岩体地下结构围岩稳定非概率可靠性的凸集合模型分析方法
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摘要
在岩体地下结构围岩稳定可靠性分析中,由于岩体的物理力学参数本身的特点,通常只能在岩体分类的基础上给出其变化的区间,要得到其概率密度分布函数和隶属函数是非常困难的。采用传统的统计概率和模糊概率模型得出的概率结论只具有理论上的意义。针对岩体地下结构围岩的特点,引进非概率的可靠性分析方法,采用凸集合模型描述基本参数的不确定性,将结构功能函数转化为仿射函数,对于给出了设计安全域的地下结构,利用仿射函数在凸集合域上求得响应输出区间,通过比较设计安全域和响应区间,确定其可靠性;对于没有明确给出设计安全域的结构,通过分析功能函数在凸集合模型上的均值与离差关系,给出其可靠性度量的非概率指标。在非概率凸集合模型分析方法中不必拟合概率密度函数和隶属函数,所需信息量少、准确度高,实例分析展示了凸集合模型分析方法的实用性。
In reliability analysis of stability of surrounding rock mass for underground engineering,due to the particular characteristics of physical and mechanical parameters of rock mass,the variation interval of these parameters can only be obtained based on rock mass classification,while it is very difficult to obtain probability density function and subjection function of these parameters for rockmass. Therefore,the stability and reliability of surrounding rock mass,calculated by traditional probabilistic statistics model and fuzzy probability model,only has theoretical significance. Based on the characteristics of surrounding rock mass of underground engineering,the convex model is adopted to simulate uncertainties of rock mass parameters and to change state equation into affine function. For the underground structure with specified design safety margin,the response output interval of structure can be calculated through affine function whose independent variable is defined in convex set. The stability and reliability of the surrounding rock mass of underground structure can be determined by comparing design safety interval with response output interval. For the underground structure without design safety margin, non-probabilistic stability reliability index is defined through the analysis of ratio of average value in limit state equation to its deviation on convex set. Probability density function and subjection function need not be fitted in non-probability convex model methods. Therefore,non-probability convex model methods need less information than traditional stability reliability analysis method. The analysis results of non-probability methods are more accurate than that of traditional method. The results of engineering analysis show the convex model method of non-probabilistic reliability is feasible.
In reliability analysis of stability of surrounding rock mass for underground engineering,due to the particular characteristics of physical and mechanical parameters of rock mass,the variation interval of these parameters can only be obtained based on rock mass classification,while it is very difficult to obtain probability density function and subjection function of these parameters for rockmass. Therefore,the stability and reliability of surrounding rock mass,calculated by traditional probabilistic statistics model and fuzzy probability model,only has theoretical significance. Based on the characteristics of surrounding rock mass of underground engineering,the convex model is adopted to simulate uncertainties of rock mass parameters and to change state equation into affine function. For the underground structure with specified design safety margin,the response output interval of structure can be calculated through affine function whose independent variable is defined in convex set. The stability and reliability of the surrounding rock mass of underground structure can be determined by comparing design safety interval with response output interval. For the underground structure without design safety margin, non-probabilistic stability reliability index is defined through the analysis of ratio of average value in limit state equation to its deviation on convex set. Probability density function and subjection function need not be fitted in non-probability convex model methods. Therefore,non-probability convex model methods need less information than traditional stability reliability analysis method. The analysis results of non-probability methods are more accurate than that of traditional method. The results of engineering analysis show the convex model method of non-probabilistic reliability is feasible.
