Generalized response displacement methods for seismic analysis of underground structures with complex cross section

The response displacement method (RDM) is recommended for the seismic analysis of underground structures in the transverse direction for many codes, including bases for design of structures-seismic actions for designing geotechnical works (ISO 23469) and code for seismic design of urban rail transit structures (GB 50909-2014). However, there are some obvious limitations in the application of RDM. Springs and the shear stress of the soil could be approximately evaluated for the structures having a simple cross section, such as rectangular and circular structures. It is necessary to propose simplified seismic analysis methods for structures with complex cross sections. This paper refers to the idea of RDM and proposes three generalized response displacement methods (GRDM). In GRDM1, a part of the soil surrounding a structure is selected to generate a generalized underground structure with a rectangular cross section, and the same analysis model as RDM is applied to analyze the responses of the structure. In GRDM2, a hollow soil model without a generalized structure is used to compute the equivalent load caused by the relative displacement of the soil, and the soil-structure interaction model is applied to calculate the responses of the structure. In GRDM3, a continuous soil model is applied to compute the equivalent load caused by the relative displacement and shear stress of the soil, and the soil-structure interaction model is applied to analyze the responses of the structure, which is the same as the model used in GRDM2. The time-history analysis method (THAM) is used to evaluate the accuracy of the proposed simplified methods. Results show that the error of GRDM1 is about 20%, while the error is only 5% for GRDM2 and GRDM3. Among the three proposed methods, GRDM3 has obvious advantages regarding calculation efficiency and accuracy. Therefore, it is recommended to use GRDM3 for the seismic response analysis of underground structures that have conventional simple or complex cross sections.