Influence of Blasting Vibration of MLEMC Shaft Foundation Pit on Adjacent High-Rise Frame Structure: A Case Study
Abstract
:1. Introduction
2. Overview of MLEMC Shaft Foundation Pit Engineering
3. Field Blasting Experiment and Vibration Monitoring Analysis
3.1. Experiments Results and Analysis
3.2. Blasting Vibration Attenuation Rule and Establishment of Prediction Model
- According to the newly obtained prediction model (Equation (11)), the surface PPV fitting degree calculated is higher than the classical Sadovski formula. This indicates that PPV attenuation is more complex due to the influence of foundation pit depth, and the classical formula has certain limitations. The prediction model can well reflect the law of vibration wave affected by depth during the ground propagation of foundation pit blasting.
- According to the PPV regression analysis, the newly established PPV prediction model has a high accuracy, and the correlation coefficient is 0.857. Therefore, the following prediction model can be used to calculate the PPV of foundation pit blasting surface.
4. Verification and Analysis of Numerical Model of High-Rise Building
4.1. Establishment of Numerical Model
4.2. Parameters of Numerical Simulation
4.2.1. Parameters of High-Rise Building
4.2.2. Explosive Parameters
4.2.3. Rock Parameters
4.2.4. Soil Parameters
4.3. Reliability Verification of Numerical Model and Parameters
5. Influence of Blasting Vibration on the High-Rise Frame Building
5.1. Modal Analysis of Natural Frequency of High-Rise Buildings
5.2. Vibration Velocity Analysis of the High-Rise Building
5.3. Dynamic Stress Analysis of the High-Rise Building
5.4. Prediction Model of Blasting Vibration Velocity of High-Rise Buildings
6. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
List of Symbols
PPV | Peak particle velocity |
Ee | Elastic modulus of reinforce concrete |
Es | Elastic modulus of steel |
At | The total area of member section |
Wbeam | The reinforcement of beam |
ρ | Density |
E | The elastic modulus |
E0 | Internal energy per unit volume |
σ0 | The yield stress |
β | Hardening parameter |
Φ | The internal friction angle |
MS | Mass matrix |
U | Displacement vector |
T | The natural vibration period of the house |
B | The width (m) of the building |
The dynamic tensile strength | |
The strain rate of concrete. | |
i | The ratio of vibration velocity between other floors and the first floor |
σ(n) | The dynamic tensile stress of floor n |
VF1 | The vibration velocity of the first floor |
JWL | Jones–Wilkens–Lee parameters |
Ec | Elastic modulus of concrete |
As | The sectional area of reinforcement |
W | Reinforcement ratio |
Wcolumn | The reinforcement of column |
μ | The Poisson ratio |
V | The relative specific volume respective |
R1, R2, A, B, ω | Material constants |
Etan | Minimum bending stiffness |
RKF | The shape parameter of failure surface |
C | The cohesion |
KS | Stiffness matrix |
Mass of nodal acceleration | |
H | The total height of the building |
α | The growth factor of dynamic tensile strength |
