1. Introduction
Steel corrosion greatly affects reinforced concrete structures, especially in harsh environments. In the United States, approximately one in seven bridges suffers from severe steel corrosion, resulting in annual expenditures of approximately USD 4 billion for maintenance and repairs [
1,
2]. These repairs not only incur high costs but also affect the performance of structures and cause public inconvenience due to the necessary closure of roads and buildings. These disturbances can cost up to ten times as much as corrosion repairs [
2]. As a result, there is a growing interest in exploring alternatives to traditional steel reinforcement, with fiber-reinforced polymer (FRP) composites emerging as a promising solution. FRP, known for its cost-effectiveness, high tensile strength, lightness, and resistance to corrosion, stands out against conventional steel [
3]. However, its adoption is limited due to its brittleness, lower elasticity, and higher initial costs [
3]. As a result, extensive research is being conducted on the structural performance of RC elements using various FRP types, such as glass, carbon, aramid, and basalt FRP. These studies aim to ensure the safety and efficiency of RC structures with FRP reinforcement and to develop comprehensive design guidelines for its wider application [
4,
5,
6,
7,
8,
9,
10].
Numerous experimental investigations have been conducted to decipher the factors influencing the structural performance of concrete beams, columns, slabs, and bridge decks reinforced with FRP. Key factors critically affecting the estimation of punching shear strength in FRP-reinforced concrete slabs include stiffness of FRP in bending and FRP–concrete bonding behavior [
11], strength characteristics of concrete [
12], dimensions of column and slab thickness [
13], proportion of FRP reinforcement [
14], arrangement of FRP within the slab [
11], and span length to depth ratio [
15]. The complexity of these parameters significantly complicates the use of traditional methods and formulas in accurately determining the punching shear capacity when FRP bars are incorporated.
The development of a punching shear strength formula for FRP bars is an ongoing task, evolving alongside the application of design codes. Studies are underway to enhance prediction formulas for FRP-reinforced concrete slabs, adapting methods from steel-reinforced slabs and considering the test-to-prediction ratio [
11,
15,
16,
17,
18]. Furthermore, several studies have focused on using the modulus ratio (the ratio of the elastic modulus of FRP bars to steel bars) to enhance precision [
19,
20,
21]. This approach has led to modified code formulas that incorporate the modulus ratio, drawing on standards like ACI 318-14 [
22] and ACI 440-98 [
20]. Drawing from a theoretical examination of the interaction between moment and shear in slabs, Theodorakopoulos and Swamy developed a model to determine the resistance to punching shear in slabs reinforced with FRP [
23]. Meanwhile, Nguyen-Minh and Rovnak [
24] introduced a prediction model grounded in fracture mechanics, effectively incorporating the impact of the span-depth ratio and dowel action. More recently, Ju et al. [
25] formulated a predictive equation utilizing both deterministic and probabilistic approaches for estimating the punching shear strength in slab–column connections reinforced with both FRP and steel. Due to the diversity in the forms of these existing design equations, which are based on different parameters, there is a notable range in the accuracy of their predictions, with some showing low precision. Consequently, there is ongoing research interest in refining and producing more accurate and consistent design methodologies for assessing the punching shear capacity in FRP–RC slab–column connections.
In recent years, the application of machine learning (ML) in predicting the structural behavior of fiber-reinforced polymer (FRP) concrete slabs has gained great interest in the field of civil engineering [
26,
27,
28,
29,
30]. A variety of studies have demonstrated the effectiveness of these ML models in enhancing the accuracy of predictions compared to traditional methods. One notable development is the development of a hybrid ML model that integrates the capabilities of a least squares support vector machine (LS-SVM) and the firefly algorithm [
30]. This model has shown significant improvement in predicting the shear capacity of FRP-reinforced panels, significantly reducing prediction errors and outperforming traditional methods. To further contribute to this field, the joint reinforcement tree model, as developed in one study, excelled in predicting the behavior of slab–column connections with FRPs [
31]. This model has high prior accuracy and low error rates and consistently exceeds the accuracy of ML and other traditional models. Another innovative approach involves the use of adaptive reinforcement in ML to enhance the prediction of shear strength in FRP-reinforced concrete slabs [
28]. This technique has proven to be more accurate than existing models and codes. Additionally, it includes SHapley Additive exPlanations (SHAP) analysis to better understand the factors that influence its forecasts and to provide some mechanical interpretation of the resulting outcomes. The use of XGBoost in ML algorithms was also an important step forward [
29]. It has demonstrated superior performance in accurately predicting the punching shear strength of FRP-RC slabs, showing higher accuracy and reliability than other ML models and existing design codes. Artificial neural networks (ANNs) have also been used in this field [
32]. A study analyzing 164 tests found that the ANN model with 6 input neurons, 15 neurons in the first hidden layer, 5 neurons in the second hidden layer, and 1 output neuron is highly accurate, with an impressive R value and mean absolute percentage error (MAPE), thus outperforming existing models. This research also led to the development of a practical graphical user interface for industry applications. Finally, the hybrid “gray box” model, which integrates modulated pressure field theory (MCFT) with a machine learning-assisted approach (genetic programming), represents a major advance [
27]. This model, which was tested using a database of 154 experiments, showed performance enhanced by an efficient correction equation, exceeding the accuracy of five other experimental models.
In this study, we have developed a gradient boosting regression tree (GBRT) model [
33] tailored for predicting the shear strength of FRP slabs. This model strategically builds additional trees, aiming to reduce prediction errors from the foundational models. The GBRT’s boosting technique is especially effective in complex situations, creating an ideal series of trees. This is particularly advantageous in cases with few samples but many input features. The model excels in comprehending the complex dynamics and non-linear behaviors of FRP slabs, thereby boosting prediction accuracy. Moreover, the GBRT method not only precisely predicts the shear strength from various features but also identifies and prioritizes the significance of each feature for a more detailed examination.
