A Projection-Coupled 2.5D THB-GIFT and Quadtree-SBIGA Formulation for Moving-Load Analysis in Semi-Infinite Media

Abstract

Moving loads in semi-infinite media generate extended wave fields while complex local structures require fine geometric and spatial resolution. This paper develops a projection-coupled two-and-a-half-dimensional (2.5D) THB-GIFT and quadtree-SBIGA computational formulation that assigns independent discretizations to these regions. The near-field THB-GIFT representation separates the geometry and analysis spaces and permits hierarchical local refinement, while the bounded propagation domain is discretized by quadtree-SBIGA with unified Bézier trace extraction and connected to the homogeneous unbounded exterior through a scaled-boundary impedance. On a common physical integration partition, an $L^2$ projection maps the nonmatching traces; Hermitian-adjoint force transfer then gives a virtual-work-consistent interface reduction. The regional dynamic operators and moving-load response reconstruction follow a single Fourier convention. Homogeneous half-space comparisons and a cylindrical-cavity analytical solution verify the components and the complete coupled system. In the cavity study, hierarchical THB refinement reduces the displacement error in the target inner band by a factor of approximately $41$. At a specified frequency--wavenumber point in the cavity benchmark, a comparison with matched outer-boundary discretization gives approximately $15\%$ lower sampled full-domain error for the coupled model, using $34\%$ fewer system degrees of freedom and $48\%$ fewer S-elements; the warm per-sample times are similar. A layered pavement with a buried conduit and twin modified-D tunnels demonstrate open, closed and multiple disconnected nonmatching interfaces and the analysis of local structural demand and dynamic interaction under moving loads.