Comparative study on interconnectivity between three-dimensional and two-dimensional discrete fracture networks: A perspective based on percolation theory

• Theoretical values of P 30 at percolation threshold of 3-D and 2-D DFNs are derived. • Relationship on interconnectivity between 3-D and 2-D DFNs is provided. • A method to obtain the percolation threshold based in PFC and Matlab is provided. Two-dimensional (2-D) discrete fracture networks (DFNs) are widely used to study the hydraulic properties of fractured rock masses. There are few studies on the reliability of 2-D DFNs reflecting the hydraulic properties of three-dimensional (3-D) rock masses. This study provides a new perspective based on percolation theory to study the interconnectivity between 3-D and 2-D DFNs quantitatively. For isotropic fractured rock masses, the corresponding value of the number of fractures in per sampled volume ( P 30 ) when 3-D DFNs achieve the percolation threshold is theoretically derived. Additionally, the corresponding value of P 30 of the original 3-D model when its 2-D DFNs on cutting planes achieve the percolation threshold is also derived for comparison. These theoretical formulas show that: (a) The corresponding values of P 30 at percolation threshold for both 3-D and 2-D DFNs are only related to the fracture diameter and inversely proportional to its third power; and (b) The corresponding value of P 30 when 2-D DFNs achieve the percolation threshold is 6.5 times of the corresponding value of P 30 when its original 3-D DFNs achieve the percolation threshold. Numerical codes and experiments based on Particle Flow Code and Matlab are developed to verify the derived theoretical equations, and the results show that the theoretical equations are validated.