On Probabilistic Method For Performance-Based Seismic Analysis Of Bridge Structures

Performance-based seismic design (PBSD) has become the main research subject in aseismic engineering and attracted a lot of research attention both in building engineering and bridge engineering. The seismic response and capacity of bridge are random because of the uncertainty of the ground motion and the geometry and material of the structure. Hence PBSD should be built on probability theory. In this paper, the probabilistic method for seismic performance analysis of bridge structures was studied systematically, including the criterion for PBSD of bridge, probability characteristics of the ductility-based seismic performance indices for reinforced concrete components, seismic hazard curve, stochastic inelastic seismic response spectra, improvement of modal pushover analysis method, and nonlinear seismic reliability analysis method for bridge under large earthquakes. The following major achievements were gained:1) Some problems concerning the seismic fortification criterion of PBSD in bridge engineering were discussed. Based on the studying of guidelines concerning seismic fortification criterion in the seismic design codes of several countries, and considering the reality of China, some proposals were put forward for the seismic fortification criterion in PBSD of bridge engineering in China, including the fortification ground motion levels, seismic performance levels, seismic importance classification of bridge structures, as well as seismic fortification objectives for bridges of variant importance.2) Five damage states with four limit states were defined for the seismic performance level of ductile reinforced concrete components, along with the strain limit definition for each limit state. Then, based on the mechanical characteristics and statistical characteristics of reinforcement and concrete, the strength and deformation characteristics of circular reinforced concrete ductile component were analyzed probabilistically for each performance level. Hereby the probabilistic distribution characteristics of the performance indices for each performance level were obtained for reinforced concrete ductile members, and the regression formula as well as probability distribution model for the performance index of each performance level were proposed, in convenient for the probabilistic analysis of seismic performance of bridge structures.3) Based on the probabilistic method for seismic hazard evaluation, according to the achievements of Seismic ground motion parameter zonation map of China and the statistical probability distribution of seismic intensity and peak ground acceleration (PGA), the conversion relationship from the basic seismic intensity and basic PGA, i.e., those presented in the Seismic ground motion parameter zonation map of China, to the seismic intensity and PGA with variant probability of exceedance in certain considering years, was deduced. Hence the seismic hazard curve that is based on the currently in effect seismic specification was obtained. In addition, the conversion relationship between seismic hazard curves of different considering years was also presented.4) The artificial seismic ground motion simulation method was improved in two aspects. Firstly, the precise integration method was adopted for the calculation of seismic response spectra of the seismic wave, which improves the calculation accuracy for high frequency domain. Then, a high order polynomial was adopted for the baseline correction of the simulated wave, which can effectively clear up the baseline-shift of the artificially simulated seismic ground motion.5) Based on a proper stochastic earthquake ground motion model, the parameters of the model that are compatible with the PGA, site classification and characteristic period grouping specified in the currently in effect zonation map in China were determined. Further more, the stochastic elastic response spectra that are based on the stochastic earthquake ground motion model and compatible with the currently in effect seismic design code were obtained.6) By utilizing the 1064 strong ground motion records obtained from the destructive events in the history, which are classified according to the site classification and characteristic period grouping specified in the design code of China, the inelastic response of SDOF systems with variant periods and ductility factors were analyzed. Then, based on the strength reduction factor model proposed by Nassar & Krawinkler, the calculation results were analyzed with statistical regression method. Thereby the strength reduction factor model that is compatible with the seismic design code of China was obtained. By the reduction of the stochastic elastic response spectra with the obtained strength reduction factor, the stochastic inelastic response spectra were obtained.7) Based on the Modal Pushover Analysis (MPA) method proposed by Chopra and the decomposition of the seismic action, as well as the energy balance equation, it was deduced and concluded that the inputted energy by the modal load was completely converted to the absorbed energy by the corresponding mode. Then the relationship between the spectral displacement increment and the energy increment in the structure under the action of modal load was deduced, which brings on the proposal of an improved Modal Pushover Analysis method-Energy Based Modal Pushover Analysis method (EMPA). As an example, a continuous rigid frame bridge was analyzed with the proposed method to illustrate its adaptability for the nonlinear seismic analysis of complex bridge structures.8) By making use of the achievements on the seismic performance level classification, probabilistic characteristics of the deformation-based performance indices for each performance level, seismic hazard curve, and simplified computation method for the stochastic inelastic seismic demand, the probabilistic method for seismic performance analysis of bridge structures was proposed.9) The probabilistic seismic performance of a realistic bridge was analyzed, by computing its determined-intensity-based aseismic reliability and 50-year-based aseismic reliability. This example illustrated the simplicity and adaptability of the proposed method for aseismic reliability analysis in the PBSD of bridge structures based on deformation-based failure criterion under large earthquake. Thus the difficulty of the conventional method for aseismic reliability analysis was avoided, which is generally performed by the huge computation of a lot of nonlinear time-history analysis by Monte Carlo simulation.