Abstract
Ultra-high-performance concrete (UHPC) is suitable for repairing and strengthening damaged normal strength concrete (NSC) structures due to its excellent qualities. However, a successful repair relies on whether the UHPC–NSC interface can offer a superb bonding performance under varying working conditions. Therefore, predicting the interface bond strength between substrate NSC and repair UHPC with sufficiently high accuracy has become essential for evaluating and maintaining NSC structures. This study utilized four different machine learning (ML) techniques, support vector machine (SVM), artificial neural network (ANN), multiple linear regression (MLR), and stepwise regression (SWR) to predict the UHPC–NSC interface bond strength. The ML models established the relationship between input variables and target bond strength and predicted the UHPC–NSC interface bond strength. Random search techniques were used to tune the selected algorithms hyperparameters, and the k-fold cross-validation technique was employed to ensure generalizability. Two datasets containing the UHPC–NSC bond strength test results from splitting-tensile and slant-shear tests were used to train and test the performance of the selected ML models. Results show that SVM and ANN models are more effective than the MLR and SWR models based on the two datasets. Besides, all the four ML models developed have better prediction accuracy than the empirical model given by the design codes. The correlation between the input variables and target bond strength was evaluated through partial dependence plots. The ML approach explored in this study has proven viable and effective in predicting UHPC–NSC bond strength and provided the basis for designing UHPC–NSC composite elements.
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Acknowledgements
This work was supported by the Hebei Transportation Science and Technology Project [grant number RW202011] and the Tianjin Transportation Science and Technology Development Plan Project [grant number 2019Bs1]. These supports are gratefully acknowledged. Any opinions, findings, conclusions, or recommendations expressed in this paper are those of the authors and do not necessarily reflect those of the sponsor.
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Appendix: The Dataset Source
Appendix: The Dataset Source
Table Splitting-tensile dataset
Reference | NSC Fc (MPa) | UHPC Age (days) | UHPC Curing Method | NSC Surface Treatment | NSC Moisture condition | Bond Strength (MPa) |
