Closed-form sensitivity of earthquake input energy to soil-structure interaction system

The input energy to a soil-structure interaction (SSI) system during earthquake shaking is taken as a structural performance measure and is formulated in the frequency domain. The purpose of this paper is to derive the closed-form expression of the sensitivity of the input energy to the SSI system with respect to uncertain parameters representing soil stiffness and damping. It is demonstrated first that the input energy expression can be of a compact form consisting of the product between the input motion component (Fourier amplitude spectrum of acceleration) and the structural model component (so-called energy transfer function). With the help of this compact form, it is shown that the formulation of earthquake input energy in the frequency domain is essential for deriving the closed-form expressions of the sensitivity of the input energy to the SSI system with respect to uncertain parameters in contrast to the time-domain formulation including inevitable numerical error and instability. This formulation is then extended to a multidegree-of-freedom superstructure model. Numerical examples support the fact that the closed-form expressions enable one to find in a reliable and efficient way the most critical combination of the uncertain parameters that leads to the maximum energy input.