Determining the minimal number of specimens for laboratory testing of rock properties

Abstract The present paper focuses on a rigorous statistical procedure referring to small-sampling theory leading to the determination of the number of specimens to test (sample size) in the laboratory for the determination of mechanical properties of rocks. From this theory, relationships between the number of specimens in a group, the coefficient of variation obtained after testing the specimens, the targeted precision index and confidence interval are given. Although this topic seems basic, the quick literature review presented shows that the situation regarding it is quite confused, and no standard and valid procedures for such an important subject can be found. An algorithm which minimizes the sample size leading to the required precision index while respecting the target confidence interval is given. The effectiveness of the algorithm is demonstrated using a series of Monte Carlo simulations from which rock properties are generated. The most important conclusion drawn from these simulations is that, all things being equal, the smallest sample size varies for given rocks and test types, or in other words, it is impossible to determine a priori the sample size required to obtain a given precision index for a certain confidence interval. If the sample size is given a priori due mainly to the limited number of samples available, the engineer must evaluate the precision index for a given confidence interval, if the knowledge of both the true mean and standard deviation intervals is required. The authors emphasize that this paper only deals with the way test data should be considered from a statistical point of view. Choosing what rock properties to test and how the values obtained are used in a design model are up to the rock engineer's judgment and experience.