Response spectrum method (RSM) has been applied in seismic analysis of underground structures considering linear soil-structure interaction (SSI). However, the RSM has two main shortcomings: it does not account for soil nonlinearity and it is computationally inefficient for processing large soil domains. This paper addresses these shortcomings by extending the RSM to consider soil nonlinearity and by simplifying the modal analysis of SSI systems. The soil nonlinearity is considered by transforming the one-dimensional (1D) frequency-domain equivalent linearization model into a modal damping linear elastic model, in which two explicit formulations of the modal damping ratio are presented. The resulting degraded shear modulus and modal damping ratio are applied to the SSI model to consider soil nonlinearity. In addition, it was found that a small number of natural frequencies and mode shapes of the SSI system are already sufficient to evaluate vibration characteristics in a typical 2D SSI analysis. Accordingly, the first three natural vibration modes of the 1D soil site are used as the loading condition to determine the effective characteristics of the SSI system by iterative static analysis of the SSI system. The effectiveness of the proposed procedure in considering soil nonlinearity and avoiding modal analysis of the SSI system is verified by comparisons with numerical examples. Finally, the extended RSM is applied to the seismic design of three prototype underground structures.

响应谱法 (RSM) 已应用于考虑线性土-结构相互作用 (SSI) 的地下结构的抗震分析。然而，RSM 有两个主要缺点：它没有考虑土壤非线性和处理大型土壤域的计算效率低下。本文通过扩展 RSM 以考虑土壤非线性和简化 SSI 系统的模态分析来解决这些缺点。通过将一维 (1D) 频域等效线性化模型转换为模态阻尼线弹性模型来考虑土壤非线性，其中给出了模态阻尼比的两个显式公式。将由此产生的退化剪切模量和模态阻尼比应用于 SSI 模型以考虑土壤非线性。此外，发现 SSI 系统的少量固有频率和振型已经足以评估典型 2D SSI 分析中的振动特性。相应地，以一维土壤场地的前三种固有振动模式作为加载条件，通过对SSI系统进行迭代静力分析来确定SSI系统的有效特性。通过与数值例子的比较，验证了所提出的程序在考虑土壤非线性和避免 SSI 系统的模态分析方面的有效性。最后，将扩展的 RSM 应用于三个原型地下结构的抗震设计。以一维土壤场地的前三种固有振动模式作为加载条件，通过对SSI系统进行迭代静力分析来确定SSI系统的有效特性。通过与数值例子的比较，验证了所提出的程序在考虑土壤非线性和避免 SSI 系统的模态分析方面的有效性。最后，将扩展的 RSM 应用于三个原型地下结构的抗震设计。以一维土壤场地的前三种固有振动模式作为加载条件，通过对SSI系统进行迭代静力分析来确定SSI系统的有效特性。通过与数值例子的比较，验证了所提出的程序在考虑土壤非线性和避免 SSI 系统的模态分析方面的有效性。最后，将扩展的 RSM 应用于三个原型地下结构的抗震设计。