工程结构通用可靠度设计与评定方法
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摘要
在土木工程领域,近似概率极限状态设计方法是国内外公认的先进设计方法,它以与失效概率相关的可靠指标度量和控制结构的可靠性,从根本上克服了过去经验方法的不足,但是在实际应用中,该方法采用的分项系数是根据事先设定的基本变量的概率特性而确定的,所考虑的设计使用年限、目标可靠指标的数值也是事先设定的,当基本变量实际的概率特性不同于设定的概率特性时,或者业主所要求的设计使用年限、目标可靠指标不同于设定的数值时,该方法便可能不再适用。这种灵活性方面的缺陷不仅使其难以满足新型结构、新材料结构设计的需要,也使其难以应用于既有结构的可靠性评定。同时,目前的设计方法仅考虑了事物变化的随机性,而未考虑人们对事物认识上的不确定性,即主观不确定性。
论文的主要目的是针对目前近似概率极限状态设计方法的缺陷,建立工程结构可靠度设计与评定的通用方法,并考虑主观不确定性对结构可靠度分析结果的影响,主要研究内容和工作包括：
1主观不确定性的数学处理方法以及考虑主观不确定性的可靠度分析方法。论文将各种人们认识上的不确定性归结为主观不确定性,并通过未确知量和信度建立了统一的主观不确定性的数学描述方法；通过对结构失效概率的信度分析,建立了考虑主观不确定性的结构可靠度分析方法,并进一步建立了综合概率与信度的可靠性度量和控制方法。
(2)工程结构可靠度设计与评定的通用表达式。目前的实用设计表达式在反映随机变量的影响方面存在着结构性的缺陷,论文根据目前国际组织JCSS推荐的计算可靠指标的JC法,直接建立了分项系数与基本变量概率特性、设计使用年限、目标可靠指标之间的函数关系,从而建立了工程结构可靠度设计与评定的通用表达式。该表达式不仅具有坚实的理论基础,而且能够灵活应用于新型结构、新材料结构的设计以及既有结构的可靠性评定,满足人们对设计使用年限、目标可靠指标的不同要求。
(3)标准灵敏度系数的确定方法。标准灵敏度系数是建立工程结构可靠度设计与评定通用方法的关键,但目前的枚举和拟合方法不仅繁琐费时,而且可能遗漏不利的情况,为此论文提出灵敏度系数边界向量和中心向量的概念,分别针对承载能力极限状态和正常使用极限状态,利用向量分析方法确定了可靠度设计的最优灵敏度系数和标准灵敏度系数,最终建立了工程结构可靠度设计与评定的通用方法,而且也为建立可靠度设计与评定方法的建立提供了解析方法。
(4)基本变量数字特征以及材料强度、抗力的推断方法。对基本变量数字特征以及材料强度、抗力的推断,是将可靠度设计与评定通用方法应用于工程实际的一项必要工作。对于既有结构而言,其当前时刻的材料强度和抗力是客观上确定但存在主观不确定性的未确知量,目前的概率统计方法并不完全适合于对它们的推断,为此论文针对既有结构的特点,提出基本变量数字特征以及材料强度、抗力的信度推断方法,这些方法不仅可以合理考虑主观不确定性的影响,而且也充分考虑了被测量本身所提供的信息。论文还针对目前变异系数推断方法的不足,提出较国家标准具有更高精度和更广适用范围的推断方法。
In the civil engineering field, the method of approximate probability limit state design is an advanced method known at domestic and overseas. The method for measure and control structural reliability is implemented by reliability index related to failure probability, overcoming the defect of the previous empirical method basically. But in practical application, partial factor was determined by predetermined probability characteristics of basic variable, design working life and target reliability index were also set beforehand. The method will not suit for reliability-based design when real probability characteristics of basic variable are different form predetermined probability characteristics, or owner's demand of design working life and target reliability index are different form setting value. Because of a lack of flexibility, this method cannot satisfy the need of design of new structures and new material structures, and can't be used in the assessment of existing structures. At the same time, the current design method only considers the randomness of things, but did not consider the uncertainty of human's recognition.
