# Seismic Performance Assessment of Ordinary Moment Resisting Frame Equipped with Viscous Dampers under Pulse-Like Earthquakes

Authors: Amir Yousefpour; Hamid Mazidababdi Farahani; Mohsen Ali Shayanfar
Journal: Shock and Vibration
 (2022)

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## Abstract

In conventional structures, the earthquake-resistant design is based on flexibility after yielding of structural members to provide a loss of earthquake input energy, while, using dampers, the input energy loss can be concentrated in predetermined points to prevent the nonlinear behavior of the main members that are also in the gravity bearing path. However, near-fault earthquakes might cause unexpected failure and severe structural damage, especially those with the pulse-like effect. A pulsed movement in the near field records in this system will, however, result in unusual behavior. Technology advances and the creation of vibration control systems have helped control this type of behavior since the earthquake forces are applied indirectly to the structure. For further investigation of this issue, in this study, some traditional two-dimensional frames were modeled for 3, 8, and 12 floors. Seven near-fault pulsed and seven far-fault nonpulsed accelerometers are applied. The structural behavior in four modes is examined: (1) without damper and soil-structure interaction effect, (2) without damper and considering soil-structure interaction effect, (3) with damper and considering soil-structure interaction, and (4) with damper without considering soil-structure interaction. Each model is analyzed in OpenSees software under incremental dynamic analysis. Then, the fragility curve is plotted based on the results. The results indicate that frame (4) reaches the failure level at a higher spectral acceleration, which means that the performance of the viscous damper in reducing drift between floors is one of the main criteria for predicting damages. It also shows the effect of soil-structure interaction on increasing the drift between floors and reaching failure at lower spectral acceleration in all models. Also, by comparing the fragility curves of the models under near-field and far-field records, it is found that the probability of failure under far-field documents (without pulse) is less than that under near-field documents (with a pulse).


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## Body

## 1. Introduction

During ground motions, much energy is applied to the structure. If this energy exceeds the capacity, it will cause damage to the member and eventually the entire network. On the other hand, long-period pulses in near-field earthquakes weaken the performance of systems. Many researchers like MacRae et al. [1], Tothong and Cornell [2], Alavi and Krawinkler [3], Hall et al. [4], Champion and Liel [5], and Özuygur and Noroozinejad [6] have examined the dynamic response of the structures in the near-fault region. The key conclusion regarding the effect of near-fault ground motions on structural response is that near-fault pulse-like records tend to increase the displacement response in structures relative to nonpulse-like movements. These displacement demands could increase structural and nonstructural damage. The pulse-like earthquake generally imposes a high seismic need on the structure, so the damper must resist the earthquake motion. Experiments have demonstrated that dampers can dissipate more than 90% of the total earthquake input energy [7].For this purpose, an energy dissipation system transfers some of the energy applied to the structure to this device, thus minimizing the damage to the structure. In recent decades, energy dissipation systems in structures have been widely used to reduce the forces caused by earthquakes and reduce the lateral displacement of buildings within the limits of the code. One type of these consumables, as passive control systems, is viscous dampers, which have attracted the attention of many researchers like Zahrai and Mohammadi [8] and Silwal et al. [9]. A viscous damper consists of a piston with some orifices inside the cylinder containing highly viscous fluid. Energy dissipation of this damper is through pushing viscous fluid out of the orifices. Luo et al. [10] examined the effects of stochastic traffic loads, corrosion, and fatigue on aging polymer composite bridges. In this study, numerical data were used to estimate the fatigue life of a PC bridge and to maintain it as it ages. According to Zhang et al. [11], the time-harmonic point-, ring-, and disc-loadings of the soil at the inner surface and the rigid foundation caused the soil layer to exhibit three-dimensional intensity Green’s functions. Liu et al. [12] examined 3-dimensional ground-penetrating radar imaging to detect road cavities in urban areas. Morai-dastjerdi et al. [13] investigated the mesh-free dynamic analysis of FGM sandwich plates resting on an elastic base. Accordingly, Ghaffarzadeh et al. [14] analyzed the seismic response of building frames supplemented with variable orifice dampers under near-fault earthquakes. They found out that the influence of the pulse effect on seismic performance of damper systems has not been well understood because of the individual differences in each near-fault earthquake record. Prasad and Mazumder [15] investigated the seismic response of a set of steel buildings with and without viscous dampers installed in the inner bay for energy