Abstract The uncertainty analysis of fractures is always an important task in studying the structures of rock masses. Traditional univariate and bivariate statistical methods have limitations for considering the dependence among fracture parameters. For this purpose, a set of simulation and analysis approaches were developed for describing the geometric uncertainties of fractures based on Copula theory. In this regard, the main contributions of this research include: (1) the applicability and advantage of Copula theory in fitting and simulating fracture parameters were validated through modeling a set of orientation data and the relationship between the length and aperture of a set of traces; (2) the difficult problem of assigning apertures to the disk fractures of a discrete fracture network (DFN) was solved by linking aperture and fracture size using “pseudo-trace” and copula functions, and then by implicitly establishing the relationship between aperture, trace length, and fracture size; and finally an enhanced DFN modeling method, oblate ellipsoid method, was proposed. Technically, the former belongs to the fundamental usage of copula, and the latter is an improvement for the Baecher disk method through increasing the dimension of fractures from 2D to 3D and is believed to be a reference for solving further problems involving rock mass fractures, such as permeability related issues, geothermal reservoirs exploitation, coalbed methane extraction, and integrity analysis.

中文翻译：

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基于Copula的岩体裂缝模拟与分析方法

摘要 裂缝的不确定性分析一直是岩体结构研究中的一项重要任务。传统的单变量和双变量统计方法在考虑裂缝参数之间的相关性方面存在局限性。为此，开发了一套基于 Copula 理论的用于描述裂缝几何不确定性的模拟和分析方法。在这方面，本研究的主要贡献包括：（1）通过对一组定向数据和一组轨迹的长度和孔径之间的关系进行建模，验证了Copula理论在拟合和模拟裂缝参数方面的适用性和优势。 ; (2)通过使用“伪迹”和copula函数将孔径和裂缝尺寸联系起来，然后通过隐式建立孔径，迹之间的关系，解决了为离散裂缝网络（DFN）的盘状裂缝分配孔径的难题长度和骨折尺寸；最后提出了一种增强的DFN建模方法，扁椭球法。从技术上讲，前者属于copula的基本用法，后者是对Baecher圆盘法的改进，将裂缝维数从2D增加到3D，相信可以作为进一步解决岩体裂缝问题的参考，如作为渗透性相关问题、地热储层开发、煤层气提取和完整性分析。然后通过隐式建立孔径、迹线长度和裂缝尺寸之间的关系；最后提出了一种增强的DFN建模方法，扁椭球法。从技术上讲，前者属于copula的基本用法，后者是对Baecher圆盘法的改进，将裂缝维数从2D增加到3D，相信可以作为进一步解决岩体裂缝问题的参考，如作为渗透性相关问题、地热储层开发、煤层气提取和完整性分析。然后通过隐式建立孔径、迹线长度和裂缝尺寸之间的关系；最后提出了一种增强的DFN建模方法，扁椭球法。从技术上讲，前者属于copula的基本用法，后者是对Baecher圆盘法的改进，将裂缝维数从2D增加到3D，相信可以作为进一步解决岩体裂缝问题的参考，如作为渗透性相关问题、地热储层开发、煤层气提取和完整性分析。