Abstract
In order to attain sustainable development, recycled concrete aggregates (RCAs) are increasingly utilized in civil engineering projects. Therefore, it is vital to study the performance of structural elements made with RCA. Shear strength is one of the main aspects in examining the structural performance of concrete beams. Shear strength is usually obtained using code calculation methods, and its exact value is obtained by experimental studies. The development of intelligent systems has provided the conditions for faster and easier calculation of this parameter. Shear strength prediction of recycled concrete beams has rarely been investigated. Therefore, in this research, the shear strength of these beams has been investigated and predicted. To achieve this goal, several methods including linear regression, regression tree, ensemble bagged trees, ensemble boosted trees, and Gaussian process regression were employed. The database used in this paper was included of 128 sets of data obtained from experimental studies. Parameters used as model inputs included percentage of recycled aggregates used in beam construction (RCA), compressive strength of concrete (\(f_{c}^{{\prime}}\)), longitudinal reinforcement ratio (\({\uprho }_{l}\)), transvers reinforcement ratio (\({\uprho }_{t}\)), yield strength of longitudinal reinforcement (\(f_{dy}\)), yield strength of transvers reinforcement (\(f_{ty}\)), width of beam (b), effective depth of beam (d), length-to–effective-depth ratio (L/d), shear span-to-effective depth ratio (a/d), and shear strength of beam (\(v_{U}\)) was output of model. Comparison of the results of the aforementioned models showed that the Gaussian process regression model had a better performance in predicting the output parameter, with a coefficient of R2, 0.91, and also had the lowest error, which indicates better performance of this proposed model, in comparison with other models.
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Appendix
Appendix
\({\text{Reference}}\) s | \({\text{ID}}\) | Input data | Output data | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
RCA | \(b\) | \(d\) | \(a/d\) | \(L/d\) | \(\rho_{l}\) | \(\rho_{t}\) | \(f_{c}^{{\prime}}\) | \(f_{dy}\) | \(f_{ty}\) | \(v_{U}\) | ||
(%) | (mm) | (mm) | (-) | (-) | (%) | (%) | (MPa) | (MPa) | (MPa) | (MPa) | ||
[18] | NS-4-CC1 | 0 | 300 | 400 | 3 | 10.75 | 1.27 | 0 | 37.3 | 449 | 0 | 1 |
NS-4-CC2 | 0 | 300 | 400 | 3 | 10.75 | 1.27 | 0 | 34.2 | 449 | 0 | 1.1 | |
NS-6-CC1 | 0 | 300 | 400 | 3 | 10.75 | 2.03 | 0 | 37.3 | 449 | 0 | 1.3 | |
