Robust estimation of fracture trace length distributions derived from underground mapping and long narrow sampling windows

Abstract

Determining the fracture trace length distribution for a rock mass is an essential and difficult step in statistical fracture modeling. This requires the collection of representative mapping data, which for many large hydropower projects includes mapping in underground exploration tunnels resulting in long and narrow sampling windows. This limits the quality of the data collected using the long narrow sampling windows, and the traditional method for estimating true trace length distribution is challenged, especially for small samples. This paper presents a modified analysis framework for determining trace length distributions for long, narrow sampling windows. The proposed framework does not require the pre-selection of a distribution function and is independent of the sampled histogram. Instead, the distribution form is identified using L-moment ratio diagrams, and the corresponding distribution parameters are estimated using the L-moments. Two graphical tools and the average weighted orthogonal distance are introduced to assist in distribution selection on the L-moment ratio diagram. The multi-scanline method used to estimate the mean trace length is improved to make it applicable to curved tunnels (i.e., curved sampling surfaces). In addition, the proposed framework emphasizes the use of contained trace lengths to replace commonly used observed trace lengths for distribution inference and parameter estimation. Specifically, we assume that the true trace lengths have the same distribution form and coefficient of variation as the contained trace lengths. Guidance and recommendations are provided on the fracture sampling strategy. Validation of the proposed framework is performed by applying it to a synthetic data set with known characteristics. The application of the framework is demonstrated for a practical engineering case using mapping data collected from a hydropower project. The results show that the proposed framework is reliable and robust.