摘要
不确定性是水工结构设计、施工、使用乃至维修报废的全生命周期中存在的客观现象，但国内真正用理论的方法加以研究，并付诸于实践起步较晚。作为解决不确定性问题的重要途径，引入随机数学的理论，用概率的观点研究重力坝结构系统在复杂环境下的结构安全性问题，成为近年来水工结构安全研究的一个重要趋势，也是多学科交叉的高坝工程设计领域的前沿课题。论文主要针对不确定环境下重力坝性态随机力学分析中的关键技术问题和体系可靠性的评估方法进行研究。主要研究内容和成果如下：
（1）研究了高坝结构性态分析的随机建模方法，建立了坝基不良地质体的材料参数完全随机场模型和约束随机场模型，解决了参数随机条件下高坝性态的合理分析和评价问题。
考虑重力坝材料参数和数值分析模型的内在随机性，以溶蚀地质条件下的典型工程问题为研究对象，阐述了基于随机场理论建立区域随机单元的方法步骤；进一步，通过Bayes信息更新原理，改进了结构参数的随机场模型，建立了区域结构的约束随机有限元力学模型，分析了区域地质体材料参数随机特性对工程结构性态的影响，解决了结构参数随机条件下高坝性态的合理分析和评价问题。
（2）研究了高坝系统地震动力灾变环境的随机描述方法及概率地震反应统计特征，建立了三层次的重力坝概率地震反应分析方法体系，提出了重力坝随机地震反应的概率特征分析方法。
针对高坝系统外部动力灾变环境的高变异随机特征，在水电工程场区地震危险性分析的基础上进行了三层次的概率地震反应参数分析，得到了重力坝典型动响应量在不同地震水准下的概率特征；同时针对地震发生时间的随机性，建立了随机地震描述的跳变概率模型，分析了动力环境下结构性能的退化规律。
（3）研究了基于Copula函数的重力坝多失效模式相关体系的联合分布模型及可靠性分析方法，推导了基于Copula函数求解相关性体系可靠度的计算式，验证了该分析模型的合理性。
不确定性范畴内的重力坝体系可靠性实质上是一个多失效模式相关的串联体系可靠度计算的问题。针对重力坝多模式相关下体系可靠度求解算法的问题，对比了区间估计法和多维数值积分解法，借鉴金融学分析中的多元联合Copula函数，推导了具有力学联系的重力坝体系不同失效模式间的概率计算式。以重力坝结构三元失效模式体系可靠性分析为例，验证了该模型在应用中的合理性。
基于Copula函数的相关性可靠度计算模型，是由多模式联合分布多重积分求解到多重差分估算一次思路上的转变。
（4）分析了坝体系统动力失稳的薄弱层面失效模式，得出了碾压混凝土重力坝坝身不同高程薄弱面的动力抗滑可靠度的变化规律；在假定条件下，推导了工程上传统的安全系数和可靠度之间的数学关系。
研究重力坝系统随机性对结构性态影响的最终目的是要评价不确定性因素对其安全（风险）的影响，即进行可靠度评价。针对重力坝动力系统随机结构体系的特点，采用刚体极限平衡方程为功能函数，以系统动力失稳的薄弱层面为失效模式，分析了重力坝动力失稳体系的可靠度，并与传统安全系数法进行了对比研究。
（5）基于极限状态方法提出了识别重力坝动力潜在失效模式的数值搜索方法，完善了复合失效模式下的碾压混凝土重力坝动力体系可靠性的分析方法体系。
针对混凝土重力坝坝身块体结构动力破损具有明显的渐进性、复杂性和复合随机性特征，人为拟定失效模式可能并不真实。从极限状态体系的力学观点出发，提出了识别重力坝动力体系潜在失效模式的数值搜索方法，并在此基础上完善了复合失效模式下的大型碾压混凝土重力坝动力体系可靠性的分析方法体系。
Uncertainty is the objective phenomenon during the whole life cycle of hydraulicstructures, including the design phase, construction phase, operation phase as well asthe scrap processing phase, but the theoretical research and practical application on itdo not have an early start. As an important way to deal with uncertainty problems,random mathematics theory is introduced, the idea of probability theory is employedto research on the safety problems of gravity dam structure system in complex anduncertain environment, which becomes an important trend of the safety of hydraulicstructures in recent years, also a front cross-discipline problem of the engineeringdesign field. The key technical problems of numerical methods for random simulationand its reliability evaluation method are studied under the new complex environmentin this paper. The behavior and the structure safety are evaluated based on the randomnumerical simulation technology and reliability analysis theory of the gravity dam, sothat the system effects of actions can be transformed from the statistical inference tothe theoretical prediction combined with statistical inference. Main contents andresults are as follows:
(1) The method of stochastic modeling is researched. Both the intervalrandom field model and constraint random field model are built to analyze thebehavior of the gravity dam under random geological material parameters.
