Percolation in three-dimensional fracture networks for arbitrary size and shape distributions

J.-F. Thovert (1, 2, 3) , Valeri V. Mourzenko (1, 2, 3) , P. M Adler (4)

1 Département FTC - Département Fluides, Thermique et Combustion [Institut Pprime]
2 CH - Combustion hétérogène et milieu poreux [Institut Pprime]
3 PPrime [Poitiers] - Institut Pprime [UPR 3346]
4 METIS - Milieux Environnementaux, Transferts et Interactions dans les hydrosystèmes et les Sols

The percolation threshold of fracture networks is investigated by extensive direct numerical simulations. The fractures are randomly located and oriented in 3d space. A very wide range of regular, irregular and random fracture shapes is considered, in monodisperse or polydisperse networks containing fractures with different shapes and/or sizes. The results are rationalized in terms of a dimensionless density. A simple model involving a new shape factor is proposed, which accounts very efficiently for the influence of the fracture shape. It applies with very good accuracy in monodisperse or moderately polydisperse networks, and provides a good first estimation in other situations. A polydispersity index is shown to control the need for a correction, and the corrective term is modelled for the investigated size distributions.

Domaines: Milieux fluides et réactifs; Mécanique des fluides [physics.class-ph]

J.-F. Thovert, Valeri V. Mourzenko, P. M Adler. Percolation in three-dimensional fracture networks for arbitrary size and shape distributions. Physical Review E , 2017, 95 (4), ⟨10.1103/PhysRevE.95.042112⟩. ⟨hal-03106028v2⟩