The tensile strength of GFRP composites with a gauge length of 400 mm were tested based on ACI guidelines 440.3R (2012) using 60 T capacity UTM. The applied tensile loads and corresponding elongations were recorded during the tests and based on that the tensile strength and modulus of elasticity of GFRP CSM and WR composites were calculated and the results are presented in Table 3.
Table 3
Tensile load test results for GFRP plain sheets and corrugated laminates
Sample Id
|
Thickness (mm)
|
C.S. area of sheet (sq.mm)
|
Tensile load (kN)
|
Tensile strength (MPa)
|
Modulus of Elasticity (MPa)
|
GFRP CSM
|
0.5
|
50
|
8.30
|
166
|
11567.57
|
GFRP WR
|
0.5
|
50
|
8.47
|
169.32
|
10135.91
|
Compressive strength of concrete cubes were tested after 28 days curing and the average compressive strength value is 31.21 MPa. The compressive strength value is more than the required value for C30 grade concrete. Thus, the quality of ingredients used for concrete preparation is suitable, and the mix proportions are appropriate.
Two point load shear strength tests on RC beams were conducted for all the beams with and without steel/ GFRP composites. From the experimental tests, failure load, corresponding mid span deflection, failure patterns are recorded and shown in Table 4.
Table 4
Sample Designation
|
Type of composites used for Externally bonding Scheme
|
Failure Load (kN)
|
Mid span deflection corresponding to failure load (mm)
|
Type of Failure
|
CB1
|
No
|
77.75
|
2.45
|
Combined shear and flexure
|
CB2
|
No
|
73.88
|
2.85
|
Shear Failure
|
EB-SS-CSM
|
CSM Strips on sides of shear area only
|
72.19
|
3.90
|
Shear Failure
|
EB-FS-CSM
|
CSM composites Full Shear Area-Sides only
|
85.22
|
3.87
|
Combined shear, flexure and concrete crushing
|
EB-SU-CSM
|
‘U’ wrap CSM Strips on
Shear Area
|
75.88
|
2.95
|
Shear Failure
|
EB-FU-CSM
|
CSM composites Full ‘U’ wrap on Shear Area
|
76.28
|
5.10
|
Combined shear and flexure
|
EB-SS-WR
|
WR Strips on sides of shear area only
|
73.59
|
3.00
|
Shear and delamination of strips
|
EB-FS-WR
|
WR composites on Full Shear Area-Sides only
|
82.13
|
6.32
|
Flexure and delamination
|
EB-SU-WR
|
‘U’ wrap WR Strips on
Shear Area
|
72.38
|
5.93
|
Shear and delamination of strips
|
EB-FU-WR
|
WR composites on Full ‘U’ wrap on Shear Area
|
87.53
|
4.55
|
Delamination
|
Note: CB – Control beam; EB – Externally bonded Beam; SS – Strips on Sides; FS – Full on Sides; SU – U wrap Strip; FU – Full U wrap; CSM – Chopped Strand Mat; WR – Woven Roving |
Failure pattern of all the ten beams are shown in Figs. 12–20. Failure pattern shows the crack propagation during the application of loading on the beam. It helps to identify the type of failure.
Beams with GFRP CSM Stirrups
The following inferences were made based on the experimental results of control beam and beams with GFRP CSM stirrups.
-
Failure load of control beam (CB1) with steel shear reinforcements is 5.24% more than that of RC beam without steel/ GFRP shear reinforcements (CB2).
-
Failure load for RC beam with GFRP CSM composites on sides of the full shear area (EB-FS-CSM) is 9.61% and 15.35% more than that of RC beams with and without steel shear reinforcements (CB1 & CB2) respectively.
-
Failure load for RC beam with CSM Strips on sides of shear area only (EB-SS-CSM) is slightly less than that of beam CB2.
-
Failure load for RC beam with CSM composites Full ‘U’ wrap on Shear Area (EB-FU-CSM) is 3.25% more than that of RC beam without steel shear reinforcements (CB2). Similarly, failure load for RC beam with ‘U’ wrap CSM Strips on shear area (EB-SU-CSM) is 2.71% more than that of CB2.
