Theoretical investigation on the impact effect in dynamic analysis of self-centering pier system based on the Hertz contact-pounding model

The self-centering (SC) pier system exhibits different mechanical behaviors under an earthquake compared with that in quasi-static experiments, especially the impact effect on the rocking interface. Published theoretical analysis and experiments had indicated that the impact events significantly affected the rocking motion, including extra energy dissipation, greater contact stress, and even more serious damage. To describe the impact mechanism more clearly and obtain the impact responses more directly, this study investigates a dynamic theoretical model considering the impact effect and its influences on the seismic responses and rocking interface. First, a dynamic theoretical model based on the Hertz contact-pounding model specific to the SC pier system is proposed, and the impact mechanism is described in detail. Subsequently, dynamic motion equations considering the impact effect are derived. The key parameters of the contact-pounding element (stiffness K-Hertz and damping C-Hertz) that significantly affect the impact process are presented. The accuracy of the proposed theoretical model is verified by test data and a finite element model (FEM). Finally, the influences of the key parameters (K-Hertz and C-Hertz) on the impact force are analyzed, and the impact effect on the rocking interface is investigated. The results indicate that the impact effect significantly increases the vertical acceleration and contact stress, particularly under near-fault earthquakes. This may cause unexpected damage on the rocking interface and should be an important consideration in the optimize design of SC pier system.