|Table of Contents|

Bayes estimation of mean and variance for shear strength parameters of loess and its application(PDF)

《建筑科学与工程学报》[ISSN:1673-2049/CN:61-1442/TU]

Issue:
2024年02期
Page:
163-172
Research Field:
岩土工程
Publishing date:

Info

Title:
Bayes estimation of mean and variance for shear strength parameters of loess and its application
Author(s):
LI Ping1; 2;  DONG Luanhua3;  ZHAO Zhiyan1; 2;  LI Jinming1; 2;  SHEN Wei1; 2;  LI Tonglu1; 2
(1. School of Geological Engineering and Geomatics, Chang'an University, Xi'an 710054, Shaanxi, China; 2. Water Cycle and Geological Environment Observation and Research Station for the Chinese Loess Plateau, Zhengning 745399, Gansu, China; 3. Shaanxi Province Institute of Water Resources and Electric Power Investigation and Design, Xi'an 710005, Shaanxi, China)
Keywords:
loess;  slope;  Bayes theory;  priori distribution;  normal inverse gamma distribution
PACS:
TU444
DOI:
10.19815/j.jace.2022.04123
Abstract:
In order to solve the problem of estimating the strength parameters of loess, 3 834 sets of Q1, Q2, Q3 loess strength parameters c(cohesive force), φ(internal friction angle)from engineering survey projects test data were collected and statistically analyzed. Without considering the correlation between the two, both the mean and variance of the parameters were used as random variables to establish normal inverse gamma priori distribution of the loess strength parameter c, φ. Based on Bayes theory, the expected value solution formulas for the posterior distribution of parameters and the posterior probability density function were derived using the conjugate prior method, and the estimation error was determined. Taking the loess slope of Jingyang in Shaanxi as an example, using the established prior distribution and the strength index of the slope soil layer test, the posterior distribution of the parameters was obtained, and the probability distribution of slope failure probability and the probability distribution of the mean stability coefficient were further estimated. The results show that at a 95% confidence level, according to the stability coefficient evaluation, the slopes are in a basically stable state, and the confidence interval of the stability coefficient is small. According to the evaluation of failure probability, the slope is close to a stable state, but the confidence interval of failure probability is relatively large. The variance of loess strength parameters controls the confidence interval of slope failure probability. Using variance as a random variable and considering variance variability can more scientifically evaluate the reliability of loess engineering.

References:

