# nvestigating considered as speed-dependent damper (Fig. 1).

nvestigating the Performance of Viscoelastic Dampers (VED) Under Near-field Earthquakes with Directivity FeatureAbstractOne of the most important factors that make structures vulnerable to earthquakes is the short distance between structures and epicenter. Near-field earthquakes have special properties, such as increasing acceleration applied to the structure, which distinguishes them from far-field earthquakes. Therefore, the absorption of input energy for structures located near the faults is very important. Hence, by rotating the acceleration-time graphs of earthquake and comparing the resulting response acceleration spectra graphs, the angle which applies the greatest force to the structure on the earthquake directivity side obtained, and then the performance of a steel structure with viscoelastic dampers (VED) under near-field earthquakes with directivity feature in two states of with directivity and without directivity is investigated. After analyzing the structure using nonlinear time history analysis, it was observed that the directivity phenomenon leads to significant increase in the force applied to the structure, but the viscoelastic dampers showed an acceptable performance in both with directivity and without directivity states.

IntroductionThe amount of energy which enters the structure depends on several factors such as the duration of the earthquake, the location of the structure, the stiffness, mass, and frequency content. Absorption of energy by lateral force resisting systems determines the performance of a structure during an earthquake. The use of dampers is one of the methods to reduce the damage to structural members due to the entry of these members into the nonlinear area. Generally, the dampers are divided into two groups, Speed-dependent and displacement-dependent dampers. In this classification, the viscoelastic damper is considered as speed-dependent damper (Fig. 1). Some of the most important advantages of this type of dampers include easy installation, cost reduction and also the proper performance during an earthquake over a wide range of ambient temperature.Figure 1- Schematic diagram of a Viscoelastic damperCox and Ashford (2002) defined near-field earthquakes as earthquakes recorded by seismograph within a distance of less than 10 km from the fault and near-field refers to the regions where their distance to fault is less than 10 km.

, but Wang et al. (2002) have determined this value to 20 km for the near-field regions. Bertero et al. (1978), during a study stated that near-field earthquakes could increase structural responses. A study was also conducted by Chopra and Chintanapakdee (2001) on a Single Degree-of-Freedom (SDOF) system, which indicated that for a certain amount of ductility, the needed resistance under the far-field earthquake records is less than the near-field earthquake records.

Somerville et al. (1997) also reported that in the near-field earthquakes, the energy caused by the earthquake can be determined in form of a large pulse at the beginning of the earthquake record. According to a study provided by Ghobarah (2004), the acceleration-time graphs recorded in near-field regions are richer in frequency content than far-field regions, i.e. it includes a greater range of frequencies, and despite far-field regions the higher frequencies did not disappear because of the adjacency to the fault. When an earthquake occurs with directivity feature, it means that the acceleration exceeds the expected value in the near-field region. This study was carried out aimed to investigate the performance of the viscoelastic damper system under near-field earthquakes with directivity feature.Determining Viscoelastic Damper SpecificationsThe viscoelastic material of 3M ISD 110 was used to determine viscoelastic dampers specifications.

This material has a loss factor of ?v = 1.2, storage modulus of G’= 0.513 Mpa and loss modulus equal to G” = 0.6156 Mpa. Based on a study by Chang et al. (1998) the effective loss factor of the viscoelastic dampers assembly is given by Equation (1) where K_b/K_v is the ratio of bracing to damper stiffness that is assumed to be 40.

The damping ratio of i-th mode of the structure is also obtained by the research carried out by Chang et al. (1992, 1995), equation (2), where ?_i and ?_si are the natural frequencies of the structure without dampers and the natural frequency of the structure with the dampers in terms of (rad / s). In this equation, the damping ratio was assumed to be 15%, which lead to ?_si to be 1.167 times ?_i.

Chang et al. (1998) provided the equations (3), (4) and (5), where the viscoelastic damper stiffness is Kv, the maximum nonlinear displacement of each damper is ?max, the Kv-b is the stiffness of the damper system with braces and hs is the height of each floor which is equal to 3 meters. Assuming the use of 2 layers of viscoelastic material and maximum allowable strain of viscoelastic material equal to 150%, its area is calculated by equation (5), where h is the thickness of viscoelastic material equal to 3cm, N is the number of dampers in each floor and n is the number of viscoelastic material layers.

Investigating Viscoelastic Damper Behavior under Near-field EarthquakesThis study was carried out on a two-dimensional eight-story steel residential building, in which viscoelastic dampers are used. This structure contains three spans, each of them is 5 meters in length and the height of floors is 3 meters (Fig. 2). The gravity load of this structure consists of dead and live loads, is applied to the structure before lateral loading.

