Evaluation of statistical uncertainty of cement-treated soil strength using Bayesian approach

The statistical parameters for the strength of cement-treated soil are evaluated by the strength of cored samples retrieved from cement-treated columns for a quality assurance procedure in the deep mixing method. The sample parameters include the statistical uncertainty associated with the statistical sample size and other factors. Therefore, a probabilistic characterization of the statistical parameters of strength is required to quantify the statistical uncertainty in the quality assurance process. This paper presents a quantitative analysis of the statistical uncertainty for the estimation of the strength of cement-treated columns. The Bayesian approach is adopted to evaluate the statistical uncertainty occurring in the determination of the statistical parameters of the strength from observed data. The inference is performed via a Markov chain Monte Carlo method, in which samples of the parameters are sequentially drawn from a joint posterior probability distribution. An example analysis is performed to illustrate the statistical uncertainty of the unconfined compressive strength of cored samples retrieved from cement-treated columns. The results show that the statistical parameters, inferred from the data with the sample size of approximately 40, include considerable uncertainty. The variability of the estimated statistical parameters is found to depend on both the sample size and the spatial correlation. The influence of the statistical uncertainty, caused in the estimation of the mean and standard deviations in strength, is examined within the framework of quality assurance in the deep mixing method.