## 3 SSI Modeling of Selected Buildings  
The effect of SSI is much more significant in low-rise and stiffer buildings with respect to high-rise long period structures [1]. Buildings considered in this study are not high-rise structures, and therefore it is expected that SSI would alter the response of examined buildings. The existing Turkish earthquake code regulations do not require engineers to consider SSI effects, whether designing new buildings or determining the seismic performances of existing buildings. Instead, the regulations mentioned above recommended the \"Fixed-Base Approach\" for both design and evaluation of buildings. As mentioned before, the primary aim of this paper is to determine SSI effects on the superstructures by considering the \"Substructure Method.\" Details of the substructure method can be found in the literature [8; 18]. \"Inertial Interactions\" and \"Kinematic Interactions\" are two components, and they should be considered in modeling of structures according to substructure method. Inertial interaction refers to the displacements and rotations occurring at the foundation level of the superstructure due to shear and moment related effects. A schematic illustration of deformations for single degree of freedom system (SDOF) caused by the lateral forces is shown in Figure 2. As a result of this interaction, an elongation of the natural vibration period of the structure is expected. Accordingly, this situation may have a dramatic effect on the seismic response of the structure. The ratio vibration periods of fixed base to SSI system for SDOF system can approximately be calculated by Equation (2). \[\frac{T^{\prime}}{T}=\sqrt{1+\frac{k}{k_{z}}+\frac{kl^{2}}{k_{yy}}} \tag{2}\]  
Figure 1: Field investigations and photos of design projects (**(a)**: Building picture, **(b)**: Plan of building, (c): reinforcement details in the RC project). In Equation (2), \(T^{\prime}\) denotes the elongated period, \(k\) is the stiffness of the structure, \(k_{z}\) is the stiffness of the vertical spring, \(h\) is the effective modal height, which can be taken as two-thirds of the structure height, and \(k_{yy}\) is the stiffness of the rotational spring about the \(y\)-axis. On the other hand, kinematic interaction defines the reduction in free-field ground motions at the base due to stiff foundation elements located on or inside the soil medium. The variation between free-field and foundation input motion (\(\text{U}_{\text{FIM}}\)) is expressed by a transfer function representing the ratio of foundation to free-field motion. Two components cause these reductions. The first one is the \"Base Slab Averaging\" which defines transition of spatially variable ground motions from soil medium to foundation due to the stiffness and strength changes caused by the foundation system [1]. The second one is the \"Embedment Effects\" in which foundation level motions are reduced because of ground motion reduction along the depth of the foundation. In the present study, three different soil types were examined, namely stiff, moderate, and soft. It should be noted that soil types are not classified as A, B or D as described in the majority of seismic codes, they are only used to represent different soil characteristics. Mean shear wave velocities (\(V_{s30}\)) corresponding to these soil types in each direction are given in Table 2[19; 20]. Selected \(V_{s30}\) values are determined according to study of ([PERSON] et al., 2013). Shear modulus of these soil conditions were calculated by using Equation (3). In this equation, \(V_{s}\) defines the shear wave velocity of soil, \(G\) denotes the soil shear modulus, and \(\rho_{s}\) denotes the soil mass density. The mechanical properties such as mass densities and Poisson's ratios of soils used in this study are given in Table 3.  
\[V_{s}=\sqrt{\frac{G}{\rho_{s}}} \tag{3}\]