Multi-Objective Optimization of Three Different SMA-LRBs for Seismic Protection of a Benchmark Highway Bridge against Real and Synthetic Ground Motions
Abstract
:1. Introduction
2. Benchmark Highway Bridge
2.1. Structural Model
2.2. Earthquake Excitations
3. Ground Motion Time Histories
- Distance to the causative fault approximately the same as the distance of the bridge to the closest active seismic fault.
- Size of the earthquake equal to the probable maximum magnitude at the closest fault.
- Soil conditions and deeper geological surroundings of the recording station similar to those beneath the bridge.
4. The SMA-LRBs
4.1. The Hysteresis Model of the LRBs
4.2. The Hysteresis Model of SMA Wires
4.2.1. SMA-LRB with Double-Cross Wires
4.2.2. SMA-LRB with Straight Wires
4.2.3. SMA-LRB with Cross Wires
4.2.4. Efficiency of Different Wire Configurations
4.2.5. Force–Displacement Curves
5. Optimizing the SMA-LRBs
6. Numerical Analysis
6.1. Base Shear
6.2. Mid-Span Acceleration
6.3. Mid-Span Displacement
6.4. Residual Mid-Span Displacement
6.5. Comparing the Three SMA-LRBs
7. Conclusions
- As for the optimized double-cross SMA-LRB, this device decreases the maximum base shear and deck acceleration of the isolated bridge from 70.29% to 87.85% and from 20.89% to 62.57%, respectively, under various records compared with the non-isolated bridge. However, LRB still leads to the largest reduction in these figures, from 77.71% to 91.07%, and from 56.85% to 82.66% under various records. Moreover, SMA-LRBs with double-cross wires reduce the maximum mid-span and residual displacements in ranges between 39.51% and 81.23% and from 52.16% to 98.67%, in turn, under different ground motions compared with the LRB isolated bridge. In brief, amongst the three SMA-LRBs, it has the largest shear force and deck acceleration, and needs the longest SMA wire, but leads to the least maximum and residual displacements. Finally, the result of the WSM method indicates that DC-SMA-LRB is the second most successful device.
- Regarding the optimized straight SMA-LRB, it decreases the maximum base shear and deck acceleration of the isolated bridge slightly more than the double-cross SMA-LRBs, from 72.50% to 88.28% and from 26.76% to 66.90%, respectively, under different records, compared with the non-isolated benchmark bridge. Besides, SMA-LRBs with straight wires reduce the maximum and residual mid-span displacement slightly less than the DC-SMA-LRBs, from 37.06% to 80.00% and from 51.55% to 94.67%, in turn, under various excitations, compared with the LRBs. Moreover, the required length of the SMA wire is the least for this configuration. Lastly, the WSM method shows that S-SMA-LRB has the best overall performance.
