Numerical study on frequency limit states in seismic performance of RC bridge pier

This study presents a numerical investigation of the natural frequency of Reinforced Concrete (RC) bridge piers, which progressively decreases as seismic damage develops. The objective was to evaluate whether variations in natural frequency can reliably identify post-seismic damage states. To this end, a numerical RC bridge pier model was developed to quantify the evolution of its natural frequency across different stages of seismic performance, considering the full range of collapse mechanisms from undamaged to severely damaged conditions. Two post-seismic indicators, such as the Frequency Reduction Coefficient and the Frequency Decay Index, were defined to characterize changes in the natural frequency of bridge piers. Based on these indicators, six progressive frequency limit states were systematically established: Cracking, Yielding, Spalling, Crushing, Buckling, and Fracturing, providing a logical framework for post-seismic structural evaluation. A backbone curve of the numerical RC bridge pier was developed to assess stiffness degradation and the evolution of natural frequency during damage progression. In addition, an extensive literature synthesis was conducted to compile an experimental database to develop a baseline RC bridge pier model for comparative analysis. Results show that the natural frequency declines consistently with increasing damage, decreasing by approximately 30% from the elastic condition to the cracking stage and by nearly 70% at the fracturing stage, corresponding to overall structural collapse. The findings confirm that natural frequency thresholds can provide a systematic framework for assessing the condition of RC bridge piers after severe earthquakes. A key contribution of this study is the proposal of initial natural frequency thresholds associated with different damage levels, offering practical guidelines for bridge structural engineers. Furthermore, the compiled tables integrate experimental and numerical frequency data from multiple studies, forming a valuable reference dataset for future research on frequency-based seismic damage assessment.