Convex Set Method For Structural Seismic Performance And Earthquake Loss Analysis

The current Performace-based earthquake engineering (PBEE) is on the basis of probabilistic reliability theory. However, when the data is insufficient to support a probabilistic assumption, the probabilistic approach is not a viable in dealing with the uncertainty in earthquake engineering. In this study, the convex set theory and convex models are applied in the treatment of uncertainty in the seismic hazard analysis and performance-based structural seismic evaluation and design, and an alternative approach is developed for analyzing the uncertainty in earthquake engineering. The main contents of this research are as follows:Firstly, the limitation of probabilistic theory and the advantage of using the convex set theory under certain condition are discussed. Basics of convex set theory and the convex analysis method are introduced. A comparison of probabilistic method and convex method is made with designed examples. The necessarity of using convex set theory in dealing with uncertainty in earthquake engineering is pointed out.Secondly, modeling the uncertainties of theb value, the annual occurrence ratev and the upper bound magnitude M uusing convex set models, a convex set-based seismic hazrd analysis approach is developed by integrating the convex theory with the probabilistic based CPSHA (China Probabilistic Seismic Hazard Analysis) theory. By the example of seismic hazard analysis of a city in southern China, this method is demonstrated with a sensitivity analysis. It is found that the uncertainty can be effectively treated by this method, and it is a better choice for seismic hazard analysis of low seismicity area.Thirdly, the uncertain sources of seismic influence coefficient maximum and the design characteristic period of ground motion are identified. The uncertainties of these two parameters are modeled with the double bounded convex set model. The bounds of earthquake demand spectrum and the shear force are obtained. A new lateral bound load method of considering the earthquake action uncertainties for Push-over analysis is proposed by combining the convex set model with SRSS load pattern, and the bound range of capacity spectrum is derived. A bound capacity spectrum method is presented by deducing the bound of inelastic earthquake demand spectrum.Fourthly, the convex theory is applied in analyzing the uncertainty in seismic risk analysis, and the uncertainties of spectrum displacement, the damage state medians and loss ratio are described by the envelope bound convex model. A new bound earthquake loss estimation method for individual building is proposed in the framework of HAZUS procedure. The earthquake loss of a hotel in southern China analyzed as an example is estimated, and the propagation of uncertainties is analyzed. This bound method enriches the tools for seismic risk analysis, and provide a new approach for earthquake loss estimation when the information is deficiency.By modeling the uncertainties of peak ground acceleration (PGA) and loss function with convex set models, the seismic risk analysis method based on Gross Domestic Product (GDP) is extended to include the associated uncertainty. Particularly, the dynamic GDP is considered by regression analysis of historical data, and a dynamic GDP earthquake loss estimation method based on convex set model is given. The earthquake loss of a city in southern China is estimated as an example, and the earthquake loss is disaggregated and the sensitivity of seismic activity parameters and loss function are analyzed. This proposed method avoids the use of subjective seismic intensity, and features the inclusion of convex theory and dynamic GDP.Finally, the envelop bound convex set model is employed to consider the uncertainties of design target displacement, seismic influence coefficient maximum and the design characteristic period of ground motion, and a new bound design method is developed based on direct displacement-based design procedure. The interval of seismic design results is obtained by considering the bound of uncertain design parameters and the reliability of designs by current seismic code and sensitivity of design results to the uncertain inputs can be checked with this method.