## 4 Effect of SSI on the Capacity and Demand Response of Existing Buildings
### Effect of SSI on the Displacement Response of Existing Buildings  
To investigate the effect of SSI on the displacement response of buildings, nonlinear dynamic analyses were performed. For this purpose, 20 real strong ground motions were selected [27]. Some attributes of selected records are given in Table 4. Response spectrum of selected records and their mean is drawn in Figure 11. The maximum spectral acceleration of the mean spectrum is around 1.14 g and elastic spectral accelerations are higher than 1 g between the periods of 0.2 s to 0.6 s.  
Effect of SSI on the displacement response of existing buildings was investigated by two different earthquake demand parameters (EDPs): roof and inter-story drift ratios. Roof displacement is one of the most widely used parameters and it has wide applicability, especially for determining the seismic performance of structures. However, seismic performance of buildings is determined according to different seismic intensity or earthquake levels. Different earthquake levels can be recommended for different performance levels according to building importance in the modern seismic codes. Earthquake levels, on the other hand, are described according to different exceeding probability levels. Considering this situation, roof drift demand ratios of existing buildings are investigated in a probabilistic manner. For this purpose, cumulative exceedance probability of drift ratios is calculated from the displacement demands of buildings which are subjected to 20 real earthquake records. In order to generalize obtained results, cumulative exceeding probabilities are provided for different building groups (new and old), story numbers and soil type which are modeled according to the substructure method. Figure 10: Decrease in structure ductility capacities with SSI effects. Figure 9: Correlation of shifted plastic limits and elongated vibration periods. In order to determine cumulative probability of exceedance curves, maximum displacement demands of each building at roof level were determined and these demands were collected in the data pool. In each data pool 100 drift ratios (5 buildings \(\times\) 20 acceleration records) corresponding to each story group of new and old buildings were obtained and then they were ranked from minimum to maximum. Minimum and maximum values in the data pool represent the drift ratios corresponding probability of exceeding 100% and 0%, respectively. In order to compare the drift demands between the fixed-base and SSI approaches, different exceedance probability levels were also considered. For this purpose, drift ratios corresponding to probability of exceeding 50% and 10% levels were used. Cumulative exceedance probabilities of three- to six-story buildings are plotted in Figures 12-15. It can be seen from the figures that roof drift probabilities of the fixed-base approach and stiff soil conditions are very similar, and they are mostly overlapped. Drift demands of moderate soil condition are closer to fixed-base and stiff soil cases with respect to soft soil condition. These figures clearly show that roof