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On the connectivity of three‐dimensional fault networks
Author(s) -
Bour Olivier,
Davy Philippe
Publication year - 1998
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/98wr01861
Subject(s) - scaling , percolation (cognitive psychology) , power law , fault (geology) , exponent , statistical physics , percolation theory , range (aeronautics) , percolation threshold , complex network , mathematics , geometry , physics , topology (electrical circuits) , geology , engineering , statistics , combinatorics , aerospace engineering , linguistics , philosophy , quantum mechanics , neuroscience , seismology , electrical resistivity and conductivity , biology
Natural fault networks involve a very broad range of fault lengths, modeled in general by a power law length distribution, n (l ) ∼ α l − a . Such a scaling law does not allow to define any a priori pertinent scale of observation for hydraulic field experiments in fractured media. To investigate the relative effects of faults depending on their length, we undertake in the spirit of percolation theory a theoretical and numerical study of the connectivity of three‐dimensional fault networks following power law length distributions. We first establish the correct analytical expression of a percolation parameter p , which describes the connectivity of the system. The parameter p is found to be dependent on the third moment of the length distribution for fault planes. It allows us to identify different regimes of connectivity depending on a , the exponent of the fault length distribution. The geometrical properties of the infinite cluster, which partly control transport properties, are also established at the percolation threshold. For natural fault networks, our theoretical analysis suggests that faults larger than a critical length scale may form a well‐connected network, while smaller faults may be not connected on average. This result, which implies an increase of the connectivity with scale, is consistent with scaling effects observed on permeability measurements.