Model of joint spacing distribution based on shadow compliance

Abstract

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. Copyright 1999 by the American Geophysical Union.