基于盲数理论的边坡可靠度分析
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摘要
针对边坡岩土体参数的多种不确定性,采用盲数理论提出一种边坡可靠度分析方法,并首次提出以边坡盲数安全系数和最小安全要求可靠度作为指标来综合评判边坡的稳定性。首先,运用响应面法和有限元强度折减法求出边坡极限状态方程,运用盲数理论建立边坡安全系数的盲数模型,解出安全系数的盲数解,并进一步求出边坡盲数安全系数和最小安全要求可靠度的计算表达式。算例分析表明,边坡盲数安全系数和最小安全要求可靠度与传统方法相比均偏低,能更安全地评价边坡的稳定性,弥补了均值安全系数和传统可靠度之间无关联的缺陷。
An analytical method is presented using the blind data theory considering a variety of uncertainties of parameters of rock and soil in slope engineering. The blind data safety factor of the slope with the reliability of minimum safety requirement is firstly presented as the comprehensive index to evaluate slope stability. Firstly,the limit state equation of the slope is solved by using the response surface method and the strength reduction method of FEM,the blind data model of safety factor is established based on the blind data theory,and the blind data solution is derived. Secondly,the expressions of blind data safety factor of the slope and reliability of minimum safety requirement are established. The blind data safety factor of the slope and reliability of minimum safety requirement obtained were smaller in comparison with ones from the traditional methods. Thus,it will be safer for engineering assessment.
An analytical method is presented using the blind data theory considering a variety of uncertainties of parameters of rock and soil in slope engineering. The blind data safety factor of the slope with the reliability of minimum safety requirement is firstly presented as the comprehensive index to evaluate slope stability. Firstly,the limit state equation of the slope is solved by using the response surface method and the strength reduction method of FEM,the blind data model of safety factor is established based on the blind data theory,and the blind data solution is derived. Secondly,the expressions of blind data safety factor of the slope and reliability of minimum safety requirement are established. The blind data safety factor of the slope and reliability of minimum safety requirement obtained were smaller in comparison with ones from the traditional methods. Thus,it will be safer for engineering assessment.
引文
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[14]张正虎,袁孟科,邓建辉,等.基于改进灰色–时序分析时变模型的边坡位移预测[J].岩石力学与工程学报,2014,33(增2):3 791–3 797.(ZHANG Zhenghu,YUAN Mengke,DENG Jianhui,et al.Displacement prediction of slope based on improved grey-time series time-varying model[J].Chinese Journal of Rock Mechanics and Engineering,2014,33(Supp.2):3 791–3 797.(in Chinese))
[15]金海元.岩石高边坡监测预警综合评价方法研究[J].长江科学院院报,2011,28(1):29–33.(JIN Haiyuan.Research on comprehensive evaluation methods of monitoring and early-warning for rock slope[J].Journal of Yangtze River Scientific Research Institute,2011,28(1):29–33.(in Chinese))
[16]赵志峰,徐卫亚.基于盲数理论的边坡安全稳定分析研究[J].岩土力学,2007,28(11):2 401–2 404.(XU Zhifeng,XU Weiya.Slope stability analysis based on the blind data theory[J].Rock and Soil Mechanics,2007,28(11):2 401–2 404.(in Chinese))
[17]董陇军,赵国彦,宫凤强,等.尾矿坝地震稳定性分析的区间模型及应用[J].中南大学学报:自然科学版,2011,42(1):164–169.(DONG Longjun,ZHAO Guoyan,GONG Fengqiang,et al.Interval analysis model of tailings dam seismic stability and its application[J].Journal of Central South University:Science and Technology,2011,42(1):164–169.(in Chinese))
[18]汪明武,李丽,金菊良.基于盲数理论的液化等级风险评价模型[J].岩土工程学报,2010,32(2):303–307.(WANG Mingwu,LI Li,JIN Juliang.Application of unascertained number theory to risk evaluation of liquefaction grade[J].Chinese Journal of Geotechnical Engineering,2010,32(2):303–307.(in Chinese))
[19]LI D,CHEN Y,LU W,et al.Stochastic response surface method for reliability analysis of rock slopes involving correlated non-normal variables[J].Computers and Geotechnics,2011,38(1):58–68.
[20]WEI W B,CHENG Y M,LI L.Three-dimensional slope failure analysis by the strength reduction and limit equilibrium methods[J].Computers and Geotechnics,2009,36(1):70–80.
[2]SAMUI P,LANSIVAARA T,KIM D.Utilization relevance vector machine for slope reliability analysis[J].Applied Soft Computing,2011,11(5):4 036–4 040.
