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The concept of inertia coupling terms among substructures was proposed. Based on the branch mode method, the superstructures and foundation soil of one soil-adjacent structure system were divided into different branches. The branch mode method was effectively introduced to real-time dynamic substructure testing (RTDST) by decomposing and transforming the motion equation of the entire system. It was also applied for the interaction coupling terms to exchange data between the physical and numerical substructures. This method decreased the degree-of-freedom of the linear substructure effectively and considered the effects of foundation translation and rotation on the upper structures. One system composed of two adjacent four-story steel structures (S1 and S2, respectively) and foundation soil was presented in this study. S1 was applied on a shaking table as the physical substructure, whereas the foundation soil and S2 were set as two numerical substructures and simulated in a computer. The seismic response of the entire coupling system was analyzed by real-time data exchange among substructures. Test results agree with numerical solutions. The RTDST based on the branch mode method is a feasible and reliable method for the investigation of soil-adjacent structure interaction (SASI) problems, and provides a new way to consider SASI problems in the RTDST.

Real-time dynamic substructure testing of soil-adjacent structure system based on branch mode method