NS-6-CC2 | 0 | 300 | 400 | 3 | 10.75 | 2.03 | 0 | 34.2 | 449 | 0 | 1.5 | |
NS-8-CC1 | 0 | 300 | 400 | 3 | 10.75 | 2.71 | 0 | 37.3 | 449 | 0 | 1.5 | |
NS-8-CC2 | 0 | 300 | 400 | 3 | 10.75 | 2.71 | 0 | 34.2 | 449 | 0 | 1.5 | |
NS-4-CC1 | 100 | 300 | 400 | 3 | 10.75 | 1.27 | 0 | 30 | 449 | 0 | 0.9 | |
NS-4-CC2 | 100 | 300 | 400 | 3 | 10.75 | 1.27 | 0 | 34.1 | 449 | 0 | 0.9 | |
NS-6-CC1 | 100 | 300 | 400 | 3 | 10.75 | 2.03 | 0 | 30 | 449 | 0 | 1.3 | |
NS-6-CC2 | 100 | 300 | 400 | 3 | 10.75 | 2.03 | 0 | 34.1 | 449 | 0 | 1.1 | |
NS-8-CC1 | 100 | 300 | 400 | 3 | 10.75 | 2.71 | 0 | 30 | 449 | 0 | 1.2 | |
NS-8-CC2 | 100 | 300 | 400 | 3 | 10.75 | 2.71 | 0 | 34.1 | 449 | 0 | 1.2 | |
[23] | EM-1.5 | 63.5 | 200 | 300 | 1.5 | 6.33 | 1 | 0 | 41.6 | 440 | 0 | 3.1 |
EM-2 | 63.5 | 200 | 300 | 2 | 7.33 | 1.5 | 0 | 41.4 | 440 | 0 | 2.8 | |
EM-2.7 | 63.5 | 200 | 309 | 2.59 | 8.41 | 1.62 | 0 | 41.6 | 440 | 0 | 1.7 | |
CL-2.7 | 0 | 200 | 309 | 2.59 | 8.41 | 1.62 | 0 | 37.95 | 440 | 0 | 1.5 | |
EM-4 | 63.5 | 200 | 305 | 3.93 | 11.15 | 2.46 | 0 | 41.6 | 440 | 0 | 1.4 | |
EV-2 | 74.3 | 200 | 300 | 2 | 7.33 | 1.5 | 0 | 49.1 | 440 | 0 | 3 | |
EV-4 | 74.3 | 200 | 305 | 3.93 | 11.15 | 2.46 | 0 | 49.1 | 440 | 0 | 1.7 | |
EM-L | 63.5 | 200 | 201 | 2.69 | 10.35 | 1.99 | 0 | 41.6 | 440 | 0 | 2.2 | |
EM-M | 63.5 | 200 | 309 | 2.59 | 8.41 | 1.62 | 0 | 41.6 | 440 | 0 | 1.7 | |
CL-M | 0 | 200 | 309 | 2.59 | 8.41 | 1.62 | 0 | 37.95 | 440 | 0 | 1.5 | |
EM-H | 63.5 | 200 | 381 | 2.73 | 8.35 | 1.83 | 0 | 41.6 | 440 | 0 | 1.3 | |
EM-VH | 63.5 | 200 | 476 | 2.73 | 7.77 | 1.68 | 0 | 41.6 | 440 | 0 | 1.1 | |
EV-H | 74.3 | 200 | 381 | 2.73 | 8.35 | 1.83 | 0 | 41.6 | 440 | 0 | 1.5 | |
EV-VH | 74.3 | 200 | 476 | 2.73 | 7.77 | 1.68 | 0 | 49.1 | 440 | 0 | 1.3 | |
[71] | S0-1a | 0 | 150 | 200 | 3.825 | 9.9 | 1.34 | 0 | 38.6 | 572 | 0 | 1.04 |
S0-1b | 0 | 150 | 200 | 3.825 | 9.9 | 1.34 | 0 | 46.5 | 572 | 0 | 1.23 | |
S0-2a | 50 | 150 | 200 | 3.825 | 9.9 | 1.34 | 0 | 40 | 572 | 0 | 1.35 | |
S0-2b | 50 | 150 | 200 | 3.825 | 9.9 | 1.34 | 0 | 39.3 | 572 | 0 | 1.41 | |
S50-1a | 100 | 150 | 200 | 3.825 | 9.9 | 1.34 | 0 | 43.8 | 572 | 0 | 1.47 | |
S50-1b | 100 | 150 | 200 | 3.825 | 9.9 | 1.34 | 0 | 38.5 | 572 | 0 | 1.3 | |
S50-2a | 0 | 150 | 200 | 3.825 | 9.9 | 1.34 | 0 | 32.6 | 572 | 0 | 1.46 | |
S50-2b | 0 | 150 | 200 | 3.825 | 9.9 | 1.34 | 0 | 50.3 | 572 | 0 | 1.37 | |
S100-1a | 50 | 150 | 200 | 3.825 | 9.9 | 1.34 | 0 | 43.6 | 572 | 0 | 1.21 | |
S100-1b | 50 | 150 | 200 | 3.825 | 9.9 | 1.34 | 0 | 40.2 | 572 | 0 | 1.27 | |
S100-2a | 100 | 150 | 200 | 3.825 | 9.9 | 1.34 | 0 | 41.4 | 572 | 0 | 1.33 | |
