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基于边界模型和广义耦合马尔可夫链模型的地层变异性模拟方法

潘敏 邓志平 蒋水华

潘敏, 邓志平, 蒋水华. 基于边界模型和广义耦合马尔可夫链模型的地层变异性模拟方法[J]. 地质科技通报, 2022, 41(2): 176-186. doi: 10.19509/j.cnki.dzkq.2022.0106
引用本文: 潘敏, 邓志平, 蒋水华. 基于边界模型和广义耦合马尔可夫链模型的地层变异性模拟方法[J]. 地质科技通报, 2022, 41(2): 176-186. doi: 10.19509/j.cnki.dzkq.2022.0106
Pan Min, Deng Zhiping, Jiang Shuihua. Simulation method of stratigraphic uncertainty using a boundary model and generalized coupled Markov chain model[J]. Bulletin of Geological Science and Technology, 2022, 41(2): 176-186. doi: 10.19509/j.cnki.dzkq.2022.0106
Citation: Pan Min, Deng Zhiping, Jiang Shuihua. Simulation method of stratigraphic uncertainty using a boundary model and generalized coupled Markov chain model[J]. Bulletin of Geological Science and Technology, 2022, 41(2): 176-186. doi: 10.19509/j.cnki.dzkq.2022.0106

基于边界模型和广义耦合马尔可夫链模型的地层变异性模拟方法

doi: 10.19509/j.cnki.dzkq.2022.0106
基金项目: 

江西省教育厅科学技术研究项目 GJJ211932

国家自然科学基金项目 52009054

国家自然科学基金项目 41867036

国家自然科学基金项目 52179103

详细信息
    作者简介:

    潘敏(1989—), 女, 现正攻读力学专业博士学位, 主要从事水工岩土工程可靠度分析与风险控制方面的研究。E-mail: panmin@nit.edu.cn

    通讯作者:

    邓志平(1990—), 男, 副教授, 主要从事水工岩土工程可靠度分析与风险控制方面的研究。E-mail: dengzhiping@nit.edu.cn

  • 中图分类号: P642

Simulation method of stratigraphic uncertainty using a boundary model and generalized coupled Markov chain model

  • 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。

     

  • 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
    下载: 导出CSV

    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
    下载: 导出CSV

    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
    下载: 导出CSV

    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
    下载: 导出CSV

    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
    下载: 导出CSV
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