-
RC beam with CSM composites on sides of the full shear area (EB-FS-CSM) performs well when compared with control beams and other beams with GFRP CSM composites. The reason for increasing the load carrying capacity of RC beam CSM composites on sides of the full shear area (EB-FS-CSM) is due to the lamination is perfectly attached with the concrete surface. But, for beams with ‘U’ wrap CSM composites, stress concentration is more near the edges. It may be the reason for the reduction of load carrying capacity for beams with ‘U’ wrap composites.
-
Figures 11–20 show the failure pattern of all the beams and based on that the control beams CB1 and CB2 failed due to combined shear & flexure and shear respectively. Category III (EB-SS-CSM) and V (EB-SU-CSM) beams failed due to shear. Category IV (EB-FS-CSM) beam with CSM composites on sides of the full shear area failed by combined shear, flexure and concrete crushing. Category VI (EB-FS-CSM) beam with ‘U’ wrap CSM composites on full shear area fails by combined shear and flexure. None of the beam failed due to delamination. However, Figs. 15 and 16, beams with ‘U’ wrap CSM composites, show that delamination started between the sides and bottom portion due to high stress concentration.
Beams with GFRP WR Stirrups
The following inferences were made based on the experimental results of control beam and beams with GFRP WR stirrups.
-
Failure load for RC beam with woven roving composites on full shear area (EB-FS-WR) is 5.63% more than that of RC beam with steel shear reinforcements (CB1). Similarly, failure load for the beam externally bonded with ‘U’ wrap composites on shear area (EB-FU-WR) is 12.58% more than that of control beam 1.
-
Failure load for RC beam with woven roving composites on full shear area (EB-FS-WR) is 11.16% more than that of RC beams without steel/ GFRP shear reinforcements (CB2). Similarly, failure load for the beam externally bonded with ‘U’ wrap woven roving ‘U’ wrap composites on full shear area (EB-FU-WR) is 18.48% more than that of control beam 2.
-
Failure load of RC beam externally bonded with GFRP WR ‘U’ wrap on full shear area (EB-FU-WR) is 20.93%, 6.57% and 18.94% more than that of beams externally bonded with ‘U’ wrap strips on shear area, sides of full shear area and strips on sides respectively.
-
Type of failure for all the RC beams with GFRP woven roving are either delamination or combination of delamination and flexure/ shear failure.
Comparative study on Beams with GFRP CSM and WR Stirrups
Failure loads for all the control and externally bonded beams were plotted and are shown in Fig. 21.
- It is clear from the Fig. 21 that the load carrying capacity of beams externally bonded with GFRP CSM and WR composites on full shear area provide better performance when compared to GFRP strips.
- For CSM category beams, beam bonded with CSM composites on full shear area (EB-FS-CSM) performed well among other beams with same composites. Similarly, For WR category beams, beam bonded with WR ‘U’ wrap on shear area performed well among other beams with same composites.
- Failure load for beam with GFRP WR ‘U’ wrap on shear area (EB-FU-WR) is 2.71% more than that of beam with GFRP CSM composites on sides of shear area (EB-FS-CSM).
- However, the percentage increased in failure loads of the beam with GFRP CSM/ WR strips on sides/ ‘U’ wrap are less, compared to the beam with composites on full shear area.
Theoretical Analysis
Theoretical analysis were carried out based on code, and American Concrete Institute (ACI) design guidelines 440.2R (2002) and Indian Standard specifications (IS456, 2000) for control and externally bonded beams. According to ACI 440.2R-02, the nominal shear strength of an FRP strengthened concrete member (Vu) is the summation of shear resistance of concrete, contribution of the FRP reinforcing and reinforcing steel. As per ACI 440.2R-02, 2002, an additional reduction factor has to be applied to the contribution of the FRP system. According to that for RC beam strengthened with three sided ‘U’ wraps or bonded face piles, the recommended additional reduction factors for FRP shear reinforcement is 0.85.
The shear contribution of the FRP shear reinforcement is then given by
For the theoretical analysis calculation, the following equation was used.
Based on IS 456-2000, maximum shear stress for concrete is 3.5 MPa for 28 days cube compressive strength with 30 MPa. Width and effective depth of beam considered for the theoretical analysis are 100 mm and 131 mm respectively. Table 5 shows the results of theoretical analysis of RC beam with and without shear steel/ GFRP reinforcements and shear force due to external load.
