Integration of damage accumulation theories into a risk-based paradigm for assessing limit states of bridge structures

The objective of this study is to develop a risk-based approach to assessing the ultimate limit state of bridge structures by integrating fundamental theories of damage accumulation (L. M. Kachanov, Yu. N. Rabotnov, A. R. Rzhanitsyn) and substantiating a new type of ultimate limit state based on kinetic criteria. 
A comparative analysis of three classical approaches is performed: L. M. Kachanov's phenomenological theory (continuity parameter), Yu. N. Rabotnov's kinetic theory (damage parameter), and A. R. Rzhanitsyn's probabilistic method (safety characteristic).  
The physical foundations of each theory are revealed, and their advantages and limitations are demonstrated as applied to bridge construction problems. A rationale is provided for the choice of a combined model combining Yu. N. Rabotnov's kinetic equations to describe the rate of damage accumulation, the Kachanov – Rabotnov damage parameter as an integral measure of degradation, and A. R. Rzhanitsyn's probabilistic apparatus to account for the random nature of loads and strength properties.  
Specific results of the study: a modified classification of risk levels with five gradations (from ‘good’ to ‘unacceptable’) and quantitative criteria for the damage parameter and its accumulation rate is proposed; a methodology for determining indicative indicators of the limit state based on increments of relative deformations using kinetic equations of damage is developed; the limit state of the third type is substantiated as the moment of reaching a critical rate of damage accumulation (in contrast to the first type, associated with a critical value of the damage parameter, and the second type with permissible deformations), which makes it possible to identify the mode of progressive destruction before the occurrence of macroscopic defects. The developed methodology can be integrated into bridge condition monitoring systems, and the proposed criteria can be used in the development of regulatory requirements for the operation of structures under increased loads and aggressive environments.  

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