|---|---|---|---|---|---|---|
Tayeh et al. [9] | 45 | 3 | 2 | 1 | 2 | 1.81 |
45 | 3 | 2 | 1 | 2 | 1.55 | |
45 | 3 | 2 | 1 | 2 | 1.66 | |
45 | 3 | 2 | 6 | 2 | 3.44 | |
45 | 3 | 2 | 6 | 2 | 2.73 | |
45 | 3 | 2 | 6 | 2 | 3.3 | |
45 | 3 | 2 | 3 | 2 | 2.49 | |
45 | 3 | 2 | 3 | 2 | 2.82 | |
45 | 3 | 2 | 3 | 2 | 2.07 | |
45 | 3 | 2 | 5 | 2 | 3.35 | |
45 | 3 | 2 | 5 | 2 | 3.84 | |
45 | 3 | 2 | 5 | 2 | 3.46 | |
45 | 3 | 2 | 2 | 2 | 2.25 | |
45 | 3 | 2 | 2 | 2 | 2.1 | |
45 | 3 | 2 | 2 | 2 | 2.62 | |
45 | 7 | 2 | 1 | 2 | 1.87 | |
45 | 7 | 2 | 1 | 2 | 1.95 | |
45 | 7 | 2 | 1 | 2 | 1.65 | |
45 | 7 | 2 | 6 | 2 | 3.07 | |
45 | 7 | 2 | 6 | 2 | 2.87 | |
45 | 7 | 2 | 6 | 2 | 3.4 | |
45 | 7 | 2 | 3 | 2 | 2.35 | |
45 | 7 | 2 | 3 | 2 | 1.94 | |
45 | 7 | 2 | 3 | 2 | 2.54 | |
45 | 7 | 2 | 5 | 2 | 3.31 | |
45 | 7 | 2 | 5 | 2 | 4.16 | |
45 | 7 | 2 | 5 | 2 | 3.13 | |
45 | 7 | 2 | 2 | 2 | 1.99 | |
45 | 7 | 2 | 2 | 2 | 2.59 | |
45 | 7 | 2 | 2 | 2 | 2.42 | |
45 | 28 | 2 | 1 | 2 | 1.87 | |
45 | 28 | 2 | 1 | 2 | 1.68 | |
45 | 28 | 2 | 1 | 2 | 2 | |
45 | 28 | 2 | 6 | 2 | 3.14 | |
45 | 28 | 2 | 6 | 2 | 3.2 | |
45 | 28 | 2 | 6 | 2 | 3.06 | |
45 | 28 | 2 | 3 | 2 | 2.55 | |
45 | 28 | 2 | 3 | 2 | 2.84 | |
45 | 28 | 2 | 3 | 2 | 2.4 | |
45 | 28 | 2 | 5 | 2 | 3.86 | |
45 | 28 | 2 | 5 | 2 | 4.09 | |
45 | 28 | 2 | 5 | 2 | 3.43 | |
45 | 28 | 2 | 2 | 2 | 3.17 |
Reference | NSC Fc (MPa) | UHPC Age (days) | UHPC Curing Method | NSC Surface Treatment | NSC Moisture condition | Bond Strength (MPa) |
|---|---|---|---|---|---|---|
45 | 28 | 2 | 2 | 2 | 2.76 | |
45 | 28 | 2 | 2 | 2 | 2.96 | |
Carbonell et al. [33] | 54.3 | 186 | 1 | 5 | 1 | 3.7 |
53.7 | 186 | 1 | 5 | 1 | 4.2 | |
59.4 | 298 | 1 | 5 | 1 | 4 | |
59.4 | 298 | 1 | 5 | 1 | 4.3 | |
54.3 | 186 | 1 | 2 | 1 | 4.1 | |
53.7 | 186 | 1 | 2 | 1 | 4.2 | |
59.4 | 298 | 1 | 2 | 1 | 2.8 | |
59.4 | 298 | 1 | 2 | 1 | 3.9 | |
54.3 | 186 | 1 | 1 | 1 | 3.6 | |
53.7 | 186 | 1 | 1 | 1 | 4.2 | |
59.4 | 298 | 1 | 1 | 1 | 3.3 | |
59.4 | 298 | 1 | 1 | 1 | 4.2 | |
54.3 | 186 | 1 | 3 | 1 | 4.1 | |
53.7 | 186 | 1 | 3 | 1 | 4.5 | |
59.4 | 298 | 1 | 3 | 1 | 4.1 | |
59.4 | 298 | 1 | 3 | 1 | 4.5 | |
54.3 | 186 | 1 | 6 | 1 | 4.8 | |
53.7 | 186 | 1 | 6 | 1 | 5.7 | |
59.4 | 298 | 1 | 6 | 1 | 5.9 | |
59.4 | 298 | 1 | 6 | 1 | 6.6 | |
Hong and Kang [38] | 19.3 | 7 | 1 | 1 | 2 | 0.96 |
19.3 | 7 | 1 | 6 | 2 | 1.12 | |
19.3 | 7 | 1 | 6 | 2 | 1.51 | |
19.3 | 7 | 1 | 4 | 2 | 1.49 | |
Baharuddin et al. [34] | 40 | 28 | 1 | 1 | 2 | 0.75 |
40 | 28 | 1 | 1 | 2 | 0.5 | |
