基于上限分析的边坡稳定可靠性评估
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摘要
从塑性极限分析出发,基于上限分析构建边坡极限状态可靠度计算模型;针对状态函数高度非线性导致常规可靠度方法求解时存在困难的问题,将响应面模型作为极限状态函数与可靠度计算间"桥梁",利用二次正交原理优化取样点,建立考虑参数相关性的二次响应面替代函数。利用JC法直接求得边坡可靠指标的一个上限解,讨论了单个及多个参数变异性对边坡可靠度的影响。
This paper starts from plastic limit analysis and builds a reliability calculation model of limiting condition for slope on the basis of the upper bound theorem. As the limit state function of the slope was too complex to be solved by the common reliability method,the response surface method is introduced as the"bridge"between the limit state function and the reliability calculation. Sampling points are optimized using quadratic orthogonal principle. The quadratic response surface function is established, which considers the correlation between parameters. An upper bound solution of reliability is achieved directly using the J-C method. Influences of variability of parameter( s) on reliability of slope were discussed.
This paper starts from plastic limit analysis and builds a reliability calculation model of limiting condition for slope on the basis of the upper bound theorem. As the limit state function of the slope was too complex to be solved by the common reliability method,the response surface method is introduced as the"bridge"between the limit state function and the reliability calculation. Sampling points are optimized using quadratic orthogonal principle. The quadratic response surface function is established, which considers the correlation between parameters. An upper bound solution of reliability is achieved directly using the J-C method. Influences of variability of parameter( s) on reliability of slope were discussed.
引文
Chen H F,Zhan S B.1995.Limit analysis and soil plasticity[M].Beijing:China Communications Press:246-248.
Gong J X.2003.Computational methods for reliability of engineering structures[M].Dalian:Dalian University of Technology.
Jiang S H,Li D Q,Zhou C B,et al.2014.Slope reliability analysis considering effect of autocorrelation functions[J].Chinese Journal of Geotechnical Engineering,36(3):508-518.
Li D Q,Zhou C B,Chen Y F,et al.2010.Reliability analysis of slope using stochastic response surface method and code implementation[J].Chinese Journal of Rock Mechanics and Engineering,29(8):1514-1523.
Li L,Liu B C.2001.Lower bound limit analysis of bearing capacity of slope and its reliability[J].Chinese Journal of Rock Mechanics and Engineering,20(4):508-513.
Li L,Yang X L.2001.Analytical solution of bearing capacity of circular shallow foundations using upper-bound theorem of limit analysis[J].Journal of the China Railway Society,23(1):94-97.
Li Y G,Zhao G F.1994.Asymptotic analysis method for structural reliability in generalized random space[J].Journal of Hydraulic Engineering,25(8):36-41.
LüQ,Low B K.2011.Probabilistic analysis of underground rock excavation using response surface method and SORM[J].Computers and Geotechnics,38(8):1008-1021.
Shu S X,Gong W H.2015.An improved fuzzy point estimate method for slope stability ananlysis based on neural network[J].Rock and Soil Mechanics,36(7):2111-2116.
Su Y H,Li X,Ding Y,et al.2012.Reliability degree method for stability of surrounding rock of tunnels based on quadratic orthogonal experimental optimization[J].Chinese Journal of Geotechnical Engineering,34(2):326-332.
Tan X H,Song C Z,Hou X L.2016.Reliability analysis of rock slope using RBFN-based response surface method[J].Chinese Journal of Underground Space and Engineering,12(1):250-255.
Tan X H,Wang J G,Liu X R,et al.2007.Finite element reliability computation and sensitivity analysis of slope stability[J].Chinese Journal of Rock Mechanics and Engineering,26(1):115-122.
Tong X L,Zhao G F.1997.The response surface method in conjunction with geometric method in structural reliability analysis[J].China Civil Engineering Journal,30(4):51-57.
Wang F,Liang X L,Du J P.2016.Stability analysis and reliability study of anti-overturning stability of rock slope under seismic load[J].Journal of Engineering Geology,24(6):1126-1135.
Wang G L,Wu F Q,Men Y M.2006.Analysis of reliability index calculation on the basis of plasticity limit analysis&slice method of soil slope[J].Journal of Engineering Geology,14(6):835-840.
Wu Z J,Wang S L,Ge X R.2010.Application of Latin hypercube sampling technique to slope reliability analysis[J].Rock and Soil Mechanics,31(4):1047-1054.
Zhang D B,Pan Q J,Yang X L,et al.2014.Upper bound solution of reliability for slope based on limit analysis method[J].Journal of Chongqing University,37(7):59-65.
Zhang Y G,Zhang B,Li P,et al.2011.Reasarch on loess slope reliability based on the point estimate method[J].Journal of Engineering Geology,19(4):615-619.
Zheng Y N,Hou X K,Li P,et al.2014.Reliability study of loess high slope stability in Xixian-Lishi area of western Shanxi province[J].Journal of Engineering Geology,22(3):372-378.
