Hybrid machine learning model and predictive equations for compressive stress-strain constitutive modelling of confined ultra-high-performance concrete (UHPC) with normal-strength steel and high-strength steel spirals

Stress-strain constitutive model for confined ultra-high-performance concrete (UHPC) plays a pivotal role in the design and modelling of UHPC structures. However, while extensive research exists on the stress-strain responses of unconfined UHPC, a notable dearth of studies focuses on the stress-strain constitutive model for confined UHPC. Accordingly, this study introduces a novel hybrid machine learning (ML)-based stress-strain constitutive model for UHPC confined with normal-strength steel (NSS) or high-strength steel (HSS) spirals. Given the limited experimental data available, a numerical model was developed and validated against experimental results of confined UHPC. Subsequently, it was employed to generate a comprehensive dataset of confined UHPC stress-strain responses, which were then used to train the hybrid ML model. Hyperparameters of the model are subsequently optimized using Optuna along with a cross-validation technique. The optimized hybrid ML model exhibited exceptional accuracy in predicting the stress-strain response of confined UHPC with NSS or HSS spirals, as demonstrated by high coefficients of determination (R2) values ranging from 0.905 to 0.999 and low error metrics across varying stress levels and datasets. Moreover, the capability of the model to simultaneously predict both stress and strain responses was further validated through canonical correlation analysis (CCA). The results of the analysis demonstrated robust predictive performance of the model, with high CCA scores that ranged between 93.3% and 99.4%. To facilitate the practical implementation of the model, an end-to-end interactive software tool is developed. In addition, this study proposes predictive equations for the peak and ultimate stress-strain responses of confined UHPC. The evaluation of the developed predictive equations demonstrates their efficacy in accurately predicting the stress-strain responses of confined UHPC, as evidenced by the high R2 values, which ranged from 83–91%.