40 | 28 | 1 | 1 | 2 | 0.75 | |
40 | 28 | 1 | 1 | 2 | 0.75 | |
40 | 28 | 1 | 1 | 2 | 0.5 | |
40 | 28 | 1 | 1 | 1 | 2.75 | |
40 | 28 | 1 | 1 | 1 | 3.25 | |
40 | 28 | 1 | 1 | 1 | 2.25 | |
40 | 28 | 1 | 1 | 1 | 2.75 | |
40 | 28 | 1 | 1 | 1 | 2.25 | |
40 | 28 | 1 | 1 | 3 | 2.25 | |
40 | 28 | 1 | 1 | 3 | 2 | |
40 | 28 | 1 | 1 | 3 | 2.25 | |
40 | 28 | 1 | 1 | 3 | 2.5 | |
40 | 28 | 1 | 1 | 3 | 2.25 | |
Abo Sabah et al. [10] | 39.9 | 7 | 2 | 6 | 2 | 5 |
39.9 | 7 | 2 | 6 | 2 | 4.41 | |
39.9 | 7 | 2 | 6 | 2 | 4.09 |
Reference | NSC Fc (MPa) | UHPC Age (days) | UHPC Curing Method | NSC Surface Treatment | NSC Moisture condition | Bond Strength (MPa) |
|---|---|---|---|---|---|---|
49.2 | 28 | 2 | 6 | 2 | 6.45 | |
49.2 | 28 | 2 | 6 | 2 | 6.63 | |
49.2 | 28 | 2 | 6 | 2 | 6.8 | |
50.76 | 90 | 2 | 6 | 2 | 6.73 | |
50.76 | 90 | 2 | 6 | 2 | 7.15 | |
50.76 | 90 | 2 | 6 | 2 | 6.97 | |
39.9 | 7 | 2 | 5 | 2 | 5.09 | |
39.9 | 7 | 2 | 5 | 2 | 4.93 | |
39.9 | 7 | 2 | 5 | 2 | 4.72 | |
49.2 | 28 | 2 | 5 | 2 | 8.15 | |
49.2 | 28 | 2 | 5 | 2 | 8.41 | |
49.2 | 28 | 2 | 5 | 2 | 8.56 | |
50.76 | 90 | 2 | 5 | 2 | 8.21 | |
50.76 | 90 | 2 | 5 | 2 | 8.53 | |
50.76 | 90 | 2 | 5 | 2 | 8.85 | |
Saddam et al. [36] | 39.9 | 7 | 2 | 5 | 2 | 4.91 |
49.2 | 28 | 2 | 5 | 2 | 8.37 | |
51.16 | 90 | 2 | 5 | 2 | 8.53 | |
39.9 | 7 | 2 | 6 | 2 | 4.5 | |
49.2 | 28 | 2 | 6 | 2 | 6.63 | |
51.16 | 90 | 2 | 6 | 2 | 6.95 | |
Zhang et al. [37] | 53 | 3 | 1 | 2 | 1 | 2.69 |
53 | 7 | 1 | 2 | 1 | 2.98 | |
53 | 28 | 1 | 2 | 1 | 3.11 | |
53 | 7 | 1 | 4 | 1 | 3.83 | |
53 | 7 | 1 | 4 | 1 | 4.08 | |
53 | 3 | 1 | 4 | 1 | 3.38 | |
53 | 7 | 1 | 4 | 1 | 3.82 | |
53 | 28 | 1 | 4 | 1 | 3.85 | |
53 | 90 | 1 | 4 | 1 | 3.72 | |
53 | 180 | 1 | 4 | 1 | 3.8 | |
53 | 28 | 1 | 1 | 1 | 2.77 | |
53 | 28 | 1 | 5 | 1 | 3.7 | |
53 | 28 | 1 | 5 | 1 | 3.73 | |
53 | 28 | 1 | 5 | 1 | 3.65 | |
53 | 28 | 1 | 2 | 3 | 2.74 | |
53 | 28 | 1 | 2 | 2 | 2.2 | |
53 | 28 | 1 | 4 | 3 | 3.44 | |
53 | 28 | 1 | 4 | 1 | 3.02 | |
53 | 28 | 2 | 1 | 1 | 2.94 | |
53 | 28 | 2 | 1 | 1 | 2.24 | |
53 | 28 | 2 | 2 | 1 | 3.19 | |
53 | 28 | 2 | 2 | 1 | 2.37 | |
53 | 28 | 2 | 4 | 1 | 3.92 | |
53 | 28 | 2 | 4 | 1 | 3.22 | |
42.2 | 28 | 1 | 4 | 1 | 3.51 | |
31.9 | 28 | 1 | 4 | 1 | 2.6 |
Slant-shear dataset
References | NSC Fc (MPa) | UHPC Age (days) | UHPC Curing Method | NSC Surface Treatment | NSC Moisture condition | Bond Strength (MPa) |
|---|---|---|---|---|---|---|
Tayeh et al. [9] | 45 | 3 | 2 | 1 | 2 | 9.68 |
45 | 3 | 2 | 1 | 2 | 7.86 | |
45 | 3 | 2 | 1 | 2 | 7.01 | |
