Prediction of Plate End Debonding of FRP-Strengthened RC Beams Based on Explainable Machine Learning

Abstract

This research explores the phenomenon of plate-end (PE) debonding in reinforced concrete (RC) beams strengthened with fiber-reinforced polymer (FRP) composites. This type of failure represents a key mechanism that undermines the structural performance and efficiency of FRP reinforcement systems. Despite the widespread use of FRP in structural repair due to its high strength and corrosion resistance, PE debonding—often triggered by shear or inclined cracks—remains a major challenge. Traditional computational models for predicting PE debonding suffer from low accuracy due to the nonlinear relationship between influencing parameters. To address this, the research employs machine learning techniques and SHapley Additive exPlanations (SHAP), to develop more accurate and explainable predictive models. A comprehensive database is constructed using key parameters affecting PE debonding. Machine learning algorithms are trained and evaluated, and their performance is compared with existing normative models. The study also includes parameter importance and sensitivity analyses to enhance model interpretability and guide future design practices in FRP-based structural reinforcement.

1. Introduction

Fiber-reinforced polymers (FRP) are characterized by their low weight, high tensile strength, and excellent resistance to corrosion, which has led to their widespread adoption in the retrofitting and strengthening of existing concrete structures [1,2]. Despite these advantages, numerous experimental investigations have demonstrated that although externally bonded FRP can effectively increase the load-carrying capacity of reinforced concrete (RC) beams, the material’s linear elastic behavior often contributes to premature debonding failures. This tendency significantly hampers the full utilization of FRP’s potential in structural applications [3,4,5]. In flexurally strengthened FRP RC beams, two primary debonding failure mechanisms are commonly observed: plate end (PE) debonding and intermediate crack (IC) debonding. In members with shorter shear spans—where the influence of bending moments is minimal and shear forces dominate—PE debonding is more likely to occur. This type of failure can manifest in two distinct forms: separation of the concrete cover and debonding at the interface near the plate end [6,7]. End-of-plate interfacial debonding typically occurs under specific conditions, such as when the FRP plate is significantly narrower than the width of the reinforced concrete beam. As a result, concrete cover separation is generally recognized as the more prevalent form of PE debonding. When the FRP reinforcement is positioned close to the support, the detachment of the concrete cover is mainly triggered by shear cracks initiating near the FRP terminus. With increasing load, these cracks propagate and induce both vertical and horizontal deformations in the beam, leading to the development of shear and normal stresses along the interface. As these stresses accumulate and the cracks extend to the level of the tension steel reinforcement, the concrete cover layer eventually separates. Conversely, when the FRP end is located at a greater distance from the support, inclined cracks tend to develop within the shear region. Upon reaching the level of the tensile reinforcement, these cracks begin to spread horizontally, ultimately resulting in the splitting of the concrete cover [8,9,10,11].

To overcome the limitations imposed by PE debonding in FRP-strengthened structures, end anchoring techniques are commonly applied to enhance the bond performance and prevent premature failure. Developing an efficient anchorage system requires a clear understanding of the shear strength at the point where PE debonding initiates. To this end, numerous studies and design guidelines have proposed different analytical models aimed at predicting PE debonding behavior. These models typically consider factors such as the shear capacity of the concrete beam and the strain level in the FRP at the onset of delamination. Such approaches provide a basis for evaluating the effectiveness of end anchorage solutions and improving the overall performance of FRP-strengthened RC beams [8,9,10,11,12,13]. However, owing to the intricate structural behavior of FRP-strengthened RC beams and the highly nonlinear interaction between PE debonding and influencing parameters, many of the existing models face challenges in terms of computational accuracy and reliability. As a result, developing a more accurate and robust nonlinear relationship that captures the complex dependencies between PE debonding and its contributing factors has become a crucial step toward improving predictive performance and supporting more effective design approaches.