Table 5 Experimental and theoretical analysis results
Sl. No.
|
Beam Designation
|
Failure Load based on Experimental Results (kN)
|
Shear Force corresponding to Failure Load (kN)
|
Shear Resistance based on Theoretical Analysis (kN)
|
Difference (%)
|
1
|
CB1
|
77.75
|
38.88
|
36.96
|
5.18
|
2
|
CB2
|
73.88
|
36.94
|
30.57
|
20.84
|
3
|
EB-SS-CSM
|
72.19
|
36.10
|
30.86
|
16.95
|
4
|
EB-FS-CSM
|
85.22
|
42.61
|
36.16
|
17.85
|
5
|
EB-SU-CSM
|
75.88
|
37.94
|
30.89
|
22.82
|
6
|
EB-FU-CSM
|
76.28
|
38.14
|
36.20
|
5.36
|
7
|
EB-SS-WR
|
73.59
|
36.80
|
31.02
|
18.61
|
8
|
EB-FS-WR
|
82.13
|
41.56
|
36.42
|
14.11
|
9
|
EB-SU-WR
|
72.38
|
36.19
|
31.02
|
16.65
|
10
|
EB-FU-WR
|
87.53
|
43.77
|
36.42
|
20.17
|
Fig. 22 portrays the comparison between experimental and shear capacity of beams predicted based on theoretical analysis.
Correlation coefficient for experimental shear force corresponding to failure load and shear capacity of beams predicted based on theoretical analysis is calculated. It benefits to measure the strength and direction of the relationship between those two variables. Correlation coefficient for the experimental and predicted failure load values is 0.779 and the value proved that strong correlation exists between them.
Machine Learning (ML) Model
Machine learning is a sub-set of artificial intelligence that uses the patterns in the data to train a model for predicting the output of classification and regression problem. Machine learning algorithms can be used for identifying the cracks using image processing and failure pattern recognition technique (Araind et al., 2021). In this paper, supervised ML technique is applied for the purpose of regression and classification. By using labelled data for the instances of different failure load and types, supervised ML can be applied to create a relationship between the features of the RC beam data and to the known failure load or types. Then, the relationships can be used for predicting failure load and classifying fault types of the unknown instances.
Random Forest
The Random Forest (RF) classifier is a nonparametric ensemble, can be used in both classification and regression model development, which comprises of a random collection or a random selection of a forest tree. RF is basically inherits the advantages of two powerful ML techniques such as bagging and random feature selection (Breiman, 2001). In this work, ML model using the RF classifier proposed in [30] is developed using Python Scikit-learn library (Fabian et al., 2011). As we know the forest consist of a number of trees, these kind of setup is used in RF model, i.e decision tree algorithm is used to build RF model. In general, the RF algorithm creates a random sample of multiple decision trees and merges them to create a forest using the input data set. In a classification problem, for classifying an unknown input each tree votes for the output class and most voted class is chosen as the final result. In case of regression problem, the mean value of all tree outputs is considered as final result. The RF model handles the missing data effectively to maintain the accuracy of the predicted results. Hence, it is widely accepted and applied in various domains (Breiman, 2001).
The parameters related to the beam and the results obtained through the experiment were considered as features to develop models for predicting the failure load, mid span deflection, shear failure, flexure, crushing and delamination. For each model construction, the following features are used for training: Type of shear reinforcement (4 types; steel, GFRP CSM, GFRP WR and none), presence and absence of strips on sides, GFRP on sides of full shear area, 'U' wrap strips, full ‘U’ wrap on shear area and steel shear reinforcement are considered as a binary input features. The features such as compressive strength of concrete (in MPa), effective span (in mm), beam cross sectional area (in sq.mm), tensile strength of steel stirrups (in MPa), cross sectional area of steel / GFRP stirrups (in sq.mm), tensile strength of main steel (in MPa) and tensile strength of FRP (in MPa) are used as features training the RF model. The prediction of failure load and mid span deflection models are considered as regression problem, shear failure, crushing, flexure failure and delamination models are considered as classification problem.
Fig. 23 shows the structure of RF model and the following steps are carried out to develop the model:
Step 1: The experimental data shown in the Table 6 is used as the primary data to generate the synthetic data set for training and testing the RF models. One thousand synthetic values for each case is generated using the experimental results. The generated values are normally distributed within ±2% variation.
