Research on Fracture Energy Prediction and Size Effect of Concrete Based on Deep Learning with SHAP Interpretability Method
Fracture energy plays a pivotal role in ensuring the safe design of concrete structures. Currently, experimental testing remains the predominant methodology for exploring fracture energy in concrete. Nevertheless, this approach is hindered by protracted sample production cycles and test loading cond...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-06-01
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| Series: | Buildings |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-5309/15/13/2149 |
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| Summary: | Fracture energy plays a pivotal role in ensuring the safe design of concrete structures. Currently, experimental testing remains the predominant methodology for exploring fracture energy in concrete. Nevertheless, this approach is hindered by protracted sample production cycles and test loading conditions that contribute to elevated expenses. Moreover, owing to the complex nonlinear behavior exhibited by concrete during the fracturing process, existing empirical formulas exhibit restricted precision when forecasting fracture energy. Therefore, in order to swiftly and accurately predict the fracture energy of concrete and investigate the impact of various factors on it, this study employs a deep learning algorithm to establish the correlation between parameters and fracture energy. Additionally, an interpretable deep learning prediction model for fracture energy is proposed, which is then compared with existing empirical formulas. Finally, the SHapley Additive exPlanations (SHAP) interpretability method is utilized to interpret and analyze the prediction results. The SHAP method can identify and visualize the contribution direction (positive/negative) and magnitude of the input features and reveal the relative importance of parameters at both local and global levels simultaneously. This analysis effectively explains the decision-making mechanism of the “black box” model and significantly improves the problem of insufficient interpretability that is common in traditional machine learning methods. The findings demonstrate that over 87% of the prediction results from the deep learning model in this study exhibit a relative error of less than 10% on the test set. The model effectively captures the intricate nonlinear relationship among characteristic parameters, exhibiting superior accuracy and generalization capabilities compared to empirical formulas. The SHAP values of the input parameters are visualized to assess their influence on fracture energy: initially, fracture energy increases and then decreases with increasing compressive strength, age, and coarse aggregate proportion; fracture energy increases with increasing maximum particle size of aggregate until it reaches 20 mm, after which it stabilizes; a high water–binder ratio reduces fracture energy; within the range of 400 mm, fracture energy increases with height, exhibiting a noticeable size effect; fracture energy increases with specimen width, but the size effect diminishes beyond 150 mm width; fracture energy decreases as span–height ratio increases; seam height ratio exhibits an initial increase followed by a decrease in fracture energy, with larger ratios showing a more pronounced size effect; an increase in ligament height enhances fracture energy while maintaining a significant size effect. |
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| ISSN: | 2075-5309 |