Research on the Vibration Response of High-Rise Buildings under Blasting Load
Abstract
:1. Introduction
2. Theory of Blasting Vibration
2.1. Theory of Blasting Seismic Wave Propagation
2.2. Resonance Theory
3. Field Test of Blasting Vibration
3.1. Overview of the Project
3.2. Monitoring Content and Methods
3.3. Monitoring Results
3.3.1. PPV and Ground Frequency
3.3.2. PPV and Frequency of the Buildings
3.4. Analysis of Monitoring Results
3.4.1. PPV
3.4.2. Frequency
4. Numerical Test of Blasting Vibration
4.1. Model and Parameters
4.1.1. Model
4.1.2. Material Parameters
4.2. Numerical Test Results
4.3. Analysis of Numerical Test Results
4.4. Comparative Analysis of Numerical and Field Tests
4.4.1. Comparison of Ground PPV
4.4.2. Comparison of Building PPV
4.5. Blasting Vibration Tests Considering Different Slope Height Differences
4.5.1. Numerical Model
4.5.2. Numerical Test Results and Analysis
4.6. Relationship between PPV and PPS
5. Discussion
6. Conclusions
- (1)
- In the context of blasting operations, the ground PPV is observed to decline as HDEC increases. This phenomenon is evidenced by the observation that the tangential PPV is less than that of the vertical PPV, which in turn is less than that of the radial PPV. The vertical PPV in high-rise buildings is observed to increase with floor elevation, exhibiting an elevation amplification effect. The magnification factor for an 18-story building with HDEC = 50 m can reach a value of 2.66. The tangential and radial PPVs of the building demonstrate a proclivity for decline and subsequent augmentation with the ascent of the floor height. The vertical vibration velocity of the building is greater than the radial and tangential vibration velocities.
- (2)
- VDEC exerts an influence on PPV. The vertical PPV of the building increases with increasing VDEC. Both the radial and tangential PPVs of the building increase with increasing VDEC, if VDEC has a negative value.
- (3)
- There is no significant pattern in the ground frequency and building frequency, which span a range of 8 Hz to 20 Hz, with a mean value of 10 Hz.
- (4)
- PPS is not proportional to PPV. As the height of a structure increases, PPS tends to decrease and fluctuate, while PPV tends to increase. The highest PPS is observed at the first floor level. It is therefore recommended that buildings be designed with an increased ground floor column section. Meanwhile, it is recommended that PPS of buildings should be included in the blasting vibration safety allowance.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Serial No. | Category of Protection Object | Safe Permissible Particle Vibration Velocity (cm/s) | ||
---|---|---|---|---|
f ≤ 10 Hz | 10 Hz < f ≤ 50 Hz | f > 50 Hz | ||
