Fragility Analysis Of Steel Frame Structures Under Mainshock-aftershock Sequences

Based on a significant amount of data on earthquake damage,it is evident that strong primary earthquakes have a high likelihood of inducing aftershocks.The incremental structural damage caused by these aftershocks can worsen the existing damage and lead to more severe consequences.However,the current domestic code species fail to consider the impact of aftershocks on post-earthquake damage assessment and seismic performance of structures,which can have negative consequences on the evaluation of the structures’ post-earthquake damage and their seismic design.To address this issue,this paper aims to establish a probabilistic failure model of steel frames under aftershock conditions using the incremental dynamic analysis(IDA)method.This involves manually simulating realistic ground shaking sequences for the main-aftershocks and analyzing the susceptibility of steel frame models with different height and width ratios to these aftershocks.The primary research contents of this study are as follows:(1)Utilizing the aftershock ground shaking prediction formula that takes into account the correlation between the ground shaking characteristics of the mainshock and aftershock,a numerical ground shaking simulation method is employed to synthesize the main aftershock type ground shaking sequence by integrating seismic setting parameters.A typical 6-story steel frame model is designed for a specific set-up level,and its finite element model is established using Open Sees software.To analyze the effect of incremental aftershock damage on the steel frame structure,three structural damage indices,namely the maximum interstory displacement angle,maximum vertex displacement,and damage index,are selected.By comparing and analyzing the changes in these indices under the combined action of mainshock alone and main aftershock,the index that can most accurately characterize the incremental damage to the structure by aftershock is chosen as the structural damage parameter for subsequent study,to determine the degree of damage to the structure.Our results indicate that the damage index is more suitable as the damage index of the steel frame structure under the action of the main aftershock.Therefore,the damage index is selected as the structural damage index for subsequent study in this paper.(2)Based on the three characteristics of ground shaking,this study classifies commonly used ground shaking intensity parameters and considers the correlation between them.Representative ground shaking characteristic parameters are selected as the research objects.Utilizing the aftershock ground vibration prediction formula,the main aftershock ground vibrations are amplitude-modulated to obtain different intensity levels of the main aftershock ground vibration sequences.The various ground vibration intensity parameters of the ground vibration records after amplitude modulation are then calculated.An elasto-plastic time analysis is performed on the research object using the amplitude-adjusted ground shaking records as excitation to calculate the corresponding structural damage indexes for different intensity levels of the main aftershock ground shaking sequences.The correlation analysis between different ground shaking intensity indexes and their corresponding structural damage indexes is carried out to select the ground shaking intensity index with the highest correlation as the parameter for characterizing the magnitude of ground shaking intensity.The study reveals that for a steel frame structure under the action of mainshock alone,selecting the maximum peak acceleration(PGA)as the ground shaking strength index is reasonable.However,for the action of main aftershock,it is more reasonable to select the maximum peak displacement(PGV)as the ground shaking strength index.(3)Following a thorough analysis,a rational structural damage index(DM)and ground vibration intensity index(IM)have been chosen.The susceptibility of the structure under the influence of the mainshock and main aftershock is assessed through incremental dynamic analysis(IDA method),and the susceptibility curves resulting from the mainshock and main aftershock are compared.The probability of the four damage index limits shows varying degrees of increase,which is well-established.Therefore,it is imperative to consider the incremental damage caused by aftershocks during the seismic analysis and design of structures.Applying the Bayesian principle,a probability model for the susceptibility of aftershocks is derived.This model is used to plot the susceptibility curves for damaged structures following the mainshock,and probability curves for aftershock damage states are drawn based on these curves.Upon comparative analysis,it is determined that the probability of damaged structures reaching the next level of damage limit increases to varying degrees after the mainshock.By utilizing the probability model for the susceptibility of damaged structures following the mainshock,the seismic performance of these structures can be rapidly evaluated,and recommendations for post-earthquake structural repairs can be provided.(4)Predictive models for susceptibility analysis have been developed for steel frame structures with varying height-to-width ratios using a linear fitting method.These models enable the establishment of seismic probability demand models for general steel frame structures and facilitate the analysis of their vulnerability to damage.The aftershock susceptibility curves and probability curves of aftershock damage states reveal that incremental damage caused by aftershocks is more likely to result in more severe damage states after the mainshock,particularly for steel frame structures with higher height-to-width ratios.This study contributes to the evaluation of the seismic performance of steel frame structures with different damage states following the mainshock.