Table 6 Input parameters of the RC beam collected through experiments
Sl. No.
|
Beam Designation
|
Input features to the RF model
|
Regression
Model
|
Classification Model
|
Type of shear reinforcement
|
50 mm Strips on sides
|
GFRP on sides of full shear area
|
50 mm U wrap strips
|
Full U wrap on shear area
|
Steel shear reinforcement
|
Compressive strength of concrete (in MPa)
|
Effective span (in mm)
|
Beam cross sectional area (in sq.mm)
|
Tensile strength of steel stirrups (in MPa)
|
Cross sectional area of steel / GFRP stirrups (in sq.mm)
|
Tensile strength of main steel (in MPa)
|
Tensile strength of GFRP (in MPa)
|
Failure Load (in kN)
|
Mid span deflection (in mm)
|
Shear Failure
|
Flexure Failure
|
Crushing
|
Delamination
|
Data set used for training and validation:
|
1
|
CB1
|
Steel
|
No
|
No
|
No
|
No
|
Yes
|
31.21
|
650.0
|
13250
|
250
|
39.72
|
454
|
0
|
77.75
|
2.45
|
Y1
|
Y1
|
N1
|
N1
|
2
|
CB2
|
None
|
No
|
No
|
No
|
No
|
No
|
31.71
|
656.8
|
13207
|
0
|
0
|
455
|
0
|
73.88
|
2.85
|
Y2
|
N2
|
N2
|
N2
|
3
|
EB-SS-CSM
|
GFRP CSM
|
Yes
|
No
|
No
|
No
|
No
|
31.19
|
646.6
|
13205
|
0
|
49.41
|
455
|
169
|
72.19
|
3.9
|
Y3
|
N3
|
N3
|
N3
|
4
|
EB-FS-CSM
|
GFRP CSM
|
No
|
Yes
|
No
|
No
|
No
|
31.48
|
661.9
|
13237
|
0
|
99.64
|
494
|
153
|
85.22
|
3.87
|
Y4
|
Y4
|
Y4
|
N4
|
5
|
EB-SU-CSM
|
GFRP CSM
|
No
|
No
|
Yes
|
No
|
No
|
31.75
|
659.4
|
13247
|
0
|
49.31
|
474
|
160
|
75.88
|
2.95
|
Y5
|
N5
|
N5
|
N5
|
6
|
EB-FU-CSM
|
GFRP CSM
|
No
|
No
|
No
|
Yes
|
No
|
31.08
|
638.0
|
13211
|
0
|
100.74
|
433
|
159
|
76.28
|
5.1
|
Y6
|
Y6
|
N6
|
N6
|
7
|
EB-SS-WR
|
GFRP WR
|
Yes
|
No
|
No
|
No
|
No
|
30.74
|
643.1
|
13224
|
0
|
49.63
|
479
|
164
|
73.59
|
3.0
|
Y7
|
N7
|
N7
|
Y7
|
8
|
EB-FS-WR
|
GFRP WR
|
No
|
Yes
|
No
|
No
|
No
|
31.28
|
659.3
|
13242
|
0
|
98.04
|
549
|
156
|
82.13
|
6.32
|
N8
|
Y8
|
N8
|
Y8
|
9
|
EB-SU-WR
|
GFRP WR
|
No
|
No
|
Yes
|
No
|
No
|
30.74
|
657.8
|
13223
|
0
|
49.31
|
485
|
175
|
72.38
|
5.93
|
Y9
|
N9
|
N9
|
Y9
|
10
|
EB-FU-WR
|
GFRP WR
|
No
|
No
|
No
|
Yes
|
No
|
31.15
|
638.5
|
13209
|
0
|
98.33
|
453
|
166
|
87.53
|
4.55
|
N10
|
N10
|
N10
|
Y10
|
11
|
CB - C15
|
Steel
|
No
|
No
|
No
|
No
|
Yes
|
17.88
|
1000
|
13200
|
415
|
56.55
|
415
|
0
|
56.31
|
10.65
|
N11
|
Y11
|
N11
|
N11
|
12
|
CB - C20
|
Steel
|
No
|
No
|
No
|
No
|
Yes
|
21.36
|
1000
|
13200
|
415
|
56.55
|
415
|
0
|
58.3
|
21.8
|
N12
|
Y12
|
N12
|
N12
|
13
|
CB - C25
|
Steel
|
No
|
No
|
No
|
No
|
Yes
|
27.03
|
1000
|
13200
|
415
|
56.55
|
415
|
0
|
66.69
|
13.0
|
N13
|
Y13
|
N13
|
N13
|
External data set used for validating the developed model:
|
14
|
S10FP [2]
|
GFRP-WR
|
No
|
No
|
No
|
Yes
|
No
|
29.8
|
900
|
13000
|
0
|
600
|
420
|
420
|
Experimental Results
|
67.4
|
9.50
|
Delamination Failure
|
ML Predicted Results
|
82.5
|
8.86
|
Delamination Failure
|
Step 2: Divide the data set into training and testing data by splitting randomly with the pre-defined ratio. The usual strategy is to consider 70% of the data as the training set, and the remaining 30% of the data as the test set.
