下穿隧道爆破荷载激励下边坡振动预测及能量分析

何理; 钟东望; 李鹏; 宋琨; 司剑峰

doi:10.11883/bzycj-2019-0255

下穿隧道爆破荷载激励下边坡振动预测及能量分析

doi: 10.11883/bzycj-2019-0255

何理^{1, 2, 3,},
钟东望^2, ,,
李鹏¹,
宋琨³,
司剑峰²

1.
长江科学院水利部岩土力学与工程重点实验室，湖北武汉 430010
2.
武汉科技大学冶金工业过程系统科学湖北省重点实验室，湖北武汉 430065
3.
三峡大学三峡库区地质灾害教育部重点实验室，湖北宜昌 443002

基金项目: 国家自然科学基金项目（51574184，51904210）；湖北省教育厅科学技术研究项目（Q20181109）；水利部岩土力学与工程重点实验室开放基金（CKWV2018473/KY）；三峡库区地质灾害教育部重点实验室开放基金（2017KDZ02）；冶金工业过程系统科学湖北省重点实验室开放基金（Y201717）

详细信息

作者简介:
何　理（1986－　），男，博士，副教授，emp-heli@hotmail.com

通讯作者:
钟东望（1963－　），男，教授，博士生导师，1057831589@qq.com

中图分类号: O389; O383.2
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出版历程
- 收稿日期: 2019-06-26
- 修回日期: 2019-12-16
- 网络出版日期: 2020-06-25
- 刊出日期: 2020-07-01

Vibration prediction and energy analysis of slope under blasting load in underpass tunnel

HE Li^{1, 2, 3
,},
ZHONG Dongwang^{2
, ,},
LI Peng¹,
SONG Kun³,
SI Jianfeng²

1.
Key Laboratory of Geotechnical Mechanics and Engineering of the Ministry of Water Resources, Yangtze River Scientific Research Institute, Wuhan 430010, Hubei, China
2.
Hubei Province Key Laboratory of Systems Science in Metallurgical Process, Wuhan University of Science and Technology, Wuhan 430065, Hubei, China
3.
Key Laboratory of Geological Hazards on Three Gorges Reservoir Area, Ministry of Education, China Three Gorges University, Yichang 443002, Hubei, China

摘要

摘要: 为解决边坡与下穿近接隧道协同爆破施工安全难题，结合某石油储备基地扩建项目，运用量纲推导、现场实验与信号分析相结合的方法，构建考虑高程影响的振动峰值速度公式，研究隧道爆破振动能量沿坡面的衰减机制。结果显示，边坡同台阶边沿处质点振速峰值大于坡脚处，坡面局部存在振动速度高程放大效应；引入相对坡度H/D的爆破振动模型对坡面质点振速预测精度高，可反映边坡角对高程放大效应的影响；振动速度及能量沿坡面均呈现出近区衰减快、远区衰减慢的传播特性，同时隧道爆破振动能量集中分布在0～300 Hz范围的多个子振频带，且高频能量沿坡面衰减更快，能量卓越频带中值以指数形式衰减，能量最终向低频带集中。
- 边坡 /
- 隧道爆破 /
- 量纲分析 /
- 峰值速度 /
- 振动能量 /
- 高程放大效应 /
- 相对坡度
Abstract: In order to solve the safety problem in the construction of slope and underpass adjacent tunnel by cooperative blasting, based on the expansion project of a domestic petroleum reserve base, the formula of peak vibration velocity considering elevation effect was established, and the vibration energy attenuation mechanism of tunnel blasting along the slope surface was systematically studied by using method combining dimension derivation, field test and signal analysis. The results show that the peak value of particle velocity at the edge of the same step is larger than that at the foot of the inner slope, and there is an elevation amplification effect of vibration velocity on the local slope surface. The blasting vibration formula with relative slope H/D has high accuracy in predicting the particle vibration velocity on the slope, and can reflect the influence of slope angle on the elevation amplification effect of vibration velocity. The vibration velocity and energy decay faster in the near region and slower in the far region with the increase of propagation distance. The energy of tunnel blasting vibration is concentrated in several Sub-vibration frequency bands in the range of 0-300 Hz, and the high frequency energy decays faster along slope surface. The median of dominant frequency band decays exponentially, and the energy concentrates in the low frequency band eventually.
- slope /
- tunnel blasting /
- dimensional analysis /
- peak velocity /
- vibration energy /
- elevation amplification effect /
- relative slope

