To investigate the dynamic response of irregular and complex connected structure, the comprehensive soil and connected structure model was developed, which is considered the site condition of different foundation soils. This study explored on the deformation law of the connected structure, and analyzing the structural displacement, acceleration, and torsional response under various seismic conditions. The findings revealed that the presence of ground fissures significantly amplifies the dynamic response of connected structures, with a greater influence from the hanging wall. Additionally, the lag effect was observed in the generation of the peak ground acceleration (PGA) in the site model considering ground fissures, but the result surpassed those in ordinary sites. During the elastic-plastic loading stage, the study observed that the maximum inter-story displacement angle remained within the limits prescribed by specifications. Due to the varying distances between column bases of the main area and ground fissures, there is a significant magnification effect in inter-story torsional angle. The incorporation of sliding supports emerged as an effective measure in mitigating the relative displacement of connected structures, consequently reducing the translational-torsional coupling effect during rarely occurred earthquake. The research results provide reference for the seismic performance analysis of connected structures under complex site conditions.