Exact higher-order sensitivity and variation of earthquake energy input in soil-structure interaction system

The energy input to a soil-structure interaction (SSI) system during an earthquake is an important measure of seismic demand. It is formulated here in the frequency domain. Exact higher-order sensitivities of the input energy to the SSI system are derived with respect to uncertain soil stiffness and damping parameters. It is shown that the input energy can be derived in a compact form through the frequency integration of the product between 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 higher-order sensitivities of the input energy to the SSI system with respect to the uncertain parameters. The exact higher-order sensitivities facilitate to express the input energy variation due to uncertainty of ground stiffness and damping, and to find the most unfavorable combination of the uncertain parameters leading to the maximum energy input.