Simulation method of stratigraphic uncertainty using a boundary model and generalized coupled Markov chain model
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摘要: 地层变异性对岩土结构物的性能评价影响显著, 地层变异性的准确表征对工程实际具有重要意义。为此, 提出了一种有效的地层变异性模拟方法, 在概率框架内, 将边界模型和广义耦合马尔可夫链模型相结合形成一种组合模型, 以综合利用两者的优势。首先, 通过贝叶斯方法识别边界模型参数, 进而采用条件随机场对地层边界进行模拟。然后, 将边界模型模拟结果作为背景信息用于广义耦合马尔可夫链模型中, 实现两种模型的结合。最后, 以香港某建筑场地地层为例, 对3种不同模型的地层变异性模拟结果进行了比较, 以阐明该组合模型的优势, 并探讨钻孔数量及其位置对所提组合模型地层变异性模拟的影响。结果表明: 相比于边界模型与广义耦合马尔可夫链模型, 该组合模型不仅能够模拟复杂的地层分布情况, 而且能够考虑边界的空间分布趋势, 能够有效地避免地质异常现象; 钻孔布置方案对地层模拟的不确定性及其实现均具有较大影响。Abstract: Stratigraphic uncertainty has a significant impact on the performance evaluation of geotechnical structures, and it is important for engineering practice to accurately characterize the uncertainty. Hence, an effective simulation method of geological uncertainty is proposed. In the framework of probability, the boundary model and the generalized coupled Markov chain model are coupled to make full use of their advantages. First, the parameters of the boundary model are identified by the Bayes method, and then the boundary of the rock-soil material is simulated by a conditional random field. Then, the boundary model simulation results are used as background information in the generalized coupled Markov chain model to realize the coupling of the two models. Finally, taking a construction site in Hong Kong as an example, the simulation results of stratigraphic uncertainties for three different models are compared, and the advantages of the combination model proposed in this paper are clarified. The effects of the number and location of boreholes on the stratigraphic uncertainty simulation are discussed. The results show that compared with the boundary model and the generalized coupled Markov chain model, the coupling model can not only simulate the complicated stratum distribution but also consider the spatial distribution trend of the boundary and effectively avoid the geological anomaly phenomenon. The borehole layout scheme has a great impact on the stratigraphic uncertainty and its realization.
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图 1 已知样本点与未知样本点之间的两种可能子方向转移
Figure 1. Two possible transfer modes between a known sample point and an unknown sample point
图 2 基于边界模型和广义耦合马尔可夫链模型的地层模拟过程
a.钻孔数据；b.背景信息(边界模型)；c.地层实现；d.岩土体类型转移方式。Sb, So, Sr, Si, Sp, Sq为相应单元的土体类型
Figure 2. Stratigraphic uncertainty simulation process using the boundary model and generalized coupled Markov charn model
图 3 香港某建筑场地钻孔位置及其揭示的地层
Figure 3. Location and soil strata of the boreholes at a construction site in Hongkong
图 4 基于不同模型的两次地层实现
a1.基于边界模型的地层实现1；b1.基于广义耦合马尔可夫链的地层实现1；c1.基于组合模型的地层实现1；a2.基于边界模型的地层实现2；b2.基于广义耦合马尔可夫链的地层实现2；c2.基于组合模型的地层实现2
Figure 4. Two stratigraphic realizations based on different models
图 5 基于不同模型的信息熵图
a.基于广义耦合马尔可夫链模型的信息熵图；b.基于组合模型的信息熵图
Figure 5. Information entropy maps based on different models
图 6 不同钻孔布置方案对应的信息熵图
Figure 6. Information entropy maps corresponding to different borehole layout schemes
图 7 不同钻孔布置方案对应的一次地层实现
Figure 7. One stratigraphic realization corresponding to different borehole layout schemes
表 1 竖直方向转移概率矩阵
Table 1. Probability matrix of vertical transfer
(a1)竖直向下转移概率矩阵 (a2)竖直向上转移概率矩阵 材料1 材料2 材料3 材料4 材料5 材料1 材料2 材料3 材料4 材料5 材料1 0.773 0.045 0.182 0 0 1.000 0 0 0 0 材料2 0 0.855 0.145 0 0 0.018 0.855 0.127 0 0 材料3 0 0.048 0.910 0.042 0 0.028 0.056 0.910 0.007 0 材料4 0 0 0.006 0.955 0.039 0 0 0.033 0.950 0.017 材料5 0 0 0 0.031 0.969 0 0 0 0.069 0.931 
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表 2 水平方向转移概率矩阵
Table 2. Probability matrix of horizontal transfer
(a1)水平向右转移概率矩阵 (a2)水平向左转移概率矩阵 材料1 材料2 材料3 材料4 材料5 材料1 材料2 材料3 材料4 材料5 材料1 0.946 0.011 0.043 0 0 0.949 0.010 0.041 0 0 材料2 0 0.968 0.032 0 0 0 0.970 0.030 0 0 材料3 0 0.010 0.981 0.009 0 0 0.009 0.982 0.008 0 材料4 0 0 0.001 0.991 0.008 0 0 0.001 0.992 0.007 材料5 0 0 0 0.006 0.994 0 0 0 0.006 0.994
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表 3 已知样本位置及边界1和2对应的深度
Table 3. Known sample locations and corresponding depths of boundaries 1 and 2
钻孔位置x/m 5.32 14.32 26.54 34.25 41.32 边界1深度z/m -19.48 -21.56 -17.10 -14.47 -17.55 边界2深度z/m -42.49 -39.51 -38.12 -34.48 -37.51
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表 4 边界模型中模型参数贝叶斯方法识别结果
Table 4. Bayesian identification results of model parameters in the boundary model
边界 线性趋势函数 标准差σ/m 波动范围δ/m 边界1 Z=0.15x-21.71 1.03 6.32 边界2 Z=0.21x-43.70 0.95 6.78
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表 5 不同的钻孔布置方案
Table 5. Different borehole layout schemes considered in this study
钻孔布置方案 钻孔1 钻孔2 钻孔3 钻孔4 钻孔5 
3 √ √ √ 4A √ √ √ √ 4B √ √ √ √ 5 √ √ √ √ √ 注：“√”代表该钻孔布置方案包含对应的钻孔
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