The static tensile strength | |
The quasi-static strain rate of concrete | |
n | The floor |
VFn | The vibration velocity of floor n. |
VF17 | The vibration velocity of the seventeenth floor |
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Experiment | Monitoring Points | Excavation Depth (m) | Standoff Distance (m) | Charge in One Delay (kg) | Vibration Velocity (cm·s−1) | Dominant Frequency (Hz) | Velocity Amplification Factor of the Top (VF17/VF1) |
---|---|---|---|---|---|---|---|
I | #1 | 16.000 | 24.083 | 0.600 | 0.493 | 43.240 | 1.190 |
#2 | 16.000 | 30.529 | 0.600 | 0.335 | 28.750 | ||
#3 | 16.000 | 37.577 | 0.600 | 0.239 | 31.250 | ||
#4 | 16.000 | — | 0.600 | 0.174 | 24.440 | ||
#5 | 16.000 | — | 0.600 | 0.284 | 18.850 | ||
II | #1 | 16.000 | 24.083 | 0.800 | 0.588 | 36.210 | 1.230 |
#2 | 16.000 | 30.529 | 0.800 | 0.379 | 28.670 | ||
#3 | 16.000 | 37.577 | 0.800 | 0.291 | 25.750 | ||
#4 | 16.000 | — | 0.800 | 0.195 | 38.450 | ||
#5 | 16.000 | — | 0.800 | 0.358 | 20.140 | ||
III | #1 | 16.000 | 24.083 | 6.000 | 1.773 | 26.470 | 1.260 |
#2 | 16.000 | 30.529 | 6.000 | 1.192 | 29.640 | ||
#3 | 16.000 | 37.577 | 6.000 | 0.790 | 51.230 | ||
#4 | 16.000 | — | 6.000 | 0.591 | 24.530 | ||
#5 | 16.000 | — | 6.000 | 0.995 | 15.760 | ||
IV | #1 | 18.000 | 25.456 | 6.000 | 1.668 | 34.870 | 1.220 |
#2 | 18.000 | 31.623 | 6.000 | 1.153 | 18.760 | ||
#3 | 18.000 | 38.471 | 6.000 | 0.753 | 43.570 | ||
#4 | 18.000 | — | 6.000 | 0.519 | 24.410 | ||
#5 | 18.000 | — | 6.000 | 0.919 | 28.340 | ||
V | #1 | 18.000 | 25.456 | 8.000 | 1.898 | 52.430 | 1.200 |
#2 | 18.000 | 31.623 | 8.000 | 1.384 | 25.760 | ||
#3 | 18.000 | 38.471 | 8.000 | 0.997 | 29.480 | ||
#4 | 18.000 | — | 8.000 | 0.608 | 28.990 | ||
#5 | 18.000 | — | 8.000 | 1.196 | 31.570 |
Experiment | Monitoring Points | Vertical Vibration Velocity (cm·s−1) | Tangential Vibration Velocity (cm·s−1) | Radial Vibration Velocity (cm·s−1) |
---|---|---|---|---|
I | #3 | 0.239 | 0.031 | 0.042 |
#4 | 0.174 | 0.024 | 0.033 | |
#5 | 0.284 | 0.051 | 0.057 | |
II | #3 | 0.291 | 0.098 | 0.101 |
#4 | 0.195 | 0.044 | 0.058 | |
#5 | 0.358 | 0.099 | 0.100 | |
III | #3 | 0.790 | 0.133 | 0.142 |
#4 | 0.591 | 0.098 | 0.112 | |
#5 | 0.995 | 0.148 | 0.267 | |
IV | #3 | 0.753 | 0.145 | 0.136 |
#4 | 0.519 | 0.084 | 0.099 | |
#5 | 0.919 | 0.184 | 0.236 | |
V | #3 | 0.997 | 0.155 | 0.234 |
#4 | 0.608 | 0.101 | 0.233 | |
#5 | 1.196 | 0.231 | 0.297 |
Category | Variables | Dimension |
---|---|---|
Dependent variable | Vibration displacement μ | L |
Peak particle velocity υ | LT−1 | |
Particle vibration acceleration α | LT−2 | |
Frequency f | T−1 | |
Independent variable | Charge Q | M |
Distance between structure and blasting source r | L | |
Foundation pit excavation depth d | L | |
Density of rock mass ρ | ML−3 | |
Phase velocity c | LT−1 | |
Detonation time t | T |
Classical Sadovski’s Formula (Equation (8)) | Correlation Coefficient | Obtained Formula (Equation (11)) | Correlation Coefficient |
---|---|---|---|
0.723 | 0.857 |
