Development of Structural Collapse Fragility Functions Considering Different Failure Modes by Fault Tree Analysis

Seismic risk assessment of structures is an important and practical tool for seismic safety assessment, earthquake consequence analysis, seismic strengthening planning and post-earthquake crisis management. This assessment consists of various parts including seismic hazard analysis, exposure evaluation, vulnerability analysis, and risk estimation. One of the most important parts of this process is the development of structural fragility functions or curves for undesired performance. Various methods have been used to determine fragility functions. In most of these methods, a general limit state such as maximum relative displacement of the floors is considered as failure mode, while in older buildings, more failure modes such as shear failure mode of structural members are usually prevailing.
In this paper, a framework for determining the fragility functions of structural collapse based on different failure modes of structural members using fault tree analysis is presented. This method includes developing the fault tree of the undesired performance of the structure (through possible failure modes in members), preparing a suitable computer model of the structure according to failure modes, selecting earthquake acceleration records for IDA analysis, determining the capacity and limit mode of failure modes based on laboratory results or standards, performing IDA analysis for the structure and forming a fragility table, calculating the fragility parameters using a suitable statistical distribution and plotting the seismic fragility curve for each of the base events in fault tree and quantifying the fault tree, and finally deriving the fragility curve of the structure.
This method was applied on a reinforced concrete building frame made in Europe according to the design criteria of the 50s and 60s, and then the results were compared with the conventional method of developing fragility functions, which is based on the general limit state of maximum relative displacement of floors. Because the main reason for the weakness of the frame under study is the weakness in shear of the columns due to the lack of seismic transverse reinforcement details at the time of their design and construction, in next stage, the fragility function of the studied frame is determined by observing the criteria of seismic transverse reinforcement and is compared with the fragility function of the existing frame without observing these criteria.
 The results show a much lower median estimate of the capacity of the fragility function due to the shear weakness of the old frames in the proposed method compared to the conventional method. The fragility curves derived from conventional methods match very well with the failure mode causing weak-storey on the first floor. This observation is in good agreement with the results presented in the references in which the main collapse mode for this frame is the failure of the weak floor in the first floor. Another observable result in the proposed method is the reduction of the dispersion of the results using this method compared to the conventional method because the fragility curve obtained from this method covers a narrower range than the conventional method.
Considering the criteria of transverse reinforcement, it was observed that in many columns, the philosophy of designing new regulations, which is flexural failure before shear failure, has occurred, which shows the high importance of transverse reinforcement in column sections. By observing the criteria of transverse reinforcement of sections, the most vulnerable part of this frame are the columns of row 2 in shear failure mode, due to the significant difference in the cross-sectional height of the columns of this row compared to other rows. This difference in the height of the sections leads to high absorption of shear force in the section, which causes the force to pass through 
the capacity much faster and as a result, its high vulnerability. Finally, comparing the fragility curves of frame collapse in two cases with considering the seismic shear reinforcement criteria and without considering it shows the significant effect of cross-section reinforcement criteria on the seismic fragility function of structures.