A three-dimensional fractal discrete fracture network (DFN) model for radon migration in fractured rocks is presented in this paper. In the model, the first-order model determines the location of fracture center and the distribution of fracture length, the von Mises-Fisher distribution is used for the fracture orientations, and the facture apertures are modeled by the aperture-length correlated method. The finite element method (FEM) is used to solve the partial differential equation of radon migration in the DFN. The model is further developed into computer software that can analyze the radon migration in fractured rocks. Radon migration in actual fractured rock at an outcrop site is predicted using the model.


Radon and its daughters are the second leading cause of lung cancer after smoking, which widely exists in fractured media such as rocks (Walsh et al., 2010; Papachristodoulou et al., 2007; Yoon et al., 2016). The study of radon migration in fractured media is of great significance to the prediction of natural disasters such as earthquakes, hurricanes and tornadoes (Minkin and Shapovalov, 2016). Some studies have found that radon can migrate and accumulate freely in micro pores, and a series of studies have been carried out on this characteristic (Rowberry et al., 2016; Ajayi et al., 2018; 2019; Holford et al., 1993). In recent years, by improving the combination of geological data and seepage model, the DFN model has been widely used in fracture seepage simulation in fractured media(Rogers and Nielson, 1991).

Fractures in rocks are so geometrically complex that it is practically impossible to obtain the true fracture structure(Mosley et al., 1997). But the geometric properties of fractures, such as fracture location, length, orientation and aperture, can be statistically distributed, and they have statistical self-similarity and fractal characteristics (Miao et al., 2015; Liu et al., 2015; Sornette et al., 1990a). In this study, a three-dimensional DFN model of radon migration in fractured rock mass is established, the radon migration equation is solved by FEM, and the model is developed into computer software which can analyze radon migration in fractured rock mass. The ability of the model to describe natural fractures is evaluated by natural fractures.

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