Investigating the Effect of Sample Size on Uncertainty in Stress Estimations

Obtaining reliable estimates of u stress, particularly principal stresses, is crucial for robust rock engineering design. However, due to the stress variability inherent in fractured rock masses, a key question that arises in practice is that of how many stress measurements are required to obtain stress estimates of acceptable reliability. In this paper, we investigate the effect of sample size – i.e., number of stress measurements – on the uncertainties associated with point estimations of both principal mean stress magnitude and orientation. We use Monte Carlo simulation in conjunction with a recently developed multivariate statistical model to simulate a large number of stress tensor samples of different sizes. We show (i) that the number of stress measurements required for obtaining estimates of acceptable reliability is practically impossible, and (ii) with the small sample sizes often used in rock engineering, large uncertainties may exist which are likely to yield misleading stress estimates.