Reliability analysis of seismic subsidence of loess foundation based on Kriging surrogate model
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摘要:
为评估黄土地基在发生地震期间出现的震陷安全水平，本文提出了一种基于Kriging代理模型的黄土地基震陷可靠度分析方法，采用拉丁超立方抽样（LHS）抽取随机变量的样本点，通过FLAC3D有限差分软件建立黄土地基数值模型并计算所抽样本点对应的响应值作为建立Kriging代理模型所需的训练样本点，结合蒙特卡罗法计算黄土地基震陷的可靠度，并分析随机变量的变异性对震陷可靠度的影响。算例分析结果表明：提出的震陷可靠度计算方法相比传统的确定性计算方法能够合理地考虑土性参数的变异性，更加符合实际情况，具有更好的可靠性和适用性。黏聚力的变异系数对震陷最大可靠度的影响更为显著。
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关键词:
- Kriging代理模型 /
- 黄土地基 /
- 震陷 /
- 可靠度 /
- Monte Carlo
Abstract:In order to evaluate the safety level of seismic subsidence of loess foundation during earthquakes, this paper proposes a reliability analysis method based on the Kriging surrogate model. The sample points of random variables are extracted based on Latin hypercube sampling (LHS). A numerical model of the loess foundation is established using FLAC3D finite difference software, and response values corresponding to the sample point is calculated as the training sample point for establishing Kriging surrogate model. The reliability of seismic subsidence of loess foundation is calculated by Monte Carlo method, and the influence of variability of random variables on seismic subsidence reliability is analyzed. The results show that the proposed seismic subsidence reliability calculation method can reasonably consider the variability of soil parameters compared to traditional deterministic methods, making it more practical with better reliability and applicability. The variation coefficient of cohesion significantly affects the maximum reliability of seismic subsidence.
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Key words:
- Kriging surrogate model /
- loess foundation /
- seismic subsidence /
- reliability /
- Monte Carlo
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表 1 不同地震波及不同峰值加速度作用下地基震陷量
Table 1. Seismic subsidence of foundation under different seismic waves and peak accelerations.
峰值加速度/g 震陷量/cm 地震波1 地震波2 地震波3 0.1 0.72 1.95 2.65 0.2 2.37 8.40 13.44 0.3 9.10 16.02 21.62 0.4 17.83 21.44 29.52 0.5 19.78 25.29 37.06 0.6 20.08 30.67 40.98 0.7 20.48 35.84 46.98 
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表 2 分布假设检验结果
Table 2. Distribution hypothesis test results
检验参数 样本量 验证结果 $ {D_{\max }} $ 可接受的临界值 $ D_n^\alpha /\left( {\alpha = 0.05} \right) $ 正态分布 对数正态分布 威布尔分布 结果 $ {D_{\max }} $ 结果 $ {D_{\max }} $ 结果 $ {D_{\max }} $ 内摩擦角 24 √ 0.180 √ 0.223 √ 0.093 0.273 黏聚力 24 √ 0.099 √ 0.125 √ 0.102 0.273 压缩模量 24 √ 0.094 √ 0.146 √ 0.164 0.273 密度 48 √ 0.150 √ 0.185 √ 0.115 0.196
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表 3 不同地震波作用下地基震陷破坏概率
Table 3. Probability of foundation subsidence failure under different seismic wave effects
加速度/g 地震波1 地震波2 地震波3 0.1 0 0 0 0.2 0 0 0 0.3 0 0 0 0.4 0 0.072 0.116 0.5 0 0.17 0.378 0.6 0 0.232 0.704 0.7 0.002 0.264 0.888
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表 4 不同地震波作用下地基震陷完好概率
Table 4. Probability of intact seismic subsidence of foundation under different seismic wave effects
加速度/g 地震波1 地震波2 地震波3 0.1 0.946 0.854 0.842 0.2 0.392 0.094 0.832 0.3 0.238 0.004 0 0.4 0.01 0 0 0.5 0.018 0 0 0.6 0.012 0 0 0.7 0.002 0 0
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表 5 各参数变异系数工况组合表
Table 5. Combination table of variation coefficient for each parameter
工况 COV 密度 弹性模量 黏聚力 摩擦角 1-1 0.01 0.3 0.2 0.3 1-2 0.05 1-3 0.1 1-4 0.15 1-5 0.2 2-1 0.05 0.05 0.2 0.3 2-2 0.1 2-3 0.2 2-4 0.3 2-5 0.4 3-1 0.05 0.3 0.05 0.3 3-2 0.1 3-3 0.2 3-4 0.3 3-5 0.4 4-1 0.05 0.3 0.2 0.1 4-2 0.2 4-3 0.3 4-4 0.4 4-5 0.5
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