USING RELATIVE POSITION DIRECT-LINK NODE POINT CLOUDS TO ANALYZE FRACTURE PATTERNS IN 2D

Fracture patterns display different types and degrees of organization of both orientation and spacing as influenced by stress fields, stress field evolution, layer thickness, temperatures, and material anisotropies. As an approximation, many fracture patterns in 2D can be characterized by fracture intersection (node) positions and linkages instead of by line segments. Scatter plots of the relative position of directly linked nodes for each node create point clouds, “node fingerprints”, that carry qualitative information about both fracture pattern orientation and spacing in the same plot. Heat maps of point cloud data density aid interpretation. A distinct cluster represents a preferred orientation with consistent spacing. As node spacing variance increases the clusters elongate into a ray or petal. Patterns with random linking orientations but even spacing create more concentric cloud shapes. Patterns also have different degrees of organization manifest as how concentrated or diffuse the cloud points are. Many pattern combinations exist, and plots from different fracture patterns appear visually distinct.

The degree of organization of the linking orientations and of the node spacings can be quantified by comparing an observed distribution against a random/uniform distribution in some manner. At present we are using Shannon (information) entropy values applied to discrete bins of observed values of linked node orientations and distances. Since results are a function of bin architecture, for comparison purposes we consistently use 18 bins. For the spacing distribution the bin structure and hence results are sensitive to selected range and to larger outliers. An overall Shannon entropy value for the point cloud can be computed, but looking at spacing and linking-orientation separately has utility given these two parameters are influenced by different factors. These plots and Shannon entropy values provide qualitative and quantitative spaces for comparing different fracture patterns, or the change of a fracture pattern within an area. Results from real world fracture patterns suggest that significant amounts of disorganization exist in many fracture patterns, especially in node spacing.