Characterization of geological uncertainties from limited boreholes using copula-based coupled Markov chains for underground construction

IF 8.2 1区 工程技术 Q1 ENGINEERING, CIVIL
Fan Wang , Heng Li , Gang Li , Zheng-Jun You , Elton J. Chen
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引用次数: 0

Abstract

This paper proposes an efficient method for quantifying the stratigraphic uncertainties and modeling the geological formations based on boreholes. Two Markov chains are used to describe the soil transitions along different directions, and the transition probability matrices (TPMs) of the Markov chains are analytically expressed by copulas. This copula expression is efficient since it can represent a large TPM by a few unknown parameters. Due to the analytical expression of the TPMs, the likelihood function of the Markov chain model is given in an explicit form. The estimation of the TPMs is then re-casted as a multi-objective constrained optimization problem that aims to maximize the likelihoods of two independent Markov chains subject to a set of parameter constraints. Unlike the method which determines the TPMs by counting the number of transitions between soil types, the proposed method is more statistically sound. Moreover, a random path sampling method is presented to avoid the directional effect problem in simulations. The soil type at a location is inferred from its nearest known neighbors along the cardinal directions. A general form of the conditional probability, based on Pickard's theorem and Bayes rule, is presented for the soil type generation. The proposed stratigraphic characterization and simulation method is applied to real borehole data collected from a construction site in Wuhan, China. It is illustrated that the proposed method is accurate in prediction and does not show an inclination during simulation.

利用基于 copula 的耦合马尔可夫链表征地下工程有限钻孔的地质不确定性
本文提出了一种基于钻孔量化地层不确定性和地质构造建模的有效方法。本文使用两条马尔可夫链来描述不同方向的土壤转换,马尔可夫链的转换概率矩阵(TPM)通过协方差进行分析表达。这种共线表达方式非常高效,因为它只需用几个未知参数就能表示大量的 TPM。由于 TPM 的分析表达式,马尔可夫链模型的似然函数以明确的形式给出。然后,TPMs 的估计被重铸为一个多目标约束优化问题,其目的是最大化两个独立马尔可夫链在一组参数约束下的似然值。与通过计算土壤类型之间的转换次数来确定 TPM 的方法不同,所提出的方法更符合统计学原理。此外,还提出了一种随机路径采样方法,以避免模拟中的方向效应问题。一个地点的土壤类型是根据其沿主方向的已知近邻推断出来的。根据皮卡德定理和贝叶斯规则,提出了土壤类型生成的条件概率一般形式。所提出的地层特征描述和模拟方法被应用于从中国武汉的一个建筑工地采集的真实钻孔数据。结果表明,所提出的方法预测准确,在模拟过程中不会出现倾斜。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Underground Space
Underground Space ENGINEERING, CIVIL-
CiteScore
10.20
自引率
14.10%
发文量
71
审稿时长
63 days
期刊介绍: Underground Space is an open access international journal without article processing charges (APC) committed to serving as a scientific forum for researchers and practitioners in the field of underground engineering. The journal welcomes manuscripts that deal with original theories, methods, technologies, and important applications throughout the life-cycle of underground projects, including planning, design, operation and maintenance, disaster prevention, and demolition. The journal is particularly interested in manuscripts related to the latest development of smart underground engineering from the perspectives of resilience, resources saving, environmental friendliness, humanity, and artificial intelligence. The manuscripts are expected to have significant innovation and potential impact in the field of underground engineering, and should have clear association with or application in underground projects.
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