Cross-correlation between length and position in real fracture networks

Abstract

By analyzing local geometrical properties of a dense multiscale fracture pattern, we characterized statistically the correlations between length and position of a fracture. Apart from some resolution effects, we show that the mean distance between a fracture center and its nearest neighbor is correlated to its length l such as d ∼ l0.3. Likewise, the average area around each fracture center within which no other fracture portion is lying has an ellipsoidal shape whose factor of anisotropy is correlated to l. The long axis, along fracture strike, is correlated to l such as d ∼ l0.25-0.3. The short axis remains invariant, about equal to the equivalent distance in a random fractal. At small scale (i.e., less than 1 m which is bed thickness) the shield area is isotropic. In addition to refining of geometrical model of fracture networks, such observations place some constraints on the stress interactions that prevail during fracture growth.