Aiming at defective in limit state design method of approximate probability, the dissertation establish general method for re liability-based design and assessment of engineering structures, and also take into account of the affections of subjective to the analysis result of structural reliability. The research contents and result includes:
1. Mathematical treatment method for subjective uncertainty and reliability analysis method based on subjective uncertainty are proposed. The dissertation induces all kinds of uncertainty in human's recognition as subjective uncertainty; to establish general mathematical treatment method for subjective uncertainty by uncertain variables and belief function. Based on be lief analysis of structural failure probability, the paper creates structural reliability analysis method considering subjective uncertainty, further to establish reliability measures and control methods with combing probability and belief.
2. General expression for the design and assessment of reliability of engineering structures are proposed. At present, there are plenty of shortcomings about reflecting the impact of the random variables in the practical design expression. In the paper, according to the JC method recommended by the international organization JCSS, functional relationships among partial factor and probabilistic characteristic of basic variable, design working life, target reliability index are founded. At last, the general expression for the design and assessment of reliability of engineering structures are proposed. Based on the solid theoretical basis, the expression can be use to design the new structure and new material structure, to assess the existing structures. So it can satisfy the different needs on the design working life and target reliability index.
3. The paper proposes determination method of standard sensitivity coefficient. The standard sensitivity coefficient is critical to establish general method of the reliability-based design and assessment of engineering structures. But current enumeration method and fitting method are not only tedious but may also to miss the adverse cases. Therefore, the boundary vector and center vector are set up for the sensitivity coefficient. Aiming at the ultimate limit states and serviceability limit states, the paper makes use of the analytical vector method to determine the optimal sensitivity coefficient and standard sensitivity coefficient of reliability-based design. At last, the general expression for the design and assessment of reliability of engineering structures are founded. At the same time, analytical method is derived to design and assessment the reliability of engineering structures.
4. The paper proposes inference rules for probability characteristics of basic variables, material strength and resistance.The research on the number characteristics of basic variables, material strength and resistance are essential to engineering practice, especially the general method of reliability-based design and assessment. The material strength and resistance at any time for the existing structures are determined objectively but uncertain and unknown variables also existing subjectively. The current methods of probability and statistics are not entirely suitable for their inference. According to the characteristics of the existing structures, the reliability inference method for the number characteristics of basic variables and material strength and resistance are proposed. The method considers the impact by subjective uncertainty reasonably and the information of the measured member. Considering the deficiency of inference method on the variation coefficient at present, new inference method is proposed. Comparing with present approximate inference method including the national standard GB/T11891-89 approximate inference method, it also has higher accuracy and widely applied.
论文的主要目的是针对目前近似概率极限状态设计方法的缺陷,建立工程结构可靠度设计与评定的通用方法,并考虑主观不确定性对结构可靠度分析结果的影响,主要研究内容和工作包括：
1主观不确定性的数学处理方法以及考虑主观不确定性的可靠度分析方法。论文将各种人们认识上的不确定性归结为主观不确定性,并通过未确知量和信度建立了统一的主观不确定性的数学描述方法；通过对结构失效概率的信度分析,建立了考虑主观不确定性的结构可靠度分析方法,并进一步建立了综合概率与信度的可靠性度量和控制方法。
(2)工程结构可靠度设计与评定的通用表达式。目前的实用设计表达式在反映随机变量的影响方面存在着结构性的缺陷,论文根据目前国际组织JCSS推荐的计算可靠指标的JC法,直接建立了分项系数与基本变量概率特性、设计使用年限、目标可靠指标之间的函数关系,从而建立了工程结构可靠度设计与评定的通用表达式。该表达式不仅具有坚实的理论基础,而且能够灵活应用于新型结构、新材料结构的设计以及既有结构的可靠性评定,满足人们对设计使用年限、目标可靠指标的不同要求。
(3)标准灵敏度系数的确定方法。标准灵敏度系数是建立工程结构可靠度设计与评定通用方法的关键,但目前的枚举和拟合方法不仅繁琐费时,而且可能遗漏不利的情况,为此论文提出灵敏度系数边界向量和中心向量的概念,分别针对承载能力极限状态和正常使用极限状态,利用向量分析方法确定了可靠度设计的最优灵敏度系数和标准灵敏度系数,最终建立了工程结构可靠度设计与评定的通用方法,而且也为建立可靠度设计与评定方法的建立提供了解析方法。
(4)基本变量数字特征以及材料强度、抗力的推断方法。对基本变量数字特征以及材料强度、抗力的推断,是将可靠度设计与评定通用方法应用于工程实际的一项必要工作。对于既有结构而言,其当前时刻的材料强度和抗力是客观上确定但存在主观不确定性的未确知量,目前的概率统计方法并不完全适合于对它们的推断,为此论文针对既有结构的特点,提出基本变量数字特征以及材料强度、抗力的信度推断方法,这些方法不仅可以合理考虑主观不确定性的影响,而且也充分考虑了被测量本身所提供的信息。论文还针对目前变异系数推断方法的不足,提出较国家标准具有更高精度和更广适用范围的推断方法。
