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Scaling of fracture connectivity in geological formations
Author(s) -
Berkowitz Brian,
Bour Olivier,
Davy Philippe,
Odling Noelle
Publication year - 2000
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1029/1999gl011241
Subject(s) - scaling , fracture (geology) , geology , fractal dimension , fractal , exponent , scale (ratio) , fault (geology) , joint (building) , power law , cusp (singularity) , statistical physics , geometry , seismology , geotechnical engineering , mathematics , physics , statistics , mathematical analysis , linguistics , philosophy , engineering , quantum mechanics , architectural engineering
A new method to quantify fracture network connectivity is developed and applied to analyze two classical examples of fault and joint networks in natural geological formations. The connectivity measure accounts for the scaling properties of fracture networks, which are controlled by the power law length distribution exponent a , the fractal dimension D and the fracture density. The connectivity behavior of fracture patterns depends on the scale of measurement, for a < D + 1, but is independent of scale for a > D + 1. Analysis of the San Andreas fault system shows that a < D +1 and that the connectivity threshold is reached only at a critical length scale. In contrast, for a typical sandstone joint pattern, a ≈ D + 1, which is on the cusp where the connectivity threshold is highly sensitive to the minimum fracture length in the system.