Abstract Geological uncertainty exists widely in nature, which has a pivotal influence on the deformation and stability of the geotechnical structure. The coupled Markov chain (CMC) model is a widely used method to simulate the variability of strata. However, the difficulty to determine the horizontal transition probability matrix (HTPM), one of the important input parameters for the CMC model, limits its direct application to geotechnical engineering problems. In this study, an analytical method for estimating the HTPM is proposed and the CMC model is enhanced by integrating the analytical HTPM estimation method for simulating geological uncertainty. The validity of the analytical method for the HTPM and the accuracy of the strata simulated by the enhanced CMC model are evaluated through a typical stratum in literature. The results show that the estimated HTPMs are in good agreement with the real values and not sensitive to borehole schemes. The CMC model enhanced by the proposed analytical method for estimating the HTPM is well capable of simulating the strata based on given borehole data.

中文翻译：

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一种模拟地质不确定性的耦合马尔可夫链水平转移概率矩阵的估计解析方法

摘要 地质不确定性在自然界中广泛存在，对岩土结构的变形和稳定性有着举足轻重的影响。耦合马尔可夫链（CMC）模型是一种广泛使用的模拟地层变异性的方法。然而，水平转移概率矩阵 (HTPM) 是 CMC 模型的重要输入参数之一，但由于难以确定，限制了其在岩土工程问题中的直接应用。在这项研究中，提出了一种估计HTPM的解析方法，并通过整合模拟地质不确定性的解析HTPM估计方法来增强CMC模型。通过文献中的典型地层评价HTPM分析方法的有效性和增强CMC模型模拟地层的准确性。结果表明，估计的 HTPM 与实际值吻合良好，对钻孔方案不敏感。通过所提出的用于估计 HTPM 的分析方法增强的 CMC 模型能够很好地基于给定的钻孔数据模拟地层。