## 4 Effect of SSI on the Capacity and Demand Response of Existing Buildings
### Effect of SSI on the Capacity Curves
The studies of [PERSON] and [PERSON] [24] and [PERSON] [25] investigated the dimensionless parameters that control the vibration period of the systems in SSI, and they showed that the most important parameter is (\(\hbar/V_{s}T\)), which is known as the structure to soil stiffness ratio. For typical reinforced concrete frame buildings on stiff soil, this ratio is usually less than 0.1 [23]. As this ratio increases, the elongation of the natural vibration period also increases. For this reason, elongation of vibration period resulting from inertial interaction should be taken into consideration when assessing the seismic behavior of structures since the vibration period of the building affects the displacement demand. The natural period of the buildings in the inventory are determined for each soil type and story groups from the analyses, and mean period values of fixed-base and elongated periods due to different soil classes are shown in Figure 6. Figure 7 also shows that vibration periods increase with increasing story numbers as expected. This situation is valid for all soil types. Comparison of values in Figures 6 and 7 have shown that the elongation of the vibration period is much more significant in the soft soil case and this behavior is identical both in new (98+) and old (98-) buildings (Figure 7). In addition to vibration periods, elongation of displacement capacities corresponding to yield and collapse limits (as shown in Figure 5) were also investigated for all buildings and soil conditions. Relation between elongation of the vibration periods (\(T^{\prime}/T\)) and change in the yield drift ratios (\(\Delta_{y}\)/\(\Delta_{y}\)) depending on the SSI are illustrated in Figure 8. In this figure, T\({}^{\prime}\) and \(\Delta_{y^{\prime}}\) notations represent the vibration periods and yield displacements of stiff, moderate and soft soil cases, respectively. T and \(\Delta_{y}\) notations, on the other hand, correspond to fixed-base case. Strong correlation between (\(T^{\prime}/T\)) and (\(\Delta_{y}\)/\(\Delta_{y}\)) values explains the effect of SSI on the capacity (yield displacement) and demand (period)-related structural parameters of the buildings. Figure 5: Capacity curves and damage limits of selected old and new buildings. The effect of SSI on the plastic deformation capacity of buildings is also investigated. For this purpose, plastic drift capacities corresponding to stiff, moderate and soft cases (\(\Delta_{p}\)\({}^{\prime}\)) were divided into the ratios of fixed-base case (\(\Delta_{p}\)) and distribution of results is presented in Figure 9. Variation of \(\Delta_{p}\)\({}^{\prime}\)/\(\Delta_{p}\) values indicates that effects of SSI on the plastic deformation capacity of buildings are insignificant and there is no correlation between plastic deformation capacities and period elongations (\(T^{\prime}\)/\(T\)) due to SSI. Effect of this situation can also be examined from the ductility capacities of buildings. Increasing yield displacements and similar plastic drift capacities requires to decrease ductility capacities of buildings. This disadvantage related with the SSI was also reported by [PERSON] and [PERSON] [26]. In order to investigate the extent of this problem, changes in the ductility ratios depending on the (\(T^{\prime}\)/\(T\)) values are presented in Figure 10. Figure 10 clearly shows the considerable decrease in building ductility capacities (\(\mu^{\prime}\)/\(u\)) due to effect of SSI [21,22,26]. Figure 8: Correlation of shifted yield points and elongated vibration periods. Figure 6: Distribution of mean vibration periods according to story numbers and soil types. Figure 7: Distribution of vibration periods for all models according to story numbers and soil types.