Behmanesh - M.Sc Student of Amirkabir University of Technology, Tehran, Iran.
Khoshnudian - Assistant Professor of Amirkabir University of Technology, Tehran, Iran.

Effects of soil structure interaction (SSI) in elastic systems have been extensively studied in the past. It was introduced in some codes and provisions like NEHRP (1997, 2000, and 2003), ASCE 2005, and originally in ATC 3-06. However those did not consider yielding behavior of structure. The latter effect has attracted few investigations. Therefore, in this paper we investigate SSI effects in inelastic structures with comprehensive study for wide ranges of non-dimensional parameters to include SSI effects in Nonlinear Static Analysis Procedures (NSP). To consider inelastic behavior of structures the last document considering SSI in inelastic structures, FEMA-440,defines an equivalent period lengthening ratio which alters the elastic period lengthening ratio by using ductility of the system to determine foundation damping from the known elastic formulation. In addition, in the whole procedure structure-soil system is replaced by rigid base SDOF system calculated by pushover analysis. Obviously that procedure cannot lead to exact responses; to evaluate it, we consider a SDOF structure with different periods changing from 0.2 to 3 seconds and different ductilities: 2, 4, and 6. This SDOF structure is located on the homogeneous half space defined by non-dimensional frequency (a0), aspect ratio (S), mass ratio and radius ration of the foundation. The SDOF with idealized bilinear behavior is used as the structural model. The soil is modeled by fundamental lumped parameters based on the concepts of cone models representing soil with a 3DOF system. The proposed 4DOF system is analyzed in time domain using average acceleration method with several ground motions recorded on very soft soil sites. First, this exact response is compared with the response of the inelastic rigid base SDOF system with initial and secondary stiffness determined by pushover analysis to evaluate the sufficiency of the basic concepts of FEMA-440: replacing fixed base structure and using of elastic damping values by equivalent period lengthening. It should be noted that the main procedure of FEMA-440 is checked too and the comparisons reveal an unsuitable estimations for exact responses, but it will not be discussed here because it has another source of error in equivalent linearization. So we use non linear analysis in calculating the response of replaced SDOF structure to achieve our own aims. Next, the accuracy of two FEMA-440 methods for determining maximum displacement demands, Equivalent Linearization and Coefficient Method are evaluated with exact results.

Soil Structure Inertial Interaction, Foundation Damping, Inelastic Structure, Equivalent Linearization, Coefficient Method