Estimating the mean trace length of rock discontinuities

Rock discontinuities appear as traces on exposures such as natural outcrops or tunnel walls. Discontinuity size which has important effects on rock mass behavior is related to trace length. This paper presents a technique for estimating mean trace length from the observations made on finite, circular sampling windows. The method takes sampling errors into account and it requires, like existing methods using rectangular sampling windows, that the numbers of discontinuities with both ends censored, with one end observed and one end censored, and with both ends observed be known. Knowledge of the lengths of the observed traces and the distribution of trace lengths is not required. A major advantage of the proposed method over the existing methods is that it does not need sampling data about the orientation of discontinuities, i.e. the proposed method is applicable to traces with arbitrary orientation distributions. To check the validity of the proposed method, theoretical relations between the mean trace length and the mean diameter of circular discontinuities, respectively for lognormal and negative exponential distributions of the diameter of discontinuities, are derived. The proposed method is then applied to analyze data simulated with the FracMan code, and the predicted results are compared to the corresponding theoretical solutions. The results show that the proposed method is satisfactory. Comparisons of the predicted mean trace length with the mean of observed trace lengths show that it is important to consider sampling biases when estimating mean trace length.