Risk$-$based bridge management involves theoretical considerations of assessing, prioritizing, and managing risks associated with the condition, performance, and functionality of bridge infrastructure assets. Develop a comprehensive theoretical framework elucidating principles of risk$-$based bridge management methodologies, including deterioration modeling, consequence assessment, and risk mitigation strategies. Explore theoretical models for evaluating bridge risks, such as bridge condition rating systems, structural health monitoring data, and consequence analysis techniques, and discuss theoretical approaches to optimizing bridge maintenance, repair, and rehabilitation decisions, aiming to enhance bridge safety, resilience, and serviceability while maximizing asset value and lifecycle performance.