dissipation. Viscous dampers were reported to reduce the displacements, which decreased the amount of steel needed for the overall stability. Wang et al. [16] used a gas physisorption test (CO2 and N2) to analyze pore heterogeneity and its underlying causes in over-mature Wufeng-Longmaxi shales and their isolated organic matter (OM). Jiang et al. [17] studied tectonothermal histories of the Dongpu Depression from thirteen wells to reconstruct Cenozoic tectonothermal histories. Zhang et al. [18] investigated the progress of friction-based seismic isolation and energy dissipation technologies.The study conducted by Balkanlou et al. [19] demonstrated that the structure with dampers could be designed optimally to justify the cost spent using dampers. Silvestri et al. [20] proposed a five-step procedure for creating viscous dampers to achieve target performance levels. Using viscous dampers to mitigate the pounding of the adjacent buildings was the subject of Milanchian and Hosseini’s research [21]. Nonlinear and linear viscous dampers interconnected the buildings to provide vertical seismic isolation. The final results did not indicate a preferable performance of nonlinear viscous dampers over linear viscous dampers. However, the authors revealed that employing appropriate link parameters proportional to mass and stiffness ratios could lead to satisfactory levels of seismic response reduction in cases of both types of dampers. De Demonico et al. [22] gave energy-based perspectives to interpret the seismic performance in terms of the dissipated energy by the viscous dampers out of the total earthquake-induced energy. Xu et al. [23] constructed a model for the coupling of water, heat, and solute transport in saline loess, taking sodium sulfate crystallization into account. Li et al. [24] investigated the feasibility and drawbacks of applying the PFDD technique to combat FDI assaults on power grid state estimates. Wang et al. [25] suggested a novel technique for bioinspired defect diagnostics based on rough sets (RSBFDM). The suggested solution outperforms existing options in experiments conducted on genuine 110 kV and 750 kV substations.Moreover, in conventional structural analysis and design, the effect of soil beneath the foundation is mainly ignored. However, Ghalami [26] indicates that soil flexibility may have a significant impact on the structural response. Amiri et al. [27] evaluated several three-dimensional steel moment-resisting frames to investigate the effect of soil-structure interaction (SSI) in structural retrofitting. The studied models were considered three-dimensional models of 3-, 7-, and 13-story steel moment-resisting frames. The analysis results showed that considering the soil-structure interaction increases the natural period of the structure. The results also show that the number of buildings’ natural period increases in soil-structure interaction. However, this effect can be ignored in low-rise structures. Šago et al. [28] have identified many of the several obstacles that occurred concurrently with the COVID-19 epidemic and the severe earthquake in Zagreb. The findings indicate that quick developments broadened our area of practice without delay during these exceedingly trying times. Xu et al. [29] used the reactive Euler equations coupled with a comprehensive chemical model to study the interactions between two ODWs created by symmetrical finite wedges in hydrogen-air mixtures. Arbabi and Tahghghi [30] simulated multistory building-foundation systems through a Winkler-based approach using OpenSees finite element framework. Four typical 4-, 8-, 12-, and 16-story steel moment-resisting frame (MRF) buildings on three hypothetically soft, medium, and hard soil sites with shear wave velocities less than 600 m/s subjected to actual ground motion records of varied hazard levels are modeled with and without SSI. It is observed that the performance level of models supported by the flexible foundation, particularly in an intense earthquake event, may alter significantly in comparison to fixed-base structures. Moreover, for MRFs on soft soil, the nonlinear foundation is found to have a significant effect on the force and displacement demands. The authors indicate the necessity of considering the SSI effect to accomplish an economical yet safe structural design.In this study, an ordinary two-dimensional moment-resisting steel frame of 3, 8, and 12 floors was designed under seven near-fault pulsed records and seven far-fault nonpulsed records. Despite the fact that ordinary moment resisting frames are widely used, they do not comply with special detailing requirements for ductile behavior. It is, therefore, essential to evaluate the behavior of these frames in the presence of dampers and SSI effects. The structural behavior was examined in four modes: (1) without damper and soil-structure interaction (SSI) effect; (2) without damper and considering SSI effect; (3) with damper and considering SSI; and (4) with damper without considering SSI. OpenSees software analyzed each model under incremental dynamic analysis (IDA). Then, based on the results of a comprehensive active study, the fragility curve was drawn. Vulnerability levels introduced in HAZUS MH-MR4 [31] were used to investigate different failure modes in the models. Finally, the performance of the building-damper system under near-fault pulsed-like earthquakes and the SSI effect are systematically investigated.