Zhu Y X.1993.Reliability analysis of slope[M].Beijing:Metallurgical Industry Press:5-8.
Zhu Y,Feng X T,Zhou H,et al.2016.Limit state surface in strength parameter space and system reliability analysis[J].Chinese Journal of Rock Mechanics and Engineering,35(S2):3473-3480.
陈惠发,詹世斌.1995.极限分析与土体塑性[M].北京:人民交通出版:246-248.
贡金鑫.2003.工程结构可靠度计算方法[M].大连:大连理工大学出版社.
蒋水华,李典庆,周创兵,等.2014.考虑自相关函数影响的边坡可靠度分析[J].岩土工程学报,36(3):508-518.
李典庆,周创兵,陈益峰,等.2010.边坡可靠度分析的随机响应面法及程序实现[J].岩石力学与工程学报,29(8):1514-1523.
李亮,刘宝琛.2001a.边坡极限承载力的下限分析法及可靠性度理论[J].岩土力学与工程学报,20(4):508-513.
李亮,杨小礼.2001b.圆形浅基础地基承载力极限分析的上限解析解[J].铁道学报,23(1):94-97.
李云贵,赵国藩.1994.广义随机空间内的结构可靠度渐近分析方法[J].水利学报,25(8):36-41.
舒苏旬,龚文惠.2015.边坡稳定分析的神经网络改进模糊点估计法[J].岩土力学,36(7):2111-2116.
苏永华,李翔,丁云,等.2012.基于二次正交试验优化的隧道围岩稳定可靠度方法[J].岩土工程学报,34(2):326-332.
谭晓慧,宋传中,侯晓亮.2016.基于径向基函数响应面法的岩质边坡可靠度分析[J].地下空间与工程学报,12(1):250-255.
谭晓慧,王建国,刘新荣,等.2007.边坡稳定的有限元可靠度计算及敏感性分析[J].岩石力学与工程学报,26(1):115-122.
佟晓利,赵国藩.1997.一种与结构可靠度分析几何法相结合的响应面方法[J].土木工程学报,30(4):51-57.
王飞,梁旭黎,杜建坡.2016.地震荷载作用下岩石边坡的抗倾覆稳定性分析及可靠度研究[J].工程地质学报,24(6):1126-1135.
王根龙,伍法权,门玉明.2006.基于土质边坡塑性极限分析条分法可靠度计算方法研究[J].工程地质学报,14(6):835-840.
吴振君,王水林,葛修润.2010.LHS方法在边坡可靠度分析中的应用[J].岩土力学,31(4):1047-1054.
张道兵,潘秋景,杨小礼,等.2014.用极限分析方法计算边坡可靠度上限值[J].重庆大学学报,37(7):59-65.
张亚国,张波,李萍,等.2011.基于点估计法的黄土边坡可靠度研究[J].工程地质学报,19(4):615-619.
郑亚楠,侯晓坤,李萍,等.2014.晋西隰县-离石地区黄土高边坡可靠度研究[J].工程地质学报,22(3):372-378.
朱勇,冯夏庭,周辉,等.2016.岩土强度参数空间中的极限状态面与系统可靠度分析[J].岩石力学与工程学报,35(增2):3473-3480.
祝玉学.1993.边坡可靠性分析[M].北京:冶金工业出版社:5-8.
Gong J X.2003.Computational methods for reliability of engineering structures[M].Dalian:Dalian University of Technology.
Jiang S H,Li D Q,Zhou C B,et al.2014.Slope reliability analysis considering effect of autocorrelation functions[J].Chinese Journal of Geotechnical Engineering,36(3):508-518.
Li D Q,Zhou C B,Chen Y F,et al.2010.Reliability analysis of slope using stochastic response surface method and code implementation[J].Chinese Journal of Rock Mechanics and Engineering,29(8):1514-1523.
Li L,Liu B C.2001.Lower bound limit analysis of bearing capacity of slope and its reliability[J].Chinese Journal of Rock Mechanics and Engineering,20(4):508-513.
Li L,Yang X L.2001.Analytical solution of bearing capacity of circular shallow foundations using upper-bound theorem of limit analysis[J].Journal of the China Railway Society,23(1):94-97.
Li Y G,Zhao G F.1994.Asymptotic analysis method for structural reliability in generalized random space[J].Journal of Hydraulic Engineering,25(8):36-41.
LüQ,Low B K.2011.Probabilistic analysis of underground rock excavation using response surface method and SORM[J].Computers and Geotechnics,38(8):1008-1021.
Shu S X,Gong W H.2015.An improved fuzzy point estimate method for slope stability ananlysis based on neural network[J].Rock and Soil Mechanics,36(7):2111-2116.
Su Y H,Li X,Ding Y,et al.2012.Reliability degree method for stability of surrounding rock of tunnels based on quadratic orthogonal experimental optimization[J].Chinese Journal of Geotechnical Engineering,34(2):326-332.