Step 3: Use the training data set to fit the RF model with the minimum number of trees in the forest (n_estimators) and maximum depth of the tree (max_depth) is as follows:
RF Regression models: n_estimators=4 and max_depth=11
RF classification models: n_estimators=4 and max_depth=5
Step 4: Predict the output using the test data input features.
Step 5: Calculate the necessary performance metrics and plot the required graphs/confusion charts.
Performance of the RF model
Fig. 24 & Fig. 25 shows the overall distribution plot of actual and fitted value of the developed model for predicting failure load and mid span deflection. In this study, the performance metrics such as coefficient of determination (R2), Mean Absolute Error (MAE) and Root Mean Square Error (RMSE) were calculated to assess the performance of the regression model. Three indicators namely R2, MAE and RMSE were calculated as follows:
where ti and oi are the target and output of ith sample, n is the number of samples.
The table 7 shows the performance metrics obtained of various regression models, and the results indicates that the developed model with the best R2 score, lowest MAE error and lowest RMSE error is presented as follows:
Table 7 Performance metrics of the regression models
Performance measures
|
Failure load
|
Mid span deflection
|
Training set
|
Testing set
|
Training set
|
Testing set
|
MAE
|
0.4527 kN
|
0.7825 kN
|
0.0386 mm
|
0.0733 mm
|
RMSE
|
0.5606 kN
|
0.9314 kN
|
0.0643 mm
|
0.1189 mm
|
R2 Score
|
1.0
|
0.99
|
1.0
|
1.0
|
Accuracy
|
|
98.94%
|
|
98.89%
|
Figs. 26 – 29 show the confusion matrix for shear failure, flexure failure, crushing and delamination of strips of RC beam with different specification. The classification models are evaluated using the accuracy, precision, recall and F1-Score, which are defined as:
where TP is true positive which is the number of accurate predictions of a specific label (actual label ‘1’, predicted as ‘1’), FP is false positive which is the number of wrong predictions of a specific label (actual label is not ‘1’, predicted as ‘1’), FN is false negative which is number of wrong prediction of specific label as other labels (actual label ‘1’, predicted as other label) and TN is true negative which is the number of the accurate predictions of the other labels with respect to TP.
Table 8 Performance metrics of the classifier model
Weighted mean of
|
Shear Failure
|
Flexure Failure
|
Crushing
|
Delamination
|
Accuracy
|
99.6%
|
99.9%
|
99.8%
|
99.9%
|
Precision
|
0.996
|
0.999
|
0.998
|
0.993
|
Recall
|
0.996
|
0.999
|
0.998
|
0.993
|
F1-Score
|
0.996
|
0.999
|
0.998
|
0.993
|
In this paper, 10-fold cross-validation approach is used to test the performance of the developed model. This means that the model is trained ten times, each time with a different 70% of the synthetic data set and the remaining 30% is used for testing the regression / classifier model. The average performance metrics of the developed models are presented as results. It is observed that all developed models are having higher prediction accuracy. The developed model is also validated using the data set from the literature [2], and the difference between failure loads, mid span deflection of experimental and ML predicted results are 22.40% and 7.22% respectively. Type of failure is delamination for both experimental and ML predicted results, it proved that the performance of ML modelling is excellent. In future work, it is planned to develop other type using Tensor flow libraries.