Efficient Identification Method of Coastal Soft Soil Stratum Based on Hierarchical Bayesian Learning
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摘要: 基于静力触探试验数据划分土层依赖于经验图表和主观判断，划分的土层剖面不可避免地存在不确定性.提出了一种基于土体分类指数Ic的土层界面快速识别和不确定性量化方法.在分层贝叶斯学习框架下，所提方法采用全高斯概率模型表征土体空间变异性，通过引入正态‒逆威沙特共轭分布实现似然函数的快速计算，高效求解模型证据，识别最可能土层数目和厚度.所提方法基于Ic的统计特性自动划分土层，提高了识别结果的可靠性.Abstract: Underground stratification based on the cone penetration test (CPT) data relies on empirical charts and subjective judgments. Uncertainties in soil profile identified from CPT data are unavoidable. In this paper it proposes a fast underground stratigraphy identification method based on soil classification index Ic, which also quantifies the identification uncertainty. Under the hierarchical Bayesian learning framework, the proposed method uses full Gaussian random field model to characterize the spatial variability of soils, and efficiently calculates the likelihood function of soil layer thicknesses given a soil layer number by introducing the Normal-Inverse Wishart conjugate distribution. By this means, the model evidence can be solved efficiently, and the most possible profile is identified. The proposed method automatically identifies the most probable soil layer profile considering the statistical characteristics of Ic, and improves the reliability of the identification results.
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图 1 土层划分示意及全高斯随机场模型
Fig. 1. Illustration of full Gaussian random field modelling of underground stratigraphy
图 2 所提土层划分方法对应的图模型
Fig. 2. Graphical model for the proposed soil stratification method
图 4 不同土层数目对应的模型证据对数值
Fig. 4. Logarithm of the evidence for different model classes with different numbers of soil layers
图 5 土层划分结果及界面深度标准差
Fig. 5. Underground stratigraphy identified from proposed approach and its uncertainty
图 7 不同土层数目对应的模型证据对数值
Fig. 7. Logarithm of the evidence of different model classes with different numbers of soil layers
图 9 不同$ \alpha $对应的土层数目识别精度
Fig. 9. Accuracy of soil layer number using different $ \alpha $ values
表 1 基于土类指数Ic的土体分类（刘松玉等，2013）
Table 1. Soil classification based on the soil behavior type index $ {I}_{c} $ (Liu et al., 2013)
土类指数$ {I}_{c} $范围 土体类型 分区 < 1.87 中砂 7 1.87~2.10 细砂 6 2.10~2.32 粉砂 5 2.32~2.65 粉土 4 2.65~2.90 粉质黏土 3 2.9~3.45且$ {Q}_{tn} > 11.8\mathrm{e}\mathrm{x}\mathrm{p}(-{F}_{r}/1.15)-0.36 $ 黏土 2 > 3.45或$ {Q}_{tn} < 11.8\mathrm{e}\mathrm{x}\mathrm{p}\left(-{F}_{r}/1.15\right)-0.36 $ 淤泥或淤泥质土 1 
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