In recent years, machine learning, particularly explainable machine learning, has been widely used in civil engineering [14]. Gharagoz et al. proposed an optimization framework for seismic retrofitting that combines eXtreme Gradient Boosting (XGBoost) with the Spring-Rotational Friction Damper (SRFD) system, and introduced explainable AI (XAI) methods to enhance model transparency, achieving data-driven design optimization tailored to specific seismic risks [15]. Zhu et al. proposed a method for predicting the shear bearing capacity of FRP-concrete interfaces based on explainable machine learning, employing eight algorithms including XGBoost combined with mechanically inspired feature engineering, and utilizing SHAP technology to achieve model explanation [16]. Li et al. proposed an explainable machine learning model based on XGBoost and SHAP technology for predicting the axial bearing capacity (Pmax) of FRP-constrained rusted reinforced concrete columns. The model was constructed using 285 experimental data points, covering 20 key input parameters, and feature importance analysis and model interpretation were achieved using the SHAP method [17]. Chu et al. constructed four machine learning models (Random Forest (RF), Support Vector Regression (SVR), Gradient Boosting Decision Tree (GBRT), and XGBoost) based on 198 sets of experimental data to predict the compressive strength of CO₂-cured concrete, and combined the SHAP method to enhance model explainability [18]. Yan et al. addressed the inaccuracy and instability issues of existing empirical formulas in predicting the shear bearing capacity of flat beam structures made of FRP-reinforced concrete without shear reinforcement. They collected 165 sets of experimental data and introduced eight key variables to establish four models: Back Propagation Artificial Neural Network (BPANN), SVR, RF, and GBRT. By combining the SHAP and (Partial Dependence Plot) PDP methods to interpret the models, it was revealed that effective plate height and column cross-sectional width-to-height ratio are the key factors influencing shear strength [19].

The subsequent procedures of this study are as follows: The second part is database construction, including parameter selection and analysis. The third part is model construction and evaluation, including the use of data collected in the second part in combination with machine learning methods to construct predictive models, evaluation of the normative recommendation model, and parameter importance and sensitivity analysis using SHAP. The fourth part is conclusions, including a summary of machine learning models, normative recommendation models, parameter analysis, and research shortcomings.

2. Database Construction

2.1. Parameter Selection

Researchers have conducted extensive experimental studies on parameters affecting PE debonding in FRP-reinforced RC beams. Ritchie et al. found that the higher the ratio of FRP width to beam width, the lower the shear force at debonding failure [20]. However, Quantrill et al. observed the opposite; in their experiments, as the ratio of FRP width to beam width increased from 0.3 to 0.8, the end shear force at PE failure increased from 12.3 kN to 17.0 kN [21]. Arduini et al. investigated the effect of FRP stiffness on shear force at debonding, finding that as FRP stiffness increased (from 217 to 434), the end shear force at PE failure decreased (from 55 kN to 45 kN) [22]. In contrast, Beber et al. reported the opposite trend. In their test on four beams, the end shear forces at PE failure were 51.1 kN and 50.3 kN for FRP stiffness of 101.2, and 62.1 kN and 62.0 kN for stiffness of 177.1 [23]. Similarly, David et al. reached the same conclusion. In tests on four FRP-strengthened beams, when FRP stiffness was 180, the shear forces at PE failure were 68.0 kN and 71.1 kN, whereas for stiffness of 360, they were 78.0 kN and 79.5 kN [24]. Additionally, Valcuende et al. studied the influence of concrete strength on PE failure, showing that as concrete strength increased from 39.5 MPa to 41.6 MPa, the end shear force at failure decreased from 39.3 kN to 35.1 kN [25]. Likewise, Hasnat et al. observed a similar trend, with shear force decreasing from 50.8 kN to 50.0 kN as concrete strength increased from 47.5 MPa to 48.3 MPa [26]. However, Gao et al. found that increasing concrete strength from 47.8 MPa to 62.1 MPa resulted in an increase in end shear force at PE failure, rising from 58.1 kN to 68.0 kN [27]. These results indicate that the relationship between various parameters and PE debonding is complex, and experimental studies alone cannot fully reveal the underlying mechanisms of PE failure.

2.2. Parameter Analysis

Based on the keywords “FRP”, “RC”, and “ plate end debonding”, a search was conducted in the Web of Science. Considering standards and data availability [6,8,9,10,11,20,21,22,23,24,25,26,27], nine parameters were selected for this study: concrete strength, the ratio of anchorage length to shear span, tensile reinforcement yield strength, stirrup yield strength, stirrup reinforcement ratio, ultimate strength of FRP, FRP stiffness, the ratio of FRP width to beam width, and the shear force at the onset of intermediate end debonding failure. A comprehensive database comprising 128 datasets of FRP-strengthened RC beams experiencing plate end debonding was established. The distribution of these parameters is illustrated in Figure 1 using histograms overlaid with density curves, while

Table 1. Statistical characteristics of parameters.

