Verification of Theoretical Model and Vibration Effect Caused by Blasting in Shallow Buried Tunnel on Mountain Slope
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摘要: 为研究位于边坡地形和浅埋土岩复合地层条件下的山岭隧道施工爆破振动效应和振动影响范围，验证并获得准确适用的振速理论模型，以国道317线下穿县城密集区的德格隧道为依托，利用现场爆破振动监测和回归分析对4组常用理论模型进行验证，同时，通过三维数值模拟及与理论模型计算、现场实测结果的比较，围绕爆破振速、振动影响范围以及存在的爆破振动效应进行分析. 研究结果表明：4组常见理论模型计算拟合度在0.15～0.86之间，其中，唐海、朱传统和周同龄理论模型公式对应不同爆心水平距离、高程差时各有优势；理论模型计算得到的爆破振动影响范围比数值计算结果更接近现场实测结果；在隧道成洞区28 m范围内爆破施工引起的“空洞效应”明显，地表垂向最大振速由起爆点处的1.98 cm/s增大到了2.23 cm/s；爆心所在横切面内顺坡向一侧距离开挖中线10～20 m范围坡面上“边坡效应”显著，最大垂向振速达1.83 cm/s之后随爆心距增大而线性减小；在逆坡向一侧5～10 m范围内随高程增加将出现“高程放大效应”，因此，上述范围内的地表建筑应作为现场监测重点并做好防震措施.Abstract: Results on the blasting vibration effect and influence range of a mountain tunnel under a slope terrain and shallow buried soil in rock composite stratum conditions are presented. The objective was to verify and obtain an accurate and applicable theoretical model of vibration velocity based on a case study by taking the De-ge tunnel in the project of No.317 national highway that passes below a densely populated county. The 4 usual theoretical models were verified by on-site blasting vibration monitoring and regression analysis. Simultaneously, the vibration velocity, the influence range of vibration and the blasting vibration effect were analyzed through 3-D numerical simulation and comparison with theoretical calculations and field measurement results. The results show that: the degree of fitting of the 4 usual theoretical models is 0.15−0.86, and the theoretical model formulas by Tang, Zhu, and Zhou can complement each other with respective advantages in terms of different blasting horizontal distance and elevation difference. The influence range of blasting vibration obtained by the theoretical model is closer to field measurements than the numerical results. The " hole effect” located on the surface within 28 m of the completed tunnel is clear and the maximum vertical vibration velocity increased from 1.98 cm/s at the initiation point up to 2.23 cm/s at the surface. The " slope effect” is remarkable in 10−20 m from the middle line on the downslope surface. The vertical velocity decreases linearly with the increase of the detonation distance when it reaches 1.83 cm/s. The " elevation amplification effect” on the adverse slope will occur within 5−10 m on the other side of the center line as the elevation increases. In the above range on the ground surface, the protected buildings should be the key points of field monitoring, and the earthquake precautions should be strengthened.
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图 2 爆破振动监测试验点
Figure 2. Schematic diagram of the plane layout of monitoring points for the blasting vibration
图 5 开挖及监测点（单位：m）
Figure 5. Schematic diagram of the excavationand monitoring (unit: m)
表 1 现场监测结果
Table 1. Results of monitoring in conducted experiment
最大段
装药量/kg监测点
编号直线距离
$R$/m水平距离
$S$/m高程差
$H$/m实测垂向
速度${V_{y{\rm{1}}}}$/（cm•s–1）实测水平
速度${V_{x1}}$/（cm•s–1）${V_0}$/（cm•s–1） 1.5 监16 25.11 2.4 25 1.462 0.825 0.740 监14 41.73 30 29 0.474 0.352 0.309 监 2 49.37 49 6 0.331 0.282 0.231 监15 43.83 39 20 0.475 0.220 0.284 1.5 监 1 66.22 64 17 0.299 0.122 0.140 监11 83.01 83 1 0.162 0.025 0.095 监 2 70.66 63 32 0.263 0.142 0.125 2.0 监14 67.19 65 17 0.248 0.123 0.136 监15 39.45 34 20 0.222 0.175 0.340 监15 49.24 45 20 0.491 0.350 0.340 监14 62.36 60 17 0.100 0.080 0.155 监 1 62.39 58 23 0.183 0.240 0.155 
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表 2 拟合结果及试验点振速计算
Table 2. Fitting results and vibration velocity calculation of test points
名称 回归方程 拟合度 试验点1 试验点2 试验点3 Vy2 Vy1 Vy2 Vy1 Vy2 Vy1 周同龄 ${{V_y} = 150{\left( {\displaystyle\frac{{{Q^{1/3}}}}{R}} \right)^{{\rm{1}}{\rm{.72}}}}{H^{0.275}}}$ 0.62 0.141 0.163 2.900 1.462 1.785 1.475 唐海 ${{V_y} = 150 \times 1.45 \times {\left( {\displaystyle\frac{{{Q^{1/3}}}}{R}} \right)^{1.72}}{\left( {\displaystyle\frac{H}{R}} \right)^{0.80}}}$ 0.86 0.008 0.163 1.503 1.462 1.062 1.475 朱传统 ${{V_y} = 150{\left( {\displaystyle\frac{{{Q^{1/3}}}}{R}} \right)^{1.72}}{\left( {\displaystyle\frac{{{Q^{1/3}}}}{H}} \right)^{{\rm{ - 0}}{\rm{.12}}}}}$ 0.75 0.130 0.163 1.997 1.462 1.066 1.475 水工技规 ${{V_y} = 150{\left( {\displaystyle\frac{{{Q^{1/3}}}}{S}} \right)^{1.72}}{\left( {\displaystyle\frac{{{Q^{1/3}}}}{H}} \right)^{{\rm{ - }}0.18}}}$ 0.15 0.133 0.163 3.392 1.462 49.817 1.475
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表 3 模型物理力学计算参数
Table 3. Physical and mechanical calculation parameters of the model
名称 Ed/GPa 泊松比 粘聚力/kPa 内摩擦角/（°） 密度/（kg•m–3） 坡洪积松散堆积体（V） 0.40 0.45 20 28 1 950 裂隙发育灰岩、片岩（Ⅳ） 15.00 0.28 80 38 2 500 混凝土 35.00 0.20 – – 2 500
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表 4 最大振速比较
Table 4. Comparison of the maximum vibration
试验点编号 式（2） 式（3） 式（4） 数值计算结果 实测结果 1 0.141 0.008 0.130 0.155 0.163 2 2.900 1.503 1.997 1.750 1.462 3 1.785 1.062 1.066 1.880 1.475
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