Our study focuses on the dynamic transient analysis of arched beam bridges over rivers, which face unique geohazards and challenges, including vibrations and dynamic loads that can affect structural integrity. The finite element software ANSYS v. 19.3 was employed to assess acceleration time histories at various bridge positions. Using MATLAB, we conducted wavelet packet decomposition to extract insights from the data, specifically isolating river-induced influences. In this article, the introduction of the wavelet packet rate index (WPERI) is presented as a novel metric for the detection of cracks in the curved bridge segments over rivers. The WPERI proves reliable in accounting for the river environment’s impact on structural integrity. Our findings highlight the sensitivity and precision of the WPERI in accurately detecting cracks and vulnerabilities in these riverine bridges. By combining WPT, finite element analysis, and signal decomposition, our research offers insights into tailored crack detection methods for riverine bridges. This study underscores the potential of WPT as a tool for identifying and characterizing cracks in curved bridge elements over rivers. The innovative WPERI provides a holistic approach to addressing structural issues, thus enhancing bridge durability amid changing environmental conditions. It contributes significantly to structural engineering and paves the way for the further exploration of river-specific crack detection techniques.