## 2. Details of Steel Frames, Modeling, and Analysis

In this research, three ordinary moments resisting steel frames of 3, 8, and 12 stories are modeled by the LRFD method [32]. Each frame has three openings with 5 meters and a floor height of 3.2 meters. The dead load in the structure’s design was 500 kg/m, and the live load was 200 kg/m [33]. HEB profile was used for column design, and IPE profile was used for beam. Double channel is used for bracing elements (see Figure 1).Figure 1
An analysis of model structures: (a) structural plans; (b) elevations of structures that include dampers [34].
(a)(b)Also, for Incremental Dynamic Analysis (IDA), by assigning values of 0.1 g to 3 g for each acceleration, the analyses were performed for four modes of the frame, frame with damper, frame with soil-structure interaction, and frame with damper and soil-structure interaction.Dampers were considered as diagonal members, as part of a chevron brace, horizontally at the top. The horizontal chevron configuration is applied here, as shown in Figure2. This system was proposed by Lu and Zhou and tested on a shaking table in 2002 [35]. Two viscous dampers are installed in a parallel way and supported by a steel chevron brace. Lead rubber bearings are installed at the top of the brace to keep the brace’s stability and dissipate the energy under minor earthquakes.Figure 2
Configuration of viscous dampers [35].The added damping ratio, reflection coefficient, seismic coefficient, and entire period of the studied buildings are summarized in Table1. It is necessary to explain that the additional damping ratio is an important indicator for evaluating the damping effect of structures with energy-dissipation devices [36].Table 1
Basic information of studied buildings.
No. StoriesFundamental periodAdded damping ratioReflection coefficientSeismic coefficient3-Story0.54540.12.750.1658-Story1.13810.11.8480.110912-Story1.54250.11.4710.0883For modeling in OpenSees software, viscous material was used to design the damper. The Winkler model (BNWF) was modeled on the soil and foundation system linearly and nonlinearly. The infinite underlying soil medium is modeled using the concept of Cone Models with vertical, horizontal, and rocking degrees of freedom, as shown in Figure3 and Table 2. A spring and a damper are introduced for each degree of freedom, which shows the effect of soil on that degree of freedom.Figure 3
Spring-dashpot-mass model with an additional internal degree of freedom for the rotational degree of freedom [37].Table 2
Detailed parameters for the springs used to consider the SSI effect.
Spring stiffnessγ0μ0Vertical4G.r0/1−u0.580.095Horizontal8G.r0/1−u0.850.27Rocking8G.r03/31−u1+8ro5p0.3/31−vm0.24Selecting the appropriate seismic and failure intensity parameters to use IDA analysis is important and influential. Also, the selection of a proper seismic intensity parameter, in addition to causing less scattering and thus greater generality of the response created in the structure under the effect of earthquake records, must include the dynamic characteristics of a document such as frequency content and energy (Vamvatsikos and Cornell, 2002) [38]. To enter the main rotation time of the structure into the field of scaling records and consider the parameters of vibration and damping time, the spectral acceleration of the first model of the structure Sa (T1) has been used as a measure of seismic intensity.In this study, failure modes defined in the HAZUS MH-MR4 guidelines were used (National Institute of Building Sciences, 2004). Failure modes were introduced in the HAZUS instruction for steel buildings with a moment frame system with low and medium. In high stories, four failure modes are considered based on the Interstory DRIFT ratio: slight mode and moderate, extensive failure mode, and complete failure mode. Numerical values for each failure mode are presented in the Table 3 (see Table3).Table 3
Interstory Drift ratio in 4 failure modes according to HAZUS.
TypeSlightModerateExtensiveCompleteS1L0.0060.0120.030.08S1M0.0040.0080.020.0533S1H0.0030.0060.0150.04The DRIFT value obtained for each model under each of the earthquake records is compared with the values presented in the table above to check the arrival or passage of each model in each PGA value to each of these failure states.(i)
Fragility curve: to draw the fragility curve, a fragility function is required. The fragility function is a conditional probability, which expresses the possibility of failure of a structure at a certain level of failure or beyond for a given earthquake intensity. When the seismic requirements and structural capacity follow the normal log probability distribution, the fragility equation according to the HAZUS instruction is given as follows:(1)PC−D≤0.0|IM=φlnSd/ScβDIM2+βC2.Respectively, the standard logarithm deviations are in capacity and need. The mean value of the limit state or seismic capacity and the mean value of the seismic requirement are the Intensity Measure (IM) function and the normal cumulative distribution function. The discount is combined according to the HAZUS instructions and converted to a parameter. Finally, the fragility relationship is written as follows:(2)Pf=φlnSd/Scβsd.The parameterSd is the average value of the seismic requirement obtained from the following equation:(3)lnSd=a.lnIM+b.In this equation, IM is the measure of seismic intensity, considered Sa(T1) in this paper. a and b are regression coefficients obtained through linear regression analysis with the number of damage situations against different Sa. The X-Axis is the spectral acceleration parameter corresponding to the structure’s first mode for each step. Its Y-axis is the logarithm of the criterion of maximum damage intensity and the relative displacement of the floors in each step. Figure 4 shows an example of the relationship between Sa (T1) and the Engineering Demand Parameter (EDP), which is the maximum relative displacement of the floors in a logarithmic environment.Figure 4
Maximum probabilistic seismic requirement for the relative displacement of floors.The values in the HAZUS MH-MR4 instruction are given for different types of constructions and other failure modes, which are shown in the following table (Tables4–7).Table 4
Different types of Steel moment frames in HAZUS MH-MR4 instruction.
Models nameType of structural systemNumber of storiesS1LSteel moment frameLow-rise1–3S1MMid-rise4–7S1HHigh-rise+8Table 5
Values provided forSc and βsd for Steel moment frames in HAZUS MH-MR4 instruction.
TypeScsdβScsdβScsdβScsdβS1L1.30.802.590.766.480.6917.280.72S1M2.160.654.320.6610.800.6728.800.74S1H3.370.646.740.6416.850.6544.930.67Table 6
Near-field earthquakes characteristics.
Record no.Earthquake nameStationOccurrence timeMagnitudeEpicentral distance (km)1Chi-chi, TaiwanTCU12019997.629.962Darfield, New ZealandLincoln School201075.283Imperial Valley-06El Centro Array #419796.534.94Kobe, JapanCEOR Station19956.93.315Morgan HillGilroy Array #619846.193.456Northridge-01Pacoima Dam19946.693.167Parkfield-02, CACSMIP station 36419200464.81Table 7
Far-field earthquakes characteristics.
Record no.Earthquake nameStationOccurrence timeMagnitudeEpicentral distance (km)8Cape MendocinoCSMIP station 8915619927.0116.549Friuli, Italy-01Bolzano19766.533.3210Imperial Valley-06Niland Fire Station19796.5335.211LandersYermo Fire Station19927.2826.9612Northridge-01LA - Saturn st19946.6927.013San FernandoOWNER station 022019716.6122.7714Tabas, IranDayhook19787.3524.07


## 3. Earthquake Excitations

The earthquake record selection should be made so that the analysis results include all the behavioral states of the structure in the range of elastic, plastic, and complete failure [39] although the soil type should be the same for the selected records so that the documents have a good resemblance to each other. The higher the number of forms used, the more valid the analysis results. On the other hand, adding the number of records will increase the analysis time and output volume. Therefore, seven near-field accelerometers and seven far-field accelerometers with the following characteristics have been used in this research [40].The selected earthquakes have the following specifications:(i)
Occur in soil type 3.(ii)
Magnitude between 6 and 9 Richter.(iii)
Epicentral distance for near-field earthquakes is below 10 km, and for far-field earthquakes, it is above 15 km.(iv)
To maintain the seismic parameter of near-fault ground motions, they are not scaled [41].


