基于截尾概率分布的基坑突涌模糊可靠度分析
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摘要
岩土工程可靠度分析中,计算参数具有随机性,稳定性评价具有模糊性。传统的Monte Carlo模拟方法计算可靠度时,往往假定参数概率分布在正负无穷之间分布,与真实情况不符,而且其计算效率也往往较低。规范推荐的基坑突涌验算公式,计算结果往往偏于保守。引入截尾概率分布的确定方法,对参数概率分布进行截尾处理;提出拉丁超立方抽样与最大熵原理结合来确定结构响应概率分布的方法,并将其与模糊可靠度原理结合,构建了基于抽样模拟的模糊可靠度计算模型;推荐了考虑土体抗剪强度的突涌验算公式。将所提方法应用于某深基坑工程突涌分析中,其结果表明,基于截尾分布的抽样可以有效避免参数抽样值为负数的情况,所提计算模型效率明显优于传统的Monte Carlo模拟方法,模糊可靠度的计算结果比经典可靠度更符合工程实际情况。
In the reliability analysis of geotechnical engineering,the calculation parameters have characteristic of random and the stability evaluation is fuzzy. It is usually assumed that the parameters are distributed between the positive and negative infinity when the Monte Carlo simulation is applied to calculate the reliability,but this is inconformity with the real case. The computational efficiency of the Monte Carlo simulation is often low. The calculation results tend to be conservative by using the formula which is recommended by the specification for check calculation the foundation pit inrush. The parameters probability distributions are truncated by utilizing the method of the truncated probability distribution. The method for determining structure response probability distribution is proposed by combing the Latin hypercube sampling method and the maximum entropy principle,and it is used in fuzzy reliability principle to establish fuzzy reliability calculation model based on sampling simulation. It is used in fuzzy reliability principle to establish fuzzy reliability calculation model based on sampling simulation. The formula which includes shear strength of soil for check calculation the foundation pit inrush is recommended. The presented method is applied to analyze deep foundation pit inrush,the results show that the sampling based on the truncated probability distribution can efficiently avoid the situation that the sampling value is negative. The efficiency of the proposed calculation model is obviously better than the traditional Monte Carlo simulation method. The result of fuzzy reliability is more accord with the engineering practice than the classical reliability result.
In the reliability analysis of geotechnical engineering,the calculation parameters have characteristic of random and the stability evaluation is fuzzy. It is usually assumed that the parameters are distributed between the positive and negative infinity when the Monte Carlo simulation is applied to calculate the reliability,but this is inconformity with the real case. The computational efficiency of the Monte Carlo simulation is often low. The calculation results tend to be conservative by using the formula which is recommended by the specification for check calculation the foundation pit inrush. The parameters probability distributions are truncated by utilizing the method of the truncated probability distribution. The method for determining structure response probability distribution is proposed by combing the Latin hypercube sampling method and the maximum entropy principle,and it is used in fuzzy reliability principle to establish fuzzy reliability calculation model based on sampling simulation. It is used in fuzzy reliability principle to establish fuzzy reliability calculation model based on sampling simulation. The formula which includes shear strength of soil for check calculation the foundation pit inrush is recommended. The presented method is applied to analyze deep foundation pit inrush,the results show that the sampling based on the truncated probability distribution can efficiently avoid the situation that the sampling value is negative. The efficiency of the proposed calculation model is obviously better than the traditional Monte Carlo simulation method. The result of fuzzy reliability is more accord with the engineering practice than the classical reliability result.
