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Statistical Approaches |
1 Department of Geological Sciences, University of Tennessee, Knoxville, TN 37996-1410, USA wdunne{at}utk.edu
2 Department of Civil & Environmental Engineering, Virginia Tech, Blacksburg, VA 24061, USA
Mechanistic and probabilistic methods are individually used to characterize and predict joint networks. Combining these two approaches yields a method where the mechanical controls are honoured and implemented probabilistically in order to efficiently model joint development at the scale of the entire network with a useful ease of implementation. For this approach, bed-normal joints are characterized not with fracture trace geometries, but rather with intersection geometries to bedding. T-intersections represent joint termination at bedding, X-intersections represent joints crossing bedding and E-intersections are those intersections at the sample window edge. Using the intersection counts as input, a new computer program was developed that uses mechanically constrained probabilities to simulate and predict the spatial distribution of bed-normal joints in profiles across bedding. Initially, simulations are compared to ideal joint geometries for one or two lithologies with one or two bed thickness values, and found to match well. Simulations are then compared to joint geometries in four natural profiles from Llantwit Major, Wales, UK and Huntingdon, PA, USA. Simulations visually resemble the natural profiles and reasonably match the natural values of the joint network for density and mean joint height. We also extend the methodology to predicting joint networks beyond sample windows by investigating the minimum count of intersections needed to produce a representative result. Based on the five natural profiles with typical joint geometries, a sample size about 50–100 intersection counts is sufficient to produce a reasonable prediction of the expected count and, hence, the joint geometry in a rock volume.