## 4. Results

In the following, the analysis results of two-dimensional 3-, 8-, and 12-story steel moment frames in the form of IDA curves in 16%, 50%, and 84% percentiles and fragility curves are presented.


### 4.1. Three-Story Frame

The summary of the IDA curve with 16%, 50%, and 84% percentiles and fragility curves in a 3-story frame under seven pairs of near-field and far-field earthquakes is presented.As can be seen, the slope of the linear region in the (a) case, with damper and without considering SSI, is less than that in other cases, which shows a softer behavior. In the case of the damper, it enters the collapse region at a higher acceleration, which indicates better performance than other cases. Considering that the criterion of damage is interstory drift, the results of the above diagram show that the frame with damper reaches the level of failure at a higher spectral acceleration, respectively, compared to the frame without soil-structure interaction, the frame with soil-structure interaction, and the damper and the frame with interaction. This indicates the damper’s performance in reducing interstory drift as one of the criteria for predicting damage and shows the effect of soil-structure interaction on increasing displacement between floors and reaching the level of failure at lower spectral acceleration. The fragility curves of 3-story frames under seven pairs of near-field acceleration are shown in Figures5 and 6.Figure 5
Summary of IDA curves for 16%, 50%, and 84% percentiles in 3-story Ordinary moment resisting frame affected by near-field earthquakes. Examined cases: (a) with damper without considering SSI; (b) without Damper and SSI effect; (c) with damper and considering SSI; (d) without damper but considering SSI effect.
(a)(b)(c)(d)Figure 6
Fragility curves in 3-story ordinary moment resisting frame affected by near-field earthquakes. Examined cases: (a) with damper without considering SSI; (b) without Damper and SSI effect; (c) with damper and considering SSI; (d) without damper but considering SSI effect.
(a)(b)(c)(d)The fragility curve shows that the probability of structural failure in low failure mode occurs in less Sa values, and moderate, extensive, and complete failure modes occur in higher Sa values. In all curves, for low and moderate failure situations, the slope of the curve is first increased and then decreased. For extensive failure mode, the angles change with an almost uniform slope. For complete failure mode, the slope changes are extremely small. According to the coefficient of acceleration scale of near field earthquakes for 3-story structures, fragility occurs at a spectral acceleration of 1.284 g for type three soil. The results also show that soil-structure interaction has a significant effect on increasing the probability of structural failure. Also, dampers in both cases with and without soil-structure interaction reduce the likelihood of failure. In the following, a summary of the IDA curve of a 3-story frame under seven pairs of far-field earthquakes is shown in Figure7.Figure 7
Summary of IDA curves for 16%, 50%, and 84% percentiles in 3-story ordinary moment resisting frame affected by far-field earthquakes. Examined cases: (a) with damper without considering SSI; (b) without Damper and SSI effect; (c) with damper and considering SSI; (d) without damper but considering SSI effect.
(a)(b)(c)(d)The slope of the linear region in case (a), with damper and without SSI, is less than that in other states, which shows a softer behavior. In the cases with the damper, it enters the collapse region at a higher acceleration, which indicates better performance than other cases. Considering that the criterion of damage is interstory drift, the results show that the frame with damper reaches the level of failure at a higher spectral acceleration, respectively, compared to other frames. This indicates the damper’s performance in reducing displacement between floors as one of the criteria for predicting damage and shows the effect of soil-structure interaction on increasing drift between floors and reaching the level of failure at lower spectral acceleration. The fragility curves of 3-story frames under seven pairs of far-field earthquakes are shown in Figure8.Figure 8
Fragility curves in 3-story ordinary moment resisting frame affected by far-field earthquakes. Examined cases: (a) with damper without considering SSI; (b) without Damper and SSI effect; (c) with damper and considering SSI; (d) without damper but considering SSI effect.
(a)(b)(c)(d)The fragility curve shows that the probability of structural failure in low failure mode occurs in less Sa values, and moderate, extensive, and complete failure modes occur in higher Sa values. In all curves, for low and moderate failure situations, the slope of the curve is first increased and then decreased. For extensive failure mode, the curves change with an almost uniform slope. For complete failure mode, the slope changes are extremely small. According to the coefficient of acceleration scale of far-field earthquakes for 3-story structures, fragility occurs at a spectral acceleration of 1.63 g for type three soil. The results also show that soil-structure interaction has a significant effect on increasing the probability of structural failure. Also, dampers in both cases with and without soil-structure interaction reduce failure likelihood.


