Nonlinear response analysis of seismic wave scattering characteristics for three-dimensional real terrain

To accurately characterize the influence of complex terrain on seismic wave scattering and site amplification effects, this paper proposes a nonlinear seismic response calculation method that accounts for actual surface topography. First, a three-dimensional geometric model is constructed based on a digital elevation model (DEM), followed by mesh generation and stringent mesh quality control. Subsequently, the improved Drucker-Prager elastoplastic constitutive model is employed to capture soil nonlinearity and is implemented within the finite element method (FEM) framework through secondary development in ABAQUS. Building upon this foundation, seismic wave input was realized using viscoelastic artificial boundaries in conjunction with the equivalent load method, thereby establishing a three-dimensional numerical model for nonlinear seismic response analysis of real-world topographic sites. The validity of the proposed method is verified by comparing simulation results with classical benchmark cases and recorded strong-motion data, demonstrating its reliability and accuracy. A systematic analysis is then conducted on the nonlinear seismic dynamic response characteristics of complex topographies. Computational results showed that, compared to simplified mountain-canyon models, the canyon model based on actual topography exhibits a 27.2 % increase in cross-valley relative displacement and a 32.5 % increase in peak maximum principal stress. High-damage zones extend outward along both the longitudinal and transverse directions of the valley floor. In basin-like terrain, central regions experience higher acceleration levels than the edges, with amplifications of 54.5 % and 27.3 %, respectively, indicating a significant focusing effect. Moreover, damage concentration is most pronounced at the basin center. Nonlinear analyses revealed a reduction in acceleration amplitudes and a mitigation of oscillatory behavior in seismic time histories compared to linear analyses, basin terrain response spectrum peaks decrease by approximately 30 %–50 %, highlighting the critical role of material nonlinearity in modifying ground motion characteristics.