考虑场地相似性的小样本边坡可靠度分析

doi:10.3724/1000-6915.jrme.2024.0666

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Abstract This paper proposes a hierarchical Bayesian method(HBM) combined with Markov Chain Monte Carlo (MCMC) to address the challenges of large statistical uncertainty in geotechnical experimental data，inaccurate probability distribution of geotechnical parameters，and unreasonable slope reliability analysis under small sample-sized conditions. The HBM comprehensively incorporates information from multiple similar geotechnical sites and integrates it with the limited measurements from the target site. This approach enables a more reasonable characterization of the probability distribution of geotechnical parameters under small sample conditions. The proposed method is validated using real datasets from several loess sites in northern Shaanxi Province，China. Based on these datasets，a reliability analysis of a loess slope is conducted to demonstrate the practical application of the HBM. The results indicate that，compared to the independent parameter model(IPM)，which does not utilize information from similar geotechnical sites，the failure probability of the loess slope is reduced from 11.6% to 4.8% when using the HBM. Additionally，extensive numerical simulations are carried out to further verify the accuracy of the HBM compared to traditional methods. The results show that，compared to IPM，the HBM improves the accuracy of geotechnical statistics by 33% to 53% and reduces uncertainty by approximately 19% to 53%.

Key words： soil mechanics probability distribution of geotechnical parameters Bayesian methods hierarchical Bayesian model reliability-based analysis

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	XU Ling
	WANG Wenlong
	ZHAO Tengyuan

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XU Ling,WANG Wenlong,ZHAO Tengyuan. Reliability analysis of slopes from sparse measurements considering sites similarity[J]. , 2025, 44(4): 977-988.

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https://rockmech.whrsm.ac.cn/EN/10.3724/1000-6915.jrme.2024.0666 OR https://rockmech.whrsm.ac.cn/EN/Y2025/V44/I4/977

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[20]	WANG M，PAN S，TAO Y，et al. Hierarchical Bayesian modelling of quasi-region-specific soil porosity[J]. Ocean Engineering，2022，266：113052.
[39]	司马丹琪，李元松，姜成潼，等. 西部“三高”地区高速公路边坡稳定性系数与失稳概率关系探讨[J]. 中国地质灾害与防治学报，2018，29(5)：32-37.(SIMA Danqi，LI Yuansong，JIANG Chengtong，et al. Relationship between highway slope's factor of safety and its failure probability in "Three High" Region of western China[J]. The Chinese Journal of Geological Hazard and Control，2018，29(5)：32-37.(in Chinese))
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[22]	CHING J，WU S，PHOON K. Constructing quasi-site-specific multivariate probability distribution using hierarchical Bayesian model[J]. Journal of Engineering Mechanics，2021，147(10)：04021069.
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[36]	ZAI D，PANG R，XU B，et al. Slope system stability reliability analysis with multi-parameters using generalized probability density evolution method[J]. Bulletin of Engineering Geology and the Environment，2021，80(11)：8 419-8 431.
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[42]	WANG Y，ZHAO T，CAO Z. Site-specific probability distribution of geotechnical properties[J]. Computers and Geotechnics，2015，70(10)：159-168.
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[26]	蒋水华，刘源，章浩龙，等. 先验概率分布及似然函数模型的选择对边坡可靠度评价影响的定量评估[J]. 岩土力学，2020，41(9)：3 087-3 097.(JIANG Shuihua，LIU Yuan，ZHANG Haolong，et al. Quantitatively evaluating the effects of prior probability distribution and likelihood function models on slope reliability assessment[J]. Rock and Soil Mechanics，2020，41(9)：3 087-3 097.(in Chinese))
[45]	MARTIN O A，KUMAR R，LAO J. Bayesian modeling and computation in Python[M]. New York：Chapman and Hall/CRC，2021：140.
[40]	曹子君，赵腾远，王宇，等. 基于贝叶斯等效样本的土体杨氏模量的统计特征确定方法[J]. 防灾减灾工程学报，2015，35(5)：581-585.(CAO Zijun，ZHAO Tengyuan，WANG Yu，et al. Characterization of young's modules of soil using bayesian equivalents samples[J]. Journal of Disaster Prevention and Mitigation Engineering，2015，35(5)：581-585.(in Chinese))
[27]	GELMAN A. Prior distributions for variance parameters in hierarchical models(comment on article by Browne and Draper)[J]. Bayesian Analysis，2006，1(3)：515-534.
[46]	ZHU C，XIAO F. A belief Hellinger distance for D-S evidence theory and its application in pattern recognition[J]. Engineering Applications of Artificial Intelligence，2021，106(11)：104452.
[41]	赵腾远，EMMAN A A，王宇. 基于贝叶斯方法的模型选择以及岩石性质概率表征[J]. 武汉大学学报：工学版，2016，49(5)：740-744.(ZHAO Tengyuan，EMMAN A A，WANG Yu，et al. Bayesian model selection and characterization for rock properties[J]. Engineering Journal of Wuhan University，2016，49(5)：740-744.(in Chinese))
[28]	BURKARDT J. The truncated normal distribution[J]. Department of Scientific Computing Website，Florida State University，2014，1(35)：58.
[42]	WANG Y，ZHAO T，CAO Z. Site-specific probability distribution of geotechnical properties[J]. Computers and Geotechnics，2015，70(10)：159-168.
[29]	范明桥，盛金保. 土强度指标 φ，c 的互相关性[J]. 岩土工程学报，1997，29(4)：100-104.(FAN Mingqiao，SHENG Jinbao. Cross correlation of soil strength indexes φ and c[J]. Chinese Journal of Geotechnical Engineering，1997，29(4)：100-104.(in Chinese))
[43]	PANARETOS V M，ZEMEL Y. Statistical aspects of Wasserstein distances[J]. Annual Review of Statistics and Its Application，2019，6(1)：405-431.
[30]	ABRIL-PLA O，ANDREANI V，CARROLL C，et al. PyMC：a modern，and comprehensive probabilistic programming framework in Python[J]. PeerJ Computer Science，2023，9：e1516. https：//doi.org/ 10.7717/peerj-cs.1516.
[44]	HELLINGER E. Neue Begründung der Theorie quadratischer Formen von unendlichvielen Veränderlichen[J]. Journal FÜR Die Reine Und Angewandte Mathematik，1909，1909(136)：210-271.
[31]	HOFFMAN M D，GELMAN A. The No-U-Turn sampler：adaptively setting path lengths in Hamiltonian Monte Carlo[J]. Journal of Machine Learning Research，2014，15(1)：593-1 623.
[45]	MARTIN O A，KUMAR R，LAO J. Bayesian modeling and computation in Python[M]. New York：Chapman and Hall/CRC，2021：140.
[32]	NEAL R M. MCMC using Hamiltonian dynamics[J]. Arxiv Preprint，2012，doi：10.48550/arXiv.1206.1901.
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