Analysis of the Effect of Mainshock-Aftershock Sequences on the Fragility of RC Bridge Columns
Abstract
:1. Introduction
2. Basic Theory of Analysis
2.1. Damage Model and Damage Index
2.2. Incremental Damage Evaluation Index
2.3. Fragility Analysis Theory
3. Numerical Model and Selection of Ground Motion
3.1. Numerical Simulation of Bridge Column
3.2. Determination of Basic Parameters of Damage Model
3.3. Selection and Synthesis of Seismic Waves
4. Damage Analysis of RC Column under MS-AS
4.1. Effect of Axial Compression Ratio on Damage of RC Column
4.2. Effect of Shear-Span Ratio on Damage of RC Column
4.3. Effect of Aftershock on Column with Different Damage Degree
5. Fragility Analysis of RC Column under MS-AS
5.1. Effect of Axial Compression Ratio on Fragility of RC Column
5.2. Effect of Shear-Span Ratio on Fragility of RC Column
6. Conclusions
- The seismic demand of the column under the action of the MS-AS sequences is greater than MS. This demand increases with the increase of axial compression ratio and decreases with the increase of reinforcement ratio. When the column is in a slight or no damage state, the effect of aftershock can be basically ignored.
- The additional damage caused by AS can be comprehensively considered in the design according to different magnitudes. When the seismic level is 7 degree, the maximum increase rate of additional damage is about 7% of MS. When the seismic level is 8 degree, the maximum increase rate of additional damage is about 13% of MS. When the seismic level is 9 degree, the maximum growth rate of additional damage is about 15% of MS.
- The additional damage caused by AS gradually decreases with the increase of axial compression ratio in different damage states. When the column is slightly damaged, the influence of aftershocks can be ignored. When the column is in a medium damaged state, the growth rate of additional damage is up to 12.7%. When the column is in a severely damaged state, the growth rate of the additional damage can be conservatively estimated to be 11% of the MS.
- The fragility of bridge piers in different damage states under the action of MS-AS is greater than that of MS. Increasing the reinforcement ratio can significantly reduce the damage probability of columns in different damage states when μ ≤ 0.1. However, the performance of reducing the fragility of columns by increasing the reinforcement ratio gradually decreases with the increase of the axial compression ratio. The effect of aftershock on the exceeding probability is lower in columns with small axial compression ratio.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Damage Level | Damage Characteristics | Damage Index |
---|---|---|
Basically intact | Microcracks appear | 0~0.1 |
Minor damage | Locally through micro cracks appear and the longitudinal bars yield | 0.1~0.25 |
Medium damage | The cracks developed significantly and the concrete protective layer began to fall off | 0.25~0.4 |
Serious injury | The crack widens sharply, and the partial concrete protective layer falls off | 0.4~0.8 |
Completely destroyed | Stirrup fracture or longitudinal reinforcement Buckling fracture, the core area concrete is crushed | ≥0.8 |
Category | d (mm) | fy (Mpa) | fu (Mpa) | εsh | εsu | Es (Mpa) | Esh (Mpa) | ρ (%) |
---|---|---|---|---|---|---|---|---|
Longitudinal | 28 | 400 | 540 | 0.04 | 0.15 | 200,000 | 4000 | 1.0~4.0 |
Stirrup | 16 | 335 | 455 | 0.04 | 0.15 | 200,000 | 4000 | 1.5 |
c (mm) | fcc (Mpa) | fcu (Mpa) | εcc | εcu | Ec (Mpa) | \ | \ | |
Confined concrete | 45 | 26.80 | 21.44 | 0.0014 | 0.004 | 32500 | \ | \ |
Cover concrete | 1510 | 41.90 | 33.52 | 0.0053 | 0.022 | 32500 | \ | \ |
Longitudinal Reinforcement Ratio | |||||||
---|---|---|---|---|---|---|---|
μ | 1.0% | 1.5% | 2.0% | 2.5% | 3.0% | 3.5% | 4.0% |
0.05 | 0.51 | 0.49 | 0.48 | 0.47 | 0.45 | 0.44 | 0.43 |
