1 INTRODUCTION

ABSTRACT

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Spatially characterizing the surface area density of fractures (Sv) in a discontinuous rock mass can provide important input for assessing stability of rock excavations, for evaluating potential rock support programs, and for describing hydrogeologic conditions. Stereological sampling and analysis of fractures based on borehole video imaging (or on measurements of drill core, if available) provide values of Sv (in m2/m3) at accessible sampling sites in a given study area. Preliminary investigations suggest that Sv is related to traditional parameters, such as RQD and fracture density. Geostatistical spatial simulations can be used to generate stochastic images of realistic Sv values throughout the rock mass of interest, providing three-dimensional information about rock mass quality. An example analysis and simulation study based on two fracture classes (flat and steep dips) is presented to illustrate the methods and their results.

Measuring, predicting, and characterizing the nature of discontinuities in a rock mass are critical to the prudent engineering design of rock excavations. Also, such information provides important input for evaluating and modeling hydrogeologic conditions in rock masses. In this context, the term [discontinuity refers to any semi-planar surface of weakness in a rock mass, including such features as fractures (i.e., joints and faults), foliations, and bedding surfaces. Geotechnical descriptions of discontinuities generally focus on orientation, frequency of occurrence, and surface conditions (i.e., filling and roughness). Traditional geotechnical fracture frequency descriptors (RQD, fracture density, discontinuity spacing, core piece size or length) often rely on one- dimensional sampling via drill holes or outcrop scans. Extending these measures to three-dimensional interpretations can be quite subjective and often relies heavily on a thorough understanding of local geologic conditions. Recent work in the area of applying stereological studies to discontinuous rock masses has indicated promising results for three-dimensional predictions of fracture frequency (Owens & others 1994). The stereological measure of primary interest is the surface area density (Sv), which defines the total surface area of particular semi-planar features (i.e., features of a given class) per unit volume of rock mass. Once Sv has been been evaluated at various sampling locations in the rock mass of interest, then geostatistical simulations can be used to describe the spatial pattern of Sv throughout the entire rock mass under study.

2 STEREOLOGICAL ANALYSIS

Stereology is a body of mathematical theory and practice that allows for simple measurements along test probes (or on planar sections) to be related to three-dimensional geometric properties of the body being sampled. The origins of Stereology can be traced to petrological studies presented by the French geologist, Delesse, in the mid-1800s (Delesse 1848). In the past several decades, major stereological advances have occurred in the fields of biology and materials science (DeHoff & Rhines 1968; Under- wood 1970; Weibel 1979-80; Russ 1986). More recently, stereological methods have been shown useful for describing rock mass discontinuities (Kanatani 1985; Owens & others 1994). Occurrences of clean, two-dimensional planar sections cutting through a rock mass are rare in practice, so stereological measurements often focus on drill-hole data.

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