下穿铁路隧道爆破振动衰减规律研究

单仁亮; 赵岩; 王海龙; 董捷; 仝潇; 李兆龙; 王东升

doi:10.11883/bzycj-2021-0324

下穿铁路隧道爆破振动衰减规律研究

doi: 10.11883/bzycj-2021-0324

单仁亮^1,,
赵岩^1, ,,
王海龙^{1, 2},
董捷²,
仝潇¹,
李兆龙¹,
王东升¹

1.
中国矿业大学(北京)力学与建筑工程学院，北京 100083
2.
河北建筑工程学院河北省土木工程诊断、改造与抗灾重点实验室，河北张家口 075000

基金项目: 国家自然科学基金（51878242）；河北省自然科学基金（E2020404007）

详细信息

作者简介:
单仁亮（1964－　），男，博士，教授，博士生导师，srl@cumtb.edu.cn

通讯作者:
赵　岩（1991－　），男，博士研究生，zhaoyanlyp@163.com

中图分类号: O389；TU751.9
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- 被引次数: 0
出版历程
- 收稿日期: 2021-07-30
- 修回日期: 2021-09-16
- 网络出版日期: 2022-07-18
- 刊出日期: 2022-09-09

Attenuation of blasting vibration in a railway tunnel

1.
School of Mechanics and Civil Engineering, China University of Mining and Technology (Beijing), Beijing 100083, China
2.
Hebei Key Laboratory of Civil Engineering Diagnosis, Reconstruction and Disaster Resistance, Hebei University of Architecture, Zhangjiakou 075000, Hebei, China

摘要

摘要: 基于Heelan短柱药包理论，引入等效作用半径的概念，得到内部瞬时激励荷载作用下爆破峰值振动速度的衰减模型方程，并通过量纲分析进行验证。结合下穿隧道爆破工程，研究不同雷管段位及不同炮孔类型对应的爆破峰值振动速度的衰减规律。此外，讨论球形装药、柱状装药条件下改进公式的药量形式表达式，结果显示，利用等效作用半径作为拟合参考变量可以综合考虑不同雷管段位及不同炮孔类型对爆破振动规律的影响。统计数据表明，利用改进公式得到的拟合效果最优，可以为类似隧道爆破振动研究提供参考。
- 爆破峰值振动速度 /
- 衰减模型 /
- 铁路隧道 /
- Heelan短柱药包理论 /
- 量纲分析 /
- 拟合效果
Abstract: In order to deeply explore the propagation and attenuation law of column charge blasting stress waves or seismic waves, and to improve the prediction model of the blasting peak vibration velocity, a theoretical study on the blasting peak vibration velocity was carried out. First of all, based on the Heelan short-column charge theory, the concept of the equivalent radius of action was introduced, and the attenuation equation for the blasting peak vibration velocity under the action of the internal instantaneous excitation load was obtained. Then, the concepts of the equivalent action radius and equivalent blasting load were applied to the theoretical derivation of the blasting peak vibration velocity. The attenuation laws of the blast-induced vibration in cutting hole sections and non-cutting hole sections were studied, respectively. Finally, based on the dimensional harmony theorem, the reliability and universality of the attenuation model were verified. Combined with an example of tunnel blasting project, the attenuation laws of the blasting peak vibration velocities corresponding to different segments of detonators and different types of blast holes were studied. The results show that the improved formula can well fit the peak velocities of the above two types of blasting vibrations, which can accurately reflect the transmission law of the tunnel blasting vibration. In addition, the expressions of the charge form of the improved formula under the conditions of spherical charge and columnar charge were discussed, and the prediction effects of various fitting models were compared. The comparison results show that using the equivalent radius of action as a fitting reference variable can comprehensively consider the influence of different detonator positions and different blast hole types on the blasting vibration attenuation law. The reference variables of the statistical data show that the fitting effect obtained by the improved formula is the best, which can provide a reference for similar research of tunnel blasting vibration.
- blasting peak vibration velocity /
- attenuation equation /
- railway tunnel /
- Heelan short-column charge theory /
- dimensional analysis /
- fitting effect

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图 1 短柱瞬时荷载作用

Figure 1. The instantaneous load action of a short column

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图 2 掏槽孔等效作用边界

Figure 2. The equivalent boundary of cutting hole blasting

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图 3 等效边界^[23]

Figure 3. The equivalent elastic boundary^[23]

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图 4 下穿隧道平面地形图

Figure 4. Topographic map of the underpass section of the tunnel

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图 5 隧道炮孔布置

Figure 5. The layout of the tunnel blast holes

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图 6 爆破振动测点布置

Figure 6. Layout of the blasting vibration measurement points

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图 7 典型的爆破振动速度波形

Figure 7. Typical blasting vibration velocity waveforms

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图 8 爆破峰值振动速度采用式(21)的拟合曲线

Figure 8. Fitting curves of equation (21) for the blasting peak vibration velocity

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图 9 爆破峰值振动速度采用式(28)的拟合曲线

Figure 9. Fitting curves of equation (28) for the blasting peak vibration velocity

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图 10 爆破峰值振动速度采用式(29)的拟合曲线

Figure 10. Fitting curves of equation (29) for the blasting peak vibration velocity

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表 1 爆破峰值振动速度的经验公式^[14]

Table 1. Prediction formulas of blasting peak vibration velocity^[14]