### 4.2. Eight Story Frame

The summary of the IDA curve with 16%, 50%, and 84% percentiles and fragility curves in an 8-story frame under seven pairs of near-field and far-field earthquakes is presented in Figure9.Figure 9
Summary of IDA curves for 16%, 50%, and 84% percentiles in 8-story ordinary moment resisting frame affected by near-field earthquakes. Examined cases: (a) with damper without considering SSI; (b) without damper and SSI effect; (c) with damper and considering SSI; (d) without damper but considering SSI effect.
(a)(b)(c)(d)In an 8-story OMRF structure, like the previous models, the slope of the linear region in case (a), with damper and without SSI, is less than that in other states, which shows a softer behavior. In the cases with the damper, it enters the collapse region at a higher acceleration, which indicates better performance than other cases. Considering that the criterion of damage is interstory drift, the results show that the frame with a damper reaches the level of failure at a higher spectral acceleration than other frames. This indicates the damper’s performance in reducing displacement between floors as one of the criteria for predicting damage and shows the effect of soil-structure interaction on increasing drift between floors and reaching the level of failure at lower spectral acceleration. The fragility curves of 8-story frames under seven pairs of near-field earthquakes are shown in Figure10.Figure 10
Fragility curves in 8-story ordinary moment resisting frame affected by near-field earthquakes. Examined cases: (a) with damper without considering SSI; (b) without damper and SSI effect; (c) with damper and considering SSI; (d) without damper but considering SSI effect.
(a)(b)(c)(d)The fragility curve shows that the probability of structural failure in low failure mode occurs in less Sa values, and moderate, extensive, and complete failure modes occur in higher Sa values. In all curves, for low and moderate failure situations, the slope of the curve is first increased and then decreased. For extensive failure mode, the curves change with an almost uniform slope. For complete failure mode, the slope changes are extremely small. According to the coefficient of acceleration scale of far-field earthquakes for 3-story structures, fragility occurs at a spectral acceleration of 1.276 g for type three soil. The results also show that soil-structure interaction has a significant effect on increasing the probability of structural failure. Also, dampers in both cases with and without soil-structure interaction reduce failure probability. A summary of the IDA curve of a 3-story frame under seven pairs of far-field earthquakes is shown in Figure11.Figure 11
Summary of IDA curves for 16%, 50%, and 84% percentiles in 8-story ordinary moment resisting frame affected by far-field earthquakes. Examined cases: (a) with damper without considering SSI; (b) without damper and SSI effect; (c) with damper and considering SSI; (d) without damper but considering SSI effect.
(a)(b)(c)(d)In the 8-story OMRF structure affected by far-field earthquakes, like the previous models, the slope of the linear region in the case (a), with damper and without SSI, is less than that in other states, which shows a softer behavior. In the cases with the damper, it enters the collapse region at a higher acceleration, which indicates better performance than other cases. Considering that the criterion of damage is interstory drift, the results show that the frame with damper reaches the level of failure at a higher spectral acceleration, respectively, compared to other frames. This indicates the damper’s performance in reducing displacement between floors as one of the criteria for predicting damage and shows the effect of soil-structure interaction on increasing drift between floors and reaching the level of failure at lower spectral acceleration. The fragility curves of 8-story frames under seven pairs of far-field earthquakes are shown in Figure12.Figure 12
Fragility curves in 8-story ordinary moment resisting frame affected by far-field earthquakes. Examined cases: (a) with damper without considering SSI; (b) without damper and SSI effect; (c) with damper and considering SSI; (d) without damper but considering SSI effect.
(a)(b)(c)(d)The figures mentioned above indicate that the probability of structural failure in low failure mode occurs in less Sa values, and moderate, extensive, and complete failure modes occur in higher Sa values. In all curves, for low and moderate failure situations, the slope of the curve is first increased and then decreased. For extensive failure mode, the curves change with an almost uniform slope. For complete failure mode, the slope changes are extremely small. According to the coefficient of acceleration scale of far-field earthquakes for 3-story structures, fragility occurs at a spectral acceleration of 2.12 g for type three soil. The results also show that soil-structure interaction has a significant effect on increasing the probability of structural failure. Also, dampers in both cases with and without soil-structure interaction reduce the likelihood of failure.