- As regards the optimized cross SMA-LRB, it results in the reduction of the base shear and deck acceleration more than the other two SMA isolators, compared with the non-isolated bridge. However, it decreases the maximum and residual displacements less than the others and uses rather long SMA wires. Eventually, by conducting WSM, it is ranked as the least successful device.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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RSN | Station | Pulse Period (s) | 5–95% Duration (s) | PGA (g) | Earthquake Year and Name | Mw | Mechanism | Rrup (km) | Vs30 (m/s) |
---|---|---|---|---|---|---|---|---|---|
8161 | “El Centro Array #12” | 8.722 | 32.9 | 0.31 | 2010, “El Mayor-Cucapah Mexico” | 7.2 | strike slip | 11.26 | 196.88 |
8606 | “Westside Elementary School” | 7.084 | 25.3 | 0.28 | 2010, “El Mayor-Cucapah Mexico” | 7.2 | strike slip | 11.44 | 242 |
Synthetic Accelerogram # for the station “El Centro Array #12” | 1st Horizontal Component | 2nd Horizontal Component | ||||||
PGA (g) | Target PGA (g) | AI (m/s) | Target AI (m/s) | PGA (g) | Target PGA (g) | AI (m/s) | Target AI (m/s) | |
1 | 0.33 | 0.27 | 2.72 | 2.75 | 0.30 | 0.31 | 3.21 | 3.20 |
2 | 0.34 | 2.75 | 0.36 | 3.42 | ||||
3 | 0.30 | 2.93 | 0.31 | 3.21 | ||||
4 | 0.32 | 2.86 | 0.35 | 3.20 | ||||
5 | 0.31 | 2.87 | 0.34 | 3.27 | ||||
Synthetic Accelerogram # for the station “Westside Elementary School” | 1st Horizontal Component | 2nd Horizontal Component | ||||||
PGA (g) | Target PGA (g) | AI (m/s) | Target AI (m/s) | PGA (g) | Target PGA (g) | AI (m/s) | Target AI (m/s) | |
1 | 0.27 | 0.26 | 1.23 | 1.22 | 0.36 | 0.28 | 1.87 | 1.93 |
2 | 0.29 | 1.27 | 0.31 | 1.99 | ||||
3 | 0.28 | 1.27 | 0.35 | 2.07 | ||||
4 | 0.22 | 1.19 | 0.31 | 1.97 | ||||
5 | 0.25 | 1.29 | 0.39 | 2.09 |
Yield Displacement(m) | Post-Yield Stiffness (kN/mm) | Initial Stiffness (kN/mm) | |
---|---|---|---|
Abutment Isolators | 0.015 | 0.6 | 4.8 |
Mid-pier Isolators | 0.015 | 1.2 | 9.6 |
Maximum Base Shear (N) | |||||
---|---|---|---|---|---|
Earthquake | Non-Isolated | LRB Isolated | DC-SMA-LRB Isolated | S-SMA-LRB Isolated | C-SMA-LRB Isolated |
RSN 8161 | 7.09 × 106 | 1.58 × 106 | 1.96 × 106 | 1.83 × 106 | 1.71 × 106 |
Synthetic #1 | 7.07 × 106 | 1.30 × 106 | 1.70 × 106 | 1.59 × 106 | 1.46 × 106 |
Synthetic #2 | 6.82 × 106 | 0.91 × 106 | 1.06 × 106 | 1.04 × 106 | 1.02 × 106 |
Synthetic #3 | 6.80 × 106 | 1.22 × 106 | 2.02 × 106 | 1.87 × 106 | 1.35 × 106 |
Synthetic #4 | 6.61 × 106 | 0.88 × 106 | 1.69 × 106 | 1.57 × 106 | 1.49 × 106 |
Synthetic #5 | 8.25 × 106 | 1.18 × 106 | 1.75 × 106 | 1.64 × 106 | 1.25 × 106 |
RSN 8606 | 7.17 × 106 | 0.64 × 106 | 0.94 × 106 | 0.84 × 106 | 0.79 × 106 |
Synthetic #1 | 6.29 × 106 | 0.97 × 106 | 1.07 × 106 | 1.06 × 106 | 1.01 × 106 |
Synthetic #2 | 6.39 × 106 | 0.84 × 106 | 1.18 × 106 | 1.13 × 106 | 1.10 × 106 |
Synthetic #3 | 7.90 × 106 | 0.72 × 106 | 0.96 × 106 | 0.94 × 106 | 0.90 × 106 |
