The significant shear acts upon reinforced concrete (RC) elements in many buildings. Various shear failures of RC buildings have been reported in previous research papers (Whittle, 2013). The shear failure of RC beams is brittle (Chalioris and Karayiannis, 2009; Karayannis et al., 2018; Deifalla et al., 2020a; Deifalla et al., 2020b), and the elevated cost of replacing infrastructure has driven research into strengthening techniques. Shear strength is vital in many projects (Gosbell and Meggs, 2002; FIB. FRP Reinforcement in RC Structures, 2007; Oller et al., 2021). The fiber-reinforced polymer (FRP) sheets have various benefits over steel plates. Thus, research has been conducted to investigate the behavior of FRP externally and internally in RC beams (De Lorenzis and Nanni, 2001; Deifalla, 2020a; Kotynia et al., 2021). FRP has been used effectively in the automotive and aerospace industries for a few decades. It has been used for new structural elements in recent years, particularly in aggressive environments including but not limited to chemical plants because it is corrosion free (Deifalla, 2015; Deifalla, 2020b; Deifalla et al., 2021). In addition, FRP can be used in situations where the use of steel would be impossible or impractical (Hassan and Deifalla, 2016; Salem and Deifalla, 2022). For instance, it can be formed on-site to fit any irregular shape. FRP fabrics can be wrapped around curves (i.e., beams’ sides, columns’ corners, or beams’ soffits). It is lighter in weight than steel but has the same strength, (Deifalla et al., 2013), and it is easy to handle and cut to the required length.

Worldwide, there is a lack of consensus on the shear strength contribution of externally bonded (EB)-FRP jackets. Several design guidelines and codes exist worldwide (fib Task group 5.1, 2019; ACI Committee 440, 2017; Construction C–AC on TR for. CNR-DT 200 R1/2013, 2013; TR-55 CSTR, 2012; JSCE Japanese Society of Civil Engineers, 2000; Abuodeh et al., 2020; Ly et al., 2020; Chalioris et al., 2020; Benzeguir and Chaallal, 2021; Kim, 2021; Isleem et al., 2021). The lack of consensus is due to the following reasons:

• The shear strength and mechanism are complex.

The sheets can be adhesively bonded in a continuous or discrete configuration. However, both U-jacket and side‐jacket schemes are vulnerable to premature debonding failure, which occurs once a critical shear crack opens and widens. In this case, the EB-FRP bonded length is not adequate to provide anchorage for the transfer of the tensile force between the FRP and the concrete; thus, the EB-FRP fails by debonding prematurely, which can be prevented using appropriate anchorage devices. The shear strength of EB-FRP beams can be calculated as the summation of the shear resistance of the transverse steel (if any), the concrete, and the EB-FRP. In addition, several guidelines add the resistance of the EB-FRP to the shear capacity of the un-strengthened element (fib Task group 5.1, 2019; ACI Committee 440, 2017; Construction C–AC on TR for. CNR-DT 200 R1/2013, 2013; TR-55 CSTR, 2012; JSCE Japanese Society of Civil Engineers, 2000). However, previous studies have shown that EB-FRP jackets will affect the effective stress level of internal steel. Thus, this superposition approach could lead to non-conservative results (Pellegrino and Modena, 2002; Bousselham and Chaallal, 2006; Bousselham and Chaallal, 2008; Chen et al., 2010; Pellegrino and Vasic, 2013). The lack of conservative results could be because of changes in concrete diagonal cracking, diagonal strut orientation, or transverse reinforcement stress.

The engineering community is increasingly using EB-FRP systems to improve the strength of existing RC beams. Recent studies have led to a worldwide execution of this technique. However, debonding of EB-FRP sheets has been the main issue for EB-FRP RC beams in shear and torsion. For EB-FRP RC beams, premature failure by EB-FRP debonding is generally a sudden type of failure; therefore, for EB-FRP RC beams, debonding is an unwanted failure mode. Two types of EB-FRP debonding were observed by Deifalla (Deifalla et al., 2013), namely end or intermediate debonding, as shown in Figure 1, which are caused by either cover spalling or concrete cracking. Although beams are rarely subjected to pure shear and shear is often accompanied by flexure, beams are usually heavily reinforced in order to avoid the effect of flexure.

The anchorage systems of EB-FRP jackets have no rational and reliable design rules. Thus, FRP design codes and guidelines specify that physical experimental testing should be conducted as a supplement for the implementation of these machine-learning techniques(fib Task group 5.1, 2019; ACI Committee 440, 2017; Construction C–AC on TR for. CNR-DT 200 R1/2013, 2013; TR-55 CSTR, 2012; JSCE Japanese Society of Civil Engineers, 2000). However, the procedure for experimental testing is not specified by existing guidelines and design codes (Pellegrino and Modena, 2002; Sas et al., 2009a; Pellegrino and Vasic, 2013). In addition, because of the time and budget constraints of projects, it is rarely possible to perform such testing. Thus, the potential benefits of FRP anchorages are usually substituted by using an additional increase in the EB-FRP, which is not economical. The experimental studies conducted in this area are limited by case dependency and usually use a small-scale model; thus, it has a small impact in understanding the behavior of the FRP.