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图 1 边坡与隧道的空间布局

Figure 1. Spatial Distribution of slope and tunnel

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图 2 隧道炮孔布置及爆破网路

Figure 2. Blasthole layout and blasting network of tunnel

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图 3 振动传感器安装基座

Figure 3. Mounting base of sensor

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图 4 坡面不同高程振动速度分布

Figure 4. Vibration velocity distribution at different elevations on slope

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图 5 归一化速度和能量随距离的变化关系

Figure 5. Relation of normalized velocity and energy with distance

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图 6 爆破振动信号各频带能量分布图

Figure 6. Energy distribution of blasting vibration signals in each frequency band

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图 7 卓越频带中值与传播距离的变化关系

Figure 7. The relation between mid-value of dominant frequency band and propagation distance

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表 1 坡面质点振动速度

Table 1. Particle vibration velocity on slope surface

振动信号	D/m	H/m	v_max/(cm·s⁻¹)
1-1	5.6	12.5	10.81
1-2	2.6	12.5	9.78
2-1	7.9	26.5	3.41
2-2	10.9	26.5	2.02
3-1	21.4	40.5	1.59
3-2	24.4	40.5	0.96
4-1	34.9	54.5	0.94
4-2	37.9	54.5	0.79
5-1	48.9	67.5	0.67
5-2	51.9	67.5	0.64
6-1	63.0	80.5	0.68
6-2	66.0	80.5	0.63
7-1	77.0	93.5	0.35
7-2	80.0	93.5	0.28
8-1	92.1	105.5	0.20
8-2	95.1	105.5	0.16
9	146.2	117.5	0.07
注：D为水平爆心距；H为垂直爆心距；v_max为质点振动速度峰值；信号编号m-n，m表示台阶级数，m=1, 2, 3, …, 9；n=1表示台阶边沿处监测点，n=2表示内侧坡脚处监测点。

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表 2 各变量量纲

Table 2. Dimension of variables

量纲	Q	D	C_p	H	E	μ	ρ	f	V
M	1	0	0	0	1	0	1	0	0
L	0	1	1	1	−1	0	−3	0	1
T	0	0	−1	0	−2	0	0	−1	−1
注：表2中M为质量量纲，L为长度量纲，T为时间量纲。

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表 3 振动速度预测模型及拟合系数

Table 3. Prediction model and correlation coefficient of vibration velocity

公式形式	振动速度预测模型	相关系数
$v = K{\left( {\dfrac{{\sqrt[3]{Q}}}{R}} \right)^\alpha }$	$v = 139.7{\left( {\dfrac{{\sqrt[3]{Q}}}{R}} \right)^{1.62}}$	0.939
$v = K{\left( {\dfrac{{\sqrt[3]{Q}}}{D}} \right)^\alpha }{\left( {\dfrac{{\sqrt[3]{Q}}}{H}} \right)^\beta }$	$v = 62.2{\left( {\dfrac{{\sqrt[3]{Q}}}{D}} \right)^{0.51}}{\left( {\dfrac{{\sqrt[3]{Q}}}{H}} \right)^{1.02}}$	0.927
$v = K{\left( {\dfrac{{\sqrt[3]{Q}}}{R}} \right)^\alpha }{\left( {\dfrac{R}{D}} \right)^\beta }$	$v = 208.5{\left( {\dfrac{{\sqrt[3]{Q}}}{R}} \right)^{1.69}}{\left( {\dfrac{R}{D}} \right)^{ - 0.21}}$	0.941
$v = K{\left( {\dfrac{{\sqrt[3]{Q}}}{R}} \right)^\alpha }{\left( {\dfrac{{\sqrt[3]{Q}}}{H}} \right)^\beta }$	$v = 70.1{\left( {\dfrac{{\sqrt[3]{Q}}}{R}} \right)^{4.61}}{\left( {\dfrac{{\sqrt[3]{Q}}}{H}} \right)^{ - 3.49}}$	0.954
$v = K'{\left( {\dfrac{{\sqrt[3]{Q}}}{D}} \right)^\alpha }{\left( {\dfrac{R}{D}} \right)^\beta }{\left( {\dfrac{H}{D}} \right)^\gamma }$	$v = 204.4{\left( {\dfrac{{\sqrt[3]{Q}}}{D}} \right)^{1.34}}{\left( {\dfrac{R}{D}} \right)^{ - 6.16}}{\left( {\dfrac{H}{D}} \right)^{4.17}}$	0.958

