Fracture spacing is commonly assumed to follow a Poisson distribution in discrete fracture network (DFN) studies. As a result, non-Poisson distributions used to describe fracture clustering are rarely considered in generating synthetic DFNs. Field observations and numerical simulations of fracture propagation, however, suggest that fractures often exhibit spatial correlation due to geomechanical interactions. This study investigates the effect of spatial clustering on solute transport. Synthetic DFNs with constant transmissivity applied to all fractures are generated for three clustering (Dc=1.6, Dc=1.8, and Dc=2.0) scenarios. For each scenario, 50 statistically equivalent networks are generated, and advective particle trajectories of a non-reactive solute are simulated. Comparison of the different scenarios indicate increases in median particle breakthrough times by 43-77% as clustering increases from Dc=2.0 (Poissonian) to Dc=1.6 (highly clustered). It is also observed that, as clustering increases, breakthrough curves within each scenario become highly variable; this effect is more pronounced for the late time arrivals and indicates that spatial clustering may significantly affect solute retention. These results suggest that realistic distributions of spatial clustering need to be considered in DFN studies to honor the degree of network complexity and flow path tortuosity observed in natural networks.
The spatial distribution of fractures is crucial in generating discrete fracture networks (DFNs). Most DFN studies assume that fracture spacing follows a Poisson distribution, which implies that the initiation of new fractures is independent of preexisting fractures (Baecher and Lanney, 1978; Dershowitz et al., 1991). The Poissonian distribution of fractures stems from previous studies where fracture spacing was measured along scanlines (Snow, 1968; Call et al., 1976; Priest and Hudson, 1976; Einstein et al., 1980; La Pointe and Hudson, 1985). In most of these studies, a negative exponential distribution (Poisson distribution) provided the best fit to fracture spacing data, and as a result fractures location are often modelled as a Poisson point process. Numerical simulations of fracture propagation also suggest that a Poisson distribution may occur in early stages of fracture development, because of the low fracture density (Rives et al., 1992). The above-mentioned studies were mostly concerned with the spacing distribution in 1D. Observations of 2D fracture networks suggest that the spatial organization of fracture is rarely Poissonian, and that fractures exhibit complex spatial correlation or clustering (Gillespie et al., 1993, 2001; Ackermann and Schlische, 1997; Odling et al., 1999; Belayneh et al., 2009; Yamaji and Sato, 2011; Reeves et al., 2014; Sanderson and Peacock, 2019). The Poisson distribution also implies that natural rock masses are homogeneous and isotropic, and does not consider the mechanical interactions between fractures.
