Tensile behavior of reinforced UHPC: Effects of autogenous shrinkage and model of tensile capacity via deep learning-based symbolic regression

The tensile capacity of reinforced ultra-high performance concrete (R-UHPC) consists of two components: the tensile resistance of steel rebar and the contribution of UHPC. Although previous experimental studies have elucidated the total tensile capacity of R-UHPC, the individual contributions of UHPC and steel rebar remain unclear. Moreover, there is limited research on the influence of autogenous shrinkage on the tensile performance of R-UHPC. Therefore, this study aims to establish a model that accurately quantifies the contributions of both components and investigates the effect of autogenous shrinkage on the tensile behavior of R-UHPC. Direct tensile tests were conducted on both reinforced conventional UHPC (R-CUHPC) and reinforced low-shrinkage UHPC (R-LUHPC) specimens (with the addition of expansive agent and shrinkage-reducing agent) at reinforcement ratios of 1.7 %, 3.0 %, and 6.8 %, respectively. The results indicated that, as the reinforcement ratio increased, the first-cracking strength of R-LUHPC specimens exhibited slight fluctuations, whereas it notably decreased in R-CUHPC specimens. Additionally, autogenous shrinkage had minimal impact on the tensile capacity of R-LUHPC specimens. To tackle the challenge of quantifying the individual contributions of UHPC and steel rebar from experimental data, a deep learning-based symbolic regression method was introduced. As a result, a highly accurate model was developed to calculate the tensile capacity of R-UHPC components, incorporating 1.157 times the steel rebar's yield strength and 0.669 times the UHPC's ultimate tensile strength. Furthermore, this model reflects the load-bearing mechanism in which the steel rebar enters strain-hardening, while the contribution of UHPC does not reach its ultimate tensile strength due to the pull-out of partial steel fibers.