A single-step recursive representation of foundation flexibility functions to soil-structure interaction using first-order IIR filters. Issue 153 (February 2022) - Du, Xianting; Nie, Yanjun; Xia, He; Zhang, Nan; Guo, Weiwei
Abstract: The rational approximation of the dynamic impedance function of the foundation plays a vital role in the soil-structure interaction (SSI) analysis in the time domain. The filter representation of the rational approximation proposed by Safak provides a multi-step recursive parameter model facilitating incorporation into the time history analysis. However, it encounters both the uncertainty of the parameter identification and numerical instability. According to the linear time-invariant system theory in signal processing, this paper presents an improved single-step recursive representation of the foundation flexibility function using first-order infinite impulse response (IIR) filters. Based on the discrete responses of the foundation to the triangular unit impulse, the well-developed technologies of the digital filter can efficiently identify the stable filter parameters. It is easy to incorporate the filters into the motion equations of the structure in the forms of additional stiffness and single-step recursive variables. A computational scheme founded on the Newmark integration method is proposed to obtain the structural responses. According to the spectral radius theory, combining the filters with the Newmark integration method produces only a single operation matrix, thus effectively making the numerical stability guaranteed. Finally, a multi-degree-of-freedom model subjected to earthquake ground motion is employed to approve the proposed scheme. Highlights: A single-step recursive representation of the foundation flexibility function is presented. Well-developed technologies identify stable parameters. Combining the representation with the New-mark integration method produces only a single operation matrix.