	Min	Max	Mean	25%	50%	75%	Standard Deviation
f’c	19.2	66.4	41.5	33.6	41.8	49.2	10.53
Lua/a	0.47	1.31	0.89	0.68	0.97	1	0.20
fy	350	611	490	427	506	562	79.06
fyv	235	738	435	350	420	537	113.50
ρsv	0.11	1.68	0.65	0.43	0.64	0.9	0.30
ffu	160	4519	3005	2400	3425	3792.5	1077.77
Eftf	25.4	434.2	128.1	77.5	96.11	187.2	82.81
bf/b	0.3	1	0.77	0.6	0.71	1	0.20

summarizes their statistical characteristics.

As shown in Figure 1, the parameters exhibit a wide range of distributions, which to some extent ensures the generalization capability of subsequent machine learning models. The compressive strength (f’_c) of concrete ranges from 21 MPa to 70 MPa (approximate values). The distribution exhibits a unimodal shape, with the main peak located in the 40–45 MPa range, and frequencies gradually decreasing on both sides. The data are concentrated in the 30–55 MPa range, accounting for over 80% of the total count. Samples in the low-strength zone (<25 MPa) and high-strength zone (>60 MPa) are scarce, containing only 2–4 data points each. The overall distribution is approximately symmetric, but shows a slight right-tail extension on the high-strength side (>55 MPa). The peak of the L_ua/a ratio occurs around 1.0. The data exhibit characteristics of an approximately normal distribution: it shows a monotonically increasing trend from 0.4 to 0.8, and a monotonically decreasing trend from 1.0 to 1.4. The measured yield strength of the tension reinforcement (f_y) ranges from 350 to 611 MPa. The distribution exhibits a pronounced unimodal pattern, with the peak concentrated in the 550–575 MPa range, indicating that this strength interval represents the typical yield strength of the samples. Additionally, the frequency declines rapidly in the low-strength region (350–450 MPa), with fewer than 5 samples, while a slight right skew is observed in the high-strength region (>575 MPa), where a small number of samples are still present at 611 MPa. The yield strength data of stirrups (f_yv) ranges from 235 to 738 MPa, with the main peak of the distribution located near 400 MPa (peak frequency of 25), and approximately 80% of the samples are concentrated in the 300–500 MPa. Additionally, the low-strength tail (<300 MPa) shows a gradual decline, with a small number of samples still present at 235 MPa, while the high-strength region (>600 MPa) exhibits a significant right skew. The stirrup reinforcement ratio (ρ_sv) ranges from 0.1% to 1.68%, exhibiting a right-skewed distribution. The main peak is located near 0.8%, and approximately 80% of the samples are concentrated in the 0.4–1.2% range. Additionally, the frequency drops sharply in the low-reinforcement region (<0.4%) to fewer than 10, with 0.1% representing the lower bound of the distribution. In the high-reinforcement region (>1.2%), the decline is gradual, with a small number of samples still present at 1.6%. The ultimate tensile strength of FRP (f_fu) ranges from 160.6 to 4519 GPa. The main peak is located in the 3500–4000 GPa range, and approximately 75% of the samples are concentrated within the 2500–4500 GPa range. Additionally, the frequency drops sharply in the low-strength region (<2000 GPa) to fewer than 10, with 160.6 GPa representing the lower bound of the distribution. In the high-strength region (>4000 GPa), the decline is gradual, with a small number of samples still present at 4519 GPa. The stiffness of FRP (E_ft_f) ranges from 25.4 to 434.2 GPa. The main peak is located in the 50–100 GPa range, and approximately 70% of the samples are concentrated within the 25–150 GPa range, indicating that low-stiffness FRP materials dominate. Additionally, the frequency drops sharply below 50 GPa, with 25.4 GPa representing the lower bound of the distribution, while a long tail extends beyond 150 GPa, with a small number of samples still present in the 300–400 GPa range. This histogram shows the statistical distribution of the ratio of FRP width to beam width (b_f/b). The measured data range from 0.3 to 1.5, exhibiting a multimodal distribution. The main peak is located in the 0.8–1.0 interval, with secondary peaks appearing in the 0.4–0.6 and 1.2–1.4 intervals. Additionally, the overall distribution is approximately symmetric, but the cumulative frequency in the 1.0–1.5 range is slightly higher than that in the 0.3–0.8 range. Furthermore, to avoid potential information overlap among parameters during the machine learning modeling process, Figure 2 presents a correlation heatmap indicating the relationships between different parameters. It can be observed from Figure 2 that the correlations among the parameters are relatively low (all below 0.5), indicating minimal redundancy of information. This makes the selected parameters suitable as inputs for subsequent machine learning modeling.

