考虑地层变异性和土体参数变异性的边坡可靠度分析
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摘要
现有边坡可靠度分析大多数只考虑土体参数的固有变异性,而忽略了地层变异性的影响。为此,提出了同时考虑地层变异性和土体参数固有变异性的边坡可靠度分析方法,利用耦合马尔可夫链模拟地层分布,采用基于乔列斯基分解的中点法离散土体参数随机场,采用有限元强度折减法计算边坡安全系数,通过蒙特卡洛法模拟进行边坡可靠度分析。利用澳大利亚珀斯市钻孔资料,以边坡可靠度问题为例阐明了同时考虑地层变异性和土体参数固有变异性的重要性,研究了钻孔布置方案对边坡可靠度的影响规律,结果表明:提出的方法能够有效地反映地层变异性和土体参数固有变异性对边坡可靠度的影响。当钻孔数目较少时,模拟的边坡土体类型分布与真实边坡土体类型分布相差较大,此时忽略地层变异性将导致边坡可靠度不精确的估计结果。钻孔布置方案对边坡失效概率和安全系数有明显的影响,钻孔应尽可能多的布置在边坡关键影响区域。边坡失效概率和安全系数统计量与钻孔数目并不呈单调关系,但是随着钻孔数目的增加,边坡失效概率和安全系数统计量逐渐收敛至"精确解"。
The inherent variability of soil properties has currently received considerable attention in slope reliability analysis. However, the geological uncertainty is often ignored in analysis. This paper proposes a method for the slope reliability analysis considering geological uncertainty and spatial variability of soil parameters. The coupled Markov chain model is adopted to simulate the geological uncertainty. The midpoint method based on the Cholesky decomposition technique is used to discretize the random fields of different soil type parameters. The safety factor is calculated using the finite element-strength reduction method. The slope reliability analysis is conducted by Mote Carlo simulation. The procedure for this method is presented. A slope reliability problem is analyzed using the borehole data in Perth, Australia to illustrate the importance of considering geological uncertainty and spatial variability of soil parameters in slope reliability analysis and investigate the effect of layout scheme of boreholes on evaluating slope reliability. The results indicate that the proposed method can effectively reflect the effect of two types of soil heterogeneity on slope reliability. When there is less number of boreholes, the difference between the simulated and the real soil type distribution of slope is large, and ignoring the geological uncertainty will result in inaccurate estimation for slope reliability. The layout scheme of boreholes has a significant effect on safety factor and failure probability of slope. Boreholes should be placed as many as possible in the critical influence zone of the slope. The relationships between the statistics of safety factor and failure probability of slope and the number of boreholes are not monotonic, but the statistics of safety factor and failure probability of the slope converge to the accurate value with the increasing borehole number.
The inherent variability of soil properties has currently received considerable attention in slope reliability analysis. However, the geological uncertainty is often ignored in analysis. This paper proposes a method for the slope reliability analysis considering geological uncertainty and spatial variability of soil parameters. The coupled Markov chain model is adopted to simulate the geological uncertainty. The midpoint method based on the Cholesky decomposition technique is used to discretize the random fields of different soil type parameters. The safety factor is calculated using the finite element-strength reduction method. The slope reliability analysis is conducted by Mote Carlo simulation. The procedure for this method is presented. A slope reliability problem is analyzed using the borehole data in Perth, Australia to illustrate the importance of considering geological uncertainty and spatial variability of soil parameters in slope reliability analysis and investigate the effect of layout scheme of boreholes on evaluating slope reliability. The results indicate that the proposed method can effectively reflect the effect of two types of soil heterogeneity on slope reliability. When there is less number of boreholes, the difference between the simulated and the real soil type distribution of slope is large, and ignoring the geological uncertainty will result in inaccurate estimation for slope reliability. The layout scheme of boreholes has a significant effect on safety factor and failure probability of slope. Boreholes should be placed as many as possible in the critical influence zone of the slope. The relationships between the statistics of safety factor and failure probability of slope and the number of boreholes are not monotonic, but the statistics of safety factor and failure probability of the slope converge to the accurate value with the increasing borehole number.
引文
[1]ELKATEB T,CHALATURNYK R,ROBERTSON PK.An overview of soil heterogeneity:quantification and implications on geotechnical field problems[J].Canadian Geotechnical Journal,2003,40(1):1–15.
[2]PHOON K K,KULHAWY F H.Characterization of geotechnical variability[J].Canadian Geotechnical Journal,1999,36(4):612–624.
[3]EVANS S G.Landslides and surficial deposits in urban areas of British Columbia:a review[J].Canadian Geotechnical Journal,1982,19(3):269–288.
[4]HANSEN L,EILERTSEN R,SOLBERG I L,et al.Stratigraphic evaluation of a Holocene clay-slide in Northern Norway[J].Landslides,2007,4(3):233–244.
