正常固结黏土边坡可靠度随机有限元分析
|
摘要
基于概率和统计理论,对适用于正常固结黏土边坡的不排水强度随机场进行模拟,得到不排水强度均值从0开始随深度线性增长的非平稳随机场模型.基于生成的非平稳随机场模型,建立考虑参数空间变异特性的正常固结黏土边坡随机有限元分析方法,从而揭示不排水强度参数空间变异特性对正常固结黏土边坡可靠度及破坏机制的影响规律.通过对比分析发现:边坡的安全系数较小时,若采用正态分布假设不排水强度,则会低估边坡的失效概率,得到非保守的结果;此时,存在一个最危险相关距离,边坡的失效概率最大.当边坡不排水强度变异系数较大时,结合随机有限元分析得到破坏机制比确定性分析得到的最深滑动面更深.
Based on probability and statistics theory,the random field of undrained strength for slopes in normally consolidated clays was simulated,and the non-stationary random field of undrained strength increasing linearly with depth from a zero value at the ground surface was obtained.Meanwhile,based on the generated non-stationary random field model,the random finite-element method for stability analysis of slopes in normally consolidated clays accounting for spatial variability of soil properties was proposed to investigate the effect of spatial variability of undrained strength on the reliability and failure mechanism of slopes in normally consolidated clays.By comparative analysis,it is found that for slopes with relatively low factors of safety,the assumption of normally distributed undrained strength may underestimate the probability of failure,leading unconservative results.Meanwhile,for slopes with relatively low factors of safety,there exists a worst-case spatial correlation length,which leads to the highest probability of failure.According to the failure mechanisms by random finite-element analysis,it is found that for slopes with relatively high coefficients of variation of undrained strength,the failure mechanism may be deeper than the deepest failure surface obtained by deterministic analysis.
Based on probability and statistics theory,the random field of undrained strength for slopes in normally consolidated clays was simulated,and the non-stationary random field of undrained strength increasing linearly with depth from a zero value at the ground surface was obtained.Meanwhile,based on the generated non-stationary random field model,the random finite-element method for stability analysis of slopes in normally consolidated clays accounting for spatial variability of soil properties was proposed to investigate the effect of spatial variability of undrained strength on the reliability and failure mechanism of slopes in normally consolidated clays.By comparative analysis,it is found that for slopes with relatively low factors of safety,the assumption of normally distributed undrained strength may underestimate the probability of failure,leading unconservative results.Meanwhile,for slopes with relatively low factors of safety,there exists a worst-case spatial correlation length,which leads to the highest probability of failure.According to the failure mechanisms by random finite-element analysis,it is found that for slopes with relatively high coefficients of variation of undrained strength,the failure mechanism may be deeper than the deepest failure surface obtained by deterministic analysis.
引文
[1]李典庆,蒋水华.边坡可靠度非侵入式随机分析方法[M].北京:科学出版社,2016.
[2]陈祖煜.建立在相对安全率准则基础上的岩土工程可靠度分析与安全判据[J].岩石力学与工程学报,2018,37(3):521-544.
[3]PHOON K K,CHING J.Risk and reliability in geotechnical engineering[M].Boca Raton:CRC Press,2015.
[4]VANMARCKE E H.Random fields analysis and synthesis[M].Cambridge:MIT Press,1983.
[5]FENTON G A,VANMARCKE E H.Simulation of random fields via local average subdivision[J].Journal of Engineering Mechanics,1990,116(8):1733-1749.
[6]FENTON G A,GRIFFITHS D V.Risk assessment in geotechnical engineering[M].Hoboken:John Wiley&Sons,2008.
[7]GRIFFITHS D V,FENTON G A.Influence of soil strength spatial variability on the stability of an undrained clay slope by finite elements[C]//GeoDenver2000 Symposium.Denver,2000:184-193.
[8]GRIFFITHS D V,ZHU D,HUANG J,et al.Observations on probabilistic slope stability analysis[C]//Proc of 6th Asian-Pacific Symposium on Structural Reliability and its Application.Shanghai:IEEE,2016:1-14.
[9]PHOON K K,KULHAWY F H.Charactering of geotechnical variability[J].Canadian Geotechnical Journal,1999,36(4):612-624.
[10]张继周,缪林昌,王华敬.土体参数不确定性描述方法的探讨[J].岩土工程学报,2009,31(12):1936-1940.