The earthquakes studied in this study are presented in Table 1. These earthquakes have a pulse-like behavior.Figure 2- Schematic of the studied structureTable 1- Specifications of the earthquakes investigatedInvestigating the Amount of Energy Absorbed by Viscoelastic DampersAccording to Fig.

3, after analyzing the considered structure using nonlinear time history analysis, viscoelastic dampers absorbed a significant amount of input energy entered into the structure, which indicates that the damper has proper performance and high efficiency during an earthquake. After reviewing the Shear Force-Displacement diagrams for viscoelastic dampers, it was observed that this type of dampers tended to the horizontal and vertical axes due to the parallel behavior of the Dashpot and the spring (Fig. 4).Figure 3- Input Energy diagramsFigure 4- Shear Force-Displacement Diagrams for the viscoelastic damper on the last floor Investigating the performance of Viscoelastic dampers under an earthquake with directivity featureEarthquake directivity phenomenon is a phenomenon in which acceleration is applied more than usual in a particular direction during a certain period of time. It should be noted that if the period of the structure and the pulse period become closer to each other, a force higher than expected value will apply to structure. The properties of the near-field earthquakes caused to form forces that were not previously seen in the design regulations.

Therefore, after studying the impact of near-field earthquakes on structures, correction coefficients were added to the codes for this purpose Like Standard No. 2800 (2015). in order to investigate this issue, we studied the Parkfield 2004 earthquake.

As shown in Figure 5, Ali Vatanshenas (2017) stated that two CA Fault Zone1 and CA Fault Zone7 stations have recorded time history of accelerations related to Parkfield 2004 earthquake. Figure 5- Location of the earthquake center and two CA Fault Zone7 and CA Fault Zone 1 stations We plotted the acceleration-time (Fig. 6) the velocity-time (Fig. 7) and response acceleration-period graphs (Fig. 8) for two stations, and compared them with each other.

As shown in Figure 6, more acceleration is recorded at CA Fault Zone 1 Station. Figure 7 also shows the pulse-like behavior in the velocity time history related to CA-Fault Zone 1. Also, in Fig. 8, a significant difference was observed between the acceleration response spectra of these two stations in a certain period of time, in such a way that the acceleration applied to existing structures on the side of the CA Fault Zone 1 station was several times that of the other side.

According to the reasons given in Figs 6,7,8 we found that the Parkfield 2004 earthquake along the CA Fault Zone 1 station has a directivity feature.Figure 6- Acceleration time history of the two Parkfield 2004 earthquake stationsFigure 7- Velocity time history of the two Parkfield 2004 earthquake stationsFigure 8-Response acceleration spectra-period related to two Parkfield 2004 Earthquake Stations To find the most critical angle of force applied to the structure due to the earthquake directivity, we plotted the response acceleration-period diagrams of the CA Fault Zone 1 station, for each 10-degree rotation of the horizontal acceleration components perpendicular to each other which are recorded by this station (Fig. 9). In fact, by doing this, instead of turning the structure, we rotated the acceleration components. Considering that the period of the first mode of the structure under study is 1.31 seconds, we found the maximum response acceleration corresponding to this period according to Fig. 9, which was 30 °. In order to compare the performance of viscoelastic damper under the earthquake with directivity feature in two stations located in the side of directivity of the earthquake and without directivity, the structure under study was subjected to the acceleration time history of 30 degree rotated (Fig.

10) and we compared the base shear (Figure 11), input energy and dissipated energy by viscoelastic dampers (Fig. 12) for these two stations. After reviewing and comparing the base shear-time diagram for two Parkfield 2004 earthquake stations, it was observed that if the structure is built in a direction where directivity occurs, a large and significant force must be tolerated relative to the direction that directivity does not occur. According to Fig. 12, the directivity phenomenon leads to generate more input energy on the structure.

But, it was observed that the viscoelastic damper in both cases of directivity and lack of directivity showed a proper performance in absorption and dissipation of the input energy.Figure 9-Response acceleration-period diagrams after rotationFigure 10- Acceleration time history of two stations after 30 degrees of rotationFig. 11- Comparison of the basic shear of the structure after rotation of acceleration time historyFigure 12- Comparison of the values of input and dissipated energy by viscoelastic dampersConclusionAfter examining the behavior of viscoelastic damper under near-field earthquakes with directivity feature, it was observed that the directivity phenomenon leads to create more acceleration, base shear, and input energy to the structure. It was observed that viscoelastic dampers in both cases of with directivity and without directivity absorbed the significant amounts of input energy, therefore, are considered as an appropriate option to control the vibrations of the structure under the near-field earthquakes.References