S100-2b | 100 | 150 | 200 | 3.825 | 9.9 | 1.34 | 0 | 35.7 | 572 | 0 | 1.2 | |
[20] | V0CC | 0 | 200 | 303 | 3.3 | 10.07 | 2.98 | 0 | 40.2 | 571 | 0 | 1.47 |
V0RC | 50 | 200 | 303 | 3.3 | 10.07 | 2.98 | 0 | 39.65 | 571 | 0 | 1.5 | |
V24RC | 50 | 200 | 303 | 3.3 | 10.07 | 2.98 | 0.12 | 39.23 | 571 | 571 | 2.71 | |
V17CC | 0 | 200 | 303 | 3.3 | 10.07 | 2.98 | 0.17 | 39.08 | 571 | 571 | 2.49 | |
V17RC | 50 | 200 | 303 | 3.3 | 10.07 | 2.98 | 0.17 | 41.49 | 571 | 571 | 2.92 | |
V13CC | 0 | 200 | 303 | 3.3 | 10.07 | 2.98 | 0.22 | 37.66 | 571 | 571 | 3.14 | |
[21] | V0CC | 0 | 200 | 303 | 3.3 | 10.07 | 2.98 | 0 | 46.77 | 571 | 0 | 1.66 |
V0RC | 50 | 200 | 303 | 3.3 | 10.07 | 2.98 | 0 | 41.45 | 571 | 0 | 1.38 | |
V24CC | 0 | 200 | 303 | 3.3 | 10.07 | 2.98 | 0.12 | 43.66 | 571 | 571 | 2.48 | |
V24RC | 50 | 200 | 303 | 3.3 | 10.07 | 2.98 | 0.12 | 43.25 | 571 | 571 | 2.43 | |
V17CC | 0 | 200 | 303 | 3.3 | 10.07 | 2.98 | 0.17 | 45.16 | 571 | 571 | 3.3 | |
V17RC | 50 | 200 | 303 | 3.3 | 10.07 | 2.98 | 0.17 | 44.49 | 571 | 571 | 3.18 | |
V13CC | 0 | 200 | 303 | 3.3 | 10.07 | 2.98 | 0.22 | 42.75 | 571 | 571 | 3.63 | |
V13RC | 50 | 200 | 303 | 3.3 | 10.07 | 2.98 | 0.22 | 41.45 | 571 | 571 | 3.34 | |
[32] | ORNm-b2 | 100 | 200 | 250 | 3.2 | 10.4 | 1.61 | 0.28 | 58.3 | 410 | 210 | 2.37 |
GNNI-b2 | 0 | 200 | 250 | 3.2 | 10.4 | 1.61 | 0.28 | 38.7 | 410 | 210 | 2.17 | |
GRNI-b2 | 100 | 200 | 250 | 3.2 | 10.4 | 1.61 | 0.28 | 39.3 | 410 | 210 | 2.33 | |
GRRI-b2 | 100 | 200 | 250 | 3.2 | 10.4 | 1.61 | 0.28 | 35.8 | 410 | 210 | 2.26 | |
GRNm-b2 | 100 | 200 | 250 | 3.2 | 10.4 | 1.61 | 0.28 | 59.6 | 410 | 210 | 2.37 | |
GNNh-b2 | 0 | 200 | 250 | 3.2 | 10.4 | 1.61 | 0.28 | 93.4 | 410 | 210 | 2.5 | |
GRNh-b2 | 100 | 200 | 250 | 3.2 | 10.4 | 1.61 | 0.28 | 89.1 | 410 | 210 | 2.42 | |
GRRh-b2 | 100 | 200 | 250 | 3.2 | 10.4 | 1.61 | 0.28 | 82.2 | 410 | 210 | 2.55 | |
BNNI-b2 | 0 | 200 | 250 | 3.2 | 10.4 | 1.61 | 0.28 | 60.8 | 410 | 210 | 2.38 | |
BRNI-b2 | 100 | 200 | 250 | 3.2 | 10.4 | 1.61 | 0.28 | 59.6 | 410 | 210 | 2.38 | |
BRRI-b2 | 100 | 200 | 250 | 3.2 | 10.4 | 1.61 | 0.28 | 57.6 | 410 | 210 | 2.36 | |
BNNh-b2 | 0 | 200 | 250 | 3.2 | 10.4 | 1.61 | 0.28 | 100.9 | 410 | 210 | 2.62 | |
BRNh-b2 | 100 | 200 | 250 | 3.2 | 10.4 | 1.61 | 0.28 | 107.8 | 410 | 210 | 2.61 | |
BRRh-b2 | 100 | 200 | 250 | 3.2 | 10.4 | 1.61 | 0.28 | 100.5 | 410 | 210 | 2.56 | |
[72] | HC-1 | 0 | 200 | 309 | 3.2 | 9.9 | 2.92 | 0 | 41.91 | 500 | 0 | 1.63 |
HC-2 | 0 | 200 | 309 | 3.2 | 9.9 | 2.97 | 0.22 | 41.91 | 500 | 500 | 3.45 | |
