Influence of Sampling Window Geometry on the Variation of Fracture Trace Density

Abstract

ABSTRACT Sampling windows are essential tools for characterizing fracture distribution from rock exposures, yet few studies have focused on their geometry and how it affects the obtained fracture trace information. In this study, we investigate the influence of window dimension and orientation on the variation of trace density, derived by the end-point estimator, using analytic and numerical approaches. We employ rectangular, square, and circular windows for sampling the trace density of fractures with various dip angles using Monte Carlo simulations. We find that, regardless of window shape, the variation of trace density decreases as window size increases. Additionally, for rectangular and square windows, fracture dip angle affects the variation of trace density, with more impact on smaller windows. The variation is also impacted by the fracture density and fracture size. Our results illustrate that window geometry and fracture characteristics should be considered when conducting window surveys to acquire fracture data with reduced variance. INTRODUCTION Fracture characterization is an essential prerequisite for the analysis of rock mass behavior in both mechanical and hydraulic aspects. To describe the fracture distribution characteristics, including fracture spacing, density, size and orientation, rock exposures are investigated through window surveys by installing sampling windows upon the rock exposure and collecting data within the window. Different sampling windows have been suggested for the purpose of acquiring various fracture data. In an early study by Kulatilake and Wu (1984), a rectangular window was used to estimate the mean number of trace midpoints per unit area. Later on, Zhang and Einstein (1998) introduced circular windows to estimate mean trace length without orientation bias, and Mauldon (1998) proposed another method for estimating mean trace length and density using convex windows. The proposed methods were applied to an outcrop in Yingxiu, China, and their results were compared (Wu et al., 2011). Song and Lee (2001) also applied rectangular and circular windows to estimate trace length distributions, and reported comparisons between the two types of windows.