引文
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[9]杨建民,郑刚.基坑降水中渗流破坏归类及抗突涌验算公式评价[J].岩土力学,2009,30(1):261-264.(Yang Jianmin,Zheng Gang.Classification of seepage failures and opinion to formula for check bursting instability in dewatering[J].Rock and Soil Mechanics,2009,30(1):261-264.(in Chinese))
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[13]许福友,陈艾荣.基于截尾概率分布的结构可靠性分析[J].工程力学,2006,23(11):52-57.(Xu Fuyou,Chen Airong.Structural reliability analysis based on truncated probabilistc distribution[J].Engineering mechanics,2006,23(11):52-57.(in Chinese))
[14]张建仁,许福友.计算结构可靠指标的子域抽样法[J].土木工程学报,2003,36(12):39-43.(Zhang Jianren,Xu Fuyou.Subdomain sampling method for calculating structural reliability index[J].China Civil Engineering Journal,2003,36(12):39-43.(in Chinese))
[15]傅旭东,赵善锐.用蒙特卡洛(Monte-Carlo)方法计算岩土工程的可靠度指标[J].西南交通大学学报,1996,31(2):164-168.(Fu Xudong,Zhang Shanrui.Applying the Monte-Carlo simulation to calculate the geotechnical reliability index[J].Journal of Southwest Jiaotong University,1996,31(2):164-168.(in Chinese))
[16]王林,徐青.基于蒙特卡罗随机有限元法的三维随机渗流场研究[J].岩土力学,2014,35(1):287-292.(Wang Lin,Xu Qing.Analysis of three dimensional random seepage field based on Monte-Carlo stochastic finite element method[J].Rock and Soil Mechanics,2014,35(1):287-292.(in Chinese))
[17]伍国军,陈卫忠,谭贤君,等.基于拉丁超立方抽样的有限元可靠度程序开发及应用[J].岩土力学,2015,36(2):550-554.(Wu Guojun,Chen Weizhong,Tan Xianjun,et al.Program development of finite element reliability method and its application based on Latin hypercube sampling[J].Rock and Soil Mechanics,2015,36(2):550-554.(in Chinese))
[18]王光远,刘玉彬.结构模糊随机可靠度的实用计算方法[J].地震工程与工程振动,1995,15(3):38-45.(Wang Guangyuan,Liu Yubin.Practical calculation method for fuzzy random reliability of structures[J].Earthquake Engineering and Engineering Vibration,1995,15(3):38-45.(in Chinese))
[19]贾厚华,贺怀建.边坡稳定模糊随机可靠度分析[J].岩土力学,2003,24(4):657-660.(Jia Houhua,He Huaijian.Analysis of fuzzy-random reliability of slope stability[J].Rock and Soil Mechanics,2003,24(4):657-660.(in Chinese))
[20]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):1157-1163.(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):1157-1163.(in Chinese))
[21]龚文惠,王元汉,郑俊杰.基于模糊理论的膨胀土路基沉降的可靠度分析[J].华中科技大学学报,2008,36(3):50-53.(Gong Wenhui,Wang Yuanhan,Zheng Junjie.Reliability analysis on settlement of expansive soil roadbed based on fuzzy theory[J].Journal of Huangzhong University of Science and Technology(Natural Science Edition),2008,36(3):50-53.(in Chinese))
[22]孙杰,张晓,牟在根.不同隶属函数对地下连续墙模糊可靠度影响的分析[J].岩土力学,2008,29(3):838-840.(Sun Jie,Zhang Xiao,Mu Zaigen.Analysis of effect of different membership function on calculation of fuzzy reliability in underground continuous wall[J].Rock and Soil Mechanics,2008,29(3):838-840.(in Chinese))
[23]郑俊杰,徐志军,刘勇,等.基于最大熵原理的基桩竖向承载力的可靠度分析[J].岩土工程学报,2010,32(11):1643-1647.(Zheng Junjie,Xu Zhijun,Liu Yong,et al.Reliability analysis for vertical bearing capacity of piles based on the maximum entropy principle[J].Chinese Journal of Geotechnical Engineering,2010,32(11):1643-1647.(in Chinese))
[24]章光,朱维申,白世伟.计算近似失效概率的最大嫡密度函数法[J].岩石力学与工程学报,1995,14(2):119-129.(Zhang Guang,Zhu Weishen,Bai Shiwei.A method of maximum entropy density funcition for calculation of approximate failure probability[J].Chinese Journal of Rock Mechanics and Engineering,1995,14(2):119-129.(in Chinese))
[25]赖雄鸣,王成,张勇,等.最大熵法在可靠度计算中的应用[J].计算力学学报,2015,32(1):41-47.(Lai Xiongming,Wang Cheng,Zhang Yong,et al.Application of maximum entropy method in reliability computation[J].Chinese Journal of Computational Mechanics,2015,32(1):41-47.(in Chinese))
