An empirical approach to estimating population parameters from censored fracture-length distributions

Most fracture data sets are length-censored because of incomplete exposure at the surface, so estimating values of parameters of the sampled populations is difficult. Unless the form of the distribution function of the population is known, or one which is analytically tractable is assumed, length-censoring presents formidable problems in determining population parameters. Tests conducted on experimental fracture patterns developed in clay samples subjected to simple shear loading are the basis of a distribution-free way to estimate population parameters. Comparison of random samples of censored and uncensored fracture lengths shows that a useful, homogeneous data set consists of those cracks which lie entirely within the sampling area (two-ended cracks). The properties of this data set can be used to estimate the mean and variance of uncensored data. Estimates of the maximum fracture length of uncensored data, using the variance and maximum length of these two-ended cracks, show good agreement with measured values. Knowledge of the mean, variance, and maximum value of fracture-length populations are of interest in engineering and hydraulic studies, as well as in remote sensing studies of the Earth and other planets. Application of these results to data on rock masses are subject to the caveat that different crack-growth mechanisms in clay and rock may affect the accuracy of the calculations.