Copula-based simulating and analyzing methods of rock mass fractures

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.