## 1 Introduction  
In the earthquake engineering field, the shaking table test is a direct and common method to study the earthquake response and failure mechanism of structures and sites. Moreover, it is also one of the important means to research and evaluate the seismic performance of a structure. When a structure and soil move integrally under an earthquake, the structural motion and soil motion mutually affect each other, that is, the soil-structure interaction (SSI). In shaking table tests, the test model of the soil-structure system is composed of a model structure and model soil. Due to the difference of geometry and material similarity ratios for two different parts (the model structure and model soil), the determination of the duration compression ratio of the input motions is a key and difficult issue in the shaking table test of a soil-structure system. The spectrum characteristics of input motions will be changed by different duration compression ratios. Therefore, the seismic responses of the structure and soil will be affected. No matter how the duration compression ratio of input motions is determined, it is difficult to satisfy the similarity requirement of the model structure and model soil simultaneously. Because there is no unified recognition in this issue, the duration compression ratios of input motions are given different values in relative shaking table tests. Much research has been carried out on shaking table tests considering the soil-structure interaction. There are three commonly used approaches to determine the duration compression ratio of input motions: time similarity ratio of model structure; time similarity ratio of model soil; and uncompressed. The duration compression ratio of input motions determined by the time similarity ratio of a model structure is widely applied in shaking table tests. [PERSON] [1] performed a series of shaking table tests to better understand the characteristics of the seismic response of nuclear power stations with fixed-base and pile-raft foundations. [PERSON] [2] studied the effects of the seismic soil-pile-structure interaction (SSPSI) on the dynamic response of a building with various heights by conducting a series of shaking table tests on 5-story, 10-story, and 25-story model structures, in which the structure was supported by an end-bearing pile foundation in soft soil. [PERSON] [3] conducted the shaking table tests of a series of soil-structure and soil-structure group systems. The influence of structure height, the number of structures, the composition of the structure group, and seismic records was considered. [PERSON] [4] set up a comparison of conventional pile types under the same test conditions, and a series of shaking table tests. The distribution and spatial variation of acceleration and the dynamic soil pressure response of a soil slope strengthened by EPS pile under earthquake action were studied. [PERSON] [5] conducted 1 g shaking table tests with a unified system consisting of a ground, a group-pile foundation, and a superstructure, and the study showed that it was impossible to satisfy all similarity laws in 1 g model tests. [PERSON] [6] studied a 1/70 scaled model of a cable-stayed bridge with a central span of 1400 m using a multiple shaking table array system. [PERSON] [7] performed a series of shaking table tests using a soil-pile model with three different sizes to verify the existing similitude law used in 1 g shaking table tests. [PERSON] [8] performed a series of model shake table tests to investigate the effect of model scale on the seismic response of prototype helical pile groups. [PERSON] [9] set up a scaled model of a building, foundation, and soil deposit on a shaking table to investigate the effects of the vibration of soil deposits and buildings. [PERSON] [10] studied the dynamic characteristics and seismic response of high-rise buildings considering the effect of the soil-structure interaction. The model soil for soil box test was sand, sandy silt, and silty clay from bottom to top.