Density ρ/(g·cm−3) | Elastic Modulus E/GPa | Poisson’s Ratio μ |
---|---|---|
2.5 | 37.5 | 0.19 |
ρ/(g·cm−3) | V/(cm·μs−1) | A/GPa | B/GPa | R1 | R2 | ω | E0/GPa |
---|---|---|---|---|---|---|---|
1.10 | 0.4 | 214.4 | 18.2 | 4.2 | 0.9 | 0.15 | 4.19 |
ρ/(g·cm−3) | E/GPa | μ | σ0/GPa | Etan/GPa | β |
---|---|---|---|---|---|
2.68 | 45 | 0.25 | 0.5 | 0.02 | 0.5 |
Category | ρ/(g·cm−3) | E/GPa | μ | RKF | φ/° | C/GPa | STR-LIM |
---|---|---|---|---|---|---|---|
Silty clay | 1.98 | 0.007 | 0.18 | 0.6 | 0.174 | 0.015 | 0.005 |
Clay crushed stone | 1.99 | 0.011 | 0.19 | 0.5 | 0.262 | 0.035 | 0.005 |
Location | Simulation | Field Experiment | Error of Deviation |
---|---|---|---|
First floor/(cm·s−1) | 0.761 | 0.790 | 3.67% |
Ninth floor/(cm·s−1) | 0.543 | 0.591 | 8.12% |
Top floor/(cm·s−1) | 1.063 | 0.995 | 6.83% |
SET | Natural Vibration Frequency/Hz | Mode of Vibration |
---|---|---|
1 | 0.70421 | |
2 | 1.25467 | |
3 | 1.63751 | |
Working Conditions | Floor Fn | Vibration Velocity VFn | i = VFn/VF1 |
---|---|---|---|
Field test I | 1 | 0.239 | 1.000 |
9 | 0.174 | 0.728 | |
17 | 0.284 | 1.188 | |
Field test II | 1 | 0.291 | 1.000 |
9 | 0.195 | 0.670 | |
17 | 0.358 | 1.230 | |
Field test III | 1 | 0.790 | 1.000 |
9 | 0.591 | 0.748 | |
17 | 0.995 | 1.259 | |
Field test IV | 1 | 0.753 | 1.000 |
9 | 0.519 | 0.689 | |
17 | 0.919 | 1.221 | |
Field test V | 1 | 0.997 | 1.000 |
9 | 0.608 | 0.610 | |
17 | 1.196 | 1.200 | |
Numerical simulation I (Excavation depth: 20 m Charge of explosives: 15 kg) | 1 | 1.552 | 1.000 |
3 | 1.369 | 0.884 | |
5 | 1.081 | 0.697 | |
7 | 0.878 | 0.568 | |
9 | 1.090 | 0.703 | |
11 | 1.282 | 0.826 | |
13 | 1.430 | 0.923 | |
15 | 1.681 | 1.084 | |
17 | 1.928 | 1.245 | |
Numerical simulation II (Excavation depth: 16 m Charge of explosives: 6 kg) | 1 | 0.761 | 1.000 |
3 | 0.635 | 0.834 | |
5 | 0.524 | 0.688 | |
7 | 0.391 | 0.514 | |
9 | 0.543 | 0.714 | |
11 | 0.605 | 0.795 | |
13 | 0.710 | 0.933 | |
15 | 0.820 | 1.077 | |
17 | 1.063 | 1.397 | |
Numerical simulation III (Excavation depth: 22 m Charge of explosives: 15 kg) | 1 | 1.353 | 1.000 |
3 | 1.158 | 0.856 | |
5 | 0.944 | 0.698 | |
7 | 0.735 | 0.543 | |
9 | 0.971 | 0.718 | |
11 | 1.154 | 0.835 | |
13 | 1.192 | 0.881 | |
15 | 1.354 | 1.001 | |
17 | 1.536 | 1.135 |
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Jiang, N.; Zhang, Y.; Zhou, C.; Wu, T.; Zhu, B. Influence of Blasting Vibration of MLEMC Shaft Foundation Pit on Adjacent High-Rise Frame Structure: A Case Study. Energies 2020, 13, 5140. https://doi.org/10.3390/en13195140
Jiang N, Zhang Y, Zhou C, Wu T, Zhu B. Influence of Blasting Vibration of MLEMC Shaft Foundation Pit on Adjacent High-Rise Frame Structure: A Case Study. Energies. 2020; 13(19):5140. https://doi.org/10.3390/en13195140
Chicago/Turabian StyleJiang, Nan, Yuqi Zhang, Chuanbo Zhou, Tingyao Wu, and Bin Zhu. 2020. "Influence of Blasting Vibration of MLEMC Shaft Foundation Pit on Adjacent High-Rise Frame Structure: A Case Study" Energies 13, no. 19: 5140. https://doi.org/10.3390/en13195140