An Improved Integral Response Deformation Method for Seismic Response Analysis of Underground Structures Considering Far-Field Effects

In the seismic analysis of underground structures, the traditional integral response displacement method may misestimate far-field constraint effects because of the empirical placement of cutoff boundaries, leading to inaccuracies and a significant increase in computational costs. This study proposes a cutoff boundary distance criterion of three times the structural size, effectively eliminating boundary reflection errors. Furthermore, by introducing artificial boundary conditions that simulate the static resistance of a semi-infinite foundation and the far-field constraint effects, an improved integral response deformation method considering the far-field effect is developed. Verification based on the dynamic time history method (implemented with the Abaqus/Explicit solver) confirms that the computational error of the proposed method is essentially controlled within 5%, and compared with that of the traditional method, the number of mesh elements and nodes is reduced by 80%~90%. This advancement provides a computationally efficient and highly accurate solution for the seismic analysis of large-scale underground structures, making it highly valuable for practical engineering applications.