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Simplified equivalent static methods are widely used in seismic design and analysis of underground structures. The relative shear deformation of the soil is usually considered as the main earthquake load in the existing simplified methods, including the free-field racking deformation method, flexible coefficient method, response displacement method, response acceleration method, and pushover analysis method. However, the inertia force of the overburden soil caused by the vertical earthquake motion does not attract sufficient attention in many design specifications. The recent studies revealed that the large vertical inertia force made a significant influence on the shear strength and deformation capacity of the support components in the underground structures, especially for the shallow buried ones. Firstly, based on the earthquake damage investigation of shallow buried rectangular underground structures and the analysis model of response displacement method (RDM), this paper proposes the vertical inertia force-response displacement method (VIF-RDM), in which the vertical inertia force of overburden soil is taken into account. The calculation methods of two critical parameters of the VIF-RDM are described in detail, including the coefficients of the foundation springs around the structure and the maximum vertical inertia force of the overburden soil. Afterwards, the integral vertical inertia force-response displacement method (IVIF-RDM) is put forward to reduce the computational complexity and calculation error of the foundation springs. The surrounding soil model is directly used to calculate the equivalent earthquake loads, which are caused by the relative displacement of the free field. The two proposed simplified methods and RDM are compared with the time-history analysis method (THAM) in a real underground structure. The results show a significant difference in the axial force of the central column between the two proposed methods and RDM. The proposed methods reflect the internal forces of the structure under the strong earthquake more accurately. Therefore, it can be used to evaluate the seismic safety performance of the shallow buried rectangular underground structures in the future. • VIF-RDM is proposed to consider the vertical inertia force of the overburden soil. • IVIF-RDM is proposed to reduce calculation error caused by the foundation springs. • The accuracy of the proposed methods is evaluated by the time-history analysis method. • The proposed methods reflect the internal forces of the structure more accurately. [ABSTRACT FROM AUTHOR]

Simplified methods are widely used in the seismic design of underground structures, but they generally ignore the influence of vertical ground motion. This can result in unreliable design because seismic earth pressure induced by vertical ground motion can have a significant adverse effect on their seismic performance. Therefore, this paper proposes an improved pushover analysis method (I-PAM) that applies distributed horizontal and vertical inertial forces to simulate the mechanical behavior of underground structures under both horizontal and vertical ground motions. The profile of load distribution and target displacement is calculated from corresponding site response analysis. A rigorous time-history dynamic analysis method (TDAM) based on the finite element numerical analysis was employed in three case studies to evaluate the performance of the developed I-PAM. The results showed that the I-PAM can accurately predict the structure's peak axial force, bending moment and displacement under the combined action of horizontal and vertical ground motions, especially for lower ground motion intensity. It was also found that the responses of the center column and middle slap were calculated with higher accuracy compared to that of the components in direct contact with soil including sidewalls and top and bottom slabs. The developed I-PAM offers a framework for further development and enhancement of simplified analysis methods for seismic design of underground structures. • The effect of vertical ground motion on daikai subway station is conducted in present study. • The mechanical model of improved pushover analysis method considering vertical ground motion is developed. • The reliability of the improved pushover analysis method is verified by comparison with the dynamic method. [ABSTRACT FROM AUTHOR]