Evaluation of the Fragility Curve for Steel Structures with Linked Columns Frame System under Sequences of Critical Earthquakes

doi:10.21203/rs.3.rs-4692635/v1

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Evaluation of the Fragility Curve for Steel Structures with Linked Columns Frame System under Sequences of Critical Earthquakes

https://doi.org/10.21203/rs.3.rs-4692635/v1

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Fragility curves as a powerful tool assess the possible damage to existing structures and estimate the probability of structural damage exceeding a given level of seismic damage for several levels of seismic ground motions. This paper tries to evaluate the seismic vulnerability of steel structures containing relatively new Linked Column Frame using the fragility curves under the critical multiple earthquakes, which are not considered by most of the seismic design codes. Therefore, 10 LCF steel frames with shear/flexural behavior and length of 2 meters have been designed and implemented in OpenSees software. After selecting consecutive critical earthquakes, the fragility curves for single and consecutive scenarios have been calculated. For more comprehensively evaluation of the mentioned structures, the effect of various parameters including the number of stories and behavior of the linked beams has been investigated. The results indicate an increase in the probability of collapse under a seismic sequence compared to a single earthquake. This increase is more obvious in the performance level corresponding to the collapse threshold. So that the collapse prevention of 7-story frame with flexural linked beam exposed to consecutive earthquakes is 17% higher than the single case.

Fragility Curves

Linked Columns Frame System (LCF)

Critical Seismic Sequences

Incremental Dynamic Analysis (IDA)

In recent years, severe financial losses for governments and people have been reported in major earthquakes. Therefore, the proper estimation of the seismic risk and the logical reduction solutions was the focus of researchers. In this regard, risk is usually known with three components: risk (earthquake), capital (structure) and the relationship between capital and risk. Due to the random nature of earthquakes, the non-deterministic parameters of the structure, that is, the relationship between the behavior of the structure and the earthquake, are always characterized by uncertainty and certainty [1] and it is different in every country based on the economic and social level of the people. Since determining the risk limit of structures improves the level of life safety and prevents the economic resources of the country from being wasted, its proper determination has particular importance for the country. Despite the efforts of researchers, there is still limited empirical information regarding the damage level and earthquake intensity levels. For this reason, the principles of seismic design based on performance can be correctly implemented for the retrofitting of existing structures and new constructions by providing the relationships that estimate the structural damage and consider the relationship between capital and earthquake intensity at the disposal of engineers. One of the useful tools to achieve this goal is fragility curves which can assess the vulnerability of structures. In addition to seismic risk assessment, it is used in other cases, such as comparing the vulnerability of different buildings, estimating the vulnerability of urban infrastructures, as well as crisis management planning. Since fragility curves show the severity of the structural vulnerability under earthquakes, it is common to determine the seismic vulnerability of buildings using these curves. The rate of vulnerability is expressed as probabilities and as a function of parameters such as the intensity of the earthquake and the probability of its occurrence. One of the advantages of these vulnerability functions is that it is possible to provide a comparison between the vulnerability of different buildings with small and reasonable values. These curves can be presented for all type of structures and depending on how the uncertainties are calculated – field tests, experimental studies or numerical simulation); there are various ways to draw them [2]. Fragility curves were extracted for the first time in 1980 for nuclear power plants [3]. Forcellini (2022) investigated the effects of soil-structure interaction using fragility curves for tall buildings. The results showed that fixed bases can increase the vulnerability of the entire structure [4]. The seismic behavior of various knee braced steel frames was compared based on incremental dynamic analysis and development of fragility curves by Yahyapour and Seyyedpour (2021). They claim that 10, 15, and 20-story structures with knee braced frames have better performance [5]. In recent years, investigation of the seismic risk of structural and non-structural buildings using the fragility curves is still in the focus of researchers. For example these curves were extracted for steel buildings exposed to fire [6], non-deformable reinforced concrete frames [7], mixed buildings [8–9], high-rise structures [10], development of fragility curves based on predictions of IDA neural network [11], non-structural buildings such as bridges and power plants [12–16] and etc. Therefore, with the introduction of new systems, the extraction of these curves will be continued. LCF system represents a novel strategy to resisting lateral and gravity forces in structures and introduced by Dusicka and Iwai [17]. This system incorporates replaceable link beams (as fuse members), which are designed to sustain structural damage during seismic events, thereby limiting damage to specific elements. This limitation aims to minimize damage to primary structural components at various levels of seismic hazard. As a result, the cost and time associated with post-earthquake repairs can significantly reduce because buildings equipped with LCF systems can quickly return to occupancy [18]. Due to the novelty of the LCF system as a dual lateral load resisting mechanism, limited researches are reported in earthquake engineering literature survey. For example, experimental evaluation of a several beam to column connections [19], the seismic behavior of LCF frames [20] and presentation of accurate methods for designation of LCF systems [20 − 21]. Moreover, the equivalent viscous damping has been investigated for this system by Mohebkhah and Tazarv [23]. Rajabi and Golestani [24] investigated the effect of seismic sequence on the performance of steel structures with LCF system expose to critical shocks and estimated R factors using artificial intelligence. In another study, Golestani et al. [25] also proposed the R factor of steel structures with LCF between 4 and 6.5. Due to the necessity of considering more comprehensive studies on the performance of the LCF lateral-resisting system, this paper evaluates the fragility curves for this structural system under critical sequence of fore-shocks, main-shocks and after-shocks. In this regard, a set of LCF steel structures and shear and flexural linked beams has been analyzed under consecutive shocks.

