A class of fracture intensity measures in one, two, and three dimensions has been defined that allows for the definition of fracture frequency without requiring reference to specific sets or orientations. Measure P?2 (fracture area per unit volume) was found to be the most useful measure for fracture intensity in three dimensions. Relationships between intensity measures are described based on solutions from the field of stochastic geometry. The use of these measures significantly improves the consistency of discrete fracture analysis and modelling for mechanical and hydrologic applications.
Fracture patterns are described in terms of distributions for orientation, size, shape, spatial location, and intensity (Dershowitz and Einstein, 1988). Of these, intensity is one of the most important, but the least well characterized. Fracture intensity is generally noted in terms of fracture spacing St, the mean distance between fractures within a given set, as measured along a particular line such as' a borehole or scanline (Figure 1). This measure is relatively easy to determine the field, but is not useful for describing fractures in two or three dimensions. It is also dependent upon the subjective definition of fracture sets in the field. In three dimensional analysis, fracture intensity is generally defined as the number of fracture centers per unit volume, P,?. This measure is useful only where fractures are much smaller than the region being analyzed, such that fracture centers represent individual fractures, rather man fragments of fractures that may be within or outside the region. In addition, Pa? can only be related to fracture spacing St through the fracture size and orientation distributions.
The goal of this paper is to define a consistent set of fracture intensity measures in one, two, and three dimensions, together with the relationships between them.