引文
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[16]郭书祥,吕震宇,冯元生.基于区间分析的结构非概率可靠性分析模型[J].计算力学学报,2001,18(1):56–61.(GuoShuxiang,LuZhenzhou,FengYuansheng.A non-probabilistic model of structural reliability based on interval analysis[J].ChineseJournal ofComputationalMechanics,2001,18(1):56–61.(inChinese))
[17]郭书祥,吕震宇.结构体系的非概率可靠性分析方法[J].计算力学学报,2002,19(3):332–335.(GuoShuxiang,LuZhenzhou.A procedure of the analysis of non-probabilistic reliability of structural systems[J].ChineseJournal ofComputationalMechanics,2002,19(3):332–335.(inChinese))
[18]何满潮,苏永华.软岩地下结构围岩稳定可靠性模型[J].岩土工程学报,2003,25(1):54–58.(HeMnachao,SuYonghua.Stability model of surrounding rock of underground structure in soft rock[J].ChineseJournal ofGeotechnicalEngineering,2003,25(1):54–58.(inChinese))
[2]黄志全,王思敬,李华晔等.岩体力学参数取值的置信度及其可靠性[J].岩石力学与工程学报,1999,18(1):33–35.(HuangZhiquan,WangSijing,LiHuaye,et al.Exactness and reliability of rock mechanics parameter[J].ChineseJournal ofRockMechanics andEngineering,1999,18(1):33–35.(inChinese))
[3]刘同有,高谦,马念杰.地下巷道工程可靠度分析[M].北京:中国矿业大学出版社,1998.(LiuTongyou,GaoQian,MaNianjie.Analysis ofReliability forUndergroundRoadwayEngineering[M].Beijing:ChinaUniversity ofMining andTechnologyPress,1998.(inChinese))
[4]何满潮,苏永华,景海河等.块状岩体工程围岩稳定可靠性分析模型及其应用[J].岩石力学与工程学报,2002,21(3):343– 348.(HeManchao,SuYonghua,JingHaihe,et al.Stability reliability analysis model of block surrounding rock for underground engineering and its application[J].ChineseJournal ofRockMechanics andEngineering,2002,21(3):343–348.(inChinese))
[5]刘宁,卓家寿.节理岩体的三维随机有限元及可靠度计算[J].岩石力学与工程学报,1995,14(4):297–305.(LiuNing,ZhuoJiashou.3D random finite element and reliability calculation for joint rockmass[J].ChineseJournal ofRockMechanics andEngineering,1995,14(4):297–305.(inChinese))
[6]安伟光.结构系统可靠性和基于可靠性的优化设计[M].北京:国防工业出版社,1997.(AnWeiguang.OptimizationDesignBased onReliability andReliability forStructureSystem[M].Beijing:NationalDefenseIndustryPress,1997.(inChinese))
[7]YakovB H.A non-probabilistic concept of reliability[J].StructuralSafety,1994,36(14):227–245.
[8]YakovB H.A non-probabilistic measure of reliability of linear systems based on expansion of convex models[J].StructuralSafety,1995,37(17):91–109.
[9]何彩英,张景会.地震响应的凸集分析.应用数学和力学[J].1997,18(10):879–884.(HeCaiying,ZhangJinghui.The convex response set of a class of mode vibration on system[J].AppliedMathematics andMechanics,1997,18(10):879–884.(inChinese))
[10]BieniawskiZ T.EngineeringRockMassClassification[M].NewYork:JohnWiley&Sons,Inc.1989.
[11]BenHaimY,ElishakoffI.ConvexModels ofUncertainty inAppliedMechanics[M].Amsterdam:ElsevierSciencePolishers,1990.
[12]徐可君,江龙平,陈景亮等.叶片震动的非概率可靠性研究[J].机械工程学报,2002,38(10):19–21.(XuKejun,JiangLongping,ChenJingliang, et al.Non-probabilistic reliability research on vibration of blades[J].ChineseJournal ofMechanicalEngineering,2002,38(10):19–21.(inChinese))
[13]ElishakoffJ,LinY K,ZhuoLP.Probabilistic andConvexModelling ofAcousticallyExcitedStructures[M].Amsterdam:ElsevierScience,1994.
[14]邱志平,顾元宪.结构静力位移的非概率凸集合理论模型的摄动数 值算法[J].固体力学学报,1997,18(1):86–89.(QiuZhiping,GuYuanxian.Perturbed numerical algorithm of non probabilistic convex set theoretical models on the static displacements of structures[J].ActaMechanicalSolidaSinica,1997,18(1):86–89.(inChinese))
[15]张海联,周建平.固体推进剂药柱结构分析的非概率凸集合理论模型[J].国防科技大学学报,2002,24(2):1–5.(ZhangHailian,ZhouJianping.No probabilistic convex set theoretic models for structure analysis of solid propellant grain[J].Journal ofNationalUniversity ofDefenseTechnology,2002,24(2):1–5.(inChinese))
[16]郭书祥,吕震宇,冯元生.基于区间分析的结构非概率可靠性分析模型[J].计算力学学报,2001,18(1):56–61.(GuoShuxiang,LuZhenzhou,FengYuansheng.A non-probabilistic model of structural reliability based on interval analysis[J].ChineseJournal ofComputationalMechanics,2001,18(1):56–61.(inChinese))
[17]郭书祥,吕震宇.结构体系的非概率可靠性分析方法[J].计算力学学报,2002,19(3):332–335.(GuoShuxiang,LuZhenzhou.A procedure of the analysis of non-probabilistic reliability of structural systems[J].ChineseJournal ofComputationalMechanics,2002,19(3):332–335.(inChinese))
[18]何满潮,苏永华.软岩地下结构围岩稳定可靠性模型[J].岩土工程学报,2003,25(1):54–58.(HeMnachao,SuYonghua.Stability model of surrounding rock of underground structure in soft rock[J].ChineseJournal ofGeotechnicalEngineering,2003,25(1):54–58.(inChinese))
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