LCF system consists of the Linked Columns (LCs) and Moment Frame. Based on Figure (1), link beams which have been located between two stories in the story level cause to LCF fully restrained to the circumambient columns through proper details. Moreover, a link beam must consider above the connected LC to foundation to supply additional stiffness [20]. Due to the necessity of elastic behavior of columns in different seismic risk levels, pin joints are considered for the connection of all columns to the foundation. During moderate seismic events, fully restrained at one end and pinned at the other end is selected for MF beams to prevent the inelastic behavior [26].

During the last two decades, evaluation of the structural vulnerability has significant progress so that the prediction of the vulnerability of existing buildings caused by future earthquakes is known as one of the most suitable solutions to reduce the seismic hazard. As mentioned before, seismic fragility curves can assess the failure probability in earthquakes with different intensities. In other words, the possibility of increasing/decreasing damage in different excitations such as strong ground motions is illustrated by these curves as a suitable method for grading the strengthening of structures. In this regards, the damage due to the rotation and inter story drifts are usually taken into consideration [27].

In the present paper, the studied frames by Golestani et al. (2023) are selected to study the seismic performance of LCF steel structures. One of the studied frame with one LC bay (2.0 meters length and shear/flexure behavior) is shown in Figure (2). For the studied models with 3,5,7,9 and 11 stories, basic seismic design assumptions, loads, geometric properties of the structural sections and location of the lateral-resisting system are similar to Golestani et al.'s study [22]. Since the interior beams and columns cannot sustain lateral forces, pin joints are considered for their beam to column connections. In some cases, the seismic provisions of eccentrically braced frames are prevailed in the primary design of the LCF system. Moreover, the suggested values for the seismic performance factors [20] were used in the preliminary design of the models. In this study, the nonlinear models and different required analyses were performed in the OpenSees software to calculate the fragility curves [28]. In this regard, the uniaxial Hysteretic material was selected for beams (Link and bending beams) and valid experimental results were used for their validation similar to Golestani et al.'s study in 2022. Columns were modeled using Steel02 which has been proposed by Menegotto and Pinto [29], because they should be remained elastic.