1 | Earth kiln caves, adobe houses, and rubble houses | 0.15–0.45 | 0.45–0.9 | 0.9–1.5 |
2 | General civil buildings | 1.5–2.0 | 2.0–2.5 | 2.5–3.0 |
3 | Industrial and commercial buildings | 2.5–3.5 | 3.5–4.5 | 4.2–5.0 |
… | … | … | … | … |
No. of Times | Monitoring Point | HDEC (m) | Radial PPV (cm/s) | Radial Frequency (Hz) | Vertical PPV (cm/s) | Vertical Frequency (Hz) | Tangential PPV (cm/s) | Tangential Frequency (Hz) |
---|---|---|---|---|---|---|---|---|
1 | 1* | 47 | 0.278 | 13.5040 | 0.266 | 8.4686 | 0.212 | 15.3351 |
2* | 97 | 0.169 | 10.9863 | 0.176 | 8.6975 | 0.165 | 15.1062 | |
3* | 147 | 0.113 | 10.5286 | 0.126 | 8.6975 | 0.113 | 8.6975 | |
4* | 197 | 0.091 | 11.9019 | 0.082 | 7.3242 | 0.076 | 9.6130 | |
5* | 247 | 0.047 | 11.9019 | 0.055 | 16.7084 | 0.041 | 13.2751 | |
2 | 1* | 43 | 0.298 | 8.6975 | 0.266 | 8.9264 | 0.218 | 17.3950 |
2* | 93 | 0.216 | 10.7574 | 0.186 | 8.9264 | 0.148 | 9.1553 | |
3* | 143 | 0.109 | 9.3842 | 0.121 | 8.9264 | 0.113 | 9.8419 | |
4* | 193 | 0.079 | 15.3351 | 0.079 | 20.8282 | 0.075 | 9.8419 | |
5* | 243 | 0.048 | 13.5040 | 0.056 | 17.3950 | 0.048 | 6.6376 | |
3 | 1* | 71 | 0.253 | 10.0708 | 0.236 | 9.1553 | 0.206 | 16.4759 |
2* | 121 | 0.162 | 9.3842 | 0.163 | 9.3842 | 0.146 | 9.3842 | |
3* | 171 | 0.116 | 9.3842 | 0.118 | 9.3842 | 0.101 | 9.3842 | |
4* | 221 | 0.082 | 16.4795 | 0.076 | 7.3242 | 0.066 | 9.3842 | |
5* | 271 | 0.046 | 9.3842 | 0.048 | 16.4795 | 0.046 | 7.0953 | |
… | … | … | … | … | … | … | … | … |
No. of Times | Motoring Point | HDEC (m) | Radial PPV (cm/s) | Radial Frequency (Hz) | Vertical PPV (cm/s) | Vertical Frequency (Hz) | Tangential PPV (cm/s) | Tangential Frequency (Hz) |
---|---|---|---|---|---|---|---|---|
1 | 5# | 50 | 0.228 | 9.6130 | 0.602 | 9.1553 | 0.185 | 20.5994 |
4# | 50 | 0.215 | 9.6130 | 0.482 | 9.1553 | 0.18 | 11.4441 | |
3# | 50 | 0.186 | 9.3842 | 0.464 | 9.1553 | 0.169 | 12.3596 | |
2# | 50 | 0.183 | 9.6130 | 0.356 | 9.1553 | 0.164 | 11.4441 | |
1# | 50 | 0.243 | 9.3842 | 0.253 | 9.1553 | 0.195 | 10.9863 | |
2 | 5# | 50 | 0.235 | 11.2152 | 0.613 | 8.6975 | 0.196 | 11.4441 |
4# | 50 | 0.202 | 11.2152 | 0.512 | 8.6975 | 0.196 | 11.4441 | |
3# | 50 | 0.182 | 14.6484 | 0.451 | 8.6975 | 0.189 | 12.3596 | |
2# | 50 | 0.176 | 11.2152 | 0.382 | 8.6975 | 0.156 | 11.4441 | |
1# | 50 | 0.232 | 11.4441 | 0.235 | 8.6975 | 0.185 | 11.2152 | |
3 | 5# | 50 | 0.201 | 9.6130 | 0.612 | 9.3842 | 0.183 | 10.9863 |
4# | 50 | 0.199 | 9.6130 | 0.501 | 9.3842 | 0.182 | 11.2152 | |
3# | 50 | 0.148 | 9.3842 | 0.446 | 9.3842 | 0.186 | 12.3596 | |
2# | 50 | 0.16 | 9.6130 | 0.354 | 9.3842 | 0.175 | 11.2152 | |
1# | 50 | 0.223 | 9.6130 | 0.198 | 9.3842 | 0.182 | 11.2152 | |
