This paper presents a methodology to predict the fracture intensity and to measure the uncertainty associated with it, which could be expressed in terms of variance or probability intervals conditioned to the information of the fractures observed on boreholes. The methodology relies on the assumption that the fracture centers are distributed according to a Poisson process and is applicable in case of lineic data (scanline) as well as cylindrical well data. The principle is to produce a set of realizations of a Poisson-Boolean model that honors the available data (conditional simulation) and to assess the fracture intensity on each realization. The conditioning to observed fractures can be made for the Poisson-Boolean model because the fractures and their locations are independent of each other, which agrees with many models that have been considered in recent researches. The numerical values obtained through the realizations can be combined to predict the fracture intensity and to measure the uncertainty in the actual values.
A comprehensive understanding of fracture systems is critical to the economic development of underground mining, open pit mining, tailing dam, oil and gas reservoirs, geothermal reservoirs, groundwater resources and underground nuclear wastes disposal. As a rock mass property, fractures must be characterized in the three-dimensional space, whereas observations are limited to 1D (boreholes) and 2D (outcrops, drift walls), moreover very often to rather short stations, so that the available data are subject to geometric, truncation and censoring biases. Fracture characteristics include the number of fracture sets and, for each set, the number, orientation, spacing, location, shape and size of the fractures must be inferred from data sampling. Some important parameters that are considered nearly in all models are the fracture intensity and fracture size.
Many authors have shown how to estimate the fracture size distribution from outcrops, drifts and tunnel walls (Baecher, 1980; Laslett, 1982, Lantuéjoul et al., 2005) and microseismic data (Tafti et al., 2011, 2012; Aminzadeh et al., 2013). In this study, we will focus on the fracture intensity, which is defined as the mean area of fractures per unit volume of rock masses and denoted as P32 (Dershowitz and Herda, 1992; Chilès and de Marsily, 1993). Fracture intensity is one of the preferred ways for describing the fracturing of a rock mass as, unlike other intensity descriptors, it is non-directional and gives an indication of the amount of fracturing of a rock mass. However, its value is derived from directionally biased methods, so, while it is a good indicator of overall fracturing, its estimation still depends on being able to compensate for known biases.