Model of joint spacing distribution based on shadow compliance

Fracture spacing is analyzed with a special reference to the functional sha pe of a shadow, which allows some presence of joints in the proximity of ex isting ones. A new term, the "shadow compliance" alpha, is mathematically d efined. A good agreement is obtained between this model and several fractur e populations. We obtained alpha similar to 1 (alpha = 0.884 +/- 0.070) for a spacing distribution that occurred in layers that were connected to thei r neighbors with major differences in mechanical properties across the lith ologic boundaries. In this situation, different strains along the boundarie s influenced joint spacing according to the Cox-Hobbs model. Their theory a sserts that stress release behaves as a first power of distance, implying, in our theory, alpha = 1. On the other hand, we obtained alpha approximate to 3 (alpha = 2.904 +/- 0.156) for a spacing distribution where fracture oc curred in layers of uniform elastic properties, which were disconnected fro m their neighboring ones by fractures, so that the stress reduction was not dependent on material properties along the boundaries. In this case the Po llard and Segall model was the appropriate one for analyzing joint spacing. Their theory asserts that stress release behaves as a third power of dista nce, which indeed implies, for our theory, alpha = 3. Our model shows that in a given joint set, alpha is not sensitive to variations in strains that were caused by a "normal mechanism." However, a mechanism of very intense j ointing can drastically change alpha either to an unrealistic range or to a state of being indefinable.