## 2 Numerical Study  
The numerical study was focused on the dynamic response of two three-story models of concrete adjacent buildings in various configurations under seismic excitation. Each building model, with lumped mass in each story, possessed the following properties: story mass of 26,500 kg, story stiffness of 350 MN/m, and building vibration period equal to 1.22 s. Damping coefficient equal to 6.82 \(\times\) 10\({}^{4}\) kg/s and damping ratio of 5% were assumed in the numerical study. Three different configurations of neighboring buildings were analyzed. In the first one, two three-story models of non-isolated buildings with the same properties were considered, while in the second arrangement, two isolated structures were taken into account (see Figure 1a,b). In the third situation, isolated and non-isolated buildings were analyzed (see Figure 1c). The initial stiffness and post yield stiffness of the isolation system was taken to be equal to 40 MN/m and 5 MN/m, which confirmed the bilinear characteristics of the isolation system. In this model, the structural vibration period of the base-isolated building was calculated to be 1.57 s.  
Linear elastic structural behavior was considered in the analysis in the case of fixed-base building. On the other hand, the base-isolated building was modeled as a nonlinear structure by defining the initial stiffness and post yield stiffness of the isolation system. The geometric and material parameters of the presented models were selected in such a way that they describe the parameters of the real building. Parameters such as building natural vibration period and damping coefficient, which depend significantly on the mass and stiffness of the stories, were confirmed numerically, allowing us to verify the accuracy of the models created (compare [37]). Other assumptions were obtained based on previously conducted studies (see [35; 36; 38]).  
The CRVK (Coefficient of Restitution, Velocity and Stiffness) program was used to perform dynamic analyses and solve impact problems (see [39] for details). The CRVK program is a computer program based on MATLAB software that was written by [PERSON] et al. at the FEUP in order to solve different mathematical relations focusing on dynamic modeling during seismic excitations. Parameters such as number of stories, lumped masses, story stiffness, damping, building vibration period, height of building and also characteristics of earthquake records are generally defined as input values. CRVK is able to collect all of these data, analyze them, and also test them so as to obtain optimal outputs. It is mainly focused on calculating the lateral displacements, velocities, and accelerations of bounding-involved responses of buildings, energy absorption and impact force. CRVK can also suggest the best outputs based on the requested data as optimum responses in different fields such as the critical distance between adjacent buildings, damping ratio, and also the number of collisions recorded during earthquakes.  
Figure 1: Arrangement scheme of two three-story models investigated in the numerical study (where m is a story mass): (**a**) two non-isolated; (**b**) two isolated; (**c**) one non-isolated and one isolated.  
Several different earthquake records (difference in frequency contents and peak ground acceleration values) were used in the study to investigate the dynamic response of two three-story adjacent buildings. In the first part of the paper, the most representative results are presented, which were those obtained for the El Centro earthquake, characterized by a peak ground acceleration of 307 cm/s\({}^{2}\).