3. Model Construction and Evaluation

3.1. Ensemble Learning Models

In this section, we employ four ensemble learning models—RF, GBDT, Light Gradient Boosting Machine (LightGBM), and XGBoost—for model construction. The data utilized for these models consists of 128 experimental datasets collected in the second part of the study, with 80% allocated to the training set and 20% reserved for the test set. Hyperparameters for the models were optimized using grid search combined with ten-fold cross-validation.

The performance of different models on the training and test sets is shown in

Table 2. The performance of different models on the training and test sets.

	Training				Test
Models	R2	MAE	RMSE	MAPE	Models	R2	MAE	RMSE	MAPE
RF	0.85	6.05	10.7	13.80%	RF	0.79	11.05	19.35	16.60%
GBDT	0.97	3.12	4.31	8.10%	GBDT	0.903	7.55	13.11	15.50%
LightGBM	0.9811	2.96	3.88	7.90%	LightGBM	0.87	8.79	15.13	16.40%
XGBoost	0.9873	2.05	3.1764	5.50%	XGBoost	0.906	7.15	12.93	14.10%

. The predicted and experimental values for each machine learning model are shown in Figure 3. As can be seen from Figure 3, the RF model performs the poorest among all the machine learning models considered, with the greatest deviation between predicted and experimental values. The performance of the other three models—GBDT, LightGBM, and XGBoost—is relatively close, though XGBoost slightly outperforms both GBDT and LightGBM.

Further analysis is provided in Figure 4, which illustrates the performance of different models on both the training and test sets using various evaluation metrics. It is evident that RF exhibits significantly poorer performance on the training set compared to the other three models, as indicated by its lowest goodness-of-fit (R²), highest mean absolute error (MAE), and root mean square error (RMSE). On the training set, XGBoost achieves the lowest MAE and RMSE, but its R² is comparable to that of GBDT and LightGBM, being marginally higher. Similar patterns are observed on the test set, where XGBoost remains the best-performing model. However, it is noteworthy that the performance of all models declines to some extent on the test set compared to their performance on the training set.

In conclusion, among all the machine learning models evaluated, XGBoost is the most suitable for predicting PE debonding failure in FRP-strengthened RC beams. This model demonstrates superior accuracy and robustness, making it a valuable tool for understanding and predicting the complex behavior of FRP-strengthened structures under various conditions.

3.2. Model Recommended by Codes

To highlight the superiority of the XGBoost model constructed in this study, we compared its performance with recommended models from various international codes based on the data collected in Section 2. The distribution of calculated values from these recommended models versus experimental values is shown in Figure 5. According to Figure 5, among all the codes, the CNR-recommended model exhibits the highest R² and the smallest coefficient of variation (Cov) between the calculated and experimental values. In contrast, the ACI-recommended model proves to be overly conservative, with all calculated values falling below 85% of the experimental values. The AS-recommended model tends to overestimate the end shear force at the time of PE failure for strengthened beams.

Moreover, it is evident that the XGBoost-based prediction model for PE debonding failure in FRP-strengthened RC beams developed in this study achieves the highest R² (0.95) and a low Cov (12.4%).

3.3. Parameter Study

From the analysis in Section 3.1 and Section 3.2, it is evident that the XGBoost model constructed in this study is most suitable for predicting PE debonding failure in FRP-strengthened RC beams. Consequently, this section employs SHAP in conjunction with XGBoost to conduct parameter importance and sensitivity analysis [28]. The parameter importance ranking based on mean absolute SHAP values is shown in Figure 6.

