Building an unequal spacing fractal probability model for layered and jointed rock mass and numerical implementation

Abstract

As the joint spacing of layered and jointed rock masses has the characteristic of discontinuous distribution, building a network model reflecting the actual distribution of joint spacing will be the research basis for calculating and analyzing the mechanical behavior of layered and jointed rock masses. A tunnel under construction in Chongqing was chosen as the background for the engineering research. The joint spacing was measured on site by scanline examination to analyze the fractal distribution pattern of the joint spacing from the perspective of fractal geometry. This enabled us to derive the fractal dimension D, which is capable of reflecting the distribution of the spacing, and the fractal distribution probability density function. We performed a Monte Carlo random simulation employing MATLAB for programming. The joint spacing simulation data obtained in this way was used to construct a three-dimensional network model of the layered and joint rock masses through the use of distinct element code (3DEC) and the internal fish programming language. The research results showed that the joint spacing of layered and jointed rock masses had a better self-similar characteristic and that the theory of fractal geometry could be used to obtain a good description of the joint spacing distribution. It was also found that the fractal distribution of joint spacing contains more spacing distribution information than the negative exponential distribution, because it more closely resembled the actual distribution. The numerical model that was built based on the fractal distribution of the unequal spacing of the layered and jointed rock mass using the Monte Carlo method had optimal statistical similarity with the actual data; thus, it offered a practical method for building a numerical model of layered and jointed rock masses. These research findings laid the foundation for subsequent research on the extent to which joint spacing distribution affects the metamorphism of wall rock, as well as changes in the locations and distribution of plastic regions when excavating a tunnel in layered and jointed rock masses.