Mean value | 5# | 50 | 0.221 | 10.147 | 0.609 | 9.079 | 0.188 | 14.343 |
4# | 50 | 0.205 | 10.147 | 0.498 | 9.079 | 0.186 | 11.368 | |
3# | 50 | 0.172 | 11.139 | 0.454 | 9.079 | 0.181 | 12.360 | |
2# | 50 | 0.173 | 10.147 | 0.364 | 9.079 | 0.165 | 11.368 | |
1# | 50 | 0.233 | 10.147 | 0.229 | 9.079 | 0.187 | 11.139 |
Density (kg/m3) | Elastic Modulus (GPa) | Poisson’s Ratio | Yield Strength (MPa) | Tangent Modulus (MPa) |
---|---|---|---|---|
2090 | 23 | 0.22 | 20 | 250 |
Density (kg/m3) | Detonation Velocity (m/s) | Detonation Pressure (GPa) | A (GPa) | B (GPa) | R1 | R2 | Internal Energy per Unit Volume (GPa) | Relative Volume | |
---|---|---|---|---|---|---|---|---|---|
1200 | 5500 | 10 | 214.4 | 0.182 | 4.2 | 0.9 | 0.15 | 4.19 | 1 |
Floor | No.1 | No.2 | No.3 | No.4 | No.5 | Floor | No.1 | No.2 | No.3 | No.4 | No.5 |
---|---|---|---|---|---|---|---|---|---|---|---|
18 | 0.562 | 0.326 | 0.223 | 0.112 | 0.076 | 8 | 0.358 | 0.223 | 0.162 | 0.085 | 0.061 |
17 | 0.553 | 0.302 | 0.221 | 0.106 | 0.072 | 7 | 0.359 | 0.202 | 0.157 | 0.086 | 0.063 |
16 | 0.520 | 0.268 | 0.213 | 0.100 | 0.074 | 6 | 0.356 | 0.186 | 0.156 | 0.085 | 0.063 |
15 | 0.501 | 0.268 | 0.201 | 0.105 | 0.072 | 5 | 0.332 | 0.185 | 0.152 | 0.082 | 0.062 |
14 | 0.485 | 0.263 | 0.192 | 0.103 | 0.068 | 4 | 0.312 | 0.176 | 0.130 | 0.079 | 0.052 |
13 | 0.462 | 0.260 | 0.190 | 0.101 | 0.071 | 3 | 0.302 | 0.172 | 0.136 | 0.078 | 0.056 |
12 | 0.452 | 0.265 | 0.182 | 0.096 | 0.068 | 2 | 0.286 | 0.165 | 0.113 | 0.072 | 0.053 |
11 | 0.416 | 0.240 | 0.167 | 0.094 | 0.065 | 1 | 0.265 | 0.168 | 0.112 | 0.075 | 0.052 |
10 | 0.412 | 0.230 | 0.169 | 0.093 | 0.065 | ground | 0.256 | 0.169 | 0.116 | 0.076 | 0.051 |
9 | 0.396 | 0.225 | 0.168 | 0.092 | 0.063 |
HDEC (m) | Field Test | Numerical Experiment | Relative Error | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
V2 (cm/s) | V1 (cm/s) | |||||||||||
Radial | Vertical | Tangential | Combined | Radial | Vertical | Tangential | Combined | Radial | Vertical | Tangential | Combined | |
50 | 0.274 | 0.247 | 0.203 | 0.421 | 0.292 | 0.256 | 0.218 | 0.445 | 6.2 | 3.5 | 6.9 | 5.5 |
100 | 0.185 | 0.165 | 0.148 | 0.289 | 0.189 | 0.169 | 0.156 | 0.298 | 2.1 | 2.4 | 5.1 | 3.0 |
150 | 0.121 | 0.116 | 0.104 | 0.197 | 0.123 | 0.116 | 0.102 | 0.197 | 1.6 | 0.0 | 2.0 | 0.1 |
200 | 0.082 | 0.074 | 0.071 | 0.131 | 0.085 | 0.076 | 0.069 | 0.133 | 3.5 | 2.6 | 2.9 | 1.5 |
250 | 0.048 | 0.050 | 0.045 | 0.083 | 0.053 | 0.051 | 0.048 | 0.088 | 9.4 | 2.0 | 6.3 | 5.9 |
Building | Floor | Field Test | Numerical Experiment | Relative Error | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
V2 (cm/s) | V1 (cm/s) | ||||||||||||
Radial | Vertical | Tangential | Combined | Radial | Vertical | Tangential | Combined | Radial | Vertical | Tangential | Combined | ||