[11]LI D Q,QI X H,PHOON K K,et al.Effect of spatially variable shear strength parameters with linearly increaseing mean trend on reliability of infinite slopes[J].Structural Safety,2014,49:45-55.
[12]ZHU D,GRIFFITHS D V,HUANG J,et al.Probabilistic stability analyses of undrained slopes with linearly increasing mean strength[J].Geotechnique,2017,67(8):733-746.
[13]JIANG S H,HUANG J.Modeling of non-stationary random field of undrained shear strength of soil for slope reliability analysis[J].Soils and Foundations,2018,58(1):185-198.
[14]李典庆,祁小辉,周创兵,等.考虑参数空间变异性的无限长边坡可靠度分析[J].岩土工程学报,2013,35(10):1799-1806.
[15]GRIFFITHS D V,YU X.Another look at the stability of slopes with linearly increasing undrained strength[J].Geotechnique,2015,65(10):824-830.
[16]HICKS M A,SAMY K.Influence of heterogeneity on undrained clay slope stability[J].Quarterly Journal of Engineering Geology and Hydrogeology,2002,35(1):41-49.
[17]GRIFFITHS D V,HUANG J,FENTON G A.Influence of spatial variability on slope reliability using 2-D random fields[J].Journal of Geotechnical and Geoenvirontal Engineering,2009,135(10):1367-1378.
[18]ZHU D,GRIFFITHS D V,FENTON G A.Worst-case spatial correlation length in probabilistic slope stability analysis[J].Geotechnique,2019,69(1):85-88.
[2]陈祖煜.建立在相对安全率准则基础上的岩土工程可靠度分析与安全判据[J].岩石力学与工程学报,2018,37(3):521-544.
[3]PHOON K K,CHING J.Risk and reliability in geotechnical engineering[M].Boca Raton:CRC Press,2015.
[4]VANMARCKE E H.Random fields analysis and synthesis[M].Cambridge:MIT Press,1983.
[5]FENTON G A,VANMARCKE E H.Simulation of random fields via local average subdivision[J].Journal of Engineering Mechanics,1990,116(8):1733-1749.
[6]FENTON G A,GRIFFITHS D V.Risk assessment in geotechnical engineering[M].Hoboken:John Wiley&Sons,2008.
[7]GRIFFITHS D V,FENTON G A.Influence of soil strength spatial variability on the stability of an undrained clay slope by finite elements[C]//GeoDenver2000 Symposium.Denver,2000:184-193.
[8]GRIFFITHS D V,ZHU D,HUANG J,et al.Observations on probabilistic slope stability analysis[C]//Proc of 6th Asian-Pacific Symposium on Structural Reliability and its Application.Shanghai:IEEE,2016:1-14.
[9]PHOON K K,KULHAWY F H.Charactering of geotechnical variability[J].Canadian Geotechnical Journal,1999,36(4):612-624.
[10]张继周,缪林昌,王华敬.土体参数不确定性描述方法的探讨[J].岩土工程学报,2009,31(12):1936-1940.
[11]LI D Q,QI X H,PHOON K K,et al.Effect of spatially variable shear strength parameters with linearly increaseing mean trend on reliability of infinite slopes[J].Structural Safety,2014,49:45-55.
[12]ZHU D,GRIFFITHS D V,HUANG J,et al.Probabilistic stability analyses of undrained slopes with linearly increasing mean strength[J].Geotechnique,2017,67(8):733-746.
[13]JIANG S H,HUANG J.Modeling of non-stationary random field of undrained shear strength of soil for slope reliability analysis[J].Soils and Foundations,2018,58(1):185-198.
[14]李典庆,祁小辉,周创兵,等.考虑参数空间变异性的无限长边坡可靠度分析[J].岩土工程学报,2013,35(10):1799-1806.
[15]GRIFFITHS D V,YU X.Another look at the stability of slopes with linearly increasing undrained strength[J].Geotechnique,2015,65(10):824-830.
[16]HICKS M A,SAMY K.Influence of heterogeneity on undrained clay slope stability[J].Quarterly Journal of Engineering Geology and Hydrogeology,2002,35(1):41-49.
[17]GRIFFITHS D V,HUANG J,FENTON G A.Influence of spatial variability on slope reliability using 2-D random fields[J].Journal of Geotechnical and Geoenvirontal Engineering,2009,135(10):1367-1378.
[18]ZHU D,GRIFFITHS D V,FENTON G A.Worst-case spatial correlation length in probabilistic slope stability analysis[J].Geotechnique,2019,69(1):85-88.