0.10 | 0.72 | 0.70 | 0.68 | 0.66 | 0.64 | 0.62 | 0.61 |
0.15 | 0.91 | 0.87 | 0.84 | 0.82 | 0.79 | 0.77 | 0.75 |
0.20 | 1.06 | 1.02 | 0.99 | 0.95 | 0.93 | 0.90 | 0.87 |
Axial Load Ratio | ||||
---|---|---|---|---|
PGA (g) | 0.05 | 0.10 | 0.15 | 0.20 |
0.10 | 6.24 | 2.87 | 3.88 | 3.49 |
0.15 | 6.01 | 5.19 | 4.73 | 5.41 |
0.20 | 6.46 | 7.85 | 7.36 | 7.84 |
0.25 | 10.41 | 9.42 | 8.77 | 8.79 |
0.30 | 12.74 | 10.16 | 8.41 | 6.55 |
0.35 | 12.09 | 9.69 | 8.40 | 5.65 |
0.40 | 11.76 | 8.42 | 5.45 | 4.35 |
Seismic Acceleration | ||||||||
---|---|---|---|---|---|---|---|---|
Period | 0.1 g | 0.15 g | 0.20 g | 0.25 g | 0.30 g | 0.35 g | 0.40 g | |
6 | 0.31 | 2.13 | 3.23 | 2.22 | 7.84 | 11.71 | 13.27 | 14.79 |
10 | 0.68 | 2.17 | 3.54 | 5.73 | 9.17 | 8.25 | 8.49 | 8.17 |
14 | 1.14 | 1.18 | 1.67 | 9.17 | 5.84 | 6.73 | 7.69 | 5.84 |
16 | 1.69 | 1.49 | 3.74 | 3.53 | 4.17 | 1.92 | 2.50 | 2.79 |
μ | ρ | MS | MS-AS | ||||
---|---|---|---|---|---|---|---|
a | Ln(b) | a | Ln(b) | ||||
0.05 | 1.0% | 1.645 | 0.600 | 0.875 | 1.679 | 0.733 | 0.885 |
1.5% | 1.513 | 0.203 | 0.871 | 1.542 | 0.318 | 0.882 | |
2.0% | 1.423 | -0.053 | 0.895 | 1.441 | 0.084 | 0.904 | |
2.5% | 1.343 | -0.254 | 0.892 | 1.346 | -0.198 | 0.901 | |
3.0% | 1.300 | -0.402 | 0.889 | 1.298 | -0.354 | 0.899 | |
3.5% | 1.273 | -0.523 | 0.884 | 1.266 | -0.480 | 0.900 | |
4.0% | 1.246 | -0.625 | 0.879 | 1.256 | -0.541 | 0.907 | |
0.10 | 1.0% | 1.558 | 1.116 | 0.844 | 1.602 | 1.256 | 0.856 |
1.5% | 1.534 | 1.031 | 0.864 | 1.565 | 1.146 | 0.874 | |
2.0% | 1.507 | 0.904 | 0.868 | 1.541 | 1.022 | 0.880 | |
2.5% | 1.457 | 0.711 | 0.868 | 1.491 | 0.826 | 0.881 | |
3.0% | 1.399 | 0.536 | 0.865 | 1.424 | 0.631 | 0.875 | |
3.5% | 1.343 | 0.386 | 0.861 | 1.372 | 0.484 | 0.878 | |
4.0% | 1.278 | 0.225 | 0.866 | 1.305 | 0.318 | 0.886 | |
0.15 | 1.0% | 1.382 | 1.181 | 0.784 | 1.399 | 1.263 | 0.801 |
1.5% | 1.401 | 1.149 | 0.815 | 1.431 | 1.257 | 0.833 | |
2.0% | 1.415 | 1.111 | 0.845 | 1.442 | 1.212 | 0.860 | |
2.5% | 1.395 | 1.047 | 0.854 | 1.425 | 1.148 | 0.866 | |
3.0% | 1.393 | 0.999 | 0.866 | 1.423 | 1.096 | 0.877 | |
3.5% | 1.387 | 0.924 | 0.868 | 1.415 | 1.020 | 0.881 | |
4.0% | 1.368 | 0.831 | 0.869 | 1.400 | 0.934 | 0.882 | |
0.20 | 1.0% | 1.297 | 1.217 | 0.765 | 1.300 | 1.272 | 0.774 |
1.5% | 1.288 | 1.190 | 0.778 | 1.300 | 1.258 | 0.792 | |
2.0% | 1.283 | 1.150 | 0.791 | 1.301 | 1.229 | 0.810 | |
2.5% | 1.286 | 1.106 | 0.812 | 1.303 | 1.184 | 0.834 | |
3.0% | 1.296 | 1.078 | 0.833 | 1.317 | 1.160 | 0.852 | |
3.5% | 1.306 | 1.048 | 0.847 | 1.330 | 1.133 | 0.863 | |
4.0% | 1.324 | 1.031 | 0.859 | 1.341 | 1.106 | 0.871 |
Earthquake Type | a | Ln(b) | ||
---|---|---|---|---|
6 | MS | 1.519 | 0.277 | 0.850 |
MS-AS | 1.590 | 0.473 | 0.869 | |
10 | MS | 1.507 | 0.904 | 0.868 |
MS-AS | 1.541 | 1.022 | 0.880 | |
14 | MS | 1.277 | 0.746 | 0.748 |
MS-AS | 1.302 | 0.842 | 0.764 | |
18 | MS | 1.164 | 0.748 | 0.683 |
MS-AS | 1.170 | 0.789 | 0.689 |
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Wang, T.; Han, Q.; Wen, J.; Wang, L. Analysis of the Effect of Mainshock-Aftershock Sequences on the Fragility of RC Bridge Columns. Buildings 2022, 12, 1681. https://doi.org/10.3390/buildings12101681
Wang T, Han Q, Wen J, Wang L. Analysis of the Effect of Mainshock-Aftershock Sequences on the Fragility of RC Bridge Columns. Buildings. 2022; 12(10):1681. https://doi.org/10.3390/buildings12101681
Chicago/Turabian StyleWang, Tongxing, Qiang Han, Jianian Wen, and Lihui Wang. 2022. "Analysis of the Effect of Mainshock-Aftershock Sequences on the Fragility of RC Bridge Columns" Buildings 12, no. 10: 1681. https://doi.org/10.3390/buildings12101681
APA StyleWang, T., Han, Q., Wen, J., & Wang, L. (2022). Analysis of the Effect of Mainshock-Aftershock Sequences on the Fragility of RC Bridge Columns. Buildings, 12(10), 1681. https://doi.org/10.3390/buildings12101681