Fracture size estimation using data from multiple boreholes

• The intersection type between the fracture and the borehole are used to estimate the mean and standard deviation of fracture size.
• We proposed a method to infer the probability density function of the fracture size from sampling on borehole matrix.
• The performance of the proposed formulae and the method was verified by Monte Carlo simulations.

The size of a fracture within a rock mass can be obtained using data sampled from boreholes or exposed surfaces. In this study, fracture sizes are estimated using data from multiple boreholes. The fractures are assumed to be elliptical, all having the same aspect ratio, but not necessarily occurring parallel to each other. Formulae for estimating the mean and standard deviation of the characteristic fracture size are developed by considering the number of intersections between the fractures and the boreholes. A method is proposed to infer the probability density function of the fracture size from the number of fractures, which is obtained by random sampling of fractures in adjacent boreholes; the fracture distribution is assumed to follow the form of a fractal, exponential, or lognormal distribution. The performance of the method is validated using Monte Carlo simulations with different inputs of size distribution, fracture density, orientation, and mean fracture size.