## 1 Introduction
A comprehensive pseudo-dynamic hybrid simulation system, UI-SimCor, was developed to conduct multi-platform hybrid simulation experiments on the soil-foundation-structure interaction system ([PERSON] et al., 2015), and four analysis platforms (Abaqus, FedeasLab, OpenSees, and Zeus-NL) were integrated into a versatile multi-platform analysis tool. A remotely collaborative substructure pseudo-dynamic test program for beam bridges, which considers soil-pile group interaction, was developed by the NetSLab method. A series of virtual substructure pseudo-dynamic tests on beam bridges were conducted, and the results were compared with the calculation results by SAP2000 ([PERSON] et al., 2015; [PERSON] et al., 2015). [PERSON] and [PERSON] presented a new algorithm for substructure pseudo-dynamic tests to simulate the SSI effect without using a physical soil box ([PERSON] et al., 2015). The SSI effect was considered according to numerical analysis, and an experiment for the superstructure mounted on shake tables was performed. The relative response of the superstructure was predicted using a third-order polynomial extrapolation and updated by solving the coupled equilibrium equations. Some simplified models of soil-structure interaction can be used to analyze the numerical substructure. The swaying-rocking model (SR) presented by [PERSON] and [PERSON] ([PERSON] and [PERSON], 2015) sets horizontal springs and rotational springs related to the horizontal displacement of the foundation at the structural base to simulate the movement of soil, in which the input ground vibration of the foundation is only the acceleration response of the foundation surface. It is a relatively simple calculation model, but its main disadvantage is that it cannot reflect the nonlinear problem between the soil and foundation under earthquake input and it is difficult to accurately determine the relevant parameters. [PERSON] and [PERSON] ([PERSON] and [PERSON], 1985) first proposed the Winkler foundation beam model. The pile is regarded as a beam in a soil medium, and the dynamic impedance of the soil to the pile is simulated by independent springs and dampers with continuous distribution. It is a very effective simplified model to study the dynamic interaction between the soil and piles because of its simplicity, practicality, clarity of physical concepts, and low computational requirements. However, the [PERSON] foundation beam model also has certain limitations, as the coefficient of spring and damper and the volume of soil involved in vibration have not been well solved. Therefore, many scholars have developed improvements based on the assumptions of the Winkler foundation beam model, and one of the most widely used is the Penzien model ([PERSON], 1985). The model can reflect the essential mass, stiffness, damping, non-uniformity, and nonlinearity of the layered soil characteristics in the soil and pile interaction, but the parameter determination in the model is complex. The model finds it difficult to deal with complex terrain, and the nonlinearity of soil is calculated by an approximate method. Calculation models for adjacent structures and only a structure with piled foundations considering PSSI (pile-soil-structure interaction) were established based on the [PERSON] model regarding the effects of PSSI on vibration control. Researchers [52; 53; 54] used the [PERSON] model to build the integral finite-element model of a long-span cable-stayed bridge to analyze the long-period seismic response of the bridge on the soft foundation. The PSSI model did not consider the dynamic nonlinearity of soil. An improved Penzien model by [PERSON] and [PERSON] [55] was utilized to simulate the soil-pile interaction effect considering the dynamic characteristics of the soil-pile system [56]. In the improved model, the horizontal spring stiffness between the piles and the layered soils was calculated using [PERSON]'s assumption and the Mindlin formula.