Abstract
A discrete fracture network (DFN) model based on non-parametric kernel density estimators (KDE) and directional-linear statistics is developed. The model provides a characterization of the fracture network with distributions of fracture orientation and size jointly. A solution to the Bertrand paradox is used for the calculation of disk sizes from trace lengths, the latter calculated from the intersection of disks and highwall faces by triangulation. A Poisson point process is applied for the generation of the model, with fractures assumed to be flat and circular in shape, the number of fractures per unit volume (P 30 ) adjusted to match the experimental length of fractures per unit area (P 21 ). Length censoring of traces due to the surface dimension is considered in the calculations by including semi-bounded traces, i.e., traces censored in one of their ends. Orientation and size biases are corrected with a weighting function in the random sampling. The truncation effect whereby no traces shorter than some cut-off length are recorded, is addressed by a randomized optimization algorithm. The joint fracture orientation-size distribution model developed is tested with trace maps of discontinuities measured from photogrammetric models of twelve highwall faces of quarry benches, with outstanding results. Computational advantages over traditional parametric fracture models are addressed.