耦合装药条件下不同孔径孔壁冲击压力的阶段特征

楼晓明; 陈诗伟; 李广斌; 牛明远; 林日宗; 姚炳金

doi:10.11883/bzycj-2022-0547

耦合装药条件下不同孔径孔壁冲击压力的阶段特征

doi: 10.11883/bzycj-2022-0547

楼晓明^{1, 2,},
陈诗伟^{1, 2, ,},
李广斌³,
牛明远⁴,
林日宗⁴,
姚炳金^{1, 2}

1.
福州大学紫金地质与矿业学院，福建福州 350116
2.
福州大学爆炸技术研究所，福建福州 350116
3.
乌拉特后旗紫金矿业有限公司，内蒙古巴彦淖尔 015543
4.
紫金矿业建设有限公司，福建龙岩 364299

基金项目: 国家自然科学基金（51679093， 51374112）

详细信息

作者简介:
楼晓明（1972－　），男，博士，教授，331261323@qq.com

通讯作者:
陈诗伟（1999－　），男，硕士研究生，1291178186@qq.com

中图分类号: O383
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- 文章访问数: 350
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- 被引次数: 0
出版历程
- 收稿日期: 2022-12-08
- 修回日期: 2023-04-20
- 网络出版日期: 2023-04-25
- 刊出日期: 2023-08-31

Stage characteristics of impact pressure of blasthole-walls with different diameters under coupled charge conditions

LOU Xiaoming^{1, 2
,},
CHEN Shiwei^{1, 2
, ,},
LI Guangbin³,
NIU Mingyuan⁴,
LIN Rizong⁴,
YAO Bingjin^{1, 2}

1.
Zijin School of Geology and mining, Fuzhou University, Fuzhou 350116, Fujian, China
2.
Institute of explosion technology, Fuzhou University, Fuzhou 350116, Fujian, China
3.
Wulate Houqi Zijin Mining Co., Ltd., Bayannur 015543, Inner Mongolia, China
4.
Zijin Mining Construction Co., Ltd., Longyan 364299, Fujian, China

摘要

摘要: 为合理减小振动并确定单孔破坏的范围，需掌握不同孔径孔壁的冲击压力规律。通过分析孔壁在爆轰作用下的运动过程，构建了孔壁在受到爆炸冲击波时不可压缩流体动力膨胀、破岩粉碎和动态膨胀等3个阶段的简化计算模型，分别确定了各阶段的孔壁压力与时间的分段函数。基于理想气体膨胀方程，确定了孔壁峰值压力的理论放大系数，在数学上统一了孔壁压力变化的阶段特征，得到了炮孔耦合装药孔壁冲击压力孔壁压力特征变化曲线。依托LS-DYNA数值模拟软件和现场工业模型试验，采用数值分析和超动态应变测试模型试验的方法对计算模型结果进行对比分析，得到了耦合装药条件下5种不同孔径（51~200 mm）的孔壁数值分析历程点的冲击压力变化曲线，试验验证了孔壁峰值压力的理论放大系数，系数误差控制在了0.7%~6.4%之间。对比分析了76、90 mm两种特定工况下的理论计算、数值分析历程点和模型试验测点数据，结果表明：理论分段函数能够有效拟合数值分析和模型试验数据，峰值压力的误差分别为6.8%、4.9%，分段时间的误差分别为7.6%、4.8%。
- 耦合装药 /
- 炮孔直径 /
- 力学模型 /
- 孔壁压力 /
- 模型试验
Abstract: In order to reduce blasting vibration reasonably and determine the damage range of single hole, it is necessary to study the impact pressure changing law of different bore diameters. By analyzing the movement process of the hole wall under the action of detonation, a simplified calculation model for three stages of dynamic expansion of the incompressible fluid, rock-breaking, and dynamic expansion of the hole wall under the action of the explosive shock wave is established, and the time history subsection function of the hole wall pressure in each stage is determined. Based on the ideal gas expansion equation, the theoretical amplification factor of peak pressure on the bore wall is determined, the stage characteristics of bore wall pressure change were mathematically unified, and the impact pressure characteristic curves of impact pressure on the bore wall of blast-hole coupling charge were obtained. Based on LS-DYNA numerical simulation software and field industrial model test, the calculation model results were compared and validated by numerical analysis and super-dynamic strain test model test. The impact pressure curves of five different pore diameters (51−200 mm) under the coupled charge condition were obtained, and the theoretical amplification coefficient of the peak pore pressure was verified by experiments. The theoretical model error is controlled between 0.7% and 6.4%. The comparison and analysis of theoretical calculation, historical point of numerical analysis, and measured point data of model test under two specific conditions of 76 and 90 mm show that the theoretical piecewise function can effectively fit the data of numerical analysis and model test. The error of peak pressure is 6.8% and 4.9%, and that of time is 7.6% and 4.8%, respectively.
- coupling charge /
- hole diameter /
- mechanical model /
- bore wall pressure /
- model test

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图 1 岩体破坏阶段图

Figure 1. Rock mass destruction stage diagram

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图 2 爆洞塑性膨胀破坏阶段

Figure 2. Blast plastic expansion destruction stage

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图 3 岩体被粉碎阶段

Figure 3. Rock mass crushing stage

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图 4 理论孔壁压力分段函数

Figure 4. Diagram of the theoretical pore wall pressure segmentation function

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图 5 计算模型剖面图

Figure 5. Computational model profile

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图 6 不同工况下的孔壁压力时程曲线

Figure 6. Time history curves of hole wall pressure under different working conditions

