Simplified Predictive Expressions of Drift Limit States for Reinforced Concrete Circular Bridge Columns

A critical component of performance-based design (PBD) is the quantification of damage states in terms of engineering demand parameters (EDPs). One of the most widely used EDPs to define damage states of reinforced concrete bridge columns is the drift ratio. Here, a fiber-based numerical model was validated by comparing its damage predictions against experimental results for large-scale tests of reinforced concrete columns subjected to reversed cyclic loading. The Monte Carlo sampling technique was adopted to generate 1,000 well-confined and flexure-dominated concrete columns, each having a unique combination of aspect ratio, axial-load ratio, longitudinal and spiral reinforcement ratios, and concrete and reinforcing steel yield strengths. The columns were analyzed numerically under static pushover loading, and the drift ratios corresponding to various strain limits were recorded. The resulting data were fit to mathematical expressions through machine learning–based symbolic regression. The proposed simplified expressions well predicted the drift ratios obtained from the numerical analysis with a minimum square of the correlation coefficient of 0.88. Also, the predicted drift ratios from the proposed expressions were comparable to those measured experimentally at key damage states, such as concrete cover spalling, concrete core crushing, and bar buckling. In particular, the predictions of the proposed expression at rebar buckling, which was based on a reinforcing steel tensile strain of 0.05, were more accurate than two widely used expressions found in the literature. Finally, the application of the proposed expressions within the context of PBD was demonstrated by a numerical example. The proposed simplified expressions are not intended to replace pushover or nonlinear time history analyses as part of the PBD, but rather provide approximate predictions of the limit states, which would significantly facilitate the development of appropriate preliminary designs, especially at early design stages. In addition, since the predictions of the proposed expressions were validated using previous experimental data, they can serve as a benchmark for the bridge engineering community when determining the limit states of reinforced concrete columns through numerical analyses.