[1] 李可飞,许 领,赵腾远,等.基于Johnson分布体系黄土滑坡影响范围的概率预测[J].工程地质学报,2021,31(2):493-501.
LI Kefei,XU Ling,ZHAO Tengyuan,et al.Probabilistic prediction of loess landslide impact range using Johnson's system[J].Journal of Engineering Geology,2021,31(2):493-501.
[2]邢鲜丽,李同录,李 萍,等.黄土抗剪强度与含水率的变化规律[J].水文地质工程地质,2014,41(3):53-59,97.
XING Xianli,LI Tonglu,LI Ping,et al.Variation regularities of loess shear strength with the moisture content[J].Hydrogeology & Engineering Geology,2014,41(3):53-59,97.
[3]杨 勇,张海峰,范 文,等.西安黄土土性相关距离的统计分布特性研究[J].工程地质学报,2014,22(1):160-165.
YANG Yong,ZHANG Haifeng,FAN Wen,et al.Statistical distribution characteristics of correlation distance of Xi'an loess[J].Journal of Engineering Geology,2014,22(1):160-165.
[4]于慧丽,龙建辉,刘海松,等.吕梁山区黄土边坡工程地质分区及强度参数选取[J].工程地质学报,2014,22(1):152-159.
YU Huili,LONG Jianhui,LIU Haisong,et al.Engineering geology division of loess slope and its strength parameter selection in Lüliang mountainous area[J].Journal of Engineering Geology,2014,22(1):152-159.
[5]倪万魁,韩启龙.黄土土性参数的统计分析[J].工程地质学报,2001,9(1):62-67.
NI Wankui,HAN Qilong.Statistical analysis of physical and mechanical indexes of the typical loess[J].Journal of Engineering Geology,2001,9(1):62-67.
[6]SIACARA A T,BECK A T,FUTAI M M.Reliability analysis of rapid drawdown of an earth dam using direct coupling[J].Computers and Geotechnics,2020,118:103336.
[7]李 萍,白健忠,GRIFFITHS D V,等.黄土边坡可靠度的随机有限元分析[J].地球科学与环境学报,2019,41(1):116-126.
LI Ping,BAI Jianzhong,GRIFFITHS D V,et al.Random finite element analysis for the reliability of loess slopes[J].Journal of Earth Sciences and Environment,2019,41(1):116-126.
[8]郭 健,王起才,李世才.基于敏感性分析的隧道围岩变形稳定可靠度计算[J].兰州交通大学学报,2017,36(6):83-90,113.
GUO Jian,WANG Qicai,LI Shicai.Calculation of stability reliability of tunnel surrounding rock deformation based on sensitivity analysis[J].Journal of Lanzhou Jiaotong University,2017,36(6):83-90,113.
[9]李典庆,唐小松,周创兵,等.基于Copula函数的并联结构系统可靠度分析[J].工程力学,2014,31(8):32-40.
LI Dianqing,TANG Xiaosong,ZHOU Chuangbing,et al.Parallel structural system reliability analysis from the copula viewpoint[J].Engineering Mechanics,2014,31(8):32-40.
[10]LOW B K,ZHANG J,TANG W H.Efficient system reliability analysis illustrated for a retaining wall and a soil slope[J].Computers and Geotechnics,2011,38(2):196-204.
[11]GRIFFITHS D V,HUANG J S,FENTON G A.Influence of spatial variability on slope reliability using 2-D random fields[J].Journal of Geotechnical and Geoenvironmental Engineering,2009,135(10):1367-1378.
[12]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):1188-1196.
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):1188-1196.
[13]TANG X S,LI D Q,WANG X G,et al.Statistical characterization of shear strength parameters of rock mass for hydropower projects in China[J].Engineering Geology,2018,245:258-265.
[14]牛草原,王乐华,许晓亮.土体抗剪强度参数统计特性对边坡可靠性影响研究[J].水利水电技术,2017,48(12):195-198,206.
NIU Caoyuan,WANG Lehua,XU Xiaoliang.Study on impact from statistical characteristics of soil mass shear strength parameters on slope reliability[J].Water Resources and Hydropower Engineering,2017,48(12):195-198,206.
[15]LI D Q,TANG X S,PHOON K K.Bootstrap method for characterizing the effect of uncertainty in shear strength parameters on slope reliability[J].Reliability Engineering & System Safety,2015,140:99-106.
[16]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.
[17]王 林,李典庆,曹子君,等.基于贝叶斯理论的土水特征曲线模型选择与参数识别方法[J].应用基础与工程科学学报,2019,27(6):1269-1284.
WANG Lin,LI Dianqing,CAO Zijun,et al.Bayesian approaches for model selection and parameter identification of soil-water characteristic curve[J].Journal of Basic Science and Engineering,2019,27(6):1269-1284.
[18]PRAKASH A,HAZRA B,SREEDEEP S.Probabilistic analysis of soil-water characteristic curve using limited data[J].Applied Mathematical Modelling,2021,89:752-770.
[19]WANG Y,CAO Z J,AU S K.Efficient Monte Carlo Simulation of parameter sensitivity in probabilistic slope stability analysis[J].Computers and Geotechnics,2010,37(7):1015-1022.
[20]CAO Z J,WANG Y.Bayesian model comparison and characterization of undrained shear strength[J].Journal of Geotechnical and Geoenvironmental Engineering,2014,140(6):04014018.