Also, the experimental results of [19] were used to calibrate link beams. Nonlinear beamcolumn element with distributed plasticity in their length was selected to model the beams in a moment frame with flexural behavior. In this regard, fiber cross sections and the developed Fatigue Material model [30] were considered for these beams and they were calibrated according to [28]. In this study, it has been tried that all the structural connections were implemented and validated with related empirical results to lead suitable accuracy in the analysis results. For this purpose, pin and rigid joints were calibrated based on [28] without consideration the effects of the floor slab [29–30] to lead the real behavior of structural connections. Moreover, P-Δ effects, panel zone and slab rigidity, the stiffness for the diaphragm and connection springs were considered in the modeling. Thus, gravity loads were performed in real emplacements; the adjacent P-Δ equivalent columns sustain the rest of gravity loads caused by the internal columns in the plan. Finally, the multi-linear hysteretic material model was selected for beams, link beams, and rigid and pinned connections, and the independent shear force-shear strain behavior in link beams. More information is available in Golestani et al [25].

In the previous studies, real and artificial accelerograms containing seismic sequences are used. It is proven that the artificial accelerograms do not have enough accuracy and most of the results are reported overestimated [31]. Therefore, most effective successive earthquakes which have been recorded consecutively by accelrograms were selected according to the effective peak acceleration (EPA) parameter [32]. Hence, among the proposed critical consecutive records by Gohdra Amiri and Rajabi [33], 15 selected records in the study of Rajabi and Golestani [24] were selected to be applied to the modeled frames. The selected successive shocks from PEER database should be occurred in the similar station and in the same direction. It should be noted that the time history analysis was extremely time-consuming using the real sequences because the real time gap between the successive shocks was usually long. Thus, the shorter time gaps were considered with zero acceleration (= 100 second) based on [34].

In the structural and earthquake engineering literature, probabilistic examination of all uncertainties and hazard levels considering the structural performance is suggested for design of existing buildings because of random nature of earthquakes. For different intensities of the earthquake, the fragility curves specify the achievement of the performance level in a probabilistic manner. For this purpose, some parameters such as the rotation and the axial deformation of the plastic hinge, the inter-story drift are usually selected as damage modes. Two factors affect the fragility curve: (1) damage from the probability function and (2) characteristics of the seismic scenarios such as Peak Ground Velocity (PGV), Peak Ground Velocity (PGV) and Peak Ground Acceleration (PGA). According to the derived probabilistic functions from intensity values for different limit states, Eq. (1) can be used as follows:

$$\:{F}_{i}\left(im\right)=p(D>{d}_{i}\left|IM=im\left)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\right(1)\right.$$

where F_i(m) is the vulnerability probability and for earthquake intensity of IM = im, D is the damage level over a specific damage mode (d_i). PGA, PGV, or PGD can be selected as IM and different range of 0 to "n" can be defined for damage levels "i" as intact and damaged structures, respectively. In this paper, fragility curves were determined based on Shinozuka et al. [35], for Immediately Occupancy (IO), Life Safety (LS), and Collapse Prevention (CP) performance levels under critical single and successive shocks (foreshock, mainshock and aftershock). In these curves, the exceeding probability of the desired damage and PGA are introduced by vertical and horizontal axes, respectively. Proposed value of 0.005, 0.01, and 0.02 was selected for IO, LS, and CP performance levels, respectively [36–37]. Based on Figures (3) to (12), when the ratio of PGA_m to PGA_a ("m" and "a" present first shock and second shock) is greater than one, the exceeding probability of the desired damage increases. The comparison of median values shows that the PGA related to the given performance levels for consecutive shocks is less than singles. In other words, the exceeding probability of structural damage caused by successive shocks shocks is larger than singles, especially in short structures. By comparing the shear and flexural performance of the structures, the probability of failure in the LCF models with shear linked beams is lower than the structures with flexural linked beams. Also, as the number of stories increases, the possibility of failure has not necessarily increased or decreased.

