Estimation of joint length distribution using window sampling

Abstract

One of the most difficult procedures in statistical joint modeling is the determination of the joint length distribution. In this study, a window sampling method was adopted to estimate the trace length distribution for the Poisson disc joint model. Four kinds of equations were derived for estimating the trace length distribution from contained or dissecting trace length distributions in a rectangular or circular window. The equations were tested for accuracy through Monte Carlo simulation and their efficiencies for estimating the trace length distribution were compared. This new technique using window sampling was compared with the method using a semi-trace or complete trace length distribution from scanline sampling. A numerical technique for determining the diameter distribution from the trace length distribution was also suggested. To check the validity of this numerical method, it was applied to solving four example cases and their results were compared with theoretical solutions.