Experimental Evaluation of Frequency- and Amplitude-Dependent Impedance Functions of Pile Groups Using the Trust Region Method

In recent soil–structure interaction (SSI) studies, the frequency-dependent impedance functions of soil–pile systems have been increasingly recognized as key factors influencing the dynamic response of structures. However, identification of these IFs directly from the total seismic re-sponse of interacting soil-pile-superstructure systems where kinematic and inertial interactions are simultaneously activated remains quite limited, even in physical model tests. This study investigates the frequency- and amplitude-dependent impedance functions of a 2×2 pile group supporting a single-degree-of-freedom structure through shaking table tests simulat-ing observed earthquake motions. From the measured responses, transfer functions between the superstructure, footing, and ground surface were derived. The impedance functions were then estimated for each frequency using the Trust Region method by fitting the experimental transfer functions with a two-degree-of-freedom model in which the superstructure, represented by a mass and a spring, is supported by the footing, and the footing is connected to the ground through a parallel spring–dashpot system representing the impedance function. The estimated impedance functions clearly exhibited frequency-dependent behavior in both stiffness and damping. With increasing input amplitude, the dynamic stiffness decreased, and the cutoff frequency shifted to lower values due to soil and interface nonlinearity, while damp-ing increased locally at higher frequencies. These results confirm that the observed behavior, including the significant reduction in static stiffness and the shift of the cutoff frequency with in-creasing amplitude, aligns with findings from prior harmonic loading experiments even under the complex interplay of coupled seismic excitations.