## 1 Introduction
[13; 14; 15] systematically addressed the error sources of the classical RDM and then advanced the Integral Response Deformation Method (IRDM), which integrates the explicit physical concepts and rigorous theoretical framework of the original approach while eliminating traditional foundation spring models. Instead, it employs an integrated soil-structure mechanical model that directly characterizes continuum interactions, thereby eliminating errors associated with spring stiffness calibration and localized spring approximations. [PERSON] et al. [16] proposed a generalized response displacement method (GRDM) based on a \"spring-stratum-structure\" framework. This approach effectively mitigates errors caused by inappropriate spring stiffness assignments, particularly for underground structures with complex cross-sectional geometries. [PERSON] et al. [17] introduced an improved RDM that accounts for the influence of overlying frame structures on the seismic responses of metro stations. [PERSON] et al. [18] theoretically demonstrated that equivalent seismic loads induced by peripheral soil stresses in the IRDM can be obtained through a single static analysis of substructure models containing only one soil layer, with minimal influence from soil inertial forces. Building on this foundation, they developed an improved IRDM implementation that eliminates the computation and application of free-field soil inertial forces while maintaining accuracy, thereby streamlining the workflow [19]. [PERSON] [20], [PERSON] et al. [21], and [PERSON] et al. [22] proposed the forced response displacement method (FRDM) using a stratum-structure model. This method simplifies seismic action application by treating stratum relative displacements at model boundaries as static inputs for finite element analysis. Expanding on this concept, [PERSON] et al. [23, 24] proposed the Integral Forced Response Displacement Method (IFRDM), which mitigates load attenuation effects by imposing stratum deformations across entire soil domains. However, existing methods typically employ fixed or free-field displacement assumptions at the cutoff boundaries, overlooking the radiation effects induced by far-field media on seismic wave propagation. This omission results in discrepancies between computational models and actual seismic environments. Insufficient boundary distances cause computational inaccuracies arising from spurious wave reflections from the far field. Furthermore, current codes lack explicit guidelines for boundary configuration in the IRDM, leading to widespread reliance on empirical estimations in practice. Although expanding the model domain can mitigate boundary effects, it disproportionately increases computational costs. In response to these challenges, this study systematically investigates the influence of the truncation distance on computational accuracy, establishing quantitative criteria for boundary configuration. By incorporating artificial boundary conditions that simulate the static resistance of semi-infinite foundations and the constraint effects of far-field media, an improved IRDM considering far-field effects is developed. Comparative analyses of representative underground structures demonstrate that the proposed method maintains precision while significantly reducing the computational scale. This methodology provides an innovative solution that balances accuracy and efficiency for the seismic design of underground infrastructure, offering substantial practical implications for advancing safety assessment and disaster mitigation in large-scale underground engineering projects.