Characterization and interpretation of rock mass joint patterns

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Abstract
New techniques for quantifying and analyzing the geometry of joint patterns are developed using conventional statistics, geostatistics, and printed circuit board analogs, and are applied to a test case in the Niagaran dolomites (Silurian) cropping out in the western flank of the Michigan Basin near Lannon, Wisconsin. Part I discusses the geometric biases inherent in traditional joint pattern studies, and illustrates how they can lead to inaccurate representations of the true joint pattern. New techniques utilizing scanline surveys and probability theory to eliminate these biases are presented. It is recommended that joints be measured along scanlines that cross one another at nearly perpendicular angles, and that the trace length, orientation, and point of intersection of every joint be recorded. The systematically introduced biases relating to trace length and the relative orientation between the joint and scanline may then be removed. The resultant unbiased orientational rosettes and stereograms are termed fundamental rosettes and fundamental stereograms, which more closely approximate the true geometry of the jointing. A means of estimating the Rock Quality Designation (RQD) from spacing histograms is proposed, as are formulas for estimating areal and volumetric joint densities from scanline or borehole measurements, and their validity verified through synthetic pattern studies. As a result, it is possible to estimate more accurately the true distributions of trace lengths and orientations, as well as the actual volumetric or areal joint density. The spatial variability of joint patterns and the extent to which their characteristics may be validly extrapolated into the surrounding rock mass is addressed through the statistics of regionalized variables, or geostatistics. The geostatistical theory required for the analysis of joint patterns is developed. Techniques for creating synthetic joint patterns based upon the characterization methods developed are presented, and illustrate (1) the validity of the equations and their attendant assumptions, (2) the interplay of fundamental geometric joint properties in forming the overall joint pattern, and (3) methods for achieving accurate characterization of joint pattern geometry. Moreover, these synthetic patterns reveal the ability of geostatistics to identify deterministic trends, such as the increase or decrease in joint density, periodicities, the “area-of-influence” of single pattern measurements, and to quantify the truly random component in the joint pattern. A new method for investigating the fluid flow properties of joint networks using printed circuit replicas of actual or synthetic joint patterns illustrates how the interaction of all the joints governs rock mass flow systems. In Part II, the techniques developed in the first section are applied to a study of jointing in Niagaran dolomites located on the western margin of the Michigan Basin near Lannon, Wisconsin. The data collection illustrates how to carry out a scanline survey in order to maximize the quality of the joint data and insure that all necessary parameters are sufficiently sampled. The measured spacing distributions are used to predict the RQD of the dolomite, and compare favorably with the measured RQD values, thereby validating the theoretical relation developed in Part I. The notion of an unbiased or fundamental rosette proposed in Part I is validated by the fact that a rosette predicted for one area of the grid based upon the jointing measured in another favorably compares with the actual rosette. Geostatistical analysis of fracture frequency, joint orientation and RQD demonstrates that (1) jointing geometry possesses systematic spatial correlation, which manifests itself in a characteristic “region-of-influence,” (2) optimal sampling schemes that are efficient and leave no portion of the rock mass under- or un-sampled can be constructed, (3) the spatial inhomogeneity properties for individual sets varies, and is likely an expression of mode and timing of formation of the different sets, and (4) that the periodicities in the semivariograms can reveal average block dimensions into which joints divide the rock mass, which is of particular advantage when rock exposure is limited. A printed circuit replica was created from photographs of jointing at Lannon. The resistance to electric current flow was measured for different directions across the joint array, and compared with predictions based upon the fracture frequency rosette and inferences drawn from regional groundwater flow patterns. The directions of principal hydraulic conductivity predicted from both the fracture frequency rosette and the printed circuit replica were consistent and align with the regional flow directions. The printed circuit analysis also points out the effects that joint terminations can have on creating strong hydraulic conductivity anisotropics. The results suggest that the direction of maximum fracture hydraulic conductivity will tend to be oriented perpendicular to the direction of the greatest fracture frequency.

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