In the civil engineering field, the method of approximate probability limit state design is an advanced method known at domestic and overseas. The method for measure and control structural reliability is implemented by reliability index related to failure probability, overcoming the defect of the previous empirical method basically. But in practical application, partial factor was determined by predetermined probability characteristics of basic variable, design working life and target reliability index were also set beforehand. The method will not suit for reliability-based design when real probability characteristics of basic variable are different form predetermined probability characteristics, or owner's demand of design working life and target reliability index are different form setting value. Because of a lack of flexibility, this method cannot satisfy the need of design of new structures and new material structures, and can't be used in the assessment of existing structures. At the same time, the current design method only considers the randomness of things, but did not consider the uncertainty of human's recognition.
Aiming at defective in limit state design method of approximate probability, the dissertation establish general method for re liability-based design and assessment of engineering structures, and also take into account of the affections of subjective to the analysis result of structural reliability. The research contents and result includes:
1. Mathematical treatment method for subjective uncertainty and reliability analysis method based on subjective uncertainty are proposed. The dissertation induces all kinds of uncertainty in human's recognition as subjective uncertainty; to establish general mathematical treatment method for subjective uncertainty by uncertain variables and belief function. Based on be lief analysis of structural failure probability, the paper creates structural reliability analysis method considering subjective uncertainty, further to establish reliability measures and control methods with combing probability and belief.
2. General expression for the design and assessment of reliability of engineering structures are proposed. At present, there are plenty of shortcomings about reflecting the impact of the random variables in the practical design expression. In the paper, according to the JC method recommended by the international organization JCSS, functional relationships among partial factor and probabilistic characteristic of basic variable, design working life, target reliability index are founded. At last, the general expression for the design and assessment of reliability of engineering structures are proposed. Based on the solid theoretical basis, the expression can be use to design the new structure and new material structure, to assess the existing structures. So it can satisfy the different needs on the design working life and target reliability index.
3. The paper proposes determination method of standard sensitivity coefficient. The standard sensitivity coefficient is critical to establish general method of the reliability-based design and assessment of engineering structures. But current enumeration method and fitting method are not only tedious but may also to miss the adverse cases. Therefore, the boundary vector and center vector are set up for the sensitivity coefficient. Aiming at the ultimate limit states and serviceability limit states, the paper makes use of the analytical vector method to determine the optimal sensitivity coefficient and standard sensitivity coefficient of reliability-based design. At last, the general expression for the design and assessment of reliability of engineering structures are founded. At the same time, analytical method is derived to design and assessment the reliability of engineering structures.
4. The paper proposes inference rules for probability characteristics of basic variables, material strength and resistance.The research on the number characteristics of basic variables, material strength and resistance are essential to engineering practice, especially the general method of reliability-based design and assessment. The material strength and resistance at any time for the existing structures are determined objectively but uncertain and unknown variables also existing subjectively. The current methods of probability and statistics are not entirely suitable for their inference. According to the characteristics of the existing structures, the reliability inference method for the number characteristics of basic variables and material strength and resistance are proposed. The method considers the impact by subjective uncertainty reasonably and the information of the measured member. Considering the deficiency of inference method on the variation coefficient at present, new inference method is proposed. Comparing with present approximate inference method including the national standard GB/T11891-89 approximate inference method, it also has higher accuracy and widely applied.
引文
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