Synthetic #4 | 6.71 × 106 | 0.66 × 106 | 0.91 × 106 | 0.84 × 106 | 0.71 × 106 |
Synthetic #5 | 6.29 × 106 | 0.60 × 106 | 1.04 × 106 | 0.96 × 106 | 0.83 × 106 |
Maximum Mid-span Acceleration (ms−2) | |||||
---|---|---|---|---|---|
Earthquake | Non-Isolated | LRB Isolated | DC-SMA-LRB Isolated | S-SMA-LRB Isolated | C-SMA-LRB Isolated |
RSN 8161 | 4.45 | 1.92 | 3.33 | 3.05 | 2.97 |
Synthetic #1 | 4.27 | 1.29 | 2.71 | 2.45 | 2.07 |
Synthetic #2 | 4.34 | 1.45 | 2.45 | 2.37 | 1.99 |
Synthetic #3 | 4.26 | 1.76 | 3.37 | 3.12 | 2.07 |
Synthetic #4 | 4.30 | 1.22 | 3.06 | 2.89 | 2.70 |
Synthetic #5 | 5.07 | 1.40 | 2.74 | 2.44 | 1.98 |
RSN 8606 | 4.50 | 1.01 | 2.00 | 1.88 | 1.39 |
Synthetic #1 | 5.71 | 0.99 | 2.14 | 1.89 | 1.47 |
Synthetic #2 | 4.02 | 1.45 | 2.24 | 2.10 | 1.87 |
Synthetic #3 | 4.90 | 1.79 | 2.20 | 2.02 | 2.01 |
Synthetic #4 | 4.23 | 1.28 | 1.90 | 1.74 | 1.47 |
Synthetic #5 | 4.04 | 1.38 | 1.98 | 1.76 | 1.75 |
Maximum Mid-Span Displacement (m) | ||||||||
---|---|---|---|---|---|---|---|---|
Non-ISOLATED | LRB Isolated | DC-SMA-LRB Isolated | S-SMA-LRB Isolated | C-SMA-LRB Isolated | ||||
Earthquake | Reduction Ratio (%) | Reduction Ratio (%) | Reduction Ratio (%) | |||||
RSN 8161 | 0.73 × 10−1 | 2.98 × 10−1 | 1.53 × 10−1 | 48.66 | 1.62 × 10−1 | 45.64 | 2.20 × 10−1 | 26.17 |
Synthetic #1 | 0.71 × 10−1 | 4.60 × 10−1 | 1.54 × 10−1 | 66.52 | 1.59 × 10−1 | 65.43 | 1.64 × 10−1 | 64.35 |
Synthetic #2 | 0.69 × 10−1 | 3.12 × 10−1 | 1.54 × 10−1 | 50.64 | 1.70 × 10−1 | 45.51 | 2.00 × 10−1 | 35.90 |
Synthetic #3 | 0.73 × 10−1 | 3.81 × 10−1 | 1.63 × 10−1 | 57.22 | 1.69 × 10−1 | 55.64 | 2.44 × 10−1 | 35.96 |
Synthetic #4 | 0.68 × 10−1 | 3.87 × 10−1 | 1.77 × 10−1 | 54.26 | 1.78 × 10−1 | 54.01 | 2.43 × 10−1 | 37.21 |
Synthetic #5 | 0.86 × 10−1 | 2.86 × 10−1 | 1.73 × 10−1 | 39.51 | 1.80 × 10−1 | 37.06 | 1.84 × 10−1 | 35.66 |
RSN 8606 | 0.75 × 10−1 | 3.92 × 10−1 | 1.15 × 10−1 | 70.66 | 1.22 × 10−1 | 68.88 | 1.25 × 10−1 | 68.11 |
Synthetic #1 | 0.42 × 10−1 | 3.45 × 10−1 | 1.31 × 10−1 | 62.03 | 1.38 × 10−1 | 60.00 | 1.48 × 10−1 | 57.10 |
Synthetic #2 | 0.69 × 10−1 | 4.81 × 10−1 | 1.19 × 10−1 | 75.26 | 1.34 × 10−1 | 72.14 | 1.84 × 10−1 | 61.75 |
Synthetic #3 | 0.81 × 10−1 | 6.50 × 10−1 | 1.22 × 10−1 | 81.23 | 1.30 × 10−1 | 80.00 | 2.17 × 10−1 | 66.62 |
Synthetic #4 | 0.70 × 10−1 | 4.06 × 10−1 | 1.21 × 10−1 | 70.20 | 1.30 × 10−1 | 67.98 | 1.80 × 10−1 | 55.67 |
Synthetic #5 | 0.68 × 10−1 | 4.79 × 10−1 | 1.00 × 10−1 | 79.12 | 1.13 × 10−1 | 76.41 | 1.97 × 10−1 | 58.87 |
Residual Mid-Span Displacement (m) | |||||||
---|---|---|---|---|---|---|---|
LRB Isolated | DC-SMA-LRB Isolated | S-SMA-LRB Isolated | C-SMA-LRB Isolated | ||||
Earthquake | Reduction Ratio (%) | Reduction Ratio (%) | Reduction Ratio (%) | ||||
RSN 8161 | 0.1182 | 0.0300 | 74.62 | 0.0349 | 70.47 | 0.0538 | 54.48 |
Synthetic #1 | 0.0657 | 0.0033 | 94.98 | 0.0035 | 94.67 | 0.0216 | 67.12 |