[26]李军,李亮亮.承压水地层基坑坑底压拉突涌评价与物理试验[J].地下空间与工程学报,2016,12(3):670-674.(Li Jun,Li Liangliang.Compressiontension failure evaluation and physical experiment for confined water foundation pit inrushing[J].Chinese Journal of Underground Space and Engineering,2016,12(3):670-674.(in Chinese))
[27]吴奇,李俊才.高承压水基坑降水对周边环境的影响分析[J].地下空间与工程学报,2015,11(增1):365-272.(Wu Qi,Li Juncai.Analysis on impact of high confined water foundation pit dewatering on the surrounding environment[J].Chinese Journal of Underground Space and Engineering,2015,11(Supp.1):365-272.(in Chinese))
[2]翁其平,王卫东.深基坑承压水控制的设计方法与工程应用[J].岩土工程学报,2008,30(增):343-348.(Weng Qiping,Wang Weidong.Design and application of control of confined groundwater in deep foundation pits[J].Chinese Journal of Geotechnical Engineering,2008,30(Supp.):343-348.(in Chinese))
[3]秦尚林,王红亮,克高果.深井降水基坑涌水涌砂原因分析及对策[J].岩土力学,2005,26(增):271-275.(Qin Shanglin,Wang Hongliang,Ke Gaoguo.Analysis of water and sand gushing out of a foundation pit and prevention countermeasures[J].Rock and Soil Mechanics,2005,26(Supp.):271-275.(in Chinese))
[4]中华人民共和国建设部.建筑地基基础设计规范(GB 50007-2002)[S].北京:中国建筑工业出版社,2002.(Ministry of Housing and Urban-Rural Development of the People’s Republic of China.Code for design of building foundation(GB 50007-2002)[S].Beijing:China Architecture&Building Press,2002.(in Chinese))
[5]梁勇然.条形基坑的突涌分析[J].岩土工程学报,1996,18(1):75-79.(Liang Yongran.Inrush analysis of strip foundation pit[J].Chinese Jounal of Geotechnical Engineering,1996,18(1):75-79.(in Chinese))
[6]马石城,印长俊,邹银生.抗承压水基坑底板的厚度分析与计算[J].工程力学,2004,21(2):204-208.(Ma Shicheng,Yin Changjun,Zou Yinsheng.Analysis and calculation of the pit base plate thickness of bearing resistance water foundation[J].Engineering Mechanics,2004,21(2):204-208.(in Chinese))
[7]潘泓,曹洪,谭泽新,等.基坑抗突涌计算方法的对比分析及应用探讨[J].岩石力学与工程学报,2006,25(增2):3529-3534.(Pan Hong,Cao Hong,Tan Zexin,et al.Discussion on comparison analysis and application of calculation methods to anti-uprush of foundation pit[J].Chinese Journal of Rock Mechanics and Engineering,2006,25(Supp.2):3529-3534.(in Chinese))
[8]孙玉永,周顺华,肖红菊.承压水基坑抗突涌稳定判定方法研究[J].岩石力学与工程学报,2012,31(2):399-405.(Sun Yuyong,Zhou Shunhua,Xiao Hongju.Study of stability judgement method of confined water in rushing in foundation pit[J].Chinese Journal of Rock Mechanics and Engineering,2012,31(2):399-405.(in Chinese))
[9]杨建民,郑刚.基坑降水中渗流破坏归类及抗突涌验算公式评价[J].岩土力学,2009,30(1):261-264.(Yang Jianmin,Zheng Gang.Classification of seepage failures and opinion to formula for check bursting instability in dewatering[J].Rock and Soil Mechanics,2009,30(1):261-264.(in Chinese))
[10]尹小涛,王水林.基于可靠度理论的滑坡稳定性及其影响因素分析[J].岩土力学,2008,29(6):1551-1556.(Yin Xiaotao,Wang Shuilin.Stability and its influential factors analysis of landslides based on reliability theory[J].Rock and Soil Mechanics,2008,29(6):1551-1556.(in Chinese))
[11]李夕兵,宫凤强.岩土力学参数概率分布的推断方法研究综述[J].长沙理工大学学报(自然科学版),2007,4(1):1-8.(Li Xibing,Gong Fengqiang.Aresearch review of the method to deduce the probability distribution of geotechnical mechanics parameters[J].Journal of Changsha University of Science and Technology(Natural Science Edition),2007,4(1):1-8.(in Chinese))
[12]张继周,缪林昌.岩土参数概率分布类型及其选择标准[J].岩石力学与工程学报,2009,28(增2):3527-3532.(Zhang Jizhou,Miao Linchang.Types and selection criteria of probability distribution of rock and soil parameters[J].Chinese Journal of Rock Mechanics and Engineering,2009,28(Supp.2):3527-3532.(in Chinese))
[13]许福友,陈艾荣.基于截尾概率分布的结构可靠性分析[J].工程力学,2006,23(11):52-57.(Xu Fuyou,Chen Airong.Structural reliability analysis based on truncated probabilistc distribution[J].Engineering mechanics,2006,23(11):52-57.(in Chinese))