6.1. Comparison of the probability of failure under seismic scenarios with and without seismic sequence

In this part, the probability of structural failure has been calculated for each model under single and consecutive records. As an example, for 5-story LCF frames with flexural linked beam (Fig. 6), the probability of failure for IO, LS and CP are 83%, 81% and 80% under single and 87%, 85% and 82% under successive records, respectively. It can be claimed that the probability of structural failure exposed to the seismic sequence phenomenon is higher than a single earthquakes. In other words, the proposed single design earthquake by the seismic design codes is not a suitable representative and the structures collapse earlier than the regulations assumptions. Because for all performance levels, the fragility curve for single shocks is lower than successive case. This means that the probability of exceeding the regulatory limits corresponding PGA for successive cases is lower than single case. Also, the probability of failure for 7-story LCF frames with flexural linked beams in IO, LS and CP are 78%, 75% and 73% under single shocks and 88%, 86% and 83% under successive shocks, respectively. Another example is for 11-story LCF frames with shear linked beam, which have the possibility of failure in IO, LS and CP are 76%, 73%, and 70% under single and 84%, 79%, and 73% under multiple records, respectively. The results indicate that the probability of failure in steel structures containing LCF exposed to consecutive accelerograms is higher than single shocks.

6.2. Comparison of the performance level under single and multiple accelerometers

In this section, in order to compare the performance level of the studied models under scenarios with and without seismic sequence for IO, LS and CP levels, the results of 5-story frame are shown in Fig. 13. In this figure, the vertical axis shows the obtained results from the performance level of the structure. According to this figure, in 5-story frame under successive records, the percentage of IO, LS and CP performance levels has increased by 4%, 4%, and 2% compared to the first shocks. The comparison of the performance level for 7 and 11 story frames is reported in Figs. 14 and 15, respectively. Based on the results of these figures, the percentage of IO, LS and CP performance levels has increased by 10%, 11%, and 8% compared to the single earthquakes. Meanwhile, the increase in results for the 11-story frame is equal to 12%, 9% and 17%, respectively.

In this paper, the seismic vulnerability of steel structures with LCF system under critical single and successive shocks has been investigated using fragility curves. For this purpose, 10 LCF steel frames with 3, 5, 7, 9 and 11 stories have been modeled in OpenSees software and increasing dynamic analysis is performed using as-recorded scenarios with/without seismic sequences. In this study, in addition to the number of stories, the influence of some parameters such as the behavior of linked beams (flexural and shear) has also been studied. In this regard, after performing the required analysis, the fragility curves have been calculated. The conclusions are drawn as follow:

The comparison of the mean values of the fragility curves indicates that the probability of failure under successive shocks is higher than the first shocks. The highest increase is calculated for 7-story frame with flexural linked beam.
Fragility curves of studied LCF models indicate an increase in the probability of collapse under multiple records compared to single earthquakes. This issue is more evident at CP performance level.
The possibility of structural failure in studied LCF structures with shear linked beams is less than the structures with flexural linked beams.
As the number of stories increases, the possibility of failure did not necessarily increase or decrease.
Comparison of the performance level of the structures shows that the seismic sequence phenomenon causes more damage to the structure.

Funding Sources

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

CRediT authorship contribution statement

No author other than ones listed made a contribution to this work.

Declarations of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability

The raw/processed data required to reproduce these findings are available from the corresponding author on reasonable request.

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Evaluation of the Fragility Curve for Steel Structures with Linked Columns Frame System under Sequences of Critical Earthquakes

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Version 1

Abstract

Figures

1. Introduction

2. Linked Columns Frame System (LCF)

3. Fragility Curves

4. Modeling

5. Critical Strong Ground Motions

6. Extraction of Fragility Curves

6.1. Comparison of the probability of failure under seismic scenarios with and without seismic sequence

6.2. Comparison of the performance level under single and multiple accelerometers

7. Conclusion

Declarations

References

Additional Declarations

Status:

Version 1