基于分形几何理论的DFN模型构建方法研究

以重庆梁-忠（梁平县-忠县）高速公路礼让隧道为工程研究背景，通过测线法调查现场节理，获得了节理产状分布概率密度函数，并从分形几何学的角度分析了节理间距及迹长的分形分布规律，推导出能反映节理间距及迹长分布状态的分形维数D及分形分布概率密度函数。在该基础上采用Matlab软件以及Monte-Carlo随机分析方法，产生节理参数随机数，结合3DEC中最新模块离散裂隙网络(DFN)技术，建立了能反映节理裂隙分布特征的离散裂隙网络模型并验证了模型的有效性，结果表明，分形分布比负指数分布包含更多的间距、迹长分布信息，更接近于实际分布；分形维数D反映了节理间距、迹长在其变化范围内的分布特征，分形维数的大小取决于小间距、小迹长部分数量在总节理数量中的比例，为节理裂隙岩体网络模型构建提供了一种新方法。

Construction method research on DFN model based on fractal geometry theory

Taking Lirang tunnel of Liang-Zhong Expressway in Chongqing city as an engineering background，based on the field joint investigation by scan line，the distribution density function of joint production is obtained; and the fractal distribution law of joint spacing and trace length is analyzed from the viewpoint of fractal geometry. In addition，the fractal dimension D from the distribution of joint spacing and trace length and fractal distribution probability density function can be derived. Based on these work，Monte Carlo stochastic simulation theory and Matlab software are adopted to obtain simulated joints data. Finally, a discrete fracture network(DFN) model which could reflect the distribution characteristics of the joints is established. The results of the study show that：the fractal distribution contain more information about the joint spacing and the trace length distribution than other distributions; and it is more close to the actual distribution. Fractal dimension D reflected the distribution of joint spacing and trace length in its variation range，and the fractal dimension D is determined depending on the ratio of the number of small spacing，the number of small trace length to the total number of joints. This study results provides a new method for the construction of the network model of jointed rock mass.