Determining optimum number of geotechnical testing samples using Monte Carlo simulations

Knowing how many samples to test to adequately characterize soil and rock units is always challenging. A large number of tests decrease the uncertainty and increase the confidence in the resulting values of design parameters. Unfortunately, this large value also adds to project costs. This paper presents a method to determine the number of samples as a function of the coefficient of variation. If, as in the case of a reliability-based design, the resistance factors are a function of the coefficient of variation of the measurements, then lowering the coefficient of variation (COV) can result in lowering of the resistance factor resulting in a less conservative design. In this study, laboratory samples were isolated by specific unified soil classification system soil type and general site location. A distribution was fitted for each of the geotechnical parameters measured. For each scenario, groups of 2, 3, 4, 5, 10, 15, 20, 30, 50, and 100 random samples were generated by using Monte Carlo simulations from the fitted distributions. For each group, the variability was calculated in terms of the COV. In all cases, the COV decreased as the sample size increased. However, the rate of decrease for the COV was the greatest at a low number of samples; it becomes increasingly smaller at a higher number of samples.