基于CPTU测试的砂质与粉质土液化概率模型与评价方法研究

段伟; 蔡国军; 赵泽宁; 刘松玉; 董晓强

doi:10.11779/CJGE20210645

基于CPTU测试的砂质与粉质土液化概率模型与评价方法研究 English Version

段伟^{1, 2, 4,},
蔡国军^{2, 3, 4, ,},
赵泽宁²,
刘松玉²,
董晓强¹

1.
太原理工大学土木工程学院, 山西太原 030024
2.
东南大学岩土工程研究所, 江苏南京 211189
3.
安徽建筑大学土木工程学院, 安徽合肥 230601
4.
安徽省智能地下探测技术研究院, 安徽合肥 230601

基金项目:

国家重点研发计划项目 2020YFC1807200

国家杰出青年科学基金项目 4222506

国家自然科学基金项目 52108332

国家自然科学基金项目 41877231

国家自然科学基金项目 42072299

安徽省智能地下探测技术研究院开放课题 AHZT2022KF001

详细信息

作者简介:
段伟(1989—)，男，山西太原人，博士，从事现代原位测试技术等方面的研究工作。E-mail: zbdxdw@163.com

通讯作者:
蔡国军, E-mail: focuscai@163.com

中图分类号: TU413
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出版历程
- 收稿日期: 2021-06-09
- 网络出版日期: 2023-02-03
- 发布日期: 2021-06-09
- 刊出日期: 2022-12-31

CPTU-based probabilistic model and evaluation method for liquefaction of sandy and silty soils

DUAN Wei^{1, 2, 4,},
CAI Guojun^{2, 3, 4, ,},
ZHAO Zening²,
LIU Songyu²,
DONG Xiaoqiang¹

1.
College of Civil Engineering, Taiyuan University of Technology, Taiyuan 030024, China
2.
Institute of Geotechnical Engineering, Southeast University, Nanjing 211189, China
3.
School of Civil Engineering, Anhui Jianzhu University, Hefei 230601, China
4.
Anhui Institute of Intelligent Underground Detection Technology, Hefei 230601, China

摘要

摘要: 无黏性土的液化与孔隙水压力密切相关，能直接测试孔隙水压力的孔压静力触探（CPTU）原位测试技术在土体液化势评价方面具有独特的优势。采用严格的数学方法推导了基于CPTU测试技术的液化概率评价模型。新的概率模型以映射函数的形式表示，该映射函数将液化概率P_L与基于CPTU的确定性模型中得到的安全系数F_s相关联，其中CPTU确定性模型是通过核极限学习机算法和稳健搜索技术建立的。该新的概率性模型考虑了模型固有的不确定性和参数的不确定性，同时对该概率模型进行对比分析。结果表明：当安全系数 ${F_{\text{S}}}$ 为1时，液化发生的概率P_L为15.2%。该新模型的明显优势在于它直接使用CPTU数据，更符合液化行为现象，同时适用于砂质土和粉质土。该新模型无需钻孔取样室内试验，即可进行完整的液化评估或初步筛选。最后用中国唐山地震液化案例说明所提新概率模型考虑模型和参数不确定性的应用。
- 孔压静力触探 /
- 孔压参数比 /
- 砂质土 /
- 粉质土 /
- 液化概率
Abstract: The liquefaction of cohesionless soils is closely related to the pore water pressure. The in situ testing technology, piezocone penetration test (CPTU) which can directly measure the pore water pressure, has unique advantages in liquefaction evaluation. In this study, a CPTU-based model for assessing the probability of liquefaction is derived by a rigorous mathematical method. The new probabilistic model is expressed in the form of a mapping function that relates the liquefaction probability mathematically to the factor of safety obtained from the CPTU-based deterministic model, which is established by the kernel extreme learning machine algorithm and the robust search technology. The new probabilistic model considers the inherent model uncertainty and parameter uncertainty, and makes a comparative analysis of the probabilistic model. The results show that the factor of safety (F_S) of 1 yields a probability of liquefaction (P_L) of 15.2%. The obvious advantage of the new model is that it directly uses the CPTU data, which is more suitable for the phenomenon of liquefaction behavior, and is suitable for sandy soil and silty soil. The new model can be used for liquefaction evaluation or preliminary screening without the need of additional sampling and laboratory testing. Finally, a liquefaction case of Tangshan earthquake in China is used to illustrate the application of the proposed probabilistic model considering the uncertainties of model and parameters.
- piezocone penetration test /
- pore pressure ratio /
- sandy soil /
- silty soil /
- probability of liquefaction

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图 1 稳健搜索技术示意图

Figure 1. Schematic diagram of robust search technology

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${P_{\text{L}}}$ 与 ${F_{\text{s}}}$ 关系图