The contribution of EB-FRP to the resistance of RC beams is affected by EB-FRP type, direction, arrangement, and allocation. The efficacy of EB-FRP is boosted by attaching the EB-FRP in a direction parallel to the maximum tensile stress. Therefore, EB-FRP arrangements change the shear capacity of strengthened RC beams. A comprehensive investigation into the shear strength of EB-FRP RC beams is rare, and many queries regarding the mechanisms involved are not yet resolved. With the following exception, many researchers have proposed idealized models similar to that used for the internal steel stirrups, which is only valid if the shear contribution of EB-FRP comes from the tensile fiber capacity at a strain close to the ultimate tensile strain of the EB-FRP.

If full FRP wrapping is not feasible, to achieve the full design capacity, anchorage systems can be used for EB-FRP-strengthened beams using FRP (Mofidi and Chaallal, 2011a; Mofidi and Chaallal, 2014). The European fib (fib Task group 5.1, 2019) code suggests that anchorage systems should be at the compressive zone of the EB-FRP RC beams; however, no further details were provided. On the other hand, the ACI (TR-55 CSTR, 2012) indicated that anchorage systems at the termination points of EB-FRP will produce larger tensile stress transfer. However, the efficiency of these anchorage systems and the developed level of tensile stress before failure should be validated using experimental testing of a scaled model before execution (TR-55 CSTR, 2012). A study by Mofidi (Mofidi and Chaallal, 2011a; Mofidi and Chaallal, 2011b; Mofidi and Chaallal, 2014) concluded that experimental testing is needed to validate the proposed anchorage factors for the end-anchorage systems. Kalfat (Kalfat et al., 2013) demonstrated the validity of upgrading the shear strength with anchoring systems for EB-FRP materials. However, there remains a lack of sufficient research in this area. A more recent review by Godat (Godat et al., 2020) has shown that further research is essential to enhance the reliability of the shear strength predictions of EB-FRP RC beams. The interaction between the FRP shear strength, strain, and parameters is required for robust design equations.

Machine learning is being implemented in various applications because it can capture the actual behavior for complex problems involving many parameters (Deifalla, Salem). This research investigation aims at developing a reliable and accurate strength model based on advanced machine-learning techniques. An extensive database was collected and used to train and validate the model, as shown in Figure 2. A machine learning model was developed and compared with available models from the existing literature. Concluding remarks were outlined.

The reliability of the existing strength models for concrete elements under shear is being questioned by many researchers, where investigations have shown a significant discrepancy and large scattering between the measured and predicted strength of the existing models, especially those used in current design guidelines (Colotti and Swamy, 2011; Lima and Barros, 2011; Isleem et al., 2022; Qaidi et al., 2022; SuhadAbd et al., 2022; Isleem et al., 2023). Thus, existing models are deemed to be inadequate and need further improvement. That shortcoming has motivated comprehensive investigations in all aspects related to shear. This current study investigates the implementation of artificial intelligence in the shear of strengthened concrete elements, which could guide further developments of design codes and mechanical models.

Relatively limited detailed studies have investigated the shear strength of RC beams; in addition, many questions regarding the strength mechanism, especially the usage of anchorage devices, are yet to be resolved. Many studies have idealized the EB-FRP jacket in a manner similar to that of steel shear reinforcements with the assumption that the contribution of the EB-FRP to shear capacity arises from the capacity of the EB-FRP to resist tensile stresses at a strain, which is less than or equal to the FRP ultimate tensile strain (Salem and Deifalla, 2022; Deifalla et al., 2013; fib Task group 5.1, 2019). Numerous experimental tests have been conducted in this field of research, and existing design codes and guidelines were available for designing EB-FRP elements (fib Task group 5.1, 2019; ACI Committee 440, 2017; Construction C–AC on TR for. CNR-DT 200 R1/2013, 2013; TR-55 CSTR, 2012; JSCE Japanese Society of Civil Engineers, 2000). Both the empirical evidence and code suggested that performance enhancement can be attained by using the EB-FRP; however, more detailed work is required to quantify its contribution to the strength of the beams under shear (fib Task group 5.1, 2019; ACI Committee 440, 2017; Construction C–AC on TR for. CNR-DT 200 R1/2013, 2013; TR-55 CSTR, 2012; JSCE Japanese Society of Civil Engineers, 2000). Many parameters influence the effective FRP strain for shear-strengthened RC beams, including but not limited to: 1) The type of fibers in terms of Young’s Modulus; 2) The fiber orientation in terms of the inclination angle to the beam longitudinal axis; 3) The fiber distributions in terms of the number of plies and thickness of the FRP fabrics; 4) The FRP bond schemes in terms of the sides the FRP is bonded to (i.e., side bonding U-jacket, and full wrapping); 5) The concrete compressive strength; 6) The usage of anchorage devices.