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[8]李典庆,蒋水华,周创兵.等.考虑参数空间变异性的边坡可靠度分析非侵入式随机有限元法[J].岩土工程学报,2013,35(8):1413–1422.(LI Dian-qing,JIANG Shui-hua,ZHOU Chuang-bing,et al.Reliability analysis of slopes considering spatial variability of soil parameters using non-intrusive stochastic finite element method[J].Chinese Journal of Geotechnical Engineering,2013,35(8):1413–1422.(in Chinese))
[9]祁小辉,李典庆,周创兵,等.考虑土体空间变异性的边坡最危险滑动面随机分析方法[J].岩土工程学报,2013,35(4):745–753.(QI Xiao-hui,LI Dian-qing,ZHOU Chuang-bing,et al.Stochastic analysis method of critical slip surfaces in soil slopes considering spatial variability[J].Chinese Journal of Geotechnical Engineering,2013,35(4):745–753.(in Chinese))
[10]邓志平,蒋水华,曹子君,等.考虑参数空间变异性边坡可靠度分析的Kriging方法[J].武汉大学学报:工学版,2014,47(6):743-749.(DENG Zhi-ping,JIANG Shui-hua,CAO Zi-jun,et al.Reliability analysis of slope stability considering spatially varying soil properties using Kriging method[J].Engineering Journal of Wuhan University,2014,47(6):743–749.(in Chinese))
[11]GRIFFITHS D V,FENTON G A,MANOHARAN N.Undrained bearing capacity of two-strip footings on spatially random soil[J].International Journal of Geomechanics,2006,6(6):421–427.
[12]CHO S E,PARK H C.Effect of spatial variability of cross-correlated soil properties on bearing capacity of strip footing[J].International Journal for Numerical and Analytical Methods in Geomechanics,2010,34(1):1–26.
[13]WANG Y,HUANG K,CAO Z.Bayesian identification of soil strata in London clay[J].Géotechnique,2014,64(3):239.
[14]EISBACHER GH.Natural slope failure,northeastern Skeena mountains[J].Canadian Geotechnical Journal,1971,8(3):384–390.
[15]TANG WH,SIDI I,GILBERT RB.Average property in random two-state medium[J].Journal of Engineering Mechanics,1989,115(1):131–144.
[16]HALIM IS.Reliability of geotechnical systems considering geological anomaly[D].Urbana–Champaign:University of Illinois at Urbana-Champaign,1991.
[17]KOHNO S,ANG A,TANG W H.Reliability evaluation of idealized tunnel systems[J].Structural Safety,1992,11(2):81–93.
[18]ELFEKI A,DEKKING M.A Markov chain model for subsurface characterization:theory and applications[J].Mathematical Geology,2001,33(5):569–589.
[19]QI X H,LI D Q,PHOON K K,et al.Simulation of geologic uncertainty using coupled Markov chain[J].Engineering Geology,2016,207:129–140.
[20]LI D Q,QI X H,CAO Z J,et al.Evaluating slope stability uncertainty using coupled Markov chain[J].Computers and Geotechnics,2016,73:72–82.
[21]HALDAR S,BABU G L S.Effect of soil spatial variability on the response of laterally loaded pile in undrained clay[J].Computers and Geotechnics,2008,35(4):537–547.
[22]SRIVASTAVA A,BABU G L S,HALDAR S.Influence of spatial variability of permeability property on steady state seepage flow and slope stability analysis[J].Engineering Geology,2010,110(3):93–101.
[23]KASAMA K,WHITTLE A J,ZEN K.Effect of spatial variability on the bearing capacity of cement-treated ground[J].Soils and Foundations,2012,52(4):600–619.
[24]蒋水华,李典庆,周创兵,等.考虑自相关函数影响的边坡可靠度分析[J].岩土工程学报,2014,36(3):508–518.(JIANG Shui-hua,LI Dian-qing,ZHOU Chuang-bing,et al.Slope reliability analysis considering effect of autocorrelation functions[J].Chinese Journal of Geotechnical Engineering,2014,36(3):508–518.(in Chinese))
[25]CHING J,PHOON K K.Effect of element sizes in random field finite element simulations of soil shear strength[J].Computers&Structures,2013,126:120–134.
[26]SIVAKUMAR BABU GL,SRIVASTAVA A,MURTHY DSN.Reliability analysis of the bearing capacity of a shallow foundation resting on cohesive soil[J].Canadian Geotechnical Journal,2006,43(2):217–223.
[2]PHOON K K,KULHAWY F H.Characterization of geotechnical variability[J].Canadian Geotechnical Journal,1999,36(4):612–624.
[3]EVANS S G.Landslides and surficial deposits in urban areas of British Columbia:a review[J].Canadian Geotechnical Journal,1982,19(3):269–288.
[4]HANSEN L,EILERTSEN R,SOLBERG I L,et al.Stratigraphic evaluation of a Holocene clay-slide in Northern Norway[J].Landslides,2007,4(3):233–244.
