Improved optimization and visualization of drilling directions for rock mass discontinuity characterization

The LSAD approach described in this note provides a method to optimize drilling directions for geotechnical exploration programs in cases where there is a priori knowledge of discontinuity orientations. By using a measure of angular dispersion that simultaneously considers both dip and dip direction, that does not become asymptotic or non-numerical, and that is quantified using geometrically sensible units, the LSAD method builds upon and increases the utility of concepts developed by such authors as Zhou and Maerz (2002). Contouring LSAD values, either in Cartesian coordinates or on a lower hemisphere projection, further allows optimal drilling directions corresponding to LSAD minima to be easily visualized and exploited when planning geotechnical exploration programs. If more than one LSAD minimum exists, drilling in any of the directions defined by the minima should yield statistically similar results. Thus, the choice of drilling direction among multiple minima can be dictated by secondary constraints, such as drilling rig accessibility or site topography. The use of contour plots also helps to identify secondarily favorable orientations in the event that project details prevent drilling in directions defined by the minima. Just as importantly, the contour plots can help to identify unfavorable directions that should be avoided. For example, Figures 7 and 8 show that in the case of a two vertical and one horizontal discontinuity set, a vertical borehole - which is the default orientation for most geotechnical exploration programs - would be the worst possible choice. In the case of a one horizontal and one vertical set, Figures 5 and 6 show that a vertical borehole would be far from optimal but would not be the worst choice (the worst choice would be a horizontal borehole parallel to both of the discontinuity sets, which would intersect neither set). In other cases, particularly when all of the discontinuities have dip angles of <45° or so, as in Figures 9 and 10, vertical boreholes may be an optimal solution. Finally, it must also be remembered that if more than one set of discontinuities exists, optimization relative to all of the sets is always a form of compromise. In some situations it may be prudent to avoid compromises and plan the drilling program with a variety of orientations, each optimized to the orientation of a single discontinuity set.