is a major difference in the dynamic properties of colliding structures [1; 29]. Also, the impact force depends on the earthquake characteristics as well as on the relation between the natural frequencies of the colliding buildings [30]. Indeed, in some studies [31; 32], bounding was found to have a greater effect on the response of the flexible structure, as compared to the stiff one, and it was found to have a greater effect on the response of the stiff structure, as compared to the flexible one, in other studies [33]. Furthermore, using the Monte Carlo simulations based on [PERSON]'s method, [PERSON] et al. [34; 35] found that the frequency ratio had the largest influence on the maximum impact force and ductility demands while the frequency and mass ratios had the largest influence on the impact impulse (mass ratio is predominant for low frequency range). The in-between seismic gap has a significant influence on the response of colliding buildings. However, increasing the seismic gap does not necessarily lead to the reduction in the effects of bounding, unless it is large enough to totally eliminate structural collisions [28; 33]. Several formulas have been suggested to evaluate the optimum seismic gap preventing bounding, i.e., the absolute sum (ABS) formula (Equation (1)) [36], square root of the sum of the squares (SRSS) formula (Equation (2)) [29], double-difference (DDC) formula (Equations (3) and (4)) [37], Australian Code formula (Equation (5)) [38], and [PERSON] et al. formula (Equations (3) and (6)) [39]. \[S=U_{1}+U_{2} \tag{1}\]  
\[S=\sqrt{{U_{1}}^{2}+{U_{2}}^{2}} \tag{2}\]  
\[S=\sqrt{{U_{1}}^{2}+{U_{2}}^{2}-2\rho U_{1}U_{2}} \tag{3}\]  
\[\rho=\frac{8\big{(}\sqrt{\xi_{1}\xi_{2}}\big{)}\big{(}\xi_{2}+\xi_{1}\frac{ \mathrm{T}_{1}}{\mathrm{H}}\big{)}\big{(}\frac{\mathrm{T}_{2}}{\mathrm{H}} \big{)}^{1.5}}{\bigg{[}1-\Big{(}\frac{\mathrm{T}_{2}}{\mathrm{H}}\Big{)}^{2} \bigg{]}^{2}+4\xi_{1}\xi_{2}\bigg{[}1+\Big{(}\frac{\mathrm{T}_{2}}{\mathrm{H} }\big{)}^{2}\bigg{]}\Big{(}\frac{\mathrm{T}_{2}}{\mathrm{H}}\Big{)}+4\Big{(} {\xi_{1}}^{2}+{\xi_{2}}^{2}\Big{)}\Big{(}\frac{\mathrm{T}_{2}}{\mathrm{H}} \Big{)}^{2}} \tag{4}\]  
\[S=0.01H_{max} \tag{5}\]  
\[\rho=\bigg{(}\frac{T_{2}}{T_{1}}\bigg{)}-10.5(T_{2}-T_{1}) \tag{6}\]  
where \(S\) is the sufficient seismic separation gap, \(U_{1}\), \(\xi_{1}\), and \(T_{1}\) are the design displacement, damping ratio, and natural period for the first building, and \(U_{2}\), \(\xi_{2}\), and \(T_{2}\) are the design displacement, damping ratio, and natural period for the second building (\(T_{1}<T_{2}\)), respectively; \(\rho\) stands for the correlation factor and \(H_{max}\) is the height of the taller structure. The DDC formula involves the evaluation of the seismic gap based on the maximum displacements of both buildings and the correlation factor. The correlation factor represents the uncertainties in earthquake-induced structural grounding. The accurate estimation of the seismic gap between adjacent buildings based on the DDC formula requires a proper consideration of the uncertainties involved in the bounding phenomena. The correlation factor depends on the natural periods of adjacent buildings, which represent the dynamic properties of the vibrating structures, including the mass and the stiffness. Most of the studies concerning earthquake-induced structural grounding ignored the soil type and the soil-structure interaction (SSI). However, the SSI and the soil type have a significant influence on the response of vibrating buildings due to the fact that the flexibility induced by soil decreases the stiffness of the colliding buildings [40]. Furthermore, in the case of braced frames, taking into account fixed base buildings is considered conservative and it is not necessary to consider SSI. However, in the case of unbraced frames resting on soft soil, the consideration of the SSI is necessary. This refers to several factors, including the fact that the SSI has a significant influence on the interstorey drifts and the lateral deflections [41].