In the numerical simulation of wave problems, it is often necessary to truncate the unbounded computational domain at a finite distance to reduce the requirement of computational resources. To manage this truncation, artificial boundaries are introduced, among which the Scaled Boundary Perfectly Matched Layer (SBPML) is regarded as a reliable strategy. In this paper, we implement the SBPML element into the commercial software ABAQUS using the User-Defined Elements (UEL) subroutine. The key equations of the SBPML, the procedures of meshing for the SBPML domain, and the implementation workflow of the subroutine are given in details. Four benchmark examples of wave propagation problems in unbounded domains are presented to demonstrate the accuracy and effectiveness of the proposed method. Furthermore, the application of the UEL in nonlinear seismic soil-structure interaction analysis is demonstrated by evaluating the seismic response of a five-layer alluvial basin in a homogeneous half space and an aboveground-underground integrated structure-multilayer soil system under obliquely incident earthquake waves. Using the proposed UEL, all wave propagation analyses can be directly implemented in ABAQUS with a seamless workflow. To facilitate the use of the proposed approach, the codes of the UEL are published in an open-source format.

This paper establishes an efficient model for simulating wave propagation in a multi-layered transversely isotropic (TI) saturated medium. The complex frequency shifted perfectly matched layer (CFSPML) is integrated into the thin layer method (TLM) framework to address instability issues associated with the classical PML in TI media. The three-dimensional closed-form fundamental solution for dynamic sources acting on a layered TI halfspace is derived in the frequency-space domain. By eliminating the necessity of double discrete Fourier transform of spatial coordinates, this approach provides an efficient and accurate tool for exploring wave propagation in saturated soils. Numerical examples are conducted to determine the parameters involved in CFSPML for an unbounded TI saturated medium across various material anisotropy ratios, including the total thickness of CFSPML domain HPML, the parameter Delta gamma related to the number of CFSPML elements, and the reflection coefficient within the discrete CFSPML domain R0. A comprehensive investigation systematically analyses the effect of material anisotropy on dynamic responses. Numerical studies highlight that the anisotropy in the shear modulus exerts the most substantial influence on the dynamic response, followed by Young's modulus and the permeability coefficient. The effect of permeability coefficient anisotropy cannot be disregarded, particularly in the context of fluid sources.

In this work, a numerical study of the effects of soil-structure interaction (SSI) and granular material-structure interaction (GSI) on the nonlinear response and seismic capacity of flat-bottomed storage silos is conducted. A series of incremental dynamic analyses (IDA) are performed on a case of large reinforced concrete silo using 10 seismic recordings. The IDA results are given by two average IDA capacity curves, which are represented, as well as the seismic capacity of the studied structure, with and without a consideration of the SSI while accounting for the effect of GSI. These curves are used to quantify and evaluate the damage of the studied silo by utilizing two damage indices, one based on dissipated energy and the other on displacement and dissipated energy. The cumulative energy dissipation curves obtained by the average IDA capacity curves with and without SSI are presented as a function of the base shear, and these curves allow one to obtain the two critical points and the different limit states of the structure. It is observed that the SSI and GSI significantly influence the seismic response and capacity of the studied structure, particularly at higher levels of PGA. Moreover, the effect of the SSI reduces the damage index of the studied structure by 4%.