A simplified estimation method for foundation coefficients in seismic response displacement method of underground structures

Foundation coefficients are critical parameters in the response displacement method (RDM) for seismic analysis of underground structures. This study investigates the influence of soil properties, structural dimensions, and burial depth on foundation coefficients. Based on these findings, a simplified formula for estimating foundation coefficient is proposed. Subsequently, the estimation method is applied to the seismic analysis of subway stations under both homogeneous and layered site conditions, with the results benchmarked against those obtained using the static finite element method prescribed in existing design codes. The computational accuracy of the proposed approach is evaluated against the traditional response displacement method (T-RDM) and the vertical inertial force one (VIF-RDM). The findings indicate a linear relationship between foundation coefficients and the elastic modulus of the soil, while variations in structural dimensions exert a significant impact on foundation coefficients of sidewalls and base slabs. Under both homogeneous and layered site conditions, the foundation coefficients determined using the proposed simplified formula align closely with those obtained from the static finite element method. Additionally, across four engineering case studies, the structural responses derived from the proposed method are consistent with those produced by the T-RDM and VIF-RDM, further validating its reliability. In study, the proposed method eliminates the need for repeated static finite element analyses, significantly enhancing computational efficiency while maintaining high accuracy. It demonstrates strong applicability to various site conditions and structural configurations, offering a valuable reference for the seismic analysis of underground structures.