Synthetic #2 | 0.0741 | 0.0349 | 52.90 | 0.0359 | 51.55 | 0.0426 | 42.51 |
Synthetic #3 | 0.1617 | 0.0150 | 90.72 | 0.0185 | 88.56 | 0.0372 | 76.99 |
Synthetic #4 | 0.0995 | 0.0476 | 52.16 | 0.0481 | 51.66 | 0.0553 | 44.42 |
Synthetic #5 | 0.1248 | 0.0348 | 72.12 | 0.0413 | 66.91 | 0.0653 | 47.68 |
RSN 8606 | 0.1882 | 0.0408 | 78.32 | 0.0414 | 78.00 | 0.0535 | 71.57 |
Synthetic #1 | 0.1818 | 0.0326 | 82.07 | 0.0599 | 67.05 | 0.0663 | 63.53 |
Synthetic #2 | 0.1374 | 0.0157 | 88.57 | 0.0226 | 83.55 | 0.0245 | 82.17 |
Synthetic #3 | 0.1319 | 0.0018 | 98.67 | 0.0089 | 93.25 | 0.0276 | 79.08 |
Synthetic #4 | 0.0834 | 0.0155 | 81.41 | 0.0227 | 72.78 | 0.0314 | 62.35 |
Synthetic #5 | 0.1481 | 0.0153 | 89.67 | 0.0451 | 69.55 | 0.0721 | 51.32 |
Criteria | Alternatives | Normalized Alternatives | Weights | Weighted Sum Matrix | ||||||
---|---|---|---|---|---|---|---|---|---|---|
DC-SMA-LRB | S-SMA-LRB | C-SMA-LRB | DC-SMA-LRB | S-SMA-LRB | C-SMA-LRB | DC-SMA-LRB | S-SMA-LRB | C-SMA-LRB | ||
Maximum Base Shear (N) | 1,960,000 | 1,830,000 | 1,710,000 | 0.87 | 0.93 | 1.00 | 0.15 | 0.13 | 0.14 | 0.15 |
Maximum mid-span Acceleration (ms−2) | 3.33 | 3.05 | 2.97 | 0.89 | 0.97 | 1.00 | 0.15 | 0.13 | 0.15 | 0.15 |
Maximum mid-span Displacement (m) | 0.153 | 0.162 | 0.22 | 1.00 | 0.94 | 0.70 | 0.3 | 0.30 | 0.28 | 0.21 |
mid-span Residual Displacement (m) | 0.03 | 0.0349 | 0.0538 | 1.00 | 0.86 | 0.56 | 0.3 | 0.30 | 0.26 | 0.17 |
Length of the SMA wire (cm) | 242.71 | 133.12 | 205.85 | 0.55 | 1.00 | 0.65 | 0.10 | 0.05 | 0.10 | 0.06 |
Performance Score | 0.92 | 0.93 | 0.74 | |||||||
Rank | 2 | 1 | 3 |
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Hosseini, R.; Rashidi, M.; Bulajić, B.Đ.; Arani, K.K. Multi-Objective Optimization of Three Different SMA-LRBs for Seismic Protection of a Benchmark Highway Bridge against Real and Synthetic Ground Motions. Appl. Sci. 2020, 10, 4076. https://doi.org/10.3390/app10124076
Hosseini R, Rashidi M, Bulajić BĐ, Arani KK. Multi-Objective Optimization of Three Different SMA-LRBs for Seismic Protection of a Benchmark Highway Bridge against Real and Synthetic Ground Motions. Applied Sciences. 2020; 10(12):4076. https://doi.org/10.3390/app10124076
Chicago/Turabian StyleHosseini, Reyhaneh, Maria Rashidi, Borko Đ. Bulajić, and Kamyar Karbasi Arani. 2020. "Multi-Objective Optimization of Three Different SMA-LRBs for Seismic Protection of a Benchmark Highway Bridge against Real and Synthetic Ground Motions" Applied Sciences 10, no. 12: 4076. https://doi.org/10.3390/app10124076
APA StyleHosseini, R., Rashidi, M., Bulajić, B. Đ., & Arani, K. K. (2020). Multi-Objective Optimization of Three Different SMA-LRBs for Seismic Protection of a Benchmark Highway Bridge against Real and Synthetic Ground Motions. Applied Sciences, 10(12), 4076. https://doi.org/10.3390/app10124076