An extensive database of 200 beams collected from existing literature was strengthened using an EB-FRP jacket under shear. The database contains results from more than 80 experimental studies. In addition, this database includes EB-FRP beams available in existing literature (Pellegrino and Vasic, 2013; Colotti and Swamy, 2011; Sas et al., 2009b; Kotynia, Oller, Mari, Kaszubska). Although the data is available in existing databases, all data was validated using the original study.

Collected parameters were related to the beam and the FRP jacket as follows: Width of beam cross-section (X1), beam height (X2), the effective depth of beam cross-section (X3), beam span (X4), shear span to depth ratio (X5), concrete compressive strength (X6), steel flexure reinforcement ratio (X7), steel shear reinforcement ratio (X8), strength technique (X9), FRP jacket height (X10), the width of FRP jacket (X11), the thickness of FRP jacket (X12), spacing between FRP strips (X13), FRP reinforcement ratio (X14), angle of fiber orientation (X15), ultimate stress of FRP in GPa (X16), FRP young’s modulus in GPa (X17), FRP rupture strain (X18), and shear strength in kN (X19). Table 1 shows the statistical measures for all parameters.

Pearson parametric method was used to determine the influence of beam details on the FRP shear strength, as shown in Figure 3. The selected parameters included X1, X2, and X3, while parameters X4, X5, X6, X7, and X8 were not chosen as they had a lower Pearson coefficient. For a more efficient and faster training and validating process, the input parameters have been normalized to be between zero and one, according to Equation 1, while FRP’s shear strength (model’s output) has been transformed according to Equation 2 for better output distribution, as shown in Figure 4. X i , n o r m = X i − X m i n X max − X min (1) where i is the number index for each input parameter, X i , n o r m is the normalized value for the input parameter; X i is the value of the input parameter before normalization; X max and X min are the values of the maximum and minimum values of the input parameter X i . S T = ln S + 1 (2)

S is the value of the added shear strength by FRP in kN while S^T is its transformed value; the input parameter for the proposed model data has been filtered and transformed to follow a normal distribution curve for a better training process to build the model, as shown in Figure 4.

A script has been developed to generate more than 6750 different artificial neural network (ANN) models to compare and boost the developed model performance using MATLAB. In addition, different combinations of various parameters have been tested, as shown in Figure 5.

During the model construction, the transfer function of the hidden and output layers were the first parameters to be determined. Then, the training function and the number of neurons in the hidden layer were optimized by plotting the number of neurons versus the correlation coefficient (R ²) and root mean square error (RMSE), as shown in Figures 6, 7.

The number of neurons was optimized to be 35 neurons in the hidden layer, while the transfer functions were TANSIG and PURELIN for the hidden and output layers, respectively (Figure 8). Based on the constricted model, a mathematical equation has been developed to predict the shear strength added by the FRP (Equation 3). S = Exp P U R E L I N ∑ i = 1 N W 2 i T A N S I G ∑ j = 1 J W 1 j × X j − X a v g X max − X min + b 1 i + b 2 − 1 (3) where Exp is the exponential function, N is the number of neurons in the hidden layer, which has been optimized to be 35 neurons; W2i is the weight of the output layer; J is the number of input variables; W1 is the weight of the hidden layer; Xj is the value of the input variable (strength configuration, X1, X2, X3, X9, X10, X11, X12, X13, X14, X15, X16, X17, and X18); b1 is the bias of the hidden layer; b2 is the bias of the output layer.

The values of the input parameters go through the input layer to be multiplied by the weights that connect the input layer with the hidden layer. The bias of the first layer is added to the multiplication results before they transform through the activation function of the hidden layer (TANSIG). The outcome of the transfer function is then multiplied by the weights of the output layer and added to the bias of the hidden layer. Finally, the product goes through the output layer’s transfer function (PURELIN) to give the predicted value of the shear strength in kN.

Later, the performance of the ANN model was boosted by 1000 epochs; the best model outcome was found to be at the 8th epoch; then, the validation check stopped the training process at the 14th epoch, as shown in Figure 9.

