Discontinuities (joints, fractures, bedding planes, faults) are ubiquitous within rock masses. Understanding and characterizing the nature of the discontinuities is the fundamental requirement of rock engineering. With a few exceptions, the engineering properties of most rock masses are influenced by the nature of the structure as opposed to the intact rock. Discontinuities govern the mechanical and hydrological behavior of the rock mass.

During site investigations, drilling and logging of boreholes is one of the most commonly used methods of investigation, because of its relatively low cost, because of the large volume of data it provides, and because boreholes can be drilled to the exact location where the rock mass needs to be characterized. Nevertheless, drilling still incurs significant costs, and in order to maximize efficiency, it is highly desirable to maximize the information content and the reliability of the borehole data. For the purposes of this article, the optimal drilling direction is defined as the direction along which the maximum number of discontinuities is intersected. Because the probability of intersecting a given discontinuity is greatest with a borehole perpendicular to that discontinuity, it follows that for every orientation of discontinuity there exists an optimum drilling direction.

This article proposes a method that can find the optimum drilling direction based on the analysis of linear sampling bias, assuming that there is some a priori knowledge of the structure. This is quantified by a linear sampling bias index (LSBI), which is a function of the relative angle between the orientation of the borehole and the mean orientation of the normals of each of the discontinuity sets. The optimum drilling direction is the direction along which the LSBI is minimized.

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