Model of joint spacing distribution based on shadow compliance

Abstract

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" a, is mathematically defined. A good agreement is obtained between this model and several fracture populations. We obtained a -1 (a = 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, a = 1. On the other hand, we obtained a • 3 (a = 2.904 _+ 0.!56) 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, a = 3. Our model shows that in a given joint set, a 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. 2.The Model Physical ConsiderationsWe assume a one-dimensional case throughout. Let x be the distance from an existing fracture, and let q(x) dx be the probability that an additional fracture appears between x and x + dx. The form of q(x) will be dealt with later. We wish to obtain the fracture spacing distribution p (e) if q (x) is known, p(e) de being the probability that starting from a given fracture, no additional fracture occurred between x = 0 and x = 4877

Joint development and tectonic stress field evolution in the southeastern Mesozoic Ordos Basin, west part of North China

“…The joint spacing histograms may reveal important aspects of the fracturing process, such as the degree of joint set development and the influence of flaws on joint distribution (Huang and Angelier, 1989;Narr and Suppe, 1991;Rives et al, 1992;Fischer, 1994;Becker and Gross, 1996;Ruf et al, 1998;Rabinovitch and Bahat, 1999;Gillespie et al, 1999). The frequency distribution histogram of normalized joint spacing requires large quantities of data to yield meaningful results, in order to eliminate the influence of layer thickness (Narr and Suppe, 1991;Gross, 1993;Ruf et al, 1998).…”

The concept of joint saturation and its application

“…and Suppe, 1991; Rabinovitch and Bahat, 1999). Therefore, understanding the effect of stress shadows on the joint-spacing distribution is critical to interpreting joint-driving mechanisms.…”

Statistics of joint spacing in rock layers

“…Shadow : An important physical term related to joint spacing is the shadow zone (Rives et al . 1992; Rabinovitch & Bahat, 1999). The term shadow zone used in the literature describes a region around an existing joint in which no new joints can occur (e.g.…”

“…1992), generally also termed an opaque shadow zone. A non-opaque shadow zone would entail the possibility of additional joints appearing in this region but only under very stringent conditions (very high stresses, Rabinovitch & Bahat, 1999). Figure 2 depicts (schematically) two joint spacing distributions for an opaque and non-opaque shadow zone, respectively.…”