Neural network. Game theory coupled approach for predicting flexural performance of fibre-reinforced concrete

Abstract

The addition of fibres to concrete is an effective solution for enhancing its post-cracking tensile strength (fctR). Currently, this property is characterized through high-cost and time-consuming experimental tests since no reliable analytical methods exist to predict this mechanical property. This study provides two neural networks for predicting the fctR obtained from flexural beam tests for crack mouth opening displacements of 0.50 mm (fR1) and 2.50 mm (fR3). Network architectures are obtained with an optimization process that involved training 1568 Multi-Layer Perceptron configurations under Monte Carlo cross-validation over 50 iterations, with a total of 78,400 trainings for each fR,i. The resulting models were evaluated using performance metrics including Coefficient of Determination (R2), Correlation Coefficient (CC), Mean Absolute Error (MAE), Root Mean Square Error (RMSE) and Scatter index (SI). High predictive accuracies were achieved for both fR1 (R2 = 0.87, CC = 0.93, MAE = 0.64 MPa, RMSE = 0.90 MPa, SI = 19.2%) and fR3 (R2 = 0.85, CC = 0.92, MAE = 0.73 MPa, RMSE = 0.95 MPa, SI = 19.8%). Furthermore, the analysis of their global and local interpretability through the game-theory-based SHAP explanation method confirms their consistency with established understandings of fibre-reinforced concrete (FRC) behaviour. Moreover, numerical expressions are proposed as an alternative to traditional testing methods, offering a tool to predict the flexural post-cracking tensile strength for pre-design and quality control purposes of FRC structures. These approaches are deemed essential for advancing FRC technology marking a significant advancement in addressing the design limitations and widespread application challenges associated with the material.