## 1 Introduction  
It is obviously seen that an insufficient seismic gap between adjacent structures may provide damages due to possible collisions between them during seismic excitations. The phenomenon, which is often called \"earthquake-induced structural bounding\", concerns mainly buildings and bridges [1; 2; 3; 4; 5; 6]. It occurs when the gap between structures, or structural members, cannot cover their relative movements, and the relative lateral displacement exceeds the seismic gap [7; 8; 9; 10; 11; 12]. Therefore, the estimation of a sufficient gap provides a safety zone between adjacent buildings, preventing structural damage often observed during previous earthquakes [13; 14; 15]. The majority of building codes suggest determining the minimum in-between gap size for providing enough space in order to prevent building collisions. For this purpose, the absolute sum method (\(ABS\)) and the sum of the squares of the modal response (\(SRSS\)) are often used (see [16; 17], for example). The formulae are defined as  
\[S=\delta_{i}+\delta_{j} \tag{1}\]  
\[S=\sqrt{\delta_{i}{}^{2}+\delta_{j}{}^{2}} \tag{2}\]  
where \(S\) is the gap size between buildings, and \(\delta_{i}\) and \(\delta_{j}\) denote the peak lateral displacement of building \(i\) and \(j\), respectively. Other codes consider the structural height to determine the sufficient seismic gap between buildings, e.g., the following formula is used [18]:  
\[S=0.05(h_{i}+h_{j}) \tag{3}\]  
where \(h_{i}\) and \(h_{j}\) are the heights of buildings \(i\) and \(j\), respectively. Some other examples of recommendations can be found in the codes of different countries:  
- Canada: sum of individual peak lateral displacements of structures calculated by elastic analyses;
- Turkey: 3 cm for 6 m of height of the building, and 1 cm should be added for every 3 m of height;
- Australia: more than 1% of the height of the structure;
- Serbia: min. 3 cm and should be increased by 1 cm for every 3 m of the height of the building;
- Peru: 3 + 0.004-(\(h-500\)) cm;
- India: \(R\) times the sum of the calculated peak lateral displacements of the structures;
- Egypt: 2 times the sum of the peak displacements of the structures or 0.004 times the height of the building. On the other hand, various researchers have generally studied different methods to evaluate the seismic gap, which is usually less conservative than the critical gap determined by the codes. Some of them suggest that the structural period and also the damping coefficient must also be considered in order to calculate the seismic gap. Consequently, the critical distance can be reduced in such a case. For example, [PERSON] et al. [19] suggested the equation based on the \(SRSS\) formula, which is described as  
\[S=\sqrt{\delta_{i}{}^{2}+\delta_{j}{}^{2}-2\rho_{op}\delta_{i}\delta_{j}} \tag{4}\]  
where \(\rho_{op}\) is the cross-correlation coefficient determined as [19]:  
\[\rho_{op}=\frac{8\sqrt{\zeta_{i}\zeta_{j}}\Big{(}\zeta_{j}+\zeta_{i}\frac{T_{ j}}{T_{i}}\Big{)}\Big{(}\frac{T_{j}}{T_{i}}\Big{)}^{\frac{3}{2}}}{\left(1- \Big{(}\frac{T_{j}}{T_{i}}\Big{)}^{2}\right)^{2}+4\zeta_{i}\zeta_{j}\Big{(}1 +\Big{(}\frac{T_{j}}{T_{i}}\Big{)}^{2}\Big{)}\Big{(}\frac{T_{j}}{T_{i}}\Big{)} ^{2}}} \tag{5}\]  
where \(T_{i}\) and \(T_{j}\) are the periods of the buildings and \(\zeta_{i}\) and \(\zeta_{j}\) denote the structural damping ratios (see also [20]). Recently, [PERSON] et al. [21] proposed a new formula for the cross-correlation coefficient, \(\rho_{op}\), as a parameter of Equation (4), based on a cyclic process by using both periods of the buildings, and investigated the accuracy of the formula for different situations and various models so as to confirm the formula. In the approach, \(\rho_{op}\) is defined in the more general form as [21]  
\[\rho_{op}=\left|\frac{T_{j}}{T_{i}}-10.5\Big{(}T_{j}-T_{i}\Big{)}\right| \tag{6}\]  
Further studies focused on the aspects of the minimum seismic gap between structures preventing their bounding were also conducted.