Structure Fragility Analysis Under Bidirectional Seismic Action

Theoretical research and earthquake damage investigation results shows that the seismic effect of structure is multi-dimensional. But in most cases, the effect of two principal axis direction of structures is considered separately in practical engineering due to the limitation of basic theory and technology, which will obviously underestimate the seismic effect of structures. In recent years, with the progress of research and development of technology, the effect of structures subjected to earthquake in two directions(even in three directions) at the same time has gradually been paid attention. But there are still some problems need to solve when the bidirectional seismic input timehistory analysis was implemented. For example, the selection of earthquake ground motion and input sample size for bidirectional analysis has not been settled appropriately. To solve this problem and compare the unidirectional and bidirectional effect of structures under seismic action roundly, the following aspects has been conducted.(1) First of all, 3 multi-story frames and 3 high-rise frames are designed according to the current design code with torsional displacement ratio of 1.5, 1.3 and 1.1 respectively. Then “random combination method” is come up to solve the selection of earthquake ground motion for bidirectional seismic input time-history analysis. Then this method is compared with common method called “natural records method” and is proved to be better. Finally, elastic and elastic-plastic time history analysis is conducted to all examples under unidirectional and bidirectional seismic input and the difference between unidirectional and bidirectional results is given. The results show that it is more reasonable to conduct elastic and elastic-plastic time history analysis bi-directionally.(2) Two optimization methods are come up to lower the variability of the results and reduce the calculation work based on “random combination method”. Then elastic and elastic-plastic time history analysis is conducted to all examples based on the two methods and the variability of the results shows that “amplitude modulation method” is better.(3) The input sample size of time history analysis is conducted based on “amplitude modulation method” and the assurance rate for each precision levels of some small samples is given in elastic and elastic-plastic state under bidirectional seismic input and suggestion is given.(4) The IDA(Incremental Dynamic Analysis, IDA) and fragility analysis are conducted based on “amplitude modulation method” and the results of input sample size research. Then the difference between the unidirectional and bidirectional IDA curves and fragility curves for not only the whole structure but also every single story is given and the distribution of the probability of failure along the height for both multi-story structure and high-rise structure is also displayed. In the meantime, the fragility curve is combined with seismic hazard curve which can show the probability distribution and annual probability of limit states under different PGA.The main innovation in this paper includes the following three points:(1) The method for the selection of earthquake ground motion for bidirectional analysis is come forward.(2) Then the difference between the effect of structures under unidirectional and bidirectional seismic action is given and the influencing factors are also analyzed.(3) Then the difference between the unidirectional and bidirectional fragility curves and annual probability of limit states of structures are given.