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图 7 成型应变砖

Figure 7. Formed strain brick

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图 8 应变片连接

Figure 8. Strain gauge connection

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图 9 应变砖布置示意图

Figure 9. Schematic diagram of strain brick layout

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图 10 实验现场图

Figure 10. Pictures of the experiment site

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图 11 膨胀半径与特征时间的拟合关系

Figure 11. Relationship between expansion radius and time

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图 12 不同孔径时模拟与理论计算孔壁压力时程曲线对比

Figure 12. Comparison of the pore wall pressure histories obtained from numerical simulation and theoretical calculation

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表 1 炸药建模参数

Table 1. Mathematical modeling parameters of explosives

炸药名称	密度ρ/(kg·m⁻³)	爆速D/(m·s⁻¹)	C-J压力/GPa	A/GPa	B/GPa	R₁	R₂	ω	初始比内能E₀/(kJ·m⁻³)	初始体积V
粒状铵油	900	2600	1.521	471	0.07	4.05	0.95	0.30	7.1	1

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表 2 围岩（片岩）建模参数

Table 2. Surrounding rock modeling parameters

密度ρ/(kg·m⁻³)	剪切模量G/GPa	完整归一化强度A/GPa	断裂归一化强度B/GPa	应变强度参数C/GPa	断裂强度参数M/GPa
2 945	0.1908	0.78	0.65	0.02	0.45

完整强度参数N/GPa	应变率$\dot \varepsilon $/s⁻¹	抗拉强度σ_t/GPa	最大断裂归一化强度σ_s/GPa	Hugoniot弹性极限	Hugoniot弹性极限压力分量
0.45	10⁻⁶	0.0292	0.35	0.0275	0.01945

断裂塑性应变参数D₁	断裂塑性应变指数D₂	体积模量K₁/GPa	第二压力系数K₂	第三压力系数K₃	失效标准
1.15	7.0	31	7.0	56.5	0

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表 3 炮孔堵塞材料（土）建模参数

Table 3. Modeling parameters of hole blockage

密度ρ/(kg·m⁻³)	剪切模量G/GPa	卸载体积模量K_x/GPa	屈服函数常数A₀	屈服函数常数A₁	屈服函数常数A₂
1 800	0.06385	78	3.4×10⁻¹³	7.033×10⁻⁷	0.3

断裂压力p_c/kN	装卸载路径	初始压力p_i	体积应变ε₁	体积应变ε₂	体积应变ε₃
−6.9	0	0	0	−0.104	−0.161

体积应变ε₄	体积应变ε₅	体积应变ε₆	体积应变ε₇	体积应变ε₈	体积应变ε₉
−0.192	−0.224	−0.246	−0.271	−0.283	−0.9

体积应变ε₁₀	体积应变ε₁对应的压力p₁/N	体积应变ε₂对应的压力p₂/N	体积应变ε₃对应的压力p₃/N	体积应变ε₄对应的压力p₄/N
−0.4	0	0.2	0.4	0.6

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表 4 流固耦合空气建模参数

Table 4. Fluid-structure interaction air modeling parameters

密度ρ/(kg·m⁻³)	多项式系数C₀	多项式系数C₁	多项式系数C₂	多项式系数C₃	多项式系数C₄
1.25	0.344	0.78	$ 0 $	$ 0 $	1.4

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表 5 不同孔径耦合装药炮孔压力模型试验测试结果

Table 5. Results of coupling charge pressure model tests with different hole diameters

试验编号	炮孔直径/mm	炸药质量/g	峰值电压/V	峰值应变/10⁻⁶	峰值时刻/μs	峰值压力/GPa
1	76	1720	5.765	28058.255	114	7.545
2	76	1720	5.932	28871.044	112	7.763
3	76	1720	4.897	23833.699	100	6.409
4	90	2544	7.542	36706.914	160	9.871
5	90	2544	7.363	35835.721	142	9.636
6	90	2544	7.433	36176.411	148	9.728

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表 6 孔壁膨胀峰值特征点数据

Table 6. Pore wall expansion peak feature point data

直径/mm	峰值压力/GPa			误差%		Z	ω
直径/mm	理论	模拟	试验	模拟	试验	Z	ω
51	3.852	3.660		5.245		0.9514	2.532
76	7.570	7.090	7.239	6.341	4.373	0.9567	4.453
90	9.608	9.130	9.745	5.237	1.426	0.9572	6.317
115	12.605	12.700		0.748		0.9602	8.287
200	21.239	22.700		6.435		0.9726	13.964

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表 7 直径76 mm时孔壁压力及时刻误差分析

Table 7. Error analysis of the hole wall pressure and time for a diameter of 76 mm

类别	峰值位移/mm	峰值时刻/μs	峰值压力/GPa	分段时刻/μs	分段压力/GPa
理论值	1.810	115.000	7.090	304.000	1.300
模拟值	1.720	120.000	7.570	329.000	1.459
试验值		127.667	7.239	333.000	1.052
模拟误差/%	5.233	4.167	6.341	7.599	10.000
实验误差/%		9.992	2.102	8.709	19.077

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表 8 直径90 mm时孔壁塑形膨胀阶段压力及时刻

Table 8. Error analysis of the hole wall pressure and time for a diameter of 90 mm

类别	峰值位移/mm	峰值时刻/μs	峰值压力/GPa	分段时刻/μs	分段压力/GPa
理论值	2.143	136.000	9.608	324.000	1.500
模拟值	2.470	140.000	9.131	309.000	1.505
试验值		150.000	9.745	330.000	1.052
模拟误差/%	13.239	2.529	4.961	4.813	0.333
试验误差/%		10.294	1.426	1.852	29.867

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