## 6 Discussion and Conclusions  
### Discussion  
A mainshock-integrated aftershock seismic fragility function model is developed in this study to estimate the probability of exceeding a damage state of a structure (bridge, building, or other civil structures) under mainshock and aftershock loads that are recorded in the past earthquakeevents, in which, the probability of collapse is conditional upon mainshock and aftershock intensity. The innovation of this work is that the developed fragility model is different from the traditional fragility function model, in which three parameters are included in the proposed model. The generated fragility curves can reflect the effect of the mainshocks on the probability of failure at a specific intensity level, which means that for a specific mainshock and aftershock intensity, the probability of exceeding a damage state is clearly presented in the fragility curves. In addition, different from the model proposed by [PERSON] et al. [7], in creating the fragility curve, the horizontal coordinate is aftershock intensity in the mainshock-integrated aftershock seismic fragility model. In reference [7], the failure probability is expressed using mainshock intensity as the horizontal coordinate (traditional fragility model function is used). In the model proposed in this work, the failure probability has an initial value, which is determined by mainshock and is included in the model proposed by [PERSON] et al. [7]. The results in this work show that when the mainshock intensity level is lower (smaller than 0.4 g) if aftershock intensity is also less than 0.4 g, the earthquake sequences have a smaller effect on the probability of collapse. However, it may affect other damage states such as moderate or major damage, which is not presented in this study. In this work, due to limited recorded ground motion sequences, the sample size of the recorded ground motion sequences is only 60. Therefore, for future research, it is suggested that more numbers of recorded or synthesized earthquake sequences are utilized in conducting fragility analysis to reduce the difference induced by sample size. In addition, the M-A recorded in more earthquake events at the same station is suggested to be used. In this study, the probability of collapse of the bridge structures under M-A sequences is emphasized. Researchers can use this model for other damage states. It is noted that the proposed modeling framework embraces sufficient flexibility, which adaptably incorporates any mainshock by parametric quadratic polynomials. Nonetheless, for future research, it is suggested that the proposed fragility model be applied for different types of real bridges or civil structures to check the applicability and validity of the model. If possible, shake-table testing may be conducted in which mainshock-aftershock sequences with variable intensities are included, and different degrees of damage can be recorded. With these data, the proposed method can be further adjusted and validated. The probability of collapse in this work has an initial value, which increases with the mainshock intensity. The initial value should also have a great correlation with the properties of the structure; therefore, it is worthy of studying the relationship between the initial value of the probability of collapse conditional on the M-A sequence with the characteristic of structures. In this work, the displacement ductility is used to judge the damage states; for future research, other damage states are suggested to be used, such as the Park-Ang model. In this study, we focus on developing a fragility function model for assessing a civil structure under earthquake sequences, and the methods for judging damage states would not affect the accuracy of the model proposed. It is worth mentioning that many aftershocks may follow a mainshock in reality. It is possible that more than one aftershocks are considered; however, this would further complicate the potential scaling relation between the mainshock and its aftershocks.