45 | 3 | 2 | 6 | 2 | 14.25 | |
45 | 3 | 2 | 6 | 2 | 14.7 | |
45 | 3 | 2 | 6 | 2 | 12.67 | |
45 | 3 | 2 | 3 | 2 | 11.78 | |
45 | 3 | 2 | 3 | 2 | 9.72 | |
45 | 3 | 2 | 3 | 2 | 11.59 | |
45 | 3 | 2 | 6 | 2 | 16.8 | |
45 | 3 | 2 | 6 | 2 | 17.57 | |
45 | 3 | 2 | 6 | 2 | 17.18 | |
45 | 3 | 2 | 6 | 2 | 11.3 | |
45 | 3 | 2 | 6 | 2 | 12.32 | |
45 | 3 | 2 | 6 | 2 | 10.69 | |
45 | 7 | 2 | 1 | 2 | 7.21 | |
45 | 7 | 2 | 1 | 2 | 8.52 | |
45 | 7 | 2 | 1 | 2 | 9.69 | |
45 | 7 | 2 | 6 | 2 | 14.83 | |
45 | 7 | 2 | 6 | 2 | 14.61 | |
45 | 7 | 2 | 6 | 2 | 12.23 | |
45 | 7 | 2 | 3 | 2 | 12.1 | |
45 | 7 | 2 | 3 | 2 | 10.12 | |
45 | 7 | 2 | 3 | 2 | 11.09 | |
45 | 7 | 2 | 6 | 2 | 16.13 | |
45 | 7 | 2 | 6 | 2 | 18.5 | |
45 | 7 | 2 | 6 | 2 | 16.88 | |
45 | 7 | 2 | 6 | 2 | 10.49 | |
45 | 7 | 2 | 6 | 2 | 13.17 | |
45 | 7 | 2 | 6 | 2 | 11.3 | |
45 | 28 | 2 | 1 | 2 | 7.38 | |
45 | 28 | 2 | 1 | 2 | 10.45 | |
45 | 28 | 2 | 1 | 2 | 8.22 | |
45 | 28 | 2 | 6 | 2 | 14.74 | |
45 | 28 | 2 | 6 | 2 | 12.34 | |
45 | 28 | 2 | 6 | 2 | 14.69 | |
45 | 28 | 2 | 3 | 2 | 11.11 | |
45 | 28 | 2 | 3 | 2 | 12.48 | |
45 | 28 | 2 | 3 | 2 | 13.22 | |
45 | 28 | 2 | 6 | 2 | 17.08 | |
45 | 28 | 2 | 6 | 2 | 18.15 | |
45 | 28 | 2 | 6 | 2 | 18.19 | |
45 | 28 | 2 | 6 | 2 | 14.13 | |
45 | 28 | 2 | 6 | 2 | 10.67 | |
45 | 28 | 2 | 6 | 2 | 13.46 | |
Carbonell et al. [33] | 44.5 | 8 | 1 | 6 | 1 | 16.1 |
44.5 | 8 | 1 | 6 | 1 | 12.1 | |
55.9 | 8 | 1 | 6 | 1 | 21.7 |
References | NSC Fc (MPa) | UHPC Age (days) | UHPC Curing Method | NSC Surface Treatment | NSC Moisture condition | Bond Strength (MPa) |
|---|---|---|---|---|---|---|
55.9 | 8 | 1 | 6 | 1 | 14.6 | |
45.6 | 8 | 1 | 6 | 1 | 17 | |
45.6 | 8 | 1 | 6 | 1 | 12.2 | |
44.5 | 8 | 1 | 6 | 1 | 17.5 | |
44.5 | 8 | 1 | 6 | 1 | 11.3 | |
56.8 | 3 | 1 | 6 | 1 | 17.8 | |
55.9 | 3 | 1 | 6 | 1 | 15.3 | |
54.5 | 3 | 1 | 6 | 1 | 9.4 | |
50.2 | 3 | 1 | 6 | 1 | 9.7 | |
50.2 | 3 | 1 | 6 | 1 | 16.7 | |
55.9 | 2 | 1 | 6 | 1 | 5.9 | |
55.9 | 2 | 1 | 6 | 1 | 3.4 | |
45.6 | 2 | 1 | 6 | 1 | 5.2 | |
Baharuddin et al. [34] | 40 | 28 | 1 | 1 | 2 | 1.35 |
40 | 28 | 1 | 1 | 2 | 1.19 | |
40 | 28 | 1 | 1 | 2 | 2.71 | |
40 | 28 | 1 | 1 | 2 | 2.23 | |
40 | 28 | 1 | 1 | 2 | 2.39 | |
40 | 28 | 1 | 1 | 1 | 3.18 | |
40 | 28 | 1 | 1 | 1 | 3.34 | |
40 | 28 | 1 | 1 | 1 | 3.5 | |
40 | 28 | 1 | 1 | 1 | 3.02 | |
40 | 28 | 1 | 1 | 1 | 3.18 | |
40 | 28 | 1 | 1 | 3 | 2.55 | |
40 | 28 | 1 | 1 | 3 | 2.55 | |
40 | 28 | 1 | 1 | 3 | 2.23 | |
40 | 28 | 1 | 1 | 3 | 2.71 | |
40 | 28 | 1 | 1 | 3 | 2.23 | |