[3]唐小松,李典庆,周创兵.基于认知聚类分区方法的边坡可靠度分析[J].岩土力学,2011,32(2):571–578.(TANG Xiaosong,LI Dianqing,ZHOU Chuangbing.Knowledge-based clustered partitioning method for reliability analysis of slope stability[J].Rock and Soil Mechanics,2011,32(2):571–578.(in Chinese))
[4]蒋水华,祁小辉,曹子君,等.基于随机响应面法的边坡系统可靠度分析[J].岩土力学,2015,36(3):809–818.(JIANG Shuihua,QI Xiaohui,CAO Zijun,et al.System reliability analysis of slope with stochastic response surface method[J].Rock and Soil Mechanics,2015,36(3):809–818.(in Chinese))
[5]薛亚东,方超,葛嘉诚.各向异性随机场下的边坡可靠度分析[J].岩土工程学报,2013,35(增2):77–82.(XUE Yadong,FANG Chao,GE Jiacheng.Slope reliability in anisotropic random fields[J].Chinese Journal of Geotechnical Engineering,2013,35(Supp.2):77–82.(in Chinese))
[6]徐辉.基于模糊集理论的边坡稳定模糊随机可靠度分析[硕士学位论文][D].杭州:浙江大学,2006.(XU Hui.Fuzzy reliability analysis of slope stable capacity based on fuzzy sets[M.S.Thesis][D].Hangzhou:Zhejiang University,2006.(in Chinese))
[7]舒苏荀,龚文惠.二维随机场下边坡稳定性的径向基函数神经网络分析法[J].岩土力学,2015,36(4):1 205–1 210.(SHU Suxun,GONG Wenhui.Radial basis function neural network-based method for slope stability analysis under two-dimensional random field[J].Rock and Soil Mechanics,2015,36(4):1 205–1 210.(in Chinese))
[8]张永杰,李侑军,李邵军,等.边坡模糊可靠性分析隶属函数取值界限研究[J].岩土力学,2014,35(4):1 157–1 163.(ZHANG Yongjie,LI Youjun,LI Shaojun,et al.Study of boundaries of membership function values for slope fuzzy reliability analysis[J].Rock and Soil Mechanics,2014,35(4):1 157–1 163.(in Chinese))
[9]周宁,傅鹤林,郭建峰,等.引入修正因子的非等时距时变参数灰色预测模型及应用[J].岩土工程学报,2006,28(6):756–760.(ZHOU Ning,FU Helin,GUO Jianfeng,et al.Correcting factor of gray with prediction model unequal intervaltime-varying parameters[J].Chinese Journal of Geotechnical Engineering,2006,28(6):756–760.(in Chinese))
[10]薛锦春,李夕兵,董陇军.边坡稳定性的聚类未确知综合识别方法及应用[J].岩土力学,2010,31(增1):293–297.(XUE Jinchun,LI Xibing,DONG Longjun.Study of rock slope stability based on clustering uncertained measurement complicated algorithm[J].Rock and Soil Mechanics,2010,31(Supp.1):293–297.(in Chinese))
[11]高荣雄,龚文惠,王元汉,等.顺层边坡稳定性及可靠度的随机有限元分析法[J].岩土力学,2009,30(4):1 165–1 169.(GAO Rongxiong,GONG Wenhui,WANG Yuanhan,et al.Analysis of stability and reliability of bedding rock slope by stochastic finite element method[J].Rock and Soil Mechanics,2009,30(4):1 165–1 169.(in Chinese))
[12]舒苏荀,龚文惠.考虑参数空间变异性的边坡模糊随机可靠度分析[J].华中科技大学学报:自然科学版,2014,42(9):93–97.(SHU Suxun,GONG Wenhui.Fuzzy random reliability analysis of slopes considering spatial variability of soil parameters[J].Journal of Huazhong University of Science and Technology:Natural Science Edition,2014,42(9):93–97.(in Chinese))
[13]谭晓慧,王建国,胡晓军,等.边坡稳定的模糊随机有限元可靠度分析[J].岩土工程学报,2009,31(7):991–996.(TAN Xiaohui,WANG Jianguo,HU Xiaojun,et al.Fuzzy random finite element reliability analysis of slope stability[J].Chinese Journal of Geotechnical Engineering,2009,31(7):991–996.(in Chinese))
[14]张正虎,袁孟科,邓建辉,等.基于改进灰色–时序分析时变模型的边坡位移预测[J].岩石力学与工程学报,2014,33(增2):3 791–3 797.(ZHANG Zhenghu,YUAN Mengke,DENG Jianhui,et al.Displacement prediction of slope based on improved grey-time series time-varying model[J].Chinese Journal of Rock Mechanics and Engineering,2014,33(Supp.2):3 791–3 797.(in Chinese))
[15]金海元.岩石高边坡监测预警综合评价方法研究[J].长江科学院院报,2011,28(1):29–33.(JIN Haiyuan.Research on comprehensive evaluation methods of monitoring and early-warning for rock slope[J].Journal of Yangtze River Scientific Research Institute,2011,28(1):29–33.(in Chinese))
[16]赵志峰,徐卫亚.基于盲数理论的边坡安全稳定分析研究[J].岩土力学,2007,28(11):2 401–2 404.(XU Zhifeng,XU Weiya.Slope stability analysis based on the blind data theory[J].Rock and Soil Mechanics,2007,28(11):2 401–2 404.(in Chinese))
[17]董陇军,赵国彦,宫凤强,等.尾矿坝地震稳定性分析的区间模型及应用[J].中南大学学报:自然科学版,2011,42(1):164–169.(DONG Longjun,ZHAO Guoyan,GONG Fengqiang,et al.Interval analysis model of tailings dam seismic stability and its application[J].Journal of Central South University:Science and Technology,2011,42(1):164–169.(in Chinese))
[18]汪明武,李丽,金菊良.基于盲数理论的液化等级风险评价模型[J].岩土工程学报,2010,32(2):303–307.(WANG Mingwu,LI Li,JIN Juliang.Application of unascertained number theory to risk evaluation of liquefaction grade[J].Chinese Journal of Geotechnical Engineering,2010,32(2):303–307.(in Chinese))
[19]LI D,CHEN Y,LU W,et al.Stochastic response surface method for reliability analysis of rock slopes involving correlated non-normal variables[J].Computers and Geotechnics,2011,38(1):58–68.
[20]WEI W B,CHENG Y M,LI L.Three-dimensional slope failure analysis by the strength reduction and limit equilibrium methods[J].Computers and Geotechnics,2009,36(1):70–80.