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.

中文翻译：

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考虑统计不确定性和空间变异性的水泥土柱整体强度的概率分析

结合随机场理论的有限元法（FEM）分析是预测具有空间变异性的深层水泥拌和技术来预测地基改良行为的有力工具。在分析中，强度的统计参数（即均值，方差和自相关距离）通常保持不变。但是，当根据从水泥处理过的土柱中提取的岩心样品的强度进行评估时，这些参数涉及统计不确定性。这项研究提出了一个概率分析框架，考虑了核心强度的统计不确定性和空间变异性，可以评估水泥处理过的土柱的整体强度。在蒙特卡洛框架中结合了贝叶斯推断分析和有限元分析以及随机场理论，可以同时考虑统计不确定性和空间变异性。核心强度的统计不确定性通过贝叶斯推断方法进行评估，该方法从观测数据中推断出统计参数的概率分布。推断的强度统计参数用于生成随机场实现，并对生成的实现进行有限元分析。进行了示例分析，以说明该方法的详细信息。