## 1 Introduction  
Seismic analysis and structural design of buildings and other engineering structures in China are often based on the assumption that the foundation is a rigid half-space and the bottoms of the structures are fixed. The NIST GCR 12-917-21 report [1] and FEMA P-58 [2] proposed the consideration of soil-structure interactions in seismic analysis. It is well known that soil-structure interaction (SSI) can significantly affect the seismic response of superstructures, especially those on soft soil foundations [3; 4; 5; 6]. Soil-structure interaction, one of the major subjects in the domain of earthquake engineering, has been paid comprehensive attention by international scholars for more than forty years, from the field's inequtive works [7; 8], analytical formulations [9; 10; 11; 12], and numerical simulations [13; 14] to recent experimental works [15; 16; 17; 18; 19]. The whole SSI system can be tested using a shaking table to simulate seismic excitation [17; 20; 21; 22]. Centrifuge tests [23; 24; 25], and forced vibration tests [26; 27; 28; 29; 30] are also used to study the SSI system. Shaking table tests and centrifuge tests have some limitations. In shaking table tests, the soil stress level is lower than that of the prototype soil because superstructures can only use small-scale models and the model size creates significant scaling effects, which results in different dynamic responses in the prototype soil and the model soil. By increasing the field acceleration of the model in the centrifuge test, the soil stress level can be simulated as equal to or close to that of the prototype soil. However, most current centrifuge equipment cannot carry out large-scale model tests, so the model size effect in centrifuge tests needs more attention [31]. Forced vibration tests cannot adequately capture the radiation of energy away within the relatively small dimensions of laboratory models ([PERSON] et al., 2015). There are many cases where seismic loading produced nonlinear SSI responses ([PERSON] et al., 2015; [PERSON] et al., 2015; [PERSON] et al., 2015). However, the forced vibration field test of shallow foundations did not cause a nonlinear soil response, which led to a substantial change in the soil properties relative to those for small-strain (elastic) conditions. Forced vibration tests are affected by field test conditions. Given the limited test conditions of these three test methods, there is another alternative test method, the substructure pseudo-dynamic test, which was first proposed in 1985 ([PERSON] et al., 2015). The whole system is divided into two coupled parts. One part is called the experimental substructure and is a particularly interesting or strong nonlinear structure in the whole structural system, which can be easily damaged by an earthquake. The rest of the system is called the numerical substructure. At present, many countries and regions have built networked laboratories for substructure pseudo-dynamic tests, for example the network for earthquake engineering simulation (NEES) in America ([PERSON] et al., 2015; [PERSON] et al., 2015), the distributed hybrid experiments at Kyoto University in Japan ([PERSON] et al., 2015; [PERSON] et al., 2015), the internet-based simulation for earthquake engineering (ISEE) developed by the National Center for Research on Earthquake Engineering (NCREE) in Taiwan ([PERSON] et al., 2015; [PERSON] et al., 2015; [PERSON] et al., 2015), and the networked structural laboratories (NetSLab) studied by Hunan University in China ([PERSON] et al., 2015; [PERSON] et al., 2015). A large number of studies have used this method to study structural dynamic responses ([PERSON] et al., 2015; [PERSON] et al., 2015), but most studies did not consider the effect of soil-structure interaction. With the development of this test method, few substructure pseudo-dynamic tests referred to the study of soil-structure interaction.