A method to truncate elastic half-plane for soil–structure interaction analysis under moving loads and its implementation to ABAQUS

Moving loads appear in many half-plane problems, including analyses involving highway or railway bridges, culverts, and embankments. Current modeling approaches are mostly analytical, which provide only limited utility in practical problems featuring embedded or supported scatterers (e.g., a tunnel). Basic applications of fully numerical/discrete approaches (e.g., the finite element method) are also complicated because of the moving inbound load(s). One approach is to use a very large domain so that the wavefield reaches a steady state prior to any significant interaction of the moving loads with the local region containing the scatterer. This scenario elevates the computational burden to impractically high levels. In the present study, we devise an approach featuring Perfectly-Matched-Layers (PMLs) and the Domain Reduction Method (DRM) for a linear elastic half-plane, which enables drastic reductions in the domain size without sacrificing accuracy. The effective nodal forces at the boundary of the truncated local domain are computed a priori for the far free-field problem. Both the scattered and otherwise outbound waves are absorbed by the PMLs. The DRM approach and the PMLs are implemented together in commercial software ABAQUS—the former with a stand-alone code that modifies the ABAQUS input file and the latter through a user-defined element (UEL) subroutine. The accuracy of the method and its implementation is verified for homogeneous half-planes with and without a rectangle-shaped hollow zone under a concentrated moving load. We also present a parametric study involving a variety of scatterer geometries, embedment depths, and load speeds. The results indicate the veracity and the utility of the DRM and PML implementations for moving loads on half-plane.