Model of joint spacing distribution based on shadow compliance

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10 Scopus citations


Fracture spacing is analyzed with a special reference to the functional shape of a shadow, which allows some presence of joints in the proximity of existing ones. A new term, the "shadow compliance" α, is mathematically defined. A good agreement is obtained between this model and several fracture populations. We obtained α ∼ 1 (α = 0.884 ± 0.070) for a spacing distribution that occurred in layers that were connected to their neighbors with major differences in mechanical properties across the lithologic boundaries. In this situation, different strains along the boundaries influenced joint spacing according to the Cox-Hobbs model. Their theory asserts that stress release behaves as a first power of distance, implying, in our theory, α = 1. On the other hand, we obtained α ≈ 3 (α = 2.904 ± 0.156) for a spacing distribution where fracture occurred in layers of uniform elastic properties, which were disconnected from their neighboring ones by fractures, so that the stress reduction was not dependent on material properties along the boundaries. In this case the Pollard and Segall model was the appropriate one for analyzing joint spacing. Their theory asserts that stress release behaves as a third power of distance, which indeed implies, for our theory, α = 3. Our model shows that in a given joint set, α is not sensitive to variations in strains that were caused by a "normal mechanism." However, a mechanism of very intense jointing can drastically change a either to an unrealistic range or to a state of being indefinable.

Original languageEnglish
Article number98JB02732
Pages (from-to)4877-4886
Number of pages10
JournalJournal of Geophysical Research: Solid Earth
Issue numberB3
StatePublished - 10 Mar 1999

ASJC Scopus subject areas

  • Geophysics
  • Geochemistry and Petrology
  • Earth and Planetary Sciences (miscellaneous)
  • Space and Planetary Science


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