Severe damages of adjacent structures due to structural pounding during earthquakes have emphasized the need to use some seismic retrofit strategy to enhance the structural performance. The purpose of this paper is to study the influence of using linear and nonlinear Fluid Viscous Dampers (FVDs) on the seismic collapse capacities of adjacent structures prone to pounding and proposing modification factors to modify the median collapse capacity of structures considering the effects of pounding.

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... e factors can be used to predict the collapse capacity of structures in pounding condition. A seismic retrofit strategy employs FVDs installed in 3-, 6-and 9-story Special Moment Resisting Frames (SMRFs). The SMRFs were assumed to have different values of separation distance according to the seismic code. To model pounding phenomenon, linear viscoelastic contact elements were used in the OpenSees software. Furthermore, to determine the seismic collapse capacities of each structure, the proposed algorithm was applied to remove the collapsed structure during the incremental dynamic analysis. The results of the analyses illustrate that the existence of FVDs can substantially improve the seismic behavior of structures having a significant influence on the collapse capacities of colliding structures. Moreover, considering the adjacent SMRFs in one or two sides of the main structure can significantly affect the median collapse capacity of the main structure itself. Finally, the proposed modification factors can be successfully used to estimate the effects of pounding on the collapse capacities of adjacent structures. j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l oc a t e / y m s s p and second, installing passive energy dissipation devices such as dampers or adding dissipative metal shear panels (see for instance [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] ). The first approach is more convenient for low-rise buildings, whereas the second one can be more effective and affordable for all types of structures. Furthermore, the strengthening option for structures may interfere with the architectural plans, while the installation of seismic dampers can play a positive role. Although previous studies were mainly focused on the strengthening option, the idea of using linear and nonlinear Fluid Viscous Dampers (FVDs) for retrofitting structures is not new. Among different passive energy dissipation systems, FVDs have some performance advantages for their ability to reduce both displacements and accelerations, which can be very important for the structures with sensitive components. Moreover, their velocity-dependent behavior makes them capable of dissipating more energy at small deformations [13, 14] ]. The response of FVDs can be linear or nonlinear, depending on the velocity exponent value, a, which usually varies from 0.15 to 1.0. Bigdeli et al. [15] investigated the optimal arrangement of a limited number of dampers that minimize the inter-story drifts. They showed that increasing the number of dampers would not necessarily improve efficiency. considered the FVDs mounted on the chevron-braced frames with different values of the velocity exponent in order to compare linear and nonlinear FVD devices. They achieved larger reductions in the peak accelerations by using the linear FVDs, whereas increasing the FVDs nonlinearity resulted in smaller damping forces. Moreover, Dall'Asta et al. [17] accomplished a similar trend of results using a probabilistic methodology. Tubaldi et al. [18, 19] proposed probabilistic performance-based procedures to quantify the risk reduction, obtained by using viscous and viscoelastic dampers, and to assess the seismic risk associated with pounding between adjacent structures. Recently, many retrofitting techniques have been introduced to improve the seismic performance of existing structures. Mansoori and Moghadam [20] investigated the possibility of controlling both accelerations and displacements of asymmetric structures. They concluded that the distribution of linear FVDs had a significant effect on structural modal properties. Kim et al. [21] considered a seismic retrofitting scheme to enhance the seismic performance of the special truss moment frame using linear FVDs. They indicated that the seismic performance of the special truss moment frame increased by adding linear FVDs in the case of slight to moderate damage state. Landi et al. [22] proposed a procedure in order to direct the determination of FVDs required for the seismic retrofit of structures without performing several iterations. Furthermore, Landi et al. [23] proposed a simplified probabilistic method for the seismic assessment of nonlinear structures equipped with nonlinear FVDs. Dall'Asta et al. [24] studied the influence of FVD properties on the probabilistic seismic performance and risk assessment. Karavasilis [25] investigated the design capacity assessment of columns in steel moment-resisting frames with linear FVDs. The results of the study indicated that steel moment-resisting frames with linear FVDs were more prone to column plastic hinging, as compared to steel moment-resisting frames. Seismic design and assessment of the steel self-centering moment-resisting frames with FVDs were also investigated by Tzimas et al. [26] . They showed that using FVDs was effective in improving the residual drift performance of steel self-centering moment-resisting frames. as well as Kazemi et al. [28] investigated the effects of using viscous dampers between two adjacent structures. They showed that this approach could be used to substantially improve structural behavior during seismic excitations and to prevent earthquake-induced structural pounding. Pounding between two adjacent structures is a source of considerable amplification of accelerations in structures. In addition, this phenomenon can substantially modify the structural response [1] . Previous studies reveal that structural characteristics, such as mass and fundamental natural period of the adjacent structure, and the fact of having the single-or doublesided pounding may both increase or decrease the structural response [29] [30] [31] . Crozet et al. [32] performed a sensitivity analysis to provide a consistent measure of the relative importance of parameters, such as the coefficient of restitution as well as mass and frequency ratios of the colliding structures, using the Monte Carlo simulations of single-degree-offreedom (SDOF) systems. It is important to utilize more precise structural models to evaluate pounding phenomenon. Therefore, some researchers used multi-degree-of-freedom (MDOF) models, with the mass of each story concentrated at the floor level [31, 33] . Favvata [34] correlated the seismic performance of 3-and 8-story structures with the minimum required separation distance for three intensity levels of seismic hazard. The most important issue in the case of the inter-story pounding conducted in that study was the local performance of exterior columns, which had a critical condition due to impact force. Also, the minimum required separation distance was found to be dependent on the level of the seismic hazard. It is also clear that considering the P-Delta effect can influence the stability of the structure. Moreover, including or excluding the P-Delta effect can result in the increase or decrease in the structural response under ground motions. Therefore, many studies investigated the influence of P-Delta effect on the seismic collapse capacity of structures [35] [36] [37] [38] [39] . Masroor and Mosqueda [40] examined the collapse probability of pounding between a base-isolated steel structure and moat wall. They concluded that the collapse margin ratio could be reduced significantly as the result of pounding. Moreover, Elwardany et al. [41, 42] studied the effect of the infill panels on the seismic response of adjacent structures prone to collisions. The results showed that the existence of infill panels could significantly affect the pounding-involved structural response during earthquakes. Nevertheless, despite considerable research in the field of earthquake-induced structural pounding, the results of studies concerning the effectiveness of different methods of modification of collapse capacities of structures, so as to improve their seismic resistance, are very limited. Therefore, the aim of this paper is to study the influence of using linear and nonlinear FVDs on the seismic collapse capacities of adjacent Special Moment Resisting Frames (SMRFs) prone to pounding. Furthermore, to extend the results of the study, comprehensive sensitivity analyses of the earthquake-induced pounding between three adjacent SMRFs are performed to investigate the effect of considering two adjacent structures on collapse capacities of the main structure. Then, the modification factors, intended to estimate the median collapse capacity, are proposed.