Probabilistic analysis of overall strength of a cement-treated soil column considering statistical uncertainty and spatial variability

A finite-element method (FEM) analysis incorporating with random field theory is a powerful tool to predict the behavior of ground improvement by deep cement mixing with spatial variability. In the analysis, statistical parameters of the strength (i.e., mean, variance, and autocorrelation distance) are normally held constant. However, these parameters involve a statistical uncertainty when evaluated from strengths of core samples retrieved from the cement-treated soil columns. This study presents a probabilistic analysis framework to evaluate the overall strength of a cement-treated soil column considering the statistical uncertainty and spatial variability of the core strength. A Bayesian inference analysis and an FEM analysis incorporating with the random field theory are combined in a Monte Carlo framework to simultaneously consider the statistical uncertainty and spatial variability. The statistical uncertainty of the core strength is evaluated by the Bayesian inference approach, where the probability distribution of the statistical parameters is inferred from the observation data. The inferred statistical parameters of the strength are used for generating random field realizations, and the FEM analysis is conducted on the generated realizations. An example analysis is conducted to illustrate the details of the approach. The results of the example simulation demonstrate that the proposed framework can provide the probabilistic characteristic of the overall strength of the cement-treated column when the statistical uncertainty and the spatial variability of the core strength need to be simultaneously considered.