Estimation of Fracture Size and Probability Density Function by Setting Scanlines in Rectangular Sampling Window

Abstract

Rock masses are very important materials in geotechnical engineering. In engineering rock mass, fracture is the relatively weak part of mechanical strength in rock mass and is the most important factor controlling the deformation, damage, and permeability of rock mass. Therefore, investigating fractures is very important for characterizing rock mass. This paper proposed a new approach by using uniformly equidistant orthogonal scanlines. Within the study context, the solution formula of fracture size is derived by establishing the space intersection model of arbitrary fracture and scanline, rectangular window, and a rectangular box with a rectangular window. Then, fractures were randomly generated in a certain size cube and compared with the traditional Kulatilake trace length integral evaluation method. The study results have shown that the proposed method is more reasonable and accurate. Then, this method was applied to an adit of Songta Hydropower Station. Finally, a new fracture diameter probability density estimation method was proposed, the fracture diameter of the normal distribution was verified, and the parameters of the probability density function obtained by the scanlines method were in agreement with the initial set parameters. In summary, the proposed scanlines method can well estimate the mean value of the fracture diameter and the probability density function of the fracture size.