Abo Sabah et al. [10] | 39.9 | 7 | 2 | 6 | 2 | 27.1 |
39.9 | 7 | 2 | 6 | 2 | 23.6 | |
39.9 | 7 | 2 | 6 | 2 | 19.1 | |
49.2 | 28 | 2 | 6 | 2 | 23.6 | |
49.2 | 28 | 2 | 6 | 2 | 19.7 | |
49.2 | 28 | 2 | 6 | 2 | 28.4 | |
50.76 | 90 | 2 | 6 | 2 | 28.4 | |
50.76 | 90 | 2 | 6 | 2 | 19.8 | |
50.76 | 90 | 2 | 6 | 2 | 29.7 | |
39.9 | 7 | 2 | 6 | 2 | 38.2 | |
39.9 | 7 | 2 | 6 | 2 | 29.5 | |
39.9 | 7 | 2 | 6 | 2 | 36.1 | |
49.2 | 28 | 2 | 6 | 2 | 28.5 | |
49.2 | 28 | 2 | 6 | 2 | 37.3 | |
49.2 | 28 | 2 | 6 | 2 | 39.7 | |
50.76 | 90 | 2 | 6 | 2 | 31 | |
50.76 | 90 | 2 | 6 | 2 | 41.2 | |
50.76 | 90 | 2 | 6 | 2 | 36.2 | |
Jafarinejad et al.[35] | 51 | 28 | 1 | 1 | 2 | 11.5 |
51 | 28 | 1 | 6 | 2 | 13.5 | |
57.4 | 28 | 1 | 6 | 2 | 19.6 | |
57.4 | 28 | 1 | 6 | 2 | 29.4 |
References | NSC Fc (MPa) | UHPC Age (days) | UHPC Curing Method | NSC Surface Treatment | NSC Moisture condition | Bond Strength (MPa) |
|---|---|---|---|---|---|---|
53.1 | 3 | 1 | 6 | 2 | 26.5 | |
53.1 | 7 | 1 | 6 | 2 | 28.6 | |
53.1 | 28 | 1 | 6 | 2 | 28.2 | |
Saddam et al. [36] | 39.9 | 7 | 2 | 6 | 2 | 34.6 |
49.2 | 28 | 2 | 6 | 2 | 35.2 | |
51.16 | 90 | 2 | 6 | 2 | 36.13 | |
39.9 | 7 | 2 | 6 | 2 | 23.27 | |
49.2 | 28 | 2 | 6 | 2 | 23.9 | |
51.16 | 90 | 2 | 6 | 2 | 25.9 | |
Zhang et al. [37] | 53 | 3 | 1 | 6 | 1 | 14.35 |
53 | 7 | 1 | 6 | 1 | 15.5.9 | |
53 | 28 | 1 | 6 | 1 | 16.09 | |
53 | 7 | 1 | 6 | 1 | 18.97 | |
53 | 7 | 1 | 6 | 1 | 20.22 | |
53 | 3 | 1 | 6 | 1 | 18.17 | |
53 | 7 | 1 | 6 | 1 | 19.85 | |
53 | 28 | 1 | 6 | 1 | 21.34 | |
53 | 90 | 1 | 6 | 1 | 21.62 | |
53 | 180 | 1 | 6 | 1 | 20.68 | |
53 | 28 | 1 | 1 | 1 | 12.06 | |
53 | 28 | 1 | 6 | 1 | 21.29 | |
53 | 28 | 1 | 6 | 1 | 21.74 | |
53 | 28 | 1 | 6 | 1 | 21.99 | |
53 | 28 | 1 | 6 | 3 | 14.68 | |
53 | 28 | 1 | 6 | 2 | 10.15 | |
53 | 28 | 1 | 6 | 3 | 20.39 | |
53 | 28 | 1 | 6 | 1 | 16.64 | |
53 | 28 | 2 | 1 | 1 | 11.4 | |
53 | 28 | 2 | 1 | 1 | 10.96 | |
53 | 28 | 2 | 6 | 1 | 15.57 | |
53 | 28 | 2 | 6 | 1 | 13.21 | |
53 | 28 | 2 | 6 | 1 | 21.81 | |
53 | 28 | 2 | 6 | 1 | 16.88 | |
42.2 | 28 | 1 | 6 | 1 | 17.93 | |
31.9 | 28 | 1 | 6 | 1 | 13.76 |
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Farouk, A.I.B., Jinsong, Z. Prediction of Interface Bond Strength Between Ultra-High-Performance Concrete (UHPC) and Normal Strength Concrete (NSC) Using a Machine Learning Approach. Arab J Sci Eng 47, 5337–5363 (2022). https://doi.org/10.1007/s13369-021-06433-6
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DOI: https://doi.org/10.1007/s13369-021-06433-6