[21]CAO Z J,HUANG K,WANG Y.Bayesian inverse analysis for geotechnical site characterisation using cone penetration test[J].International Journal of Reliability and Safety,2014,8(2/3/4):97-116.
[22]JIANG S H,LI D Q,CAO Z J,et al.Efficient system reliability analysis of slope stability in spatially variable soils using Monte Carlo simulation[J].Journal of Geotechnical and Geoenvironmental Engineering,2015,141(2):04014096.
[23]夏增选,李 萍,曹 博,等.边坡可靠度的Bayes估计及后验稳健性[J].河海大学学报(自然科学版),2020,48(3):238-244.
XIA Zengxuan,LI Ping,CAO Bo,et al.Bayesian estimation and posterior robustness of slope reliability[J].Journal of Hohai University(Natural Sciences),2020,48(3):238-244.
[24]VO B N,DROVANDI C C,PETTITT A N.Bayesian parametric bootstrap for models with intractable likelihoods[J].Bayesian Analysis,2019,14(1):211-234.
[25]ESIN K B,SAMET K.A simulation study of the Bayes estimator for parameters in Weibull distribution[J].Sigma Journal of Engineering and Natural Sciences,2020,38(3):1609-1621
[26]ZHANG Y Y.The Bayes rule of the variance parameter of the hierarchical normal and inverse gamma model under Stein's loss[J].Communications in Statistics — Theory and Methods,2017,46(14):7125-7133.
[27]WANG Y,QIN Z W,LIU X,et al.Probabilistic analysis of post-failure behavior of soil slopes using random smoothed particle hydrodynamics[J].Engineering Geology,2019,261:105266.
[28]周方明,王 锋,谷明晗,等.基于蒙特卡罗法的缓变型防洪风险分析[J].水资源与水工程学报,2018,29(5):180-185.
ZHOU Fangming,WANG Feng,GU Minghan,et al.Analysis of flood control risk of slow type based on Monte Carlo method[J].Journal of Water Resources and Water Engineering,2018,29(5):180-185.
[29]陈悦丽,陈德辉,李泽椿,等.基于Monte Carlo-SHALSTAB模型的滑坡危险性评价:以福建省德化县为例[J].灾害学,2015,30(4):101-106.
CHEN Yueli,CHEN Dehui,LI Zechun,et al.Assessment of landslide hazard based on Monte carlo-SHALSTAB model[J].Journal of Catastrophology,2015,30(4):101-106.
[30]ZHANG J,LI J Y,CHEN X H,et al.Geological structure-guided hybrid MCMC and Bayesian linearized inversion methodology[J].Journal of Petroleum Science and Engineering,2021,199:108296.
[31]ZHAO C,ZHANG G Z,ZHANG J J.Probabilistic inversion for compressional modulus and shear modulus based on QA-MCMC algorithm with joint probability distribution[J].Journal of Applied Geophysics,2020,178:104070.
[32]张茺喨,田茂再.基于贝叶斯的Bootstrap置信区间[J].统计与决策,2020,36(1):32-35.
ZHANG Chongliang,TIAN Maozai.Bootstrap confidence interval based on Bayes[J].Statistics & Decision,2020,36(1):32-35.
[33]骆 飞,罗 强,蒋良潍,等.小样本岩土参数的Bootstrap估计及边坡稳定分析[J].岩石力学与工程学报,2017,36(2):370-379.
LUO Fei,LUO Qiang,JIANG Liangwei,et al.Bootstrap estimation for geotechnical parameters of small samples and slope stability analysis[J].Chinese Journal of Rock Mechanics and Engineering,2017,36(2):370-379.
[34]孙慧玲,胡伟文,杨美妮.Bayes Bootstrap方法在小样本参数估计中的应用[J].计算机与数字工程,2016,44(5):788-790,808.
SUN Huiling,HU Weiwen,YANG Meini.Application of Bayes Bootstrp method in small samples parameter estimation[J].Computer & Digital Engineering,2016,44(5):788-790,808.
[35]李 萍,黄丽娟,李振江,等.甘肃黄土高边坡可靠度研究[J].岩土力学,2013,34(3):811-817.
LI Ping,HUANG Lijuan,LI Zhenjiang,et al.Study of reliability for loess high slopes in Gansu area[J].Rock and Soil Mechanics,2013,34(3):811-817.
[36]高德彬.公路黄土路堑高边坡稳定性研究[D].西安:长安大学,2008.
GAO Debin.Study on stability of highway loess cutting high slope[D].Xi'an:Chang'an University,2008.
[37]侯晓坤,李同录,赵 谦,等.黄土地区路堑高边坡可靠度设计标准研究[J].工程地质学报,2015,23(增):132-139.
HOU Xiaokun,LI Tonglu,ZHAO Qian,et al.Research on reliability criteria applying high cutting loess slope design[J].Journal of Engineering Geology,2015,23(S):132-139.
[38]李 萍,张 波,李同录.黄土高原边坡特征与破坏规律的分区研究[J].地球科学与环境学报,2012,34(3):89-98.
LI Ping,ZHANG Bo,LI Tonglu.Study on regionalization for characteristic and destruction rule of slope in Loess Plateau[J].Journal of Earth Sciences and Environment,2012,34(3):89-98.
[39]盛 骤.概率论与数理统计[M].3版.北京:高等教育出版社,2001.
SHENG Zhou.Probability and mathematical statistics[M].3rd ed.Beijing:Higher Education Press,2001.
[40]GELMAN A,CARLIN J B,STERN H S,et al.Bayesian data analysis[M].3rd ed.London:Chapman and Hall,2013.
[42]DUNCAN J M.Factors of safety and reliability in geotechnical engineering[J].Journal of Geotechnical and Geoenvironmental Engineering,2000,126(4):307-316.

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Last Update: 2024-03-25