### 4.3. 12-Story Frame

The summary of the IDA curve with 16%, 50%, and 84% fractiles and fragility curves in a 12-story frame under seven pairs of near-field and far-field earthquakes is presented in Figure13.Figure 13
Summary of IDA curves for 16%, 50%, and 84% percentiles in 12-story ordinary moment resisting frame affected by near-field earthquakes. Examined cases: (a) with damper without considering SSI; (b) without damper and SSI effect; (c) with damper and considering SSI; (d) without damper but considering SSI effect.
(a)(b)(c)(d)In the 12-story OMRF structure affected by near-field earthquakes, like the other models, the slope of the linear region in the case (a), with damper and without SSI, is less than that in other states, which shows a softer behavior. In the cases with the damper, it enters the collapse region at a higher acceleration, which indicates better performance than other cases. Considering that the criterion of damage is interstory drift, the results show that the frame with a damper reaches the level of failure at a higher spectral acceleration than other frames. This indicates the damper’s performance in reducing displacement between floors as one of the criteria for predicting damage and shows the effect of soil-structure interaction on increasing drift between floors and reaching the level of failure at lower spectral acceleration. The fragility curves of 12-story frames under seven pairs of near-field acceleration are shown in Figure14.Figure 14
Fragility curves in 12-story ordinary moment resisting frame affected by near-field earthquakes. Examined cases: (a) with damper without considering SSI; (b) without damper and SSI effect; (c) with damper and considering SSI; (d) without damper but considering SSI effect.
(a)(b)(c)(d)The fragility curve shows that the probability of structural failure in low failure mode occurs in less Sa values, and moderate, extensive, and complete failure modes occur in higher Sa values. In all curves, for low and moderate failure situations, the slope of the curve is first high and then decreased. For extensive failure mode, the curves change with an almost uniform slope. For complete failure mode, the slope changes are extremely small. According to the coefficient of acceleration scale of far-field earthquakes for 3-story structures, fragility occurs at a spectral acceleration of 1.344 g for type three soil. The results also show that soil-structure interaction has a significant effect on increasing the probability of structural failure. Also, dampers in both cases with and without soil-structure interaction reduce failure likelihood. In the following, a summary of the IDA curve of a 3-story frame under seven pairs of far-field earthquakes is shown in Figure15.Figure 15
Summary of IDA curves for 16%, 50%, and 84% percentiles in 12-story ordinary moment resisting frame affected by far-field earthquakes. Examined cases: (a) with damper without considering SSI; (b) without damper and SSI effect; (c) with damper and considering SSI; (d) without damper but considering SSI effect.
(a)(b)(c)(d)In the 8-story OMRF structure affected by far-field earthquakes, like the previous models, the slope of the linear region in the case (a), with damper and without SSI, is less than that in other states, which shows a softer behavior. In the cases with the damper, it enters the collapse region at a higher acceleration, which indicates better performance than other cases. Considering that the criterion of damage is interstory drift, the results show that the frame with a damper reaches the level of failure at a higher spectral acceleration than other frames. This indicates the damper’s performance in reducing displacement between floors as one of the criteria for predicting damage and shows the effect of soil-structure interaction on increasing drift between floors and reaching the level of failure at lower spectral acceleration. The fragility curves of 12-story frames under seven pairs of far-field earthquakes are shown in Figure16.Figure 16
Fragility curves in 12-story ordinary moment resisting frame affected by far-field earthquakes. Examined cases: (a) with damper without considering SSI; (b) without damper and SSI effect; (c) with damper and considering SSI; (d) without damper but considering SSI effect.
(a)(b)(c)(d)The fragility curve shows that the probability of structural failure in low failure mode occurs in less Sa values, and moderate, extensive, and complete failure modes occur in higher Sa values. In all curves, for low and moderate failure situations, the slope of the curve is first high and then decreased. For extensive failure mode, the curves change with an almost uniform slope. For complete failure mode, the slope changes are extremely small. According to the coefficient of acceleration scale of far-field earthquakes for 3-story structures, fragility occurs at a spectral acceleration of 2.12 g for type three soil. The results also show that soil-structure interaction has a significant effect on increasing the probability of structural failure. Also, dampers in both cases with and without soil-structure interaction reduce the probability of failure.


## 4.1. Three-Story Frame

The summary of the IDA curve with 16%, 50%, and 84% percentiles and fragility curves in a 3-story frame under seven pairs of near-field and far-field earthquakes is presented.As can be seen, the slope of the linear region in the (a) case, with damper and without considering SSI, is less than that in other cases, which shows a softer behavior. In the case of the damper, it enters the collapse region at a higher acceleration, which indicates better performance than other cases. Considering that the criterion of damage is interstory drift, the results of the above diagram show that the frame with damper reaches the level of failure at a higher spectral acceleration, respectively, compared to the frame without soil-structure interaction, the frame with soil-structure interaction, and the damper and the frame with interaction. This indicates the damper’s performance in reducing interstory drift as one of the criteria for predicting damage and shows the effect of soil-structure interaction on increasing displacement between floors and reaching the level of failure at lower spectral acceleration. The fragility curves of 3-story frames under seven pairs of near-field acceleration are shown in Figures5 and 6.Figure 5
Summary of IDA curves for 16%, 50%, and 84% percentiles in 3-story Ordinary moment resisting frame affected by near-field earthquakes. Examined cases: (a) with damper without considering SSI; (b) without Damper and SSI effect; (c) with damper and considering SSI; (d) without damper but considering SSI effect.
(a)(b)(c)(d)Figure 6
Fragility curves in 3-story ordinary moment resisting frame affected by near-field earthquakes. Examined cases: (a) with damper without considering SSI; (b) without Damper and SSI effect; (c) with damper and considering SSI; (d) without damper but considering SSI effect.
(a)(b)(c)(d)The fragility curve shows that the probability of structural failure in low failure mode occurs in less Sa values, and moderate, extensive, and complete failure modes occur in higher Sa values. In all curves, for low and moderate failure situations, the slope of the curve is first increased and then decreased. For extensive failure mode, the angles change with an almost uniform slope. For complete failure mode, the slope changes are extremely small. According to the coefficient of acceleration scale of near field earthquakes for 3-story structures, fragility occurs at a spectral acceleration of 1.284 g for type three soil. The results also show that soil-structure interaction has a significant effect on increasing the probability of structural failure. Also, dampers in both cases with and without soil-structure interaction reduce the likelihood of failure. In the following, a summary of the IDA curve of a 3-story frame under seven pairs of far-field earthquakes is shown in Figure7.Figure 7
Summary of IDA curves for 16%, 50%, and 84% percentiles in 3-story ordinary moment resisting frame affected by far-field earthquakes. Examined cases: (a) with damper without considering SSI; (b) without Damper and SSI effect; (c) with damper and considering SSI; (d) without damper but considering SSI effect.
(a)(b)(c)(d)The slope of the linear region in case (a), with damper and without SSI, is less than that in other states, which shows a softer behavior. In the cases with the damper, it enters the collapse region at a higher acceleration, which indicates better performance than other cases. Considering that the criterion of damage is interstory drift, the results show that the frame with damper reaches the level of failure at a higher spectral acceleration, respectively, compared to other frames. This indicates the damper’s performance in reducing displacement between floors as one of the criteria for predicting damage and shows the effect of soil-structure interaction on increasing drift between floors and reaching the level of failure at lower spectral acceleration. The fragility curves of 3-story frames under seven pairs of far-field earthquakes are shown in Figure8.Figure 8
Fragility curves in 3-story ordinary moment resisting frame affected by far-field earthquakes. Examined cases: (a) with damper without considering SSI; (b) without Damper and SSI effect; (c) with damper and considering SSI; (d) without damper but considering SSI effect.
(a)(b)(c)(d)The fragility curve shows that the probability of structural failure in low failure mode occurs in less Sa values, and moderate, extensive, and complete failure modes occur in higher Sa values. In all curves, for low and moderate failure situations, the slope of the curve is first increased and then decreased. For extensive failure mode, the curves change with an almost uniform slope. For complete failure mode, the slope changes are extremely small. According to the coefficient of acceleration scale of far-field earthquakes for 3-story structures, fragility occurs at a spectral acceleration of 1.63 g for type three soil. The results also show that soil-structure interaction has a significant effect on increasing the probability of structural failure. Also, dampers in both cases with and without soil-structure interaction reduce failure likelihood.