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表 4 各振动信号总能量

Table 4. Total energy of vibration signals

信号编号	1-1	1-2	2-1	2-2	3-1	3-2	4-1	4-2	5-1	5-2	6-1	6-2	7-1	7-2	8-1	8-2	9
总能量/mJ	1518.2	1770.9	262.3	122.9	33.3	15.8	11.2	7.6	5.0	3.8	3.8	4.9	2.8	1.8	1.5	1.2	0.2

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表 5 信号能量集中频带的分布

Table 5. Energy distribution in energy concentrated bands

信号	能量集中频带1		能量集中频带2		能量集中频带3		能量集中频带4		卓越频带/Hz
信号	频率/Hz	能量占比/%	频率/Hz	能量占比/%	频率/Hz	能量占比/%	频率/Hz	能量占比/%	卓越频带/Hz
1-1	54.6～64.35	17.1	115.05～126.75	24.6	179.40～202.80	20.7	232.05～251.55	17.4	115.05～126.75
1-2	39.00～62.40	24.9	118.95～126.75	44.6	187.20～196.95	18.2	−	−	118.95～126.75
2-1	107.25～126.75	20.4	187.20～202.80	36.1	243.75～251.55	26.2	−	−	187.20～202.80
2-2	62.40～78.00	11.1	189.15～202.80	21.9	235.95～249.60	18.7	−	−	189.15～202.80
3-1	31.20～48.75	17.3	62.40～81.90	22.9	93.60～105.30	9.1	189.15～202.80	10.8	62.40～81.90
3-2	21.45～50.70	21.4	62.40～81.90	26.9	93.60～109.20	28.7	−	−	93.60～109.20
4-1	33.15～109.20	81.7	187.20～241.80	5.9	−	−	−	−	33.15～109.20
4-2	17.55～46.80	31.1	60.45～78.00	11.3	95.55～111.15	35.7	−	−	95.55～111.15
5-1	29.25～64.35	34.7	93.6～117.00	42.4	189.15～202.80	8.6	−	−	93.60～117.00
5-2	29.25～54.60	22.6	93.6～109.20	43.4	189.15～195.00	10.4	−	−	93.60～109.20
6-1	17.55～23.40	14.3	33.15～64.35	42.6	101.40～109.20	20.2	−	−	33.15～64.35
6-2	17.55～23.40	11.3	31.2～58.50	72.3	93.60～101.40	5.2	−	−	31.20～58.50
7-1	29.25～54.60	71.9	93.6～105.30	9.4	−	−	−	−	29.25～54.60
7-2	17.55～46.80	69.8	95.55～101.4	11.4	−	−	−	−	17.55～46.80
8-1	0～3.90	13.7	19.50～50.70	68.9	−	−	−	−	19.5～50.70
8-2	0～3.90	19.9	17.55～23.40	22.9	29.25～35.10	17.7	42.90～54.60	21.7	17.55～23.40
9	17.55～33.15	62.1	48.75～62.40	26.2	−	−	−	−	17.55～33.15

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