Analysis of Earthquake Energy Input in Soil-Pile-Structure System with Uncertain Soil Parameter

The energy flow in a soil-pile-structure (SPS) system during an earthquake is an important consideration in seismic-resistant design. The energy input to the structure is formulated here in the frequency domain. The frequency-domain approach enables the exact and complete treatment of frequency-dependent stiffness and damping properties. It is shown that the input energy can be derived in a compact form through the frequency integration of the product of the ground-motion input component and the structural model component. By taking full advantage of this compact form, it is demonstrated that the formulation of earthquake input energy in the frequency domain is essentially appropriate for deriving the exact first and second-order sensitivities of the input energy with respect to an uncertain soil stiffness parameter. The sensitivity expressions derived for swaying-rocking models with independent uncertain parameters are used here for the efficient formulation in a new model. The exact second-order sensitivities facilitate the expression of input energy variation due to uncertainty in ground stiffness, which is useful seismic design data.