Are Three to Ten Tests Enough to Characterize a Rock Property?

Abstract

The geotechnical literature contains claims that testing as few as three to 10 samples suffices for characterizing such rock properties as unconfined compressive strength, but from the perspective of basic statistics, such small numbers are unlikely to provide acceptable estimates of true means and standard deviations and are even less likely to yield accurate assessments of normality. Statistically based decisions are overly risky when based on dubious statistics: problematic estimates may be tolerable for reconnaissance studies, evaluation of small sites, projects with minimal hazards and risk, or when combined with high factor-of-safety designs, but not when potential loss is considerable, designs are less conservative, or statistical work depends on assumptions of normality, such as in the case of confidence intervals, t-tests, statistical power, and standard risk analysis. In this study, bootstrapping experiments with artificial populations confirm that 30 to 300 samples are appropriate with Gaussian distributions, depending on needs, but higher numbers may be required for populations with irregular or skewed distributions. Planning for large projects, trying to improve economy without loss of safety in designs, and statistical research (e.g., creating accurate regression models) all require more information than is likely to be available about the amounts and patterns of variability exhibited by specific rock units. Therefore, a national registry or state registries of engineering test results would comprise a valuable advance for the engineering geology profession.