Simulation of geological uncertainty using modified generalized coupled Markov chain
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摘要: 传统的广义耦合马尔可夫链模型是地层变异性模拟一种有效的工具。然而,由于岩土工程地质勘探过程中钻孔分布的稀疏性,广义耦合马尔可夫链水平方向转移概率矩阵不能直接估计,传统的广义耦合马尔可夫链模型不能直接用于地层变异性模拟。为此,提出了基于钻孔资料广义耦合马尔可夫链水平两方向转移概率矩阵的极大似然估计方法,验证了该方法的有效性,在此基础上采用信息熵图量化地层变异性。以爱尔兰地区都柏林市丹拉海尔港口处的一组钻孔资料为例进行地层变异性模拟,分析了钻孔布置方案对水平方向转移概率矩阵估计的影响,探讨了钻孔布置方案对地层变异性模拟的影响规律。结果表明：提出的水平方向转移概率矩阵极大似然估计方法能够有效地估计水平方向转移概率矩阵,从而为基于钻孔资料的地层不确定性分析奠定了基础。钻孔布置方案对各方向上转移概率矩阵的估计和地层变异性的模拟结果都十分重要,为获得准确的转移概率矩阵应提供足够的钻孔数据。钻孔位置对地层变异性模拟有明显的影响,应将钻孔布置于重点研究区域,尽量减少地层模拟不确定性。信息熵图能够直观地量化地层模拟的不确定性,可用于指导钻孔方案的布置。Abstract: The traditional generalized coupled Markov chain (GCMC) is an effective model for the simulation of geological uncertainty. However, it cannot be directly applied to geotechnical problems. The reason lies in that one important parameter of GCMC, namely horizontal transition probability matrix (HTPM), is hard to be estimated due to the typical large distance between boreholes. Hence, In the framework of GCMC, a maximum likelihood estimation method for HTPMs based on borehole data is proposed. The validity of the method is verified. On this basis, the information entropy plot is adopted herein to quantify geological uncertainty. In addition, the borehole data from Dun Laoghaire Harbour, Dublin City, Ireland is used to simulate the geological uncertainty. The influences of layout schemes of boreholes on HTPMs are investigated. Moreover, those on simulation of geological uncertainty are explored. The results show that the proposed method can effectively estimate HTPM, which lays a foundation for analysis of geological uncertainty based on borehole data. The layout scheme of boreholes is very important for the estimation of the transition probability matrix in all directions and the simulated results of the geological uncertainty. Adequate borehole data should be provided to obtain accurate transition probability matrices. The boreholes should be designed in the key research area to minimize the simulation of geological uncertainty. The information entropy plot can visually quantify the stratigraphic simulation uncertainty, which can be used to guide the design of borehole schemes.
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Keywords:
- geological uncertainty /
- generalized coupled /
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