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systems.” Earthquake Eng. Struct. Dyn., 32, 121–138.
Wolf, J. P. 1985. Soil-structure interaction, Prentice-Hall, Englewood
Cliffs, N.J.
Wolf, J. P. 1988. Soil-structure-interaction analysis in time domain,
Prentice-Hall, Englewood Cliffs, N.J.
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Seismic History Analysis of Asymmetric Buildings
with Soil–Structure Interaction
Jui-Liang Lin1; Keh-Chyuan Tsai2; and Eduardo Miranda3
Abstract: An efficient approximate method that uses the multi-degrees-of-freedom MDOF modal equations of motion for the seismic response history analysis of asymmetric elastic buildings with soil–structure interaction SSI is presented in this paper. The systems considered are two-way asymmetric shear buildings resting on the surface of an elastic half-space, which are excited by two-directional seismic ground motions. The SSI forces were simulated using frequency-independent soil springs and dashpots. First, the MDOF modal equations of motion for the SSI systems were derived. The modal response histories were obtained by solving the MDOF modal equations of motion using the step-by-step integration method. Subsequently, the seismic response histories of the whole SSI system were deter-mined from the arithmetic summation of the modal response histories. The MDOF modal equations of motion retain the property of nonproportional damping of the original SSI system. The proposed method has the advantages of the conventional modal response history analysis, which requires only the first few vibration modes to obtain accurate analytical results. Finally, the efficiency of the proposed method was validated using numerical examples of a two-way asymmetric four-story building with large and small SSI effects.
DOI: 10.1061/ASCE0733-94452009135:2101
CE Database subject headings: Modal analysis; Soil-structure interaction; Asymmetry; Seismic analysis; Approximation methods.
Introduction
The seismic responses of linear symmetric buildings with soil–structure interaction SSI have been well investigated in the past decades Veletsos and Meek 1974; Wolf 1985, 1988; Gupta and Trifunac 1991. The complexity of the SSI effect arises from two aspects: the frequency-dependent interaction forces, and the non-proportional damping of the soil–structure system. In order to deal with the frequency-dependent interaction forces, the SSI problem was processed in the frequency domain using either Fou-rier transformation or Laplace transformation Bielak 1971; Cas-telloni 1970; Chopra and Gutierrez 1974; Meek and Veletsos 1972; Gupta and Trifunac 1991. However, frequency domain analysis is only capable of dealing with linear responses and is not popular among practicing structural engineers Wolf 1988. To facilitate the analysis of the stated problem in the time domain, the soil springs and dashpots were approximated by frequency-independent expressions Parmelee 1967; Richart et al. 1970; Bielak 1976. Although such approximations may perform satis-factorily for the analysis of typical multistory buildings, they may not be adequate for other types of structures, such as concrete
gravity dams Vaish and Chopra 1973. To deal with the nonpro-portional damping of SSI systems, equivalent modal damping was calculated to facilitate the conventional modal response history analysis. The equivalent modal damping was estimated either by quantifying the dissipated energy in the soil Roesset et al. 1973; Novak and Hifnawy 1983 or by matching the approximate nor-mal mode solution with the rigorous solution for a certain struc-tural location Tsai 1974; Balendra et al. 1982.
Conventional modal response history analysis, which neglects the off-diagonal terms of the transformed damping matrix for a nonproportionally damped one-way asymmetric building resting on a rigid base, is one of the common approximation approaches. However, this approximation approach may result in unacceptable errors under certain conditions Goel 2001. The two-degrees-of-freedom modal equations of motion preserve the property of non-proportional damping for the original one-way asymmetric building system resting on a rigid base Lin and Tsai 2007. Using these modal equations of motion, it was verified that the modal response history analysis results in analytical results that are more accurate than those obtained using the conventional modal re-sponse history analysis Lin and Tsai 2007.