Assessment of rock unit variability through use of spatial variograms

All rock units contain a certain degree of variability, which is an intrinsic property of the material. This variability can present itself in differences in mineralogy, grain size, grain shape, porosity, or a number of other ways. This presents a challenge when attempting to identify the number of specimens required in order to capture the geomechanical variability of a rock unit. For instance, while a homogeneous granite may only require a few specimens to characterize the spectrum of geomechanical behavior anticipated within the unit, a moderately to highly metamorphosed rock unit such as a gneiss, a schist, or a meta-igneous or meta-sedimentary rock may require a significantly larger number of specimens. This discrepancy can lead to over-testing, which induces an unnecessary excess cost, or under-testing, which could lead to an under-representation of the geomechanical variability possible within a rock unit. While previous works have considered robust statistical approaches such as Monte Carlo simulations and confidence interval analysis with large data sets, this work presents a practical empirical methodology of assessing geologic and geomechanical variability by analyzing images and the respective uniaxial compressive strength (UCS) of core specimens. Once corrected for lighting irregularities and other deleterious influences, two-dimensional covariance maps and one-dimensional variogram samples are calculated for each rock core and used to extract several metrics for rock unit geologic variability. These metrics are then correlated to geomechanical variability based on UCS testing results. Ultimately, these correlations can be used to find the number of specimens required to estimate the rock unit's mean UCS within a specified margin of error. This methodology allows one to quickly analyze core images of a specific rock type and evaluate how many specimens are required for testing.