After the model construction, the model was used to predict the shear strength for FRP in kN; then, the predicted value versus the actual values was plotted, as shown in Figure 10. In addition, statistical tests have been conducted to test the accuracy of the newly developed model. Training, validating, and overall datasets have been evaluated using average relative error (ARE), average absolute relative error (AARE), relative deviation (RD), standard deviation (SD), RMSE, and R2 according to equations three to eight. Also, a comparison between the actual and predicted values is presented in Figure 11 Figure 12. Moreover, the ratio between the predicted and actual values has been calculated according to Equation 9 for both the training and validating datasets and is presented in Figure 13. A R E = 1 N × ∑ i = 1 N S P r e d i c t e d − S A c t u a l S A c t u a l × 100 (4) A A R E = 1 N × ∑ i = 1 N S P r e d i c t e d − S i A c t u a l S i A c t u a l × 100 (5) R D = S P r e d i c t e d − S A c t u a l S A c t u a l × 100 (6) S D = 1 N − 1 × ∑ i = 1 N S P r e d i c t e d − S A c t u a l S A c t u a l 2 0.5 (7) R M S E = 1 N × ∑ i = 1 N S P r e d i c t e d − S A c t u a l 2 0.5 (8) R 2 = 1 − ∑ i = 1 N S P r e d i c t e d − S A c t u a l 2 S A c t u a l M e a n − S A c t u a l 2 (9) R a t i o = F P r e d i c t e d F A c t u a l (10) where N is the number of tested data points, S^Predicted is the predicted shear strength value in kN; S^Actual is the corresponding actual shear strength value in kN; S A c t u a l M e a n is the average of the actual shear strength value in kN.

The model showed excellent performance as it has R ² and RMSE of 0.91 and 17.45 for the overall dataset, respectively. The R ², RMSE, ARE, AARE, and SD statistical tests are summarized and listed in Figures 13–17, respectively. In addition, the results of the different datasets were compared to check the fitting of the proposed model, while RD versus the actual shear strength was plotted and is presented in Figure 18.

After validating the model and demonstrating its credibility in predicting the shear strength value added by the FRP, the model was then used to conduct a parametric study to study the impact of each parameter individually. When investigating a certain parameter, the rest of the variables were set to a constant at their average value while changing the value of the tested parameter. X10, X14, X15, and X17 were investigated, and their values versus the model outcome were plotted, as shown in Figures 19–22.

In 2020, machine learning was used to predict the FRP shear strength capacity with a certain accuracy [50]. In this work, the proposed model performance has been evaluated and compared to the models from the existing literature. R ² is one of the essential statistical parameters that can determine the accuracy of any model regardless of the values of the used data. R ² for the overall datasets and the number of data used in developing the new model have been compared with their corresponding values from the previous model, as shown in Figure 23. The model from this work was constructed using a larger number of dataset points, giving the model a wide range of applicability. In addition, R ² shows better performance and more accurate results than the models from the existing literature for all datasets.

Table 2 shows the statistical measures for various selected models’ safety ratios, namely average and coefficient of variation. The safety ratio was defined as the ratio between the measured and the calculated FRP contribution. At the same time, selected models include the proposed model, the Fib 90 (fib Task group 5.1, 2019), the ACI (ACI Committee 440, 2017), the CNR (Construction C–AC on TR for. CNR-DT 200 R1/2013, 2013), the TR-55 (TR-55 CSTR, 2012), and the JSCE (JSCE Japanese Society of Civil Engineers, 2000). The proposed model captured the behavior of FRP-strengthened beams and precited the FRP contribution accurately and consistently. The range of the average was from 0.98 to 1.14, and the range of the coefficient of variation was from 24% to 36%. The range of the selected models’ average was from 0.48 to 4.46, and the range of the coefficient of variation was from 35% to 95%.

Based on the findings from this current study, the following is recommended:

- The use of artificial intelligence methods to predict the true strength as it provides more accurate strength compared to other methods.

Based on the findings from this current study, the following are recommended for the strength modeling of shear-strengthened beams:

- Using anchorage strengthening schemes.

An artificial intelligence model for the shear strength of FRP-strengthened elements was proposed, which accounts for the following parameters: the width of the beam cross-section, beam height, the effective depth of beam cross-section, strength technique, FRP jacket height, the width of FRP jacket, the thickness of FRP jacket, spacing between FRP strips, angle of fiber orientation, ultimate stress of FRP, FRP young’s modulus, and FRP rupture strain. The model’s accuracy compared to the existing model is superior, where statistical tests R ², RMSE, ARE, AARE, and SD were found to be 0.91, 17.45, 0.048, 0.23, and 0.91, respectively, for the overall dataset. A parametric study was conducted to study the influence of the FRP jacket height, the width of the FRP jacket, the thickness of the FRP jacket, spacing between FRP strips, angle of fiber orientation, ultimate stress of FRP, FRP young’s modulus, and FRP rupture strain.