[5]刘润,闫澍旺.渤海湾地基土随机场特性及可靠度分析[J].岩土工程学报,2004,26(4):464–467.(LIU Run,YAN Shu-wang.Random field model and reliability analysis of foundation soil in Bohai gulf[J].Chinese Journal of Geotechnical Engineering,2004,26(4):464–467.(in Chinese))
[6]朱红霞,闫澍旺.天津港地基土随机场特性及可靠度分析[J].岩石力学与工程学报,2007,26(增刊2):3959–3965.(ZHU Hong-xia,YAN Shu-wang.Random field model and reliability analysis of foundation soil in Tianjin port[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(S2):3959–3965.(in Chinese))
[7]张继周,缪林昌.基于随机场理论的地基概率沉降分析[J].岩土工程学报,2010,32(7):1059–1064.(ZHANG Ji-zhou,MIAO Lin-chang.Probabilistic foundation settlement based on random field theory[J].Chinese Journal of Geotechnical Engineering,2010,32(7):1059–1064.(in Chinese))
[8]李典庆,蒋水华,周创兵.等.考虑参数空间变异性的边坡可靠度分析非侵入式随机有限元法[J].岩土工程学报,2013,35(8):1413–1422.(LI Dian-qing,JIANG Shui-hua,ZHOU Chuang-bing,et al.Reliability analysis of slopes considering spatial variability of soil parameters using non-intrusive stochastic finite element method[J].Chinese Journal of Geotechnical Engineering,2013,35(8):1413–1422.(in Chinese))
[9]祁小辉,李典庆,周创兵,等.考虑土体空间变异性的边坡最危险滑动面随机分析方法[J].岩土工程学报,2013,35(4):745–753.(QI Xiao-hui,LI Dian-qing,ZHOU Chuang-bing,et al.Stochastic analysis method of critical slip surfaces in soil slopes considering spatial variability[J].Chinese Journal of Geotechnical Engineering,2013,35(4):745–753.(in Chinese))
[10]邓志平,蒋水华,曹子君,等.考虑参数空间变异性边坡可靠度分析的Kriging方法[J].武汉大学学报:工学版,2014,47(6):743-749.(DENG Zhi-ping,JIANG Shui-hua,CAO Zi-jun,et al.Reliability analysis of slope stability considering spatially varying soil properties using Kriging method[J].Engineering Journal of Wuhan University,2014,47(6):743–749.(in Chinese))
[11]GRIFFITHS D V,FENTON G A,MANOHARAN N.Undrained bearing capacity of two-strip footings on spatially random soil[J].International Journal of Geomechanics,2006,6(6):421–427.
[12]CHO S E,PARK H C.Effect of spatial variability of cross-correlated soil properties on bearing capacity of strip footing[J].International Journal for Numerical and Analytical Methods in Geomechanics,2010,34(1):1–26.
[13]WANG Y,HUANG K,CAO Z.Bayesian identification of soil strata in London clay[J].Géotechnique,2014,64(3):239.
[14]EISBACHER GH.Natural slope failure,northeastern Skeena mountains[J].Canadian Geotechnical Journal,1971,8(3):384–390.
[15]TANG WH,SIDI I,GILBERT RB.Average property in random two-state medium[J].Journal of Engineering Mechanics,1989,115(1):131–144.
[16]HALIM IS.Reliability of geotechnical systems considering geological anomaly[D].Urbana–Champaign:University of Illinois at Urbana-Champaign,1991.
[17]KOHNO S,ANG A,TANG W H.Reliability evaluation of idealized tunnel systems[J].Structural Safety,1992,11(2):81–93.
[18]ELFEKI A,DEKKING M.A Markov chain model for subsurface characterization:theory and applications[J].Mathematical Geology,2001,33(5):569–589.
[19]QI X H,LI D Q,PHOON K K,et al.Simulation of geologic uncertainty using coupled Markov chain[J].Engineering Geology,2016,207:129–140.
[20]LI D Q,QI X H,CAO Z J,et al.Evaluating slope stability uncertainty using coupled Markov chain[J].Computers and Geotechnics,2016,73:72–82.
[21]HALDAR S,BABU G L S.Effect of soil spatial variability on the response of laterally loaded pile in undrained clay[J].Computers and Geotechnics,2008,35(4):537–547.
[22]SRIVASTAVA A,BABU G L S,HALDAR S.Influence of spatial variability of permeability property on steady state seepage flow and slope stability analysis[J].Engineering Geology,2010,110(3):93–101.
[23]KASAMA K,WHITTLE A J,ZEN K.Effect of spatial variability on the bearing capacity of cement-treated ground[J].Soils and Foundations,2012,52(4):600–619.
[24]蒋水华,李典庆,周创兵,等.考虑自相关函数影响的边坡可靠度分析[J].岩土工程学报,2014,36(3):508–518.(JIANG Shui-hua,LI Dian-qing,ZHOU Chuang-bing,et al.Slope reliability analysis considering effect of autocorrelation functions[J].Chinese Journal of Geotechnical Engineering,2014,36(3):508–518.(in Chinese))
[25]CHING J,PHOON K K.Effect of element sizes in random field finite element simulations of soil shear strength[J].Computers&Structures,2013,126:120–134.
[26]SIVAKUMAR BABU GL,SRIVASTAVA A,MURTHY DSN.Reliability analysis of the bearing capacity of a shallow foundation resting on cohesive soil[J].Canadian Geotechnical Journal,2006,43(2):217–223.
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