Advances in Structural Engineering Vol. 7 No. 6 2004 503 1. INTRODUCTION It has been demonstrated repeatedly in past devastating earthquakes that the ground surface motions are greatly affected by the surface ground properties and building damage is therefore influenced by those surface ground properties. It is therefore rational to define a design earthquake as outcropping motion at the bottom of the surface ground. Since soil exhibits a great deal of nonlinearity during vibrations of large amplitude, nonlinear surface ground amplification is one of the major subjects in earthquake engineering and seismic resistant design to be investigated from the view point of reliable building structural design. This philosophy has been incorporated in the new Japanese seismic-resistant design code (June 2000). However, the scenario of its implementation is not necessarily presented explicitly. The conventional treatment of surface ground nonlinearities is based on the combination of the deterministic equivalent linearization technique and the one-dimensional wave propagation theory represented by the SHAKE program (Schnabel et al. 1972). The validity of this approach in a practical sense has been Response Spectrum Method for Nonlinear Surface Ground Analysis Izuru Takewaki* Department of Urban & Environmental Engineering, Graduate School of Engineering, Kyoto University, Sakyo, Kyoto 606-8501, Japan (Received: 3 March 2004; Received revised form: 15 June 2004; Accepted: 16 June 2004) Abstract: An equivalent linear response spectrum approach is proposed for nonlinear surface ground analysis. In contrast to the conventional method which deals with only a single ground motion for equivalent linearization of soil properties, it is argued in this paper that a design response spectrum defined at the upper level (bottom of the surface ground) of an engineering bedrock can be handled as the target design earthquake. The effective shear strain in each soil layer is evaluated by means of a response spectrum method in which the mean peak shear strain is computed by a response spectrum mode- superposition procedure. The soil hysteretic damping is substituted by the corresponding viscous damping. The stiffness coefficient and damping ratio of each soil layer are obtained iteratively from the nonlinear relation of stiffness reduction factors and damping ratios with respect to the strain level. After the evaluation of the equivalent stiffness coefficient and damping ratio of every soil layer, the surface ground response can be described via the one-dimensional wave propagation theory. The reliability and accuracy of the proposed analysis method is examined through comparison with the results obtained by the conventional method (represented by the SHAKE program) for many simulated spectrum-compatible ground motions. Key words: surface ground analysis, nonlinear surface ground amplification, response spectrum method, one- dimensional wave propagation, equivalent linear model, complex modal analysis *Corrresponding author. Email address: takewaki@archi.kyoto-u.ac.jp; Fax: +81-75-753-5748; Tel: +81-75-753-4762. ASE 7(6)-272 20/12/04 3:57 pm Page 503