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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摘要针对小样本条件下岩土试验数据统计不确定性大、岩土体参数概率分布不准确、边坡可靠度分析不合理的问题，通过综合考虑多个工程场地的相似特点，使用分层贝叶斯模型(HBM)，充分借助相似工程场地的数据信息，并结合马尔科夫链蒙特卡洛(MCMC)，实现小样本条件下目标场地岩土参数多维概率分布的合理刻画。采用陕北多个黄土工程场地的真实c，?数据，验证HBM方法对于小样本条件下构建岩土参数概率分布的有效性。并在此基础上，开展某黄土边坡的可靠度分析。结果表明：与独立参数模型(IPM)(不考虑相似工程场地数据信息)相比，HBM对应的边坡失效概率从11.6%降低到4.8%。此外，为了进一步验证HBM的相较传统方法的准确性，还通过大量模拟数据进行试验。结果表明：相比于IPM而言，HBM所得结果准确度能够提升33%～53%，不确定性降低19%～53%。

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	许领
	王文龙
	赵腾远

关键词 ：土力学, 土体参数的概率分布, 贝叶斯方法, 分层贝叶斯模型, 可靠度理论

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

引用本文:

许领，王文龙，赵腾远. 考虑场地相似性的小样本边坡可靠度分析[J]. 岩石力学与工程学报, 2025, 44(4): 977-988.
XU Ling，WANG Wenlong，ZHAO Tengyuan. Reliability analysis of slopes from sparse measurements considering sites similarity. , 2025, 44(4): 977-988.

链接本文:

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

[1]	祝玉学. 边坡可靠性分析[M]. 北京：冶金工业出版社，1993：21-25.(ZHU Yuxue. Slope reliability analysis[M]. Beijing：Metallurgical Industry Press，1993：21-25.(in Chinese))
[2]	张文生，罗强，蒋良潍，等. 小样本岩土参数下考虑矩估计偏差的土质边坡可靠度分析[J]. 岩土力学，2019，40(1)：315-324.(ZHANG Wensheng，LUO Qiang，JIANG Liangwei，et al. Reliability analysis of soil slope considering moment estimation bias using small sample geotechnical parameters[J]. Rock and Soil Mechanics，2019，40(1)：315-324.(in Chinese))
[3]	蒋良潍，赵晶，罗强，等. 小样本岩土参数下土质边坡可靠度分析的条件概率法[J]. 工程地质学报，2021，29(1)：205-213. (JIANG Liangwei，ZHAO Jing，LUO Qiang，et al. Conditional probability method for soil slope stability with small sample[J]. Journal of Engineering Geology，2021，29(1)：205-213.(in Chinese))
[4]	LIU X，TANG X，LI D，et al. Jackknifing for modeling sampling properties of soil statistics for geotechnical reliability analysis[J]. Computers and Geotechnics，2020，125：103685.
[5]	舒苏荀，张东升，潘天久，等. 小样本条件下基于Bootstrap方法的边坡非概率可靠度分析[J]. 土木工程与管理学报，2023，40(3)：96-103.(SHU Suxun，ZHANG Dongsheng，PAN Tianjiu，et al. Bootstrap method-based non-probabilistic reliability analysis for slope with small samples[J]. Journal of Civil Engineering and Managment，2023，40(3)：96-103.(in Chinese))
[6]	MA J，SU A，ZHANG J，et al. Reliability analysis for a large and complex landslide in the three gorges reservoir area(China) based on incomplete information[J]. Geomatics，Natural Hazards and Risk，2018，10(1)：181-196.
[7]	PANDIT B，TIWARI G，LATHA G M，et al. Probabilistic characterization of rock mass from limited laboratory tests and field data：associated reliability analysis and its interpretation[J]. Rock Mechanics and Rock Engineering，2019，52(9)：2 985-3 001.
[8]	唐小松，李典庆，周创兵，等. 基于Bootstrap方法的岩土体参数联合分布模型识别[J]. 岩土力学，2015，36(4)：913-922.(TANG Xiaosong，LI Dianqing，ZHOU Chuangbing，et al. Bootstrap method for joint probability distribution identification of correlated geotechnical parameters[J]. Rock and Soil Mechanics，2015，36(4)：913-922.(in Chinese))
[9]	唐小松，李典庆，周创兵，等. 基于Copula函数的抗剪强度参数间相关性模拟及边坡可靠度分析[J]. 岩土工程学报，2012，34(12)：2 284-2 291.(TANG Xiaosong，LI Dianqing，ZHOU Chuangbing，et al. Modeling dependence between shear strength parameters using Copulas and its effect on slope reliability[J]. Chinese Journal of Geotechnical Engineering，2012，34(12)：2 284-2 291.(in Chinese))
[10]	CAO J，WANG T，SHENG M，et al. Assessment of multi-dimensional joint probability distribution for uncertain mechanical strength parameters under small sample test data[J]. Probabilistic Engineering Mechanics，2023，74：103511.
[11]	ZHANG L，LI D，TANG X，et al. Bayesian model comparison and characterization of bivariate distribution for shear strength parameters of soil[J]. Computers and Geotechnics，2018，95：110-118.
[12]	KUMAR A，TIWARI G. Bayesian multimodel probabilistic methodology for stability analysis of rock structures with limited data of Copula-Dependent Inputs[J]. ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems，Part A：Civil Engineering，2023，9(3)：04023025.
[13]	ALADEJARE A E，AKEJU V O，WANG Y. Data-driven characterization of the correlation between uniaxial compressive strength and Youngs’ modulus of rock without regression models[J]. Transportation Geotechnics，2022，32：100680.
[14]	BOZORGZADEH N，HARRISON J P. Reliability-based design in rock engineering：Application of Bayesian regression methods to rock strength data[J]. Journal of Rock Mechanics and Geotechnical Engineering，2019，11(3)：612-627.
[15]	TANG X，HUANG H，LIU X，et al. Efficient Bayesian method for characterizing multiple soil parameters using parametric bootstrap[J]. Computers and Geotechnics，2023，156：105296.
[16]	吴越，刘东升，孙树国，等. 岩土强度参数正态-逆伽马分布的最大后验估计[J]. 岩石力学与工程学报，2019，38(6)：1 188- 1 196.(WU Yue，LIU Dongsheng，SUN Shuguo，et al. Maximum posteriori estimation of strength parameters for geotechnical material obeying normal-inverse Gamma distribution[J]. Chinese Journal of Rock Mechanics and Engineering，2019，38(6)：1 188-1 196.(in Chinese))
[17]	LIU J，JIANG Q，CHEN T，et al. Bayesian estimation for probability distribution of rock?s elastic modulus based on compression wave velocity and deformation warning for large underground cavern[J]. Rock Mechanics and Rock Engineering，2022，55(6)：3 749-3 767.
[18]	BOZORGZADEH N，BATHURST R J. Hierarchical Bayesian approaches to statistical modelling of geotechnical data[J]. Georisk：Assessment and Management of Risk for Engineered Systems and Geohazards，2020，16(3)：452-69.
[19]	LU S，ZHANG J，ZHOU S，et al. Reliability prediction of the axial ultimate bearing capacity of piles：A hierarchical Bayesian method[J]. Advances in Mechanical Engineering，2018，10(11)：1687814018811054.
[20]	WANG M，PAN S，TAO Y，et al. Hierarchical Bayesian modelling of quasi-region-specific soil porosity[J]. Ocean Engineering，2022，266：113052.
[21]	BOZORGZADEH N，HARRISON J P，ESCOBAR M D. Hierarchical Bayesian modelling of geotechnical data：application to rock strength[J]. Géotechnique，2019，69(12)：1 056 - 70.
[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.
[23]	CHING J，PHOON K. Measuring similarity between site-specific data and records from other sites[J]. ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems，Part A：Civil Engineering，2020，6(2)：04020011.
[24]	GELMAN A，CARLIN J B，STERN H S，et al. Bayesian data analysis[M]. 3rd ed. [S. l.]：Chapman and Hall/CRC，2021：78.
[25]	中华人民共和国住房和城乡建设部. GB 50068—2018建筑结构可靠性设计统一标准[S]. 北京：中国建筑工业出版社，2018.(Ministry of Housing and Urban-Rural Development of thr People's Republic of China. GB 50068—2018 Unified standard for reliability design of building structures[S]. Beijing：China Architecture and Building Press，2018.(in Chinese))
[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))
[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.
[28]	BURKARDT J. The truncated normal distribution[J]. Department of Scientific Computing Website，Florida State University，2014，1(35)：58.
[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))
[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.
[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.
[32]	NEAL R M. MCMC using Hamiltonian dynamics[J]. Arxiv Preprint，2012，doi：10.48550/arXiv.1206.1901.
[33]	ANG A H S，TANG W H. Probability concepts in engineering：emphasis on applications to civil and environmental engineering，2e instructor site[M]. [S. l.]：Wiley，2007：202-204.
[34]	陈将宏，李建林，许晓亮，等. 相关变量生成算法及边坡可靠度Monte Carlo模拟[J]. 岩土力学，2017，38(11)：3 341-3 346.(CHENG Jianghong，LI Jianling，XU Xiaoliang，et al. Algorithm for generation correlative variables and Monte Carlo simulation of slope reliability[J]. Rock and Soil Mechanics，2017，38(11)：3 341-3 346.(in Chinese))
[35]	ANG A H，TANG W H. Probability concepts in engineering planning and design，vol. 2：Decision，risk，and reliability[M]. [S. l.]：John Wiley & Sons Inc.，1984.
[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.
[37]	LIU Y，LI X，LIU X，et al. A combined shear strength reduction and surrogate model method for efficient reliability analysis of slopes[J]. Computers and Geotechnics，2022，152：105021.
[38]	XU L，ZHOU G，ZHAO T，et al. Characterization of inherent spatial variability of loess deposit properties in Shaanxi Province，China[J]. Journal of Soils and Sediments，2023，23(7)：2 862-2 877.
[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))
[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))
[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))
[42]	WANG Y，ZHAO T，CAO Z. Site-specific probability distribution of geotechnical properties[J]. Computers and Geotechnics，2015，70(10)：159-168.
[43]	PANARETOS V M，ZEMEL Y. Statistical aspects of Wasserstein distances[J]. Annual Review of Statistics and Its Application，2019，6(1)：405-431.
[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.
[45]	MARTIN O A，KUMAR R，LAO J. Bayesian modeling and computation in Python[M]. New York：Chapman and Hall/CRC，2021：140.
[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.