## 4.2. Eight Story Frame

The summary of the IDA curve with 16%, 50%, and 84% percentiles and fragility curves in an 8-story frame under seven pairs of near-field and far-field earthquakes is presented in Figure9.Figure 9
Summary of IDA curves for 16%, 50%, and 84% percentiles in 8-story ordinary moment resisting frame affected by near-field earthquakes. Examined cases: (a) with damper without considering SSI; (b) without damper and SSI effect; (c) with damper and considering SSI; (d) without damper but considering SSI effect.
(a)(b)(c)(d)In an 8-story OMRF structure, like the previous models, the slope of the linear region in case (a), with damper and without SSI, is less than that in other states, which shows a softer behavior. In the cases with the damper, it enters the collapse region at a higher acceleration, which indicates better performance than other cases. Considering that the criterion of damage is interstory drift, the results show that the frame with a damper reaches the level of failure at a higher spectral acceleration than other frames. This indicates the damper’s performance in reducing displacement between floors as one of the criteria for predicting damage and shows the effect of soil-structure interaction on increasing drift between floors and reaching the level of failure at lower spectral acceleration. The fragility curves of 8-story frames under seven pairs of near-field earthquakes are shown in Figure10.Figure 10
Fragility curves in 8-story ordinary moment resisting frame affected by near-field earthquakes. Examined cases: (a) with damper without considering SSI; (b) without damper and SSI effect; (c) with damper and considering SSI; (d) without damper but considering SSI effect.
(a)(b)(c)(d)The fragility curve shows that the probability of structural failure in low failure mode occurs in less Sa values, and moderate, extensive, and complete failure modes occur in higher Sa values. In all curves, for low and moderate failure situations, the slope of the curve is first increased and then decreased. For extensive failure mode, the curves change with an almost uniform slope. For complete failure mode, the slope changes are extremely small. According to the coefficient of acceleration scale of far-field earthquakes for 3-story structures, fragility occurs at a spectral acceleration of 1.276 g for type three soil. The results also show that soil-structure interaction has a significant effect on increasing the probability of structural failure. Also, dampers in both cases with and without soil-structure interaction reduce failure probability. A summary of the IDA curve of a 3-story frame under seven pairs of far-field earthquakes is shown in Figure11.Figure 11
Summary of IDA curves for 16%, 50%, and 84% percentiles in 8-story ordinary moment resisting frame affected by far-field earthquakes. Examined cases: (a) with damper without considering SSI; (b) without damper and SSI effect; (c) with damper and considering SSI; (d) without damper but considering SSI effect.
(a)(b)(c)(d)In the 8-story OMRF structure affected by far-field earthquakes, like the previous models, the slope of the linear region in the case (a), with damper and without SSI, is less than that in other states, which shows a softer behavior. In the cases with the damper, it enters the collapse region at a higher acceleration, which indicates better performance than other cases. Considering that the criterion of damage is interstory drift, the results show that the frame with damper reaches the level of failure at a higher spectral acceleration, respectively, compared to other frames. This indicates the damper’s performance in reducing displacement between floors as one of the criteria for predicting damage and shows the effect of soil-structure interaction on increasing drift between floors and reaching the level of failure at lower spectral acceleration. The fragility curves of 8-story frames under seven pairs of far-field earthquakes are shown in Figure12.Figure 12
Fragility curves in 8-story ordinary moment resisting frame affected by far-field earthquakes. Examined cases: (a) with damper without considering SSI; (b) without damper and SSI effect; (c) with damper and considering SSI; (d) without damper but considering SSI effect.
(a)(b)(c)(d)The figures mentioned above indicate that the probability of structural failure in low failure mode occurs in less Sa values, and moderate, extensive, and complete failure modes occur in higher Sa values. In all curves, for low and moderate failure situations, the slope of the curve is first increased and then decreased. For extensive failure mode, the curves change with an almost uniform slope. For complete failure mode, the slope changes are extremely small. According to the coefficient of acceleration scale of far-field earthquakes for 3-story structures, fragility occurs at a spectral acceleration of 2.12 g for type three soil. The results also show that soil-structure interaction has a significant effect on increasing the probability of structural failure. Also, dampers in both cases with and without soil-structure interaction reduce the likelihood of failure.