As illustrated in Figure 6, the yield strength of tensile reinforcement has the greatest impact on PE debonding failure, followed by the stiffness of the FRP, and then the ratio of anchorage length to shear span. The importance of concrete strength, stirrup reinforcement ratio, and yield strength of stirrups in influencing PE failure are relatively similar, indicating comparable roles in the failure mechanism. Moreover, the ratio of FRP width to beam width has the least influence on PE debonding failure among the parameters considered. It should be noted that in the end debonding failure of FRP-strengthened concrete beams, the influence of steel yield strength (fy) is often considered the most significant. This is not because fy acts directly on the debonding interface, but because it determines the timing of steel yielding. A lower yield strength causes the steel to yield earlier, accelerating crack development and beam deformation. This significantly increases stress concentration at the ends of the FRP, thereby triggering debonding failure prematurely. Consequently, fy exerts a high level of influence in predictive models by controlling the overall loading process and the sequence of failure events.

This detailed analysis not only underscores the critical parameters affecting PE debonding but also provides valuable insights for optimizing the design and strengthening strategies of FRP-reinforced concrete structures. Utilizing these findings can lead to more effective and reliable structural enhancements, minimizing the risk of premature failure and improving overall structural performance. In this study, the yield strength of the reinforcement, the stiffness of the FRP, and the ratio of anchorage length to shear span length have significant influences on PE failure. These three parameters should be given particular consideration in future strengthening designs.

The parameter sensitivity analysis based on SHAP values is depicted in Figure 7. In this figure, points to the right of the vertical axis indicate a positive influence of the parameter on PE debonding failure, while points signify a negative influence. The color scale represents the magnitude of the feature, with red indicating high values and blue indicating low values. Taking FRP stiffness as an example, most points to the right of the axis are red, suggesting that as the stiffness increases, the end shear force at which PE debonding occurs also increases. This implies that higher FRP stiffness leads to greater resistance against PE debonding under similar conditions.

Conversely, for the ratio of anchorage length to shear span, most points to the right of the axis are blue. This indicates that as the ratio increases, the end shear force at which PE debonding occurs decreases, meaning that with a larger ratio, PE debonding is more likely to happen under the same conditions.

3.4. Graphical User Interface

The Graphical User Interface (GUI) is a way that allows users to interact with electronic devices through graphical elements such as windows, icons, buttons, and other visual indicators. Compared to text-based user interfaces or command-line interfaces, a GUI provides a more intuitive and user-friendly method for operating software applications and operating systems. For non-technical users, interacting directly with command lines or code can be challenging. With a GUI, users can interact with the model through an intuitive interface without needing to understand the underlying technical details.

Therefore, a GUI for PE debonding prediction was constructed in this section. As shown in Figure 8, the end shear force at the time of PE failure in FRP-strengthened RC beams can be obtained simply by inputting the required parameters.

4. Conclusions

This study established a database and developed predictive models for PE debonding failure in FRP-strengthened RC beams using ensemble learning methods. Evaluations of the models and parameter analysis using SHAP led to the following conclusions:

(1) Among machine learning models, XGBoost exhibited the best performance in predicting PE debonding failures in FRP-strengthened RC beams, achieving the highest goodness-of-fit, lowest mean absolute error, and lowest root mean square error on both training and test sets.

(2) Among the code-recommended models, the CNR-recommended model showed the highest goodness-of-fit between calculated and experimental values, along with the smallest coefficient of variation. In contrast, the ACI-recommended model was overly conservative, with all calculated values falling below 85% of the experimental values. The AS-recommended model had a tendency to overestimate the end shear force at the time of PE failure.

(3) The yield strength of tensile reinforcement had the most significant impact on PE debonding failure, whereas the ratio of FRP width to beam width had the least influence among the parameters considered.

These findings provide valuable references for the design of FRP-strengthened RC beams. However, considering that this study was based on a relatively limited set of experimental data, it is necessary to expand the database in future research to enhance the reliability and robustness of the models. This will ensure more accurate predictions and better-informed design decisions for FRP-strengthened concrete structures.