Integrating strain-orthogonal phase-field modeling and machine learning for fracture prediction in steel fiber reinforced concrete

Abstract

This paper aims to investigate the effects of steel fiber position, inclination angle and length on the fracture behavior of steel fiber reinforced concrete (SFRC), while reducing the computational burden associated with high-fidelity phase-field fracture simulations. A computational framework integrating phase-field modeling (PFM) and machine learning (ML) is developed. A strain-orthogonal phase-field formulation is employed to simulate interfacial damage and crack propagation in SFRC across different concrete grades and fiber configurations. Based on these simulations, a dataset of 357 samples is generated, comprising peak load (Pmax), critical displacement (U) and mechanical work (W). Gradient-boosting algorithms, including CatBoost, LightGBM and XGBoost, are trained and optimized using Bayesian optimization with five-fold cross-validation to construct efficient surrogate models. The results show that CatBoost consistently provides the highest prediction accuracy, achieving test R2 values of 0.999 for peak load, 0.986 for critical displacement, and 0.942 for mechanical work. The developed ML surrogates enable near-instantaneous prediction of fracture responses, offering a substantial reduction in computational cost compared with standalone phase-field simulations. Model interpretation based on SHAP reveals that matrix stiffness and initial crack length dominate peak load, while fiber inclination plays a more significant role in post-peak mechanical work and energy dissipation. This study proposes a hybrid phase-field–machine learning framework for efficient fracture analysis of SFRC. By exploiting high-fidelity numerical simulations as a data source for surrogate modeling, the proposed approach enables rapid parametric studies and optimization of fiber-reinforced concrete systems within a computational engineering context.