模型	公式
Sadov’s formula	v_max=k(Q^1/3/R)^α
USBM	v_max=k(Q^1/2/R)^α
Indian Institute of Standards	v_max=k(Q/R^2/3)^α
Langefors, et al	v_max=k(Q/R^2/3)^α/2
Ghosh, et al	v_max=k(Q^1/3/R)^−αe^−βR
Roy	v_max=kQ^1/2/R+n
Gupta, et al	v_max=k(Q/R^3/2)^α/2e^−βR

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表 2 隧道爆破装药情况

Table 2. Charges for tunnel blasting

炮孔类型	炮孔深度/m	雷管段位	炮孔数量	单孔装药量/kg	总装药量/kg
掏槽孔	4.0	H1	16	2.7	43.2
辅助孔	3.5	H3	14	2.4	33.6
辅助孔	3.5	H5	17	1.8	30.6
辅助孔	3.5	H7	25	1.5	37.5
辅助孔	3.5	H9	30	1.5	45.0
周边孔	2.5	H11	25	1.2	30.0
底板孔	2.5	H13	2	2.1	4.2
合计			129		224.1

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表 3 爆破峰值振动速度及相关参数

Table 3. Blasting peak vibration velocity and related parameters

测点	监测次序	爆心距/m	爆破峰值振动速度/(cm·s⁻¹)
			掏槽孔	辅助孔				周边孔	底板孔
			H1	H3	H5	H7	H9	H11	H13
M5	1	27.58	1.99	1.04	1.22	1.29	1.58	0.84	0.38
M4		30.48	1.66	0.87	0.91	1.08	1.27	0.73	0.25
M3		36.89	1.54	0.72	0.46	0.89	1.23	0.62	0.20
M2		40.31	1.11	0.64	0.58	0.80	0.92	0.57	0.22
M1		49.24	0.98	0.56	0.48	0.61	0.76	0.46	0.23
M5	2	20.39	2.33	1.20	1.61	1.68	1.95	1.25	0.70
M4		21.54	2.22	1.03	1.24	1.65	1.67	0.99	0.48
M3		25.26	2.01	0.97	1.15	1.50	2.02	1.14	0.44
M2		28.28	1.96	0.88	0.91	1.16	1.35	0.85	0.34
M1		36.48	1.55	0.89	0.80	1.12	1.28	0.69	0.26
M5	3	30.55	1.86	0.85	1.14	1.15	1.35	0.65	0.27
M4		36.22	1.53	0.71	0.90	0.97	1.16	0.59	0.18
M3		42.16	1.46	0.67	0.65	0.84	1.01	0.46	0.16
M2		50.32	1.20	0.50	0.72	0.70	0.83	0.38	0.13
M1		57.84	0.92	0.45	0.63	0.64	0.74	0.33	0.12
M5	4	25.01	2.02	0.98	1.19	1.24	1.45	0.68	0.30
M4		31.33	1.62	0.86	1.18	1.12	1.32	0.63	0.27
M3		38.54	1.49	0.71	0.93	0.93	1.09	0.51	0.18
M2		41.66	1.30	0.69	0.86	0.88	1.02	0.42	0.15
M1		47.20	1.20	0.60	0.75	0.69	0.87	0.39	0.14
M5	5	29.02	1.92	0.90	1.15	1.18	1.41	0.62	0.26
M4		33.45	1.70	0.81	1.05	1.06	1.25	0.59	0.23
M3		38.04	1.52	0.73	0.93	0.94	1.11	0.50	0.17
M2		45.55	1.31	0.59	0.82	0.80	0.95	0.39	0.14
M1		50.03	1.17	0.56	0.75	0.73	0.83	0.32	0.10

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表 4 爆破峰值振动速度采用式(21)的拟合效果

Table 4. Fitting effects of equation (21) for the blasting peak vibration velocity

炮孔类型	雷管段位	拟合方程	相关系数r²
掏槽孔	H1	v_max=30.205(r_d/R)^0.934	0.942
辅助孔	H3	v_max=10.755(r_d/R)^0.935	0.844
	H5	v_max=13.401(r_d/R)^1.053	0.819
	H7	v_max=11.764(r_d/R)^0.998	0.947
	H9	v_max=10.692(r_d/R)^0.961	0.922
周边孔	H11	v_max=6.876(r_d/R)^1.124	0.940
底板孔	H13	v_max=3.721(r_d/R)^1.354	0.907

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表 5 爆破峰值振动速度的拟合效果

Table 5. Fitting effects of the blasting peak vibration velocity

拟合公式	炮孔类型	拟合方程	相关系数r²
式(21)	掏槽孔	v_max= 30.205(r_d/R)^0.934	0.942
	辅助孔	v_max=9.845(r_d/R)^0.916	0.875
	周边孔	v_max=6.876(r_d/R)^1.124	0.940
	底板孔	v_max=3.721(r_d/R)^1.354	0.907
式(28)	掏槽孔	v^max=10.957(Q^1/3/R)^0.851	0.896
	辅助孔	v_max=5.197(Q^1/3/R)^0.694	0.646
	周边孔	v_max=11.705(Q^1/3/R)^1.234	0.837
	底板孔	v_max=26.762(Q^1/3/R)^1.534	0.789
式(29)	掏槽孔	v_max=7.308(Q^1/2/R)^0.682	0.788
	辅助孔	v_max=3.016(Q^1/2/R)^0.567	0.446
	周边孔	v_max= 5.812(Q^1/2/R)^1.234	0.878
	底板孔	v_max=19.298(Q^1/2/R)^1.534	0.802

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