## 4.3. 12-Story Frame

The summary of the IDA curve with 16%, 50%, and 84% fractiles and fragility curves in a 12-story frame under seven pairs of near-field and far-field earthquakes is presented in Figure13.Figure 13
Summary of IDA curves for 16%, 50%, and 84% percentiles in 12-story ordinary moment resisting frame affected by near-field earthquakes. Examined cases: (a) with damper without considering SSI; (b) without damper and SSI effect; (c) with damper and considering SSI; (d) without damper but considering SSI effect.
(a)(b)(c)(d)In the 12-story OMRF structure affected by near-field earthquakes, like the other models, the slope of the linear region in the case (a), with damper and without SSI, is less than that in other states, which shows a softer behavior. In the cases with the damper, it enters the collapse region at a higher acceleration, which indicates better performance than other cases. Considering that the criterion of damage is interstory drift, the results show that the frame with a damper reaches the level of failure at a higher spectral acceleration than other frames. This indicates the damper’s performance in reducing displacement between floors as one of the criteria for predicting damage and shows the effect of soil-structure interaction on increasing drift between floors and reaching the level of failure at lower spectral acceleration. The fragility curves of 12-story frames under seven pairs of near-field acceleration are shown in Figure14.Figure 14
Fragility curves in 12-story ordinary moment resisting frame affected by near-field earthquakes. Examined cases: (a) with damper without considering SSI; (b) without damper and SSI effect; (c) with damper and considering SSI; (d) without damper but considering SSI effect.
(a)(b)(c)(d)The fragility curve shows that the probability of structural failure in low failure mode occurs in less Sa values, and moderate, extensive, and complete failure modes occur in higher Sa values. In all curves, for low and moderate failure situations, the slope of the curve is first high and then decreased. For extensive failure mode, the curves change with an almost uniform slope. For complete failure mode, the slope changes are extremely small. According to the coefficient of acceleration scale of far-field earthquakes for 3-story structures, fragility occurs at a spectral acceleration of 1.344 g for type three soil. The results also show that soil-structure interaction has a significant effect on increasing the probability of structural failure. Also, dampers in both cases with and without soil-structure interaction reduce failure likelihood. In the following, a summary of the IDA curve of a 3-story frame under seven pairs of far-field earthquakes is shown in Figure15.Figure 15
Summary of IDA curves for 16%, 50%, and 84% percentiles in 12-story ordinary moment resisting frame affected by far-field earthquakes. Examined cases: (a) with damper without considering SSI; (b) without damper and SSI effect; (c) with damper and considering SSI; (d) without damper but considering SSI effect.
(a)(b)(c)(d)In the 8-story OMRF structure affected by far-field earthquakes, like the previous models, the slope of the linear region in the case (a), with damper and without SSI, is less than that in other states, which shows a softer behavior. In the cases with the damper, it enters the collapse region at a higher acceleration, which indicates better performance than other cases. Considering that the criterion of damage is interstory drift, the results show that the frame with a damper reaches the level of failure at a higher spectral acceleration than other frames. This indicates the damper’s performance in reducing displacement between floors as one of the criteria for predicting damage and shows the effect of soil-structure interaction on increasing drift between floors and reaching the level of failure at lower spectral acceleration. The fragility curves of 12-story frames under seven pairs of far-field earthquakes are shown in Figure16.Figure 16
Fragility curves in 12-story ordinary moment resisting frame affected by far-field earthquakes. Examined cases: (a) with damper without considering SSI; (b) without damper and SSI effect; (c) with damper and considering SSI; (d) without damper but considering SSI effect.
(a)(b)(c)(d)The fragility curve shows that the probability of structural failure in low failure mode occurs in less Sa values, and moderate, extensive, and complete failure modes occur in higher Sa values. In all curves, for low and moderate failure situations, the slope of the curve is first high and then decreased. For extensive failure mode, the curves change with an almost uniform slope. For complete failure mode, the slope changes are extremely small. According to the coefficient of acceleration scale of far-field earthquakes for 3-story structures, fragility occurs at a spectral acceleration of 2.12 g for type three soil. The results also show that soil-structure interaction has a significant effect on increasing the probability of structural failure. Also, dampers in both cases with and without soil-structure interaction reduce the probability of failure.


## 5. Conclusion

In this study, three two-dimensional models of 3-, 8-, and 12-story ordinary steel moment frames were studied to evaluate the fragility of steel frames equipped with viscous dampers and consider SSI under near and far-field earthquakes. Each model was analyzed in OpenSees software. To draw the IDE curve, Sa (T1, 5%) was considered a parameter of seismic intensity, and interstory drift as a measure of damage intensity was selected. Then, the HAZUS instruction was used to draw the fragility curve based on the interstory drift ratio in 4 modes of slight, moderate, extensive, and complete failure. Therefore, the seismic response of the abovementioned structures is summarized as follows:(1)
The frame equipped with dampers, compared to other models, reaches the level of failure at a higher spectral acceleration, which indicates the damping function in reducing interstory drift.(2)
The effect of soil-structure interaction on increasing the displacement of stories and reaching the level of failure at spectral acceleration was less evident in all models.(3)
As the number of floors increases, the level of failure occurs at lower spectral acceleration.(4)
The level of failure occurs in the lower spectral acceleration in far-field earthquakes than in near-field earthquakes.(5)
In all models, low failure probability occurs in less Sa values (T1, 5%), and moderate, extensive, and complete failure modes occur in higher Sa values (T1, 5%), respectively.The results support that as the number of floors of the studied structures increases, the probability of failure also increases. By comparing the fragility curves of the studied models under near-field and far-field accelerometers, it is clear that the probability of failure under far-field accelerometers is less than near-field [42].



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*Source: 2924836-2022-03-31.xml*