Abstract
Trace intensity is defined as mean total trace length of discontinuities per unit area, which is an important geometric parameter to describe fracture networks. The probability of each trace appearing in the sampling surface is different since discontinuity orientation has a scatter and is probabilistically distributed, so this factor should be taken into account in trace intensity estimation. This paper presents an approach to estimate the two-dimensional trace intensity by considering unequal appearing probability for discontinuities sampled by rectangular windows. The estimation method requires the number of discontinuities intersecting the window, the appearing probability of discontinuities with both ends observed, one end observed, and both ends censored, and the mean trace length of discontinuities intersecting the window. The new estimator is validated by using discontinuity data from an outcrop in Wenchuan area in China. Similarly, circular windows are used along with Mauldon’s equation to calculate trace intensity using discontinuity trace data of the same outcrop as a contrast. Results indicate that the proposed new method based on rectangular windows shows close accuracy and less variability than that of the method based on circular windows due to the influence of finite sample size and the variability of location of the window and has advantage in application to sampling surfaces longer in one direction than in the other such as tunnel cross sections and curved sampling surfaces such as outcrops that show some curvature.
Highlights
Results indicate that the proposed new method based on rectangular windows shows close accuracy and less variability than that of the method based on circular windows due to the influence of finite sample size and the variability of location of the window and has advantage in application to sampling surfaces longer in one direction than in the other such as tunnel cross sections and curved sampling surfaces such as outcrops that show some curvature
Based on previous studies on mean trace length estimation [27, 28], this paper focuses on the areal trace intensity estimation based on rectangular windows, which has advantage in application to sampling surfaces longer in one direction than in the other such as tunnel cross sections and curved sampling surfaces such as outcrops that show some curvature. e proposed new estimator is validated by using discontinuity data from an outcrop in Wenchuan area in China
Location 4 Location 5 Zero line (b) on rectangular windows. e coefficient of variation values depicted in Tables 1 and 2 indicates that the estimation results based on the proposed method show less variability than that of the method based on circular windows due to the variability of window location and size. e proposed method allows one to incorporate the relative frequency of each trace appearing on the exposure
Summary
A New Approach for Estimating Rock Discontinuity Trace Intensity Based on Rectangular Sampling Windows. Trace intensity is defined as mean total trace length of discontinuities per unit area, which is an important geometric parameter to describe fracture networks. Is paper presents an approach to estimate the two-dimensional trace intensity by considering unequal appearing probability for discontinuities sampled by rectangular windows. Trace intensity defined as mean total trace length of discontinuities per unit area, which is a pattern characteristic that incorporates both fracture density and mean length. Researches focus on volumetric intensity (discontinuity area per unit volume of rock mass). Zhang and Einstein [12] proposed an equation to calculate the mean fractures area per unit volume of the rock mass. No research has been done on estimation of trace intensity studied in this paper based on rectangular sampling windows
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