Keywords: seismic analysis, multistory frames, soil-structure interaction.

It is common practice to ignore the effects of soil-structure interaction on the seismic analysis of usual multistory frames under the assumption that the motion of relatively flexible and lightweight structures causes negligible deformation to the supporting soil. As a result, the seismic analysis of such structures is usually performed using fixed boundary conditions at their base. These analyses yield, in general, conservative estimates for the design variables of interest, e.g. member forces and stresses. However, the inaccuracies associated with these analyses become more evident for heavier structures and softer soil media [1].

In this work, the effect of the soil-foundation (SFI) and foundation-soil-foundation interaction (FSFI) on the dynamic response of multistory buildings is studied. For this purpose a typical 2-D six-story, three bay, concrete frame structure is considered. It has been designed for static loads and complies to usual code provisions. The supporting soil medium is idealized as a homogeneous, elastic half space, with varying mechanical properties that correspond to a wide range of soil conditions, from the "very soft" to the "very hard". The structural model is based on a standard FEM discretization. The simulation of the soil is based on approximate models that utilize discrete spring and dashpot elements. The interaction between the soil and the structure (SFI) is achieved by considering vertical, horizontal and rocking spring and dashpot elements, under the assumption that each foundation acts independently, i.e. it is located far away from adjacent foundations. Furthermore, in this work the through-the-soil interaction (FSFI) of neighboring foundations is also considered via discrete spring and dashpot elements connecting each foundation to rest of the foundations of the structure. For the SFI the combination of frequency independent spring, dashpot and virtual mass constants adopted by Mulliken and Karabalis [2] are used, which have been partly developed by Gazetas [3] and Wolf [1]. For the FSFI the vertical, horizontal, and rocking spring and dashpot elements developed by Mulliken and Karabalis [2] are employed. These, also frequency independent, discrete elements are functions of the ratio of the distance (d) between the through-the-soil interacting foundations to the half side (a) of the rectangular foundations, and they have been presented in explicit form. The above spring, dashpot, and virtual mass elements, providing for FSI and FSFI, are attached to the structural FEM model at the soil-foundation interface level. All the subsequent analyses are performed using the commercial program MSC/NASTRAN v 68.2.

A detailed eigenvalue analysis of the chosen frame is performed using the entire range of boundary conditions. Thus, for six different types of realistic soil profiles the fixed base, FSI and FSFI support conditions are used. For each case, the variation of the first six eigenvalues is plotted versus the dimensionless ratio . The basic conclusion drawn from these results is that there are substantial differences in the computed eigenvalues between the analyses using simple fixed base conditions and those using FSI or FSFI support conditions. For the "softer" soils these differences can be easily observed in the range . For the first three eigenvalues are identical for all support conditions and for all soil profiles used in this work. In general, it is the higher eigenvalues where the stronger differences between the various support conditions are evident. Also, as it was expected, "softer" soils yield reduced eigenvalues when FSI or FSFI conditions are introduced. In all cases, the values of the FSFI results lay between those of the fixed base and the SFI analyses, as the FSFI represents an intermediate constraint between the other two cases.

A study on the transient behavior of the chosen frame for the above three types of support conditions and a selected range of "softer" soils is also presented. For this purpose an artificially produced acceleration time history is used which is compatible with the seismic spectrum specified in Eurocode 8. In all cases, the same acceleration time history is applied in the horizontal direction to all the nodal points at the base of the structure and the horizontal displacement of a nodal point at the top of the structure is plotted versus time. It becomes apparent, from these last results, that not only the structure vibrates at entirely different frequencies depending on the type of support conditions assumed but, in addition, when soil-structure interaction is considered, the calculated displacements are four to five times larger than those computed using the traditional fixed base assumption.

The results produced in this work provide strong evidence that for certain soil conditions, soil-structure interaction in the form of FSI or FSFI should be taken into consideration in most structural designs of everyday practice. This is in contrast to the standard notion that such considerations apply only to rare and unusual type of structures, such as nuclear reactors, heavy dams, etc.

1

Wolf, J.P. "Soil-Structure Interaction", Prentice Hall, Englewood Cliffs, New Jersey, 1985.

2

Mulliken, J.S. and Karabalis, D.L., "Discrete models for through-soil coupling of foundations and structures", Earthquake Engineering and Structural Dynamics, 27, 687-710, 1998. doi:10.1002/(SICI)1096-9845(199807)27:7<687::AID-EQE752>3.0.CO;2-O

3

Gazetas, G., "Analysis of machine foundation vibrations: State-of-the-art review", Soil Dynamics and Earthquake Engineering, 2, 2-42, 1983. doi:10.1016/0261-7277(83)90025-6

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