For the randomness of the material parameter and numerical analysis model ofthe hydraulic gravity dam, take the typical engineering problems of the dissolutionfoundation for example, methods and procedures are illustrated to establish randomelements based on the random field theory, which is applicable to all of the stochasticstructure systems. Then stochastic mechanics analysis is proposed by using the SFEM.On the other hand, according to information updating theory of bayes formula, theInterval random field model is improved to be the constrained one, so that theinfluence of the randomness of the material parameters on the behavior of the dam isanalyzed and the evaluation problem is also solved.
(2) Stochastic description method and probability seismic responsecharacteristics are researched. Three levels of procedure are presented for seismic response and its probability characteristic analysis, and then the methodof probability seismic response characteristics is put forward.
For the high variability of the dynamic loads, the probability seismic demandsanalysis (PSDA) is made based on seismic risk analysis of the engineering sites to getthe probability distribution characteristics of the dynamic response. On the otherhands, jumping degradation probability model of the structure performance underrandom seismic loads is built and the structure performance is described.
(3) System reliability analysis method for multiple failure patterns of gravitydam is put forward based on the Copula function. The joint distribution model isestablished using Copula function of stability between layers of gravity dam, thecomputational formula of this system reliability analysis method is deducedtheoretically，and the new analysis model is verified.
System reliability of the gravity dam is essentially system reliability calculationconsidering multiple correlated failure modes. Comparative study is made betweeninterval estimation method and the numerical integration method and thecomputational formula of this system reliability analysis method is deducedtheoretically based on the Copula function, which is also an ideas change from themeans of integrates to the difference method. At last, the rationality of the applicationis proved through an engineering example.
(4) Failure modes between layers for the dynamic system of the gravity damare analyzed and the law of stability reliability against sliding of different layerswith the elevation. And the mathematical relationship is deduced between thetraditional safety coefficient and the reliability index under the assumedconditions.
Reliability analysis is the ultimate purpose to evaluate the influence ofuncertainty factors to the dam safety. Failure modes between layers for the dynamicsystem of the gravity dam are assumed based on the engineering experience accordingto the characters of the dynamic dam system. The limit equilibrium equation is choseto establish the limit state equation then the stability reliability against sliding of thedam is analyzed and compared with the traditional safety coefficient.
(5) Numerical search method to recognize the potential failure modes of thedynamical dam system based on the limit state system is put forward. Reliabilityanalysis method of the dynamical dam system is established under the compositefailure modes.
For failure mode identification, considering the material heterogeneity, seismicvariation as well as the uncertainty of the fracture model and the constitutive modal ofthe concrete for numerical simulation is established based on the dynamical limit statesystem, on the other hand, for the quantification of the failure probability,mathematical model for system reliability analysis is established according to thecharacteristics of gravity dam, then the calculation formulas of failure probability,which consist of three levels(the element failure-path failure-system failure), arederived.
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