The aim of this study is to use the GBRT model with a much larger dataset than previous models to enhance accuracy in predicting the behavior of fiber-reinforced polymer (FRP) reinforced concrete panels. This expanded dataset approach was designed to overcome limitations encountered in previous studies, which often relied on smaller, less diverse data. By using a more comprehensive dataset, we expect to not only improve the accuracy and reliability of predictive models but also improve ML algorithms through more robust training and validation. Furthermore, this approach facilitates comprehensive comparison with previous studies, showcasing advances in predictive capabilities while enhancing the generalizability of the results. A larger dataset will also likely reveal new insights and trends, deepening our understanding of the factors that influence FRP-reinforced concrete slabs. In addition to providing more accurate, reliable, and universally applicable predictive models, this study also aims to develop a user-friendly graphical user interface (GUI) tool. This tool will be accessible via the web, allowing engineers to easily apply our findings and predictive models in their work, significantly advancing the current understanding and application in this field.
3. Database Used
For this investigation, a dataset of 238 experimental observations on FRP-reinforced concrete slabs under punching shear was gathered from a range of literature sources [
11,
14,
15,
16,
18,
20,
24,
37,
51,
52,
53,
54,
55,
56,
57,
58,
59,
60,
61,
62,
63,
64,
65,
66,
67,
68,
69,
70,
71,
72,
73,
74,
75,
76,
77,
78,
79,
80,
81,
82,
83,
84,
85,
86,
87,
88,
89]. It is worth mentioning that most of the experimental data included in our database was also part of the comparative study conducted by [
90]. The findings from previous work [
32] revealed that there is a significant impact of a number of critical variables on the punching shear of FRP-reinforced concrete slabs. These variables include the cross-section area of the column (
A), the perimeter of the critical section in the RC slab (
b0), which can be calculated based on 0.5
de and 1.5
de and is named
b0,0.5de (
k = 1) and
b0,1.5de (
k = 3), as demonstrated in
Figure 4. The effective depth of the RC slab is denoted as de, while
fc represents the compressive strength of the utilized concrete in the RC slab. The modulus of elasticity and the reinforcement ratio of the steel and FRP rebars are respectively indicated as
Er and
ρr. As a result, ML models that estimate the shear strength of FRP-reinforced concrete slabs are built using these discovered parameters as their foundation.
The dataset encompasses a range of values for each parameter: the cross-section area of the column (A) ranging from 6.25 to 1587.5 cm2, the perimeter of the critical section in the RC slab (b0,0.5de) ranging from 280 to 2470 mm, and (b0,1.5de) ranging from 640 to 4608 mm. The effective depth of the RC slab (de) ranges from 36 to 284 mm, the compressive strength of the utilized concrete in the RC slab (fc) ranges from 22.16 to 179 MPa, the reinforcement ratio (ρr) ranges from 0.13 to 3.76%, the modulus of elasticity of the steel and FRP rebars (Er) ranges from 28.4 to 230 GPa, and the ultimate shear strength (Vu) ranges from 24 to 1600 kN. Square and circular columns are among the test specimens. They consist of flat slab-column connections constructed of FRP-reinforced concrete without drop panels, column capitals, or shear reinforcement.
The statistical parameters summarizing the properties of the variables in the database are presented in
Table 1, while
Figure 5 illustrates the distribution of each parameter. Additionally, the correlation matrix plot in
Figure 6 displays the association between shear capacity and the six input parameters. This figure graphically represents the pairwise correlations between the parameters, each associated with a corresponding correlation coefficient. It is evident that while parameters
fc,
ρr, and
Er show a weaker connection with shear strength, parameters
b0,0.5de,
b0,1.5de, de, and
A exhibit a significant correlation with shear strength.
6. Conclusions
Structural engineers face a major challenge in predicting the shear strength of FRP-reinforced flat concrete slabs, which underscores the need for reliable and accurate ML algorithms. Using a database of 283 FRP flat slab models, this paper proposes a gradient-boosted regression tree (GBRT) model to predict the shear strength of FRP-reinforced flat concrete slabs. The input space for the present dataset consists of seven basic parameters: cross-sectional area of the column, critical cross-sectional perimeter in the RC slab at k = 1 and k = 3, effective depth of the level slab, compressive strength of concrete, FRP longitudinal reinforcement ratio, and modulus of elasticity. The model assessment employs 5-fold cross-validation and statistical measures. An overview of the study’s conclusions and observations is provided in this section:
Based on the fivefold cross-validation results, the GBRT model demonstrated consistency and reliability across the performance metrics used in this analysis.
The higher prediction accuracy of the GBRT was demonstrated by its better performance in terms of three specified metrics (i.e., Mean Absolute Error (MAE), root mean square error (RMSE), and coefficient of determination (R2)) when compared to the KNN and LASSO models. Furthermore, compared to the LASSO model, the KNN model typically produced superior predictions.
Using an experimental database, the GBRT model was compared to several well-known equations, including Ospina et al. [
11], El-Gamal et al. [
37], El-Ghandour et al. [
19], and Ju et al. [
25]. The results indicated that the GBRT model provided more accurate results than the other models. The GBRT model exhibited a reduced standard deviation, coefficient of variation, and average for a given χ value when compared to the other formulations.
The perimeter of the critical section was the most influential of the seven input factors in determining the punching shear resistance of FRP flat slabs without shear reinforcement. Additionally, the punching shear prediction of the FRP flat slabs was significantly impacted by the slab effective depth.
Based on the GBRT model, a graphical user interface was created to forecast punching shear strength, offering a useful platform for the practical design of FRP flat slabs.