Tan X H,Song C Z,Hou X L.2016.Reliability analysis of rock slope using RBFN-based response surface method[J].Chinese Journal of Underground Space and Engineering,12(1):250-255.
Tan X H,Wang J G,Liu X R,et al.2007.Finite element reliability computation and sensitivity analysis of slope stability[J].Chinese Journal of Rock Mechanics and Engineering,26(1):115-122.
Tong X L,Zhao G F.1997.The response surface method in conjunction with geometric method in structural reliability analysis[J].China Civil Engineering Journal,30(4):51-57.
Wang F,Liang X L,Du J P.2016.Stability analysis and reliability study of anti-overturning stability of rock slope under seismic load[J].Journal of Engineering Geology,24(6):1126-1135.
Wang G L,Wu F Q,Men Y M.2006.Analysis of reliability index calculation on the basis of plasticity limit analysis&slice method of soil slope[J].Journal of Engineering Geology,14(6):835-840.
Wu Z J,Wang S L,Ge X R.2010.Application of Latin hypercube sampling technique to slope reliability analysis[J].Rock and Soil Mechanics,31(4):1047-1054.
Zhang D B,Pan Q J,Yang X L,et al.2014.Upper bound solution of reliability for slope based on limit analysis method[J].Journal of Chongqing University,37(7):59-65.
Zhang Y G,Zhang B,Li P,et al.2011.Reasarch on loess slope reliability based on the point estimate method[J].Journal of Engineering Geology,19(4):615-619.
Zheng Y N,Hou X K,Li P,et al.2014.Reliability study of loess high slope stability in Xixian-Lishi area of western Shanxi province[J].Journal of Engineering Geology,22(3):372-378.
Zhu Y X.1993.Reliability analysis of slope[M].Beijing:Metallurgical Industry Press:5-8.
Zhu Y,Feng X T,Zhou H,et al.2016.Limit state surface in strength parameter space and system reliability analysis[J].Chinese Journal of Rock Mechanics and Engineering,35(S2):3473-3480.
陈惠发,詹世斌.1995.极限分析与土体塑性[M].北京:人民交通出版:246-248.
贡金鑫.2003.工程结构可靠度计算方法[M].大连:大连理工大学出版社.
蒋水华,李典庆,周创兵,等.2014.考虑自相关函数影响的边坡可靠度分析[J].岩土工程学报,36(3):508-518.
李典庆,周创兵,陈益峰,等.2010.边坡可靠度分析的随机响应面法及程序实现[J].岩石力学与工程学报,29(8):1514-1523.
李亮,刘宝琛.2001a.边坡极限承载力的下限分析法及可靠性度理论[J].岩土力学与工程学报,20(4):508-513.
李亮,杨小礼.2001b.圆形浅基础地基承载力极限分析的上限解析解[J].铁道学报,23(1):94-97.
李云贵,赵国藩.1994.广义随机空间内的结构可靠度渐近分析方法[J].水利学报,25(8):36-41.
舒苏旬,龚文惠.2015.边坡稳定分析的神经网络改进模糊点估计法[J].岩土力学,36(7):2111-2116.
苏永华,李翔,丁云,等.2012.基于二次正交试验优化的隧道围岩稳定可靠度方法[J].岩土工程学报,34(2):326-332.
谭晓慧,宋传中,侯晓亮.2016.基于径向基函数响应面法的岩质边坡可靠度分析[J].地下空间与工程学报,12(1):250-255.
谭晓慧,王建国,刘新荣,等.2007.边坡稳定的有限元可靠度计算及敏感性分析[J].岩石力学与工程学报,26(1):115-122.
佟晓利,赵国藩.1997.一种与结构可靠度分析几何法相结合的响应面方法[J].土木工程学报,30(4):51-57.
王飞,梁旭黎,杜建坡.2016.地震荷载作用下岩石边坡的抗倾覆稳定性分析及可靠度研究[J].工程地质学报,24(6):1126-1135.
王根龙,伍法权,门玉明.2006.基于土质边坡塑性极限分析条分法可靠度计算方法研究[J].工程地质学报,14(6):835-840.
吴振君,王水林,葛修润.2010.LHS方法在边坡可靠度分析中的应用[J].岩土力学,31(4):1047-1054.
张道兵,潘秋景,杨小礼,等.2014.用极限分析方法计算边坡可靠度上限值[J].重庆大学学报,37(7):59-65.
张亚国,张波,李萍,等.2011.基于点估计法的黄土边坡可靠度研究[J].工程地质学报,19(4):615-619.
郑亚楠,侯晓坤,李萍,等.2014.晋西隰县-离石地区黄土高边坡可靠度研究[J].工程地质学报,22(3):372-378.
朱勇,冯夏庭,周辉,等.2016.岩土强度参数空间中的极限状态面与系统可靠度分析[J].岩石力学与工程学报,35(增2):3473-3480.
祝玉学.1993.边坡可靠性分析[M].北京:冶金工业出版社:5-8.
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