HC-3 | 0 | 200 | 309 | 3.2 | 9.9 | 2.97 | 0.17 | 41.91 | 500 | 500 | 2.86 | |
HR25-1 | 25 | 200 | 309 | 3.2 | 9.9 | 2.92 | 0 | 42.38 | 500 | 0 | 1.68 | |
HR25-2 | 25 | 200 | 309 | 3.2 | 9.9 | 2.97 | 0.22 | 42.38 | 500 | 500 | 3.02 | |
HR25-3 | 25 | 200 | 309 | 3.2 | 9.9 | 2.97 | 0.17 | 42.38 | 500 | 500 | 2.73 | |
HR50-1 | 50 | 200 | 309 | 3.2 | 9.9 | 2.92 | 0 | 41.34 | 500 | 0 | 1.44 | |
HR50-2 | 50 | 200 | 309 | 3.2 | 9.9 | 2.97 | 0.22 | 41.34 | 500 | 500 | 3.56 | |
HR50-3 | 50 | 200 | 309 | 3.2 | 9.9 | 2.97 | 0.17 | 41.34 | 500 | 500 | 2.85 | |
HR100-1 | 100 | 200 | 309 | 3.2 | 9.9 | 2.92 | 0 | 39.75 | 500 | 0 | 1.36 | |
HR100-2 | 100 | 200 | 309 | 3.2 | 9.9 | 2.97 | 0.22 | 39.75 | 500 | 500 | 3.07 | |
HR100-3 | 100 | 200 | 309 | 3.2 | 9.9 | 2.97 | 0.17 | 39.76 | 500 | 500 | 2.64 | |
[77] | B2 | 25 | 100 | 180 | 2 | 9.4 | 1.9 | 0 | 30.42 | 560 | 0 | 2.4 |
B3 | 50 | 100 | 180 | 2 | 9.4 | 1.9 | 0 | 29.58 | 560 | 0 | 1.97 | |
B4 | 0 | 100 | 180 | 2 | 9.4 | 1.9 | 0.3 | 31.67 | 560 | 305 | 2.47 | |
B5 | 25 | 100 | 180 | 2 | 9.4 | 1.9 | 0.3 | 36.25 | 560 | 305 | 2.76 | |
B6 | 50 | 100 | 180 | 2 | 9.4 | 1.9 | 0.3 | 29.58 | 560 | 305 | 2.33 | |
B8 | 25 | 100 | 180 | 2 | 9.4 | 1.9 | 0.5 | 36.25 | 560 | 305 | 3.39 | |
B11 | 25 | 100 | 180 | 2.5 | 9.4 | 1.9 | 0.3 | 30.42 | 560 | 305 | 2.63 | |
B12 | 50 | 100 | 180 | 2.5 | 9.4 | 1.9 | 0.3 | 29.58 | 560 | 305 | 1.9 | |
[78] | 35-A-0-0 | 0 | 150 | 388 | 3 | 7.47 | 0.79 | 0 | 35.8 | 534 | 0 | 0.946 |
35-A-0-100 | 100 | 150 | 388 | 3 | 7.47 | 0.79 | 0 | 31 | 534 | 0 | 0.74 | |
35-A-0-10 | 10 | 150 | 388 | 3 | 7.47 | 0.79 | 0 | 34.3 | 534 | 0 | 0.774 | |
35-A-0-20 | 20 | 150 | 388 | 3 | 7.47 | 0.79 | 0 | 34.1 | 534 | 0 | 0.698 | |
35-A-0-20r | 20 | 150 | 388 | 3 | 7.47 | 0.79 | 0 | 34.2 | 534 | 0 | 0.85 | |
35-A-0-35 | 35 | 150 | 388 | 3 | 7.47 | 0.79 | 0 | 32.5 | 534 | 0 | 0.784 | |
35-A-0-50 | 50 | 150 | 388 | 3 | 7.47 | 0.79 | 0 | 34.4 | 534 | 0 | 0.816 | |
35-A-0-75 | 75 | 150 | 388 | 3 | 7.47 | 0.79 | 0 | 33.7 | 534 | 0 | 0.824 | |
35-S-0-05 (10) | 5 | 150 | 388 | 3 | 7.47 | 0.79 | 0 | 39 | 534 | 0 | 0.972 | |
35-S-0-10 (20) | 10 | 150 | 388 | 3 | 7.47 | 0.79 | 0 | 37.3 | 534 | 0 | 0.912 | |
35-S-0-16 (35) | 16 | 150 | 388 | 3 | 7.47 | 0.79 | 0 | 37.4 | 534 | 0 | 0.941 | |
35-S-0-23(50) | 23 | 150 | 388 | 3 | 7.47 | 0.79 | 0 | 37.1 | 534 | 0 | 0.821 | |
35-S-0-35(75) | 35 | 150 | 388 | 3 | 7.47 | 0.79 | 0 | 36.4 | 534 | 0 | 0.74 | |
[79] | 0-30 | 30 | 150 | 200 | 3 | 9.75 | 2.09 | 0.15 | 20.9 | 560 | 560 | 2.7 |
30-0 | 30 | 150 | 200 | 3 | 9.75 | 2.09 | 0.15 | 22 | 560 | 560 | 2.58 | |
