Response spectrum method for nonlinear surface ground analysis

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.