Relationship between ${P_{\text{L}}}$ and ${F_{\text{s}}}$

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图 3 概率模型对比

Figure 3. Comparison of probabilistic models

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图 4 场地T1的CPTU剖面

Figure 4. CPTU sounding profiles at location T1 in site

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图 5 场地T1的液化结果分析

Figure 5. Analysis of liquefaction results of T1 in site

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图 6 CSR_7.5和CRR_7.5变异系数与液化概率标准差的关系

Figure 6. Relationship between coefficient of variation of CSR and CRR and standard deviation of liquefaction probability

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表 1 不同模型液化判别训练集结果对比

Table 1 Comparison among different machine learning models

模型	训练集				测试集
模型	O/%	p/%	r/%	F_β=1	O/%	p/%	r/%	F_β=1
KELM	97.1	97.2	98.9	0.980	89.1	91.7	94.3	0.930
RF	86.8	90.4	85.7	0.880	87.0	86.7	92.9	0.893
SVM	96.1	95.6	99.4	0.975	85.5	86.9	91.2	0.890
LM-BP	89.4	88.5	96.1	0.922	83.6	86.5	90.9	0.886

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表 2 混淆矩阵

Table 2 Confusion matrix

模型预测	实际
模型预测	液化	非液化
液化	${T_{\text{P}}}$	${F_{\text{P}}}$
非液化	${F_{\text{N}}}$	${T_{\text{N}}}$

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表 3 模型评价结果汇总

Table 3 Summary of evaluation results by models

Z分布	δ模型	d	BIC
正态分布	M₁	2	162.65
正态分布	M₂	3	165.33
对数正态分布	M₁	2	164.92
对数正态分布	M₂	3	166.58
极值分布	M₁	2	166.44
极值分布	M₂	3	167.98

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表 4 所提液化概率模型性能的统计测试

Table 4 Statistical measurement of performance of proposed probabilistic model for liquefaction

分类	A	p	r	F
砂性土(I_{c, BJ} < 2.58)	0.78	0.76	0.90	0.83
砂性土和粉质土	0.80	0.80	0.92	0.85

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表 5 液化概率分类^[18]

Table 5 Classification of probability of liquefaction

${P_{\text{L}}}$ 范围	对应 ${F_{\text{s}}}$	等级	描述
0.85≤ ${P_{\text{L}}}$	${F_{\text{s}}}$ ≤0.17	5	几乎可以肯定它会液化
0.65≤ ${P_{\text{L}}}$ < 0.85	0.17 < ${F_{\text{s}}}$ ≤0.43	4	很可能液化
0.35≤ ${P_{\text{L}}}$ < 0.65	0.43 < ${F_{\text{s}}}$ ≤0.74	3	液化和非液化的可能相等
0.15≤ ${P_{\text{L}}}$ < 0.35	0.74 < ${F_{\text{s}}}$ ≤1.00	2	液化可能性不大
0.00≤ ${P_{\text{L}}}$ < 0.15	${F_{\text{s}}}$ > 1.00	1	几乎可以肯定它不会液化

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表 6 部分确定性误判案例的概率分析结果

Table 6 Probabilistic evaluation results of some cases misclassified by deterministic model

地震	测点	是否液化	${q_{{\text{t1N}}}}$	${I_{{\text{c, BJ}}}}$	${F_{\text{s}}}$	${P_{\text{L}}}$	等级
Hyogoken-Nanbu	Taito Kobe Factory	液化	37.5	1.57	0.300	0.761	4
Chi-Chi	NT-C2	非液化	134.1	1.66	0.734	0.356	3
Chi-Chi	YL-C1	非液化	69.8	2.22	0.913	0.209	2
Loma Prieta	McGowan 136	非液化	55.1	1.88	0.900	0.218	2

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表 7 输入参数的变化引起液化概率的变化

Table 7 Change of liquefaction probability with change of input parameters

CSR_7.5变异系数	CRR_7.5变异系数	$P_{\text{L}}^ +$	$P_{\text{L}}^ -$
0	0.02	0.774	0.719
0.05	0.02	0.791	0.690
0.10	0.02	0.804	0.653
0.15	0.02	0.816	0.605
0	0.04	0.799	0.689
0.05	0.04	0.813	0.655
0.10	0.04	0.824	0.613
0.15	0.04	0.833	0.559
0	0.06	0.823	0.658
0.05	0.06	0.834	0.620
0.10	0.06	0.843	0.573
0.15	0.06	0.850	0.513
0	0.08	0.844	0.625
0.05	0.08	0.853	0.583
0.10	0.08	0.860	0.531
0.15	0.08	0.865	0.466

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