30-30 | 30 | 150 | 200 | 3 | 9.75 | 2.09 | 0.15 | 22.1 | 560 | 560 | 2.85 | |
0-100 | 100 | 150 | 200 | 3 | 9.75 | 2.09 | 0.15 | 25.7 | 560 | 560 | 2.87 | |
100-100 | 100 | 150 | 200 | 3 | 9.75 | 2.09 | 0.15 | 19.6 | 560 | 560 | 2.27 | |
[80] | B1-2-0-0 | 0 | 150 | 250 | 2 | 8 | 2.1 | 0 | 28.8 | 420 | 0 | 2.37 |
B2-2-15-0 | 15 | 150 | 250 | 2 | 8 | 2.1 | 0 | 28.2 | 420 | 0 | 2.19 | |
B2-2-30-0 | 30 | 150 | 250 | 2 | 8 | 2.1 | 0 | 26.9 | 420 | 0 | 2.04 | |
B3-2-45-0 | 45 | 150 | 250 | 2 | 8 | 2.1 | 0 | 25 | 420 | 0 | 1.92 | |
B3-1-30-0 | 30 | 150 | 250 | 1 | 8 | 2.1 | 0 | 26.9 | 420 | 0 | 2.33 | |
B3-3-30-0 | 30 | 150 | 250 | 3 | 8 | 2.1 | 0 | 26.9 | 420 | 0 | 1.51 | |
[81] | 35-1.1-0 | 0 | 150 | 388 | 3 | 7.47 | 1.38 | 0.39 | 33.2 | 565 | 308 | 1.26 |
35-1.7-0 | 0 | 150 | 388 | 3 | 7.47 | 1.38 | 0.61 | 35 | 565 | 308 | 1.42 | |
35-2-0 | 0 | 150 | 388 | 3 | 7.47 | 1.38 | 0.75 | 34 | 565 | 308 | 2.13 | |
35-2.6-0 | 0 | 150 | 388 | 3 | 7.47 | 1.38 | 0.97 | 35 | 565 | 308 | 1.86 | |
35-3.2-0 | 0 | 150 | 388 | 3 | 7.47 | 1.38 | 1.16 | 34 | 565 | 308 | 2.54 | |
35-3.7-0 | 0 | 150 | 388 | 3 | 7.47 | 1.38 | 1.37 | 33.2 | 565 | 308 | 2.46 | |
35-1.1-20 | 20 | 150 | 388 | 3 | 7.47 | 1.38 | 0.39 | 35.1 | 565 | 308 | 1.16 | |
35-1.7-20 | 20 | 150 | 388 | 3 | 7.47 | 1.38 | 0.61 | 35.7 | 565 | 308 | 1.34 | |
35-2-20 | 20 | 150 | 388 | 3 | 7.47 | 1.38 | 0.75 | 35.4 | 565 | 308 | 2.03 | |
35-2.6-20 | 20 | 150 | 388 | 3 | 7.47 | 1.38 | 0.97 | 35.7 | 565 | 308 | 2.05 | |
35-3.2-20 | 20 | 150 | 388 | 3 | 7.47 | 1.38 | 1.16 | 35.4 | 565 | 308 | 2.45 | |
35-3.7-20 | 20 | 150 | 388 | 3 | 7.47 | 1.38 | 1.37 | 35.1 | 565 | 308 | 2.33 | |
35-1.1-100 | 100 | 150 | 388 | 3 | 7.47 | 1.38 | 0.39 | 32.7 | 565 | 308 | 1.13 | |
35-1.7-100 | 100 | 150 | 388 | 3 | 7.47 | 1.38 | 0.61 | 32.7 | 565 | 308 | 1.43 | |
35-2-100 | 100 | 150 | 388 | 3 | 7.47 | 1.38 | 0.75 | 33.8 | 565 | 308 | 1.79 | |
35-2.6-100 | 100 | 150 | 388 | 3 | 7.47 | 1.38 | 0.97 | 32.7 | 565 | 308 | 1.81 | |
35-3.2-100 | 100 | 150 | 388 | 3 | 7.47 | 1.38 | 1.16 | 33.8 | 565 | 308 | 2.24 | |
35-3.7-100 | 100 | 150 | 388 | 3 | 7.47 | 1.38 | 1.37 | 32.7 | 565 | 308 | 2.07 | |
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Omidinasab, F., Sahraei Moghadam, A. & Dowlatshahi, M.B. Predictive model for shear strength estimation in reinforced concrete beams with recycled aggregates using Gaussian process regression. Neural Comput & Applic 35, 8487–8503 (2023). https://doi.org/10.1007/s00521-022-08126-z
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DOI: https://doi.org/10.1007/s00521-022-08126-z