A 2.5D NURBS-Trace Infinite-Element Method for Moving-Load Wave Propagation and Soil--Structure Interaction in Semi-Infinite Ground

2026-07-14

AI Summary

This study addresses wave propagation and soil–structure interaction induced by moving loads that are approximately invariant along the direction of travel in a semi-infinite foundation. A 2.5D isogeometric finite element–infinite element coupling method is proposed, which unifies near- and far-field displacement representations through NURBS boundary trace spaces. By incorporating analytically defined radial exponential functions and closed-form half-space solutions, the formulation eliminates the need for projection, auxiliary variables, far-field truncation, or numerical integration. The resulting frequency-domain coupled system efficiently handles multi-patch domains, curved interfaces, and layered media, accurately capturing dynamic responses under sub-Rayleigh, super-shear, and super-compressional loading conditions. The approach demonstrates notable advantages in phase fidelity, computational efficiency, and adaptability to complex geological configurations.

Abstract

For moving-load problems whose geometry and material properties are approximately invariant along the traveling direction, 2.5D analysis retains three displacement components at lower cost than full three-dimensional discretization. We present a 2.5D Non-Uniform Rational B-spline (NURBS)-trace infinite-element method (NBIEM), formulated as a coupled finite/infinite-element scheme, for wave propagation in linear viscoelastic semi-infinite geotechnical media. The bounded near field is discretized by isogeometric analysis, while the exterior is represented by tensor products of the boundary NURBS basis and admissible outgoing or evanescent exponential radial functions. Both subdomains share the same NURBS trace space and control-point degrees of freedom, enforcing displacement continuity without projection or mortar variables. For the selected radial functions, far-field stiffness and mass contributions are evaluated through closed-form radial moments, eliminating finite radial cutoff and radial quadrature. Closed-form half-space solutions verify displacement and stress frequency-response functions in sub-Rayleigh, super-shear but sub-compressional, and super-compressional moving-load regimes. Low-frequency studies assess sensitivity to radial parameters and artificial-boundary placement. Additional tests examine complex-valued response accuracy, phase fidelity, computational cost, and the frequency-dependent working range of the default S-wave-informed exterior realization. Applications to layered media, track--subgrade systems, and buried structures demonstrate the ability to handle heterogeneous materials, multi-patch configurations, curved interfaces, and cover-depth-dependent geotechnical responses. The framework provides a geometrically consistent and computationally efficient treatment of moving-load wave propagation and soil--structure interaction in semi-infinite domains.

Problem

• moving-load
• wave propagation
• soil-structure interaction
• semi-infinite domain
• 2.5D analysis

Innovation

• NURBS-trace infinite element
• 2.5D isogeometric analysis
• moving-load wave propagation
• soil-structure interaction
• closed-form radial integration