Predicting critical crack propagation length in sustainable additive-enhanced concrete using explainable machine learning

Abstract

Predicting the critical crack propagation length (CCPL) of sustainable additive-enhanced concrete (SAEC) is a significant challenge in structural durability analysis and fracture mechanics. Experimental and numerical techniques often face limitations of complexity, cost, and computational inefficiency. To overcome these limitations, this paper presents a comprehensive machine learning framework that integrates ensemble, kernel-based, and deep learning models. A high-quality experimental dataset of 800 SAEC samples, incorporating nine key features and controlled curing, mixing, and fracture testing, was prepared. Model performance was evaluated using different statistical indices under both hold-out and k-fold cross-validation. Among all the machine learning models, the novel Neural Tangent Kernel Gaussian Process (NTK-GP) achieved the best predictive performance with R² = 0.95‒0.96, RMSE = 0.74‒0.90 mm, MAPE = 0.09‒0.14, and VAF = 0.95‒0.96. The NTK-GP's hybrid architecture, which unites the flexibility of neural representations with Bayesian uncertainty quantification, enabled accurate, smooth, and stable predictions even under nonlinear, high-dimensional data. Statistical significance tests, such as the Friedman and Nemenyi tests, confirmed that the NTK-GP is statistically comparable to several state-of-the-art models. Explainable AI analysis using SHAP revealed that fiber type (FT) and fiber volume content (FVC) are the most influential features, accounting for over 65% of the model's variance in CCPL. SHAP interaction and dependency plots showed strong combined influences between FT and FVC, especially with steel and basalt fibers at higher volumes. This supports the idea that these fibers bridge cracks and dissipate energy. Bootstrap-based 95% confidence intervals were applied for uncertainty quantification, confirming the predictive reliability by showing consistent coverage across the dataset. This study pioneers the use of NTK-GP for fracture mechanics. It demonstrates that integrating explainable machine learning with uncertainty-aware regression provides a data-efficient, robust, and interpretable alternative to experimental and numerical methods. The proposed framework not only enhances CCPL prediction accuracy and computational efficiency but also contributes to the broader goal of designing sustainable, fracture-resistant concrete materials through intelligent and data-driven modeling.

Keywords: Critical crack propagation length; Machine learning; Statistical analysis; Sustainable additive-enhanced concrete; Uncertainty quantification.

Fig. 1

Detailed laboratory arrangement illustrating materials, equipment, and specimen preparation steps for SAEC specimens.

Fig. 2

Three-point bending test.

Fig. 3

Box plots of the numerical features (a) before and (b) after outlier removal.

Fig. 4

Pearson correlation matrix of the numerical parameters.

Fig. 5

Distance correlation scores with target variable (CCPL).

Fig. 6

Feature selection using FeatureCuts‒PSO technique.

Fig. 7

NTK-GP training curve.

Fig. 8

Comparison of machine learning algorithms’ performance in predicting the CCPL of SAEC using statistical evaluation criteria.

Fig. 9

Residual plots of all machine learning models during the hold-out validation phase.

Fig. 10

CD diagram of machine learning models.

Fig. 11

Force plot for a local interpretation of three sample points using the NTK-GP model.

Fig. 12

Total sensitivity index of input parameters on the NTK-GP model.

Fig. 13

Grouped SHAP feature importance analysis for the NTK-GP model.

Fig. 14

SHAP heatmap based on the NTK-GP model.

Fig. 15

Global SHAP values based on the NTK-GP model.

Fig. 16

SHAP dependency and interaction plots based on the NTK-GP model.

Fig. 17

NTK-GP predictions with bootstrapped 95% CIs.