Estimation of a joint diameter distribution by an implicit scheme and interpolation technique

A new technique to estimate the diameter distribution of a joint set from the contained trace length distribution is suggested. This technique obtains the diameter distribution directly from the sample histogram of the contained trace lengths without using any information about the trace length distribution of an infinite window. Compared with the previous method of Song and Lee [Estimation of joint length distribution using window sampling. Int J Rock Mech Mining Sci 2001; 38: 519–28], it is more accurate for small-size joint samples. To obtain more accurate estimates, we adopt an interpolation technique of B-spline to smooth out the sampled contained trace length distribution. The effect of the B-spline as a function of three kinds of predefined diameter distributions is examined by Monte Carlo simulations.