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**Name**:

# Random Mathematical Analysis on the Dynamic Behavior of the Gravity Dam

**Author**: WangChao

**Tutor**: ZhangSheRong

**School**: Tianjin University

**Course**: Hydraulic Structure Engineering

**Keywords**: Gravity dam,Dynamic behavior,Random mathematical analysis,Reliability analysis t

**CLC**: TV642.3

**Type**: PhD thesis

**Year**: 2012

Abstract:

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.

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.

Dissertation URL:http://www.topresearch.org/showinfo-172-677247-0.html

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