NO.1 | 18 | 0.221 | 0.609 | 0.188 | 0.675 | 0.248 | 0.562 | 0.196 | 0.645 | 10.8 | 8.4 | 4.1 | 4.6 |
13 | 0.205 | 0.498 | 0.186 | 0.570 | 0.235 | 0.462 | 0.182 | 0.549 | 12.6 | 7.9 | 2.2 | 3.8 | |
9 | 0.172 | 0.454 | 0.181 | 0.518 | 0.206 | 0.396 | 0.168 | 0.477 | 16.5 | 14.6 | 7.9 | 8.6 | |
5 | 0.173 | 0.364 | 0.165 | 0.435 | 0.203 | 0.332 | 0.175 | 0.427 | 14.8 | 9.6 | 5.7 | 2.1 | |
1 | 0.233 | 0.229 | 0.187 | 0.376 | 0.263 | 0.265 | 0.201 | 0.424 | 11.5 | 13.7 | 6.8 | 11.3 | |
NO.2 | 18 | 0.209 | 0.344 | 0.166 | 0.435 | 0.186 | 0.326 | 0.163 | 0.409 | 12.5 | 5.4 | 1.8 | 6.4 |
13 | 0.190 | 0.265 | 0.157 | 0.362 | 0.185 | 0.260 | 0.152 | 0.353 | 2.7 | 1.9 | 3.3 | 2.4 | |
9 | 0.177 | 0.230 | 0.147 | 0.325 | 0.172 | 0.225 | 0.142 | 0.317 | 2.9 | 2.2 | 3.5 | 2.7 | |
5 | 0.157 | 0.190 | 0.133 | 0.280 | 0.152 | 0.185 | 0.128 | 0.272 | 3.3 | 2.7 | 3.9 | 3.2 | |
1 | 0.173 | 0.183 | 0.131 | 0.283 | 0.168 | 0.168 | 0.148 | 0.280 | 3.0 | 8.6 | 11.7 | 1.3 | |
NO.3 | 18 | 0.149 | 0.242 | 0.123 | 0.310 | 0.136 | 0.223 | 0.118 | 0.287 | 9.8 | 8.7 | 4.5 | 8.2 |
13 | 0.137 | 0.195 | 0.114 | 0.264 | 0.132 | 0.190 | 0.109 | 0.256 | 3.5 | 2.5 | 4.9 | 3.2 | |
9 | 0.129 | 0.173 | 0.111 | 0.242 | 0.124 | 0.168 | 0.106 | 0.234 | 3.8 | 2.8 | 5.0 | 3.5 | |
5 | 0.121 | 0.157 | 0.085 | 0.215 | 0.116 | 0.152 | 0.085 | 0.209 | 4.0 | 3.1 | 0.4 | 2.9 | |
1 | 0.126 | 0.109 | 0.086 | 0.187 | 0.119 | 0.112 | 0.102 | 0.193 | 5.6 | 2.7 | 15.4 | 2.7 | |
… | … | … | … | … | … | … | … | … | … | … | … | … | … |
Value of PPS (MPa) | |||||||||
---|---|---|---|---|---|---|---|---|---|
Floor | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
Value | 21.0 | 17.8 | 11.7 | 10.2 | 14.0 | 12.3 | 15.8 | 20.3 | 13.7 |
Floor | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 |
Value | 15.3 | 15.6 | 14.0 | 12.5 | 16.4 | 9.7 | 10.6 | 12.0 | 7.2 |
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Yuan, Y.; Gao, Z.; He, L.; Lei, Z. Research on the Vibration Response of High-Rise Buildings under Blasting Load. Mathematics 2024, 12, 3165. https://doi.org/10.3390/math12203165
Yuan Y, Gao Z, He L, Lei Z. Research on the Vibration Response of High-Rise Buildings under Blasting Load. Mathematics. 2024; 12(20):3165. https://doi.org/10.3390/math12203165
Chicago/Turabian StyleYuan, Yubao, Zhenghua Gao, Lu He, and Zhen Lei. 2024. "Research on the Vibration Response of High-Rise Buildings under Blasting Load" Mathematics 12, no. 20: 3165. https://doi.org/10.3390/math12203165
APA StyleYuan, Y., Gao, Z., He, L., & Lei, Z. (2024). Research on the Vibration Response of High-Rise Buildings under Blasting Load. Mathematics, 12(20), 3165. https://doi.org/10.3390/math12203165