Geostatistics can be used to make local estimates of spatially correlated rock mass properties. Local estimates, used as design inputs, allow a geotechnical design to make local adjustments to locally varying rock mass conditions. The use of geostatistics for local estimation of design inputs is illustrated using rock joint orientation data for slope stability analysis of a surface mine. The local inputs suggest local designs which are significantly different from the design made using site-wide averages composited from all sampled locations within the mine.
Geotechnical design requires characterization of rock mass mechanical properties. Rock mass properties are rarely uniform throughout the portion of a rock mass in which large geotechnical structures are often built. However, large structures are often designed using inputs which are averages of sample taken from throughout the rock mass. Using site-wide, or global, averages as design inputs does not allow the design to take into account localized deviations of rock mass properties from average conditions. Thus, a particular design based on global inputs may lead to failure for some local subregions while also being too conservative for other subregions of the rock mass. Geostatistics can be used to create local estimates of rock mass properties without extensive sampling. Geostatistics uses the variogram to characterize the spatial variability of rock mass properties. The geostatistical estimation procedure, kriging, produces local estimates which take into account the spatial variability of the rock mass properties and the spatial locations of sample values. Besides providing an estimation procedure, geostatistics also provides a means of testing to insure that the estimation procedure is performing as expected.
Measures of geologic phenomena show spatial correlation. In general, samples taken at two nearby locations tend to be more similar than samples taken from two distant locations. Spatial correlation results from natural controls acting on nearby points such as temperature of rock formation, magnitude and direction of fracture causing stress fields or proximity to a source of mineralizing fluids. In addition to spatial correlation, spatial variability may include a random component which shows no apparent correlation, even over small distances. When a global average is used as a design input, the designer assumes that over any local subregion, any deviations from the global mean will average out to zero over the particular subregion. However, when the rock property shows a high degree of spatial correlation, large subregions of the rock mass may have a significant deviation from the mean measured from throughout the rock mass. Several studies (Baecher 1984, LaPointe 1980, Miller 1979, Silva 1985, Young and Hoerget 1986) have demonstrated that many geotechnical properties display a high level of spatial correlation. Geostatistics takes advantage of spatial correlation to make estimates which accurately reflect local rock mass properties. (mathematical equation)(available in full paper)