This paper presents an analytical model for quantifying the uncertainty of three-dimensional fracture intensity measurements (P32), which measure fracture area per sampling volume, and for determining the geometrical representative elementary volume (REV) of fractured rock. The analytical model for estimating the variance of P32 is derived from the probability of a given number of fractures in a sample of rock. This model is validated through numerical simulations of fractured rock masses based on the discrete fracture network method. A series of parametric studies are conducted considering the dip angle, dip direction, Fisher constant, size and shape of the rock mass space, specimen volume, fracture diameter, and P32. Based on the results of the analytical model and the parametric studies, a simple model to quantify the coefficient of variation (COV) of P32 is established, which requires only the data of specimen volume, fracture diameter, and P32. Four engineering applications of the proposed analytical model are presented, including two case studies of estimating the geometrical REV at a given COV, one of assessing the variation of mechanical properties, and another of determining the variation of permeability.
|期刊||Bulletin of Engineering Geology and the Environment|
|出版狀態||已出版 - 1月 2022|