Estimating the intensity of rock discontinuities

This paper presents an approach for estimating the intensity of discontinuities and formulating intensity and orientation as a fracture tensor. Specifically the size distribution and the number of discontinuities are estimated first, from which the fracture tensor is then derived. Discontinuity size distribution is inferred from the trace data sampled in circular windows by using a general stereological relationship between the true trace length distribution and the discontinuity diameter distribution assuming circular shaped discontinuities. Because the measured trace lengths are biased, a method is proposed to estimate the true trace length distribution for circular window sampling. Circular window sampling has the advantage of automatically eliminating the orientation bias when estimating the true trace lengths. A method is then presented with which the total number of discontinuities in an objective volume can be estimated from the number of discontinuities observed in normal-size boreholes and using the inferred discontinuity diameter from the circular window sampling on the rock surface. With the derived size distribution and number of discontinuities, the intensity of discontinuities, which is the total surface area of discontinuities per unit volume, can then be calculated and included in a new definition of a fracture tensor. An application of the approach to analyze simulated discontinuities produces satisfactory results.