Damping in the platform models for soil-structure interaction problems: Rayleigh damping options and limitations in modal analysis

Abstract

Modal approach is widely used in seismic analysis. Moreover, spectral theory used in seismic codes all over the world is based on this modal approach. However, modal approach has an implicit limitation – relatively small or homogeneous damping. Otherwise the equations of motion in the ‘main coordinates’ remain coupled through the damping matrix even after decoupling through inertia and stiffness matrices. Due to this coupling, the results obtained using decoupled 1D modal equations of motion are incorrect. Practical example of such a situation is a platform model of the soil-structure system used for the analysis of soil-structure interaction (SSI) controlling seismic response of main NPP structures. Here, we see considerable damping in the ‘soil’ dashpots, completely different from structural damping. The difficulty with modal damping in SSI problems was realized in 1970s, and several suggestions have been made in order to save conventional modal approach. The author discusses these suggestions using a very simple 1D model and proposes to address the difficulties using combined asymptotic method (CAM). In CAM, a new platform model with homogeneous damping is analysed (thus enabling modal approach), and the difference between ‘true’ damping and artificial ‘platform’ damping is accounted for in the modified platform excitation.