该坝区建基岩体裂隙迹长的分布区间具有良好的分形特征,且迹长区间分布的分形维数可以很好地定量表征裂隙的空间发育特征。

The key to rock mass stability lies in the structural characteristics of the rock mass,and which are controlled by the geometric characteristics of the rock mass structural plane.Study on the geometric characteristics of rock mass structural plane has been one of the most important and difficult problems in geotechnical engineering.In the 1970 s,the establishment of fractal theory provided a good mathematical tool for the analysis of the geometric characteristics of structural planes,and it was widely used in the study of the geometric characteristics of rock mass structural planes.The research results fully demonstrate the superiority of fractal theory in quantitatively describing the geometric characteristics of structural surfaces,which makes the research on geometric characteristics of structural surfaces gradually shift from qualitative description to quantitative analysis.On the basis of summarizing and discussing the previous research results,this paper taking a large-scale hydropower station project in southwest China as an example,using fractal theory and analogy to the inhomogeneous Cantor set,the trace length distribution interval of seven groups of dominant fissures in the foundation rock mass on the left and right banks of the dam area was analyzed.Statistical and fractal research results show that the distribution interval of the fracture trace length of the foundation rock mass in the dam area has good fractal characteristics,and the fractal dimension of the distribution of the trace length interval can well quantitatively characterize the spatial development characteristics of the fractures.