## 1 Introduction  
Dynamic interaction between the soil and structure (SSI) [1] is a complex issue due to the fact that its influence factors such as the structure frequency, soil property, and seismic record, etc. are numerous and mutually coupled. Compared with a fixed-base structure, SSI can significantly alter the seismic demands of a structure built on soft soil, which has been widely investigated by scholars. Since SSI can lengthen the natural period and increase the damping of the structure, previous studies [2] generally agreed that the seismic demands of structures considering SSI are smaller than those of fixed-base structures. Therefore, many codes [3; 4; 5; 6] adopt the assumption of a fixed base, where MHURD-PRC, NBCC, and IBC stipulate that the design base shears of structures can be reduced when considering SSI. Moreover, in the earthquake damage evaluation of cities or regions, the SSI effect on the responses of structures has usually been neglected [7; 8] to improve the computational efficiency. However, as research continues, increasingly more scholars [9; 10] have noticed that the horizontal movement and rotation of the foundation may increase the lateral deformation and story drift of the superstructure, and SSI can provide pejorative conditions for structural seismic vulnerability [11; 12; 13; 14]. Therefore, further investigations on the SSI effect can provide technical support for improving the conventional seismic design method and urban earthquake damage evaluation method, which has significant application value. Numerical methods considering the SSI effect can be divided into two groups: the direct method [15] and substructure method [16; 17]. In the direct method, the soil, structure,and foundation are modeled together to fully consider the coupling effects among the soil, foundation, and superstructure. Since the direct method can consider the complicated model shape and load condition and the nonlinearity of the soil, foundation, superstructure, and soil-foundation contact, it has the advantage of wide application while it has the disadvantage of a long computation time. In the substructure method, the soil, foundation, and superstructures are solved separately, and the coupling among the soil, foundation, and superstructures is considered using the compatibility conditions of the force and displacement on the interface. The substructure method has a high computation efficiency while the mathematical definition of the simplified soil model is complex and the nonlinear coupling effect of SSI systems is difficult to consider [18]. [PERSON] et al. [19] evaluated the SSI effect on the seismic performance of hypothetical plane tall buildings and earthquake-induced losses using a direct method, finding that SSI changed the seismic demands such as the maximum story drift and peak story horizontal accelerations, and the addition of the SSI effect to the tall structures triggered larger losses compared with fixed-base structures in normal situations. [PERSON] and [PERSON] [20] investigated the effects of soil conditions and near-fault earthquakes (NFEs) on the responses of 6-story and 20-story plane RC frame structures using a substructure method. They found that the SSI effect on the responses of structures subjected to NFE ground motions was more pronounced in soft and medium soil properties and the roof displacements and inter-story drifts of structures considering SSI exceeded those of fixed-base structures under certain near-fault records and soil conditions. [PERSON] and [PERSON] [21] studied the seismic responses of 20-, 30-, and 40-story plane high-rise frame-core tube structures constructed on soil with class \(E_{e}\) (based on Australian Standards) under different seismic records. They pointed out that SSI can increase the lateral deflections and story drift and decrease the story shear forces of structures, and the seismic responses of SSI systems under near- and far-field earthquakes were considerably different.