Exploring explicit formula for shear transfer strength of concrete joints using dictionary learning

Shear transfer strength (STS) is a critical mechanical property of cast-in-place concrete joints (CCJs) widely used in engineering structures. However, its calculation by existing formulas still lacks accuracy and stability, partly due to inadequate CCJ parameters and insufficient data. This study aims to discover a more accurate and stable formula in an explicit form by considering more CCJ parameters using a machine learning algorithm called constrained probabilistic dictionary learning (CPDL). The “dictionary” means the establishment of a customized dictionary based on the mechanical knowledge of the STS of the CCJs. The “constrained” represents coefficient restriction and data treatments to improve the stability of the formula. The “probabilistic” stands for the ensemble-based technique to transform the formulas into a probabilistic scheme with confidence intervals. The performance of the discovered formulas was compared with seven existing mechanistic formulas and were systematically evaluated through assumption check, contribution rank, coefficient confidence, and sensitivity analysis to verify their feasibility. Results show the discovered formulas achieved better accuracy with lower variance compared with existing formulas while maintain the unit consistency. Contribution ranking identifies the influential function terms in the formulas, where shear contributions of the concrete substrate, stirrups, and longitudinal bar were quantified. Posterior analysis testified the narrow distributions of the coefficients of the function term, displaying high stability. Sensitivity analysis revealed that the discovered formulas capture the trend of dominant parameters conforming to experimental results and also shed light on the trend on previously overlooked parameters like concrete aggregate size and specimen configurations.