[14]张建仁,许福友.计算结构可靠指标的子域抽样法[J].土木工程学报,2003,36(12):39-43.(Zhang Jianren,Xu Fuyou.Subdomain sampling method for calculating structural reliability index[J].China Civil Engineering Journal,2003,36(12):39-43.(in Chinese))
[15]傅旭东,赵善锐.用蒙特卡洛(Monte-Carlo)方法计算岩土工程的可靠度指标[J].西南交通大学学报,1996,31(2):164-168.(Fu Xudong,Zhang Shanrui.Applying the Monte-Carlo simulation to calculate the geotechnical reliability index[J].Journal of Southwest Jiaotong University,1996,31(2):164-168.(in Chinese))
[16]王林,徐青.基于蒙特卡罗随机有限元法的三维随机渗流场研究[J].岩土力学,2014,35(1):287-292.(Wang Lin,Xu Qing.Analysis of three dimensional random seepage field based on Monte-Carlo stochastic finite element method[J].Rock and Soil Mechanics,2014,35(1):287-292.(in Chinese))
[17]伍国军,陈卫忠,谭贤君,等.基于拉丁超立方抽样的有限元可靠度程序开发及应用[J].岩土力学,2015,36(2):550-554.(Wu Guojun,Chen Weizhong,Tan Xianjun,et al.Program development of finite element reliability method and its application based on Latin hypercube sampling[J].Rock and Soil Mechanics,2015,36(2):550-554.(in Chinese))
[18]王光远,刘玉彬.结构模糊随机可靠度的实用计算方法[J].地震工程与工程振动,1995,15(3):38-45.(Wang Guangyuan,Liu Yubin.Practical calculation method for fuzzy random reliability of structures[J].Earthquake Engineering and Engineering Vibration,1995,15(3):38-45.(in Chinese))
[19]贾厚华,贺怀建.边坡稳定模糊随机可靠度分析[J].岩土力学,2003,24(4):657-660.(Jia Houhua,He Huaijian.Analysis of fuzzy-random reliability of slope stability[J].Rock and Soil Mechanics,2003,24(4):657-660.(in Chinese))
[20]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):1157-1163.(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):1157-1163.(in Chinese))
[21]龚文惠,王元汉,郑俊杰.基于模糊理论的膨胀土路基沉降的可靠度分析[J].华中科技大学学报,2008,36(3):50-53.(Gong Wenhui,Wang Yuanhan,Zheng Junjie.Reliability analysis on settlement of expansive soil roadbed based on fuzzy theory[J].Journal of Huangzhong University of Science and Technology(Natural Science Edition),2008,36(3):50-53.(in Chinese))
[22]孙杰,张晓,牟在根.不同隶属函数对地下连续墙模糊可靠度影响的分析[J].岩土力学,2008,29(3):838-840.(Sun Jie,Zhang Xiao,Mu Zaigen.Analysis of effect of different membership function on calculation of fuzzy reliability in underground continuous wall[J].Rock and Soil Mechanics,2008,29(3):838-840.(in Chinese))
[23]郑俊杰,徐志军,刘勇,等.基于最大熵原理的基桩竖向承载力的可靠度分析[J].岩土工程学报,2010,32(11):1643-1647.(Zheng Junjie,Xu Zhijun,Liu Yong,et al.Reliability analysis for vertical bearing capacity of piles based on the maximum entropy principle[J].Chinese Journal of Geotechnical Engineering,2010,32(11):1643-1647.(in Chinese))
[24]章光,朱维申,白世伟.计算近似失效概率的最大嫡密度函数法[J].岩石力学与工程学报,1995,14(2):119-129.(Zhang Guang,Zhu Weishen,Bai Shiwei.A method of maximum entropy density funcition for calculation of approximate failure probability[J].Chinese Journal of Rock Mechanics and Engineering,1995,14(2):119-129.(in Chinese))
[25]赖雄鸣,王成,张勇,等.最大熵法在可靠度计算中的应用[J].计算力学学报,2015,32(1):41-47.(Lai Xiongming,Wang Cheng,Zhang Yong,et al.Application of maximum entropy method in reliability computation[J].Chinese Journal of Computational Mechanics,2015,32(1):41-47.(in Chinese))
[26]李军,李亮亮.承压水地层基坑坑底压拉突涌评价与物理试验[J].地下空间与工程学报,2016,12(3):670-674.(Li Jun,Li Liangliang.Compressiontension failure evaluation and physical experiment for confined water foundation pit inrushing[J].Chinese Journal of Underground Space and Engineering,2016,12(3):670-674.(in Chinese))
[27]吴奇,李俊才.高承压水基坑降水对周边环境的影响分析[J].地下空间与工程学报,2015,11(增1):365-272.(Wu Qi,Li Juncai.Analysis on impact of high confined water foundation pit dewatering on the surrounding environment[J].Chinese Journal of Underground Space and Engineering,2015,11(Supp.1):365-272.(in Chinese))