Structural Global Reliability Methods And Nonlinear Global Seismic Reliability Analysis Of RC Frames

Performance-based earthquake engineering (PBEE) and performance-basedseismic design (PBSD), proposed by the Pacific Earthquake Engineering ResearchCenter (PEER), are a new-generation seismic design concept, method and technique.They have been warmly responded by the world-wide earthquake engineeringresearchers and engineers. Due to the strong randomness in occurring time, spaceand intensity of earthquakes, and also because of a lot of uncertainties in bothseismic demand and seismic capacity of civil engineering structures, it is necessaryto build a probabilistic framework of PBEE and PBSD based on structuralreliability theory. Nowadays, the probabilistic seismic performance evaluationbased on reliability has become one of the main research points of PBEE and PBSD.Seismic reliability of structural systems is a quantitative measure ofprobabilistic seismic risk of civil infrastructures. Recently, a new trend of systemreliability analysis based on structural global limit states has emerged. Furthermore,the new-generation PBEE also takes the systematic seismic risk based on structuralglobal reliability as the main research objective. Based on the above considerations,in this dissertation, two efficient global reliability methods, i.e. the generalized firstorder reliability method (FORM) and the improved higher order moment method(HOMM), are developed from the viewpoint of the basic variable model and thestate variable model, respectively. And then, three reinforced concrete (RC) framestructures are designed according to Chinese codes, which are taken as the researchobjects of case studies in this dissertation. The seismic reliability of these RCframes is the main research contents of this dissertation, and the assessment ofseismic safety of these RC frames is the ultimate research goal of this thesis. Usingthe developed generalized FORM and improved HOMM, the global reliability androbustness of the case-study RC frames are systematically and deeply studied fromthe aspects of four global limit states, i.e., global load carrying capacity, globaldeformation capacity, global seismic damage and global progressive collapse,respectively. The main research contents of this dissertation are summarized asfollows:1) The traditional Nataf transformation based on normal distributions isextended to the generalized Nataf transformation based on Copula functions. Thenan extended first order reliability method (EFORM) using the generalized Nataftransformation is developed to consider the nonlinear dependence among therandom variables. Furthermore, a fuzzy first order reliability method (FFORM)considering parameter uncertainties is put forward. For the basic variable model of structural global reliability, the generalized FORM (EFORM and FFORM) isrealized in the software MATLAB and the FEA platform OpenSees. It isdemonstrated through the numerical examples that the proposed generalized FORMcan effectively take into account the nonlinear dependence among the randomvariables and the epistemic uncertainty of parameters of random variables.2) An improved point estimate method (IPEM), which can incorporate themarginal distributions and the correlation information of random variables, ispresented based on the generalized Nataf transformation. And then, an improvedhigher order moment method (IHOMM) is developed by combining the IPEM withthe maximum entropy principle. For the state variable model of structural globalreliability, the improved HOMM is realized in the software MATLAB and the FEAplatform OpenSees. It is demonstrated through the numerical examples that thedeveloped higher order moment method (IHOMM) has the same accuracy as FORM,while the former is more efficient than the latter.3) Three RC frame buildings with different floors under the same seismicfortification intensity are designed according to the current Chinese codes. Thesestructures are modeled in the platform OpenSees. Through comparing with the testdata of RC elements (columns) and a global structure shaking table test in TsinghuaUniversity, the developed OpenSees models are verified and validated to beadequate to describe the nonlinear behavior of the case-study structures. Thedeterministic seismic performance analysis is carried out for the three structures,and their main seismic behaviors and properties are obtained.4) The global load-carrying capacity limit state equation is established for theRC frame structures. Through the combination of the generalized FORM and theimproved HOMM with the deterministic Pushover analysis, a FORM-based design-point pushover method and a HOMM-based random pushover method aredeveloped, respectively. It is illustrated through the comparative study that the twomethods have a good agreement. The two approaches are then applied to thenonlinear static seismic reliability analysis of structural global load carryingcapacity limit state, and the variation rules of global seismic reliability indices andsensitivity factors are obtained. Furthermore, the static seismic fragility curves arederived for the global load carrying capacity.5) The global deformation capacity limit state equation is set up for the RCframe structures. By way of the combination of the generalized FORM and theimproved HOMM with the deterministic capacity-spectrum method (CSM), theFORM-based design-point CSM and HOMM-based random CSM are presented,respectively. Comparative study shows that the two methods have a goodconsistency. The two methods are then applied to the nonlinear static seismicreliability analysis of structural global deformation capacity limit state, and the changing regularities of global seismic reliability indices and sensitivity factors areobtained. Furthermore, the static seismic fragility curves corresponding to differentdamage states are given for the global deformation capacity.6) The global seismic damage limit state equation is established for the RCframe structures. A new probability density evolution approach for structuraldynamic responses based on the improved point estimation method (IPEM) isproposed. Using20real earthquake records and2artificial earthquake records asinputs, the global dynamic response and the global parameter sensitivity ofstructures are analyzed using the IPEM, and the probabilistic density evolutioncurves of structural global dynamic responses are derived. Employing the improvedHOMM, the first-passage criteria and the cumulative damage criteria, the nonlineardynamic seismic reliability analysis are implemented for global seismic damagelimit state of structures; and the change rules of global dynamic reliability indicesof structures are discovered.7) A new definition of structural robustness is given from four aspects ofoccasional event, local damage, disproportional failure, and failure consequences. Aglobal progressive collapse limit state equation is established for the RC framestructures. A method for identifying the most probable failure members is proposedbased on local seismic reliability analysis of structural members. A randompushdown method and a random vertical IDA method are presented via the couplingof the IPEM with the deterministic pushdown analysis (PDA) and verticalincremental dynamic analysis (IDA). The two methods are used to analyze theprobabilistic progressive collapse resistant capacity and the parameter sensitivitiesof the intact structures and the damaged structures. With the total probabilitytheorem, the progressive collapse probability with the consideration of seismichazard is derived. On the basis of the above computations, the robustness indicesbased on the conditional reliability and the global reliability are evaluatedrespectively, and the changing rules of structural robustness are studied, in whichthe relationships between global robustness and local damage of structures arequantitatively revealed.