不同典型形状落石冲击砂垫层试验与量纲分析

闫鹏; 方秦; 张锦华; 张亚栋; 陈力; 范俊余

doi:10.11883/bzycj-2020-0219

不同典型形状落石冲击砂垫层试验与量纲分析

doi: 10.11883/bzycj-2020-0219

闫鹏^1,,
方秦¹,
张锦华^{2, 3, ,},
张亚栋^{2, 3},
陈力^{2, 3},
范俊余^{2, 3}

1.
中国人民解放军陆军工程大学，江苏南京 210007
2.
东南大学爆炸安全防护教育部工程研究中心，江苏南京，211189
3.
东南大学土木工程学院，江苏南京 211189

基金项目: 国家自然科学基金（51778623）

详细信息

作者简介:
闫　鹏（1991－　），男，博士研究生，yanpeng007@126.com

通讯作者:
张锦华（1981－　），男，博士，教授，zhangjh@seu.edu.cn

中图分类号: O347; U213.1
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- 被引次数: 0
出版历程
- 收稿日期: 2020-06-30
- 修回日期: 2020-08-03
- 网络出版日期: 2021-07-05
- 刊出日期: 2021-07-05

Experimental study of different typical shape falling-rocks impacting on the sand cushion and dimensionless analysis

YAN Peng^1
,,
FANG Qin¹,
ZHANG Jinhua^{2, 3
, ,},
ZHANG Yadong^{2, 3},
CHEN Li^{2, 3},
FAN Junyu^{2, 3}

1.
PLA Army Engineering University, Nanjing 210007, Jiangsu, China
2.
Engineering Research Center of Safety and Protection of Explosion and Impact of Ministry of Education (ERCSPEIME), Southeast University, Nanjing 211189, Jiangsu, China
3.
School of Civil Engineering, Southeast University, Nanjing 211189, Jiangsu, China

摘要

摘要: 开展了球形、锥形和平头3种典型形状落石撞击垫层的冲击力及侵入深度的试验研究。结果表明，落石形状对冲击试验结果有显著影响：相同条件下，平头落石的冲击力最大，侵入深度和冲击力峰值时间最短，锥形落石反之，而球形落石介于两者之间。采用无量纲化分析方法，将落石的质量、速度、形状、特征尺寸，垫层的强度、密度转换为无量纲强度冲击因子I、密度冲击因子λ和形状冲击因子ψ，并对冲击因子与侵入深度的试验数据进行了相关性分析，结果表明：（1）冲击因子I和λ在决定最终侵深z_m/d 中所起到的作用比较相近；（2）冲击因子I和λ对侵入深度的影响分析表明，I和λ的相对独立性较强，相互影响较小，在不同的λ值下，I对侵入深度的影响规律基本一致。
- 落石形状 /
- 冲击力 /
- 侵入深度 /
- 无量纲化 /
- 垫层
Abstract: An experimental study on the impact force and penetration of falling rocks with three typical shapes, including spherical, conical and flat shapes, against the cushion was carried out. The experimental results show that the shape of the falling rock has a significant influence on the impact results. Under the same conditions, the flat blocks have the highest impact force, the lowest penetration depth and the shortest peak impact time, and the opposite for the conical falling rocks, with spherical blocks are between the two. The dimensionless analysis method was adopted to convert the mass, velocity, shape, size of the falling rock, the strength and density of the cushion layer into the dimensionless strength impact factor I, density impact factor λ and shape impact factor ψ. The correlation analysis between the impact factors and penetration test data shows that: (1) The effects of the impact factors I and λ on the final depth of penetration z_m/d are similar. (2) The analysis of the impact factors I and λ effects on penetration depth shows that I and λ are relatively independent. The pattern of the I effects on the depth of penetration is generally consistent for different λ values.
- falling rock’s shape /
- impact force /
- penetration depth /
- dimensionless /
- cushion

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图 1 落石冲击试验系统

Figure 1. Rockfall impact test system

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图 2 落石冲击试验数据测量方法

Figure 2. Measurement method of rockfall impact test data

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图 3 试验所用落石形状及尺寸

Figure 3. Shapes and sizes of the falling rocks used in the test

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图 4 砂土垫层强度静力载荷试验及结果

Figure 4. Static load test and results of strength of sand cushion

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图 5 不同形状落石侵入深度对比

Figure 5. Comparison of the penetration depth of falling rocks with different shapes

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图 6 不同形状下落石冲击力时程曲线

Figure 6. Time history curves of impact force for falling rocks with different shapes

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图 7 不同形状落石相对冲击力时程曲线

Figure 7. Time history curves of relative impact force for falling rocks with different shapes

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图 8 落石形状对冲击力、峰值时间和冲量的影响

Figure 8. Effects of falling rock’s shape on impact force, peak time and impulse

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图 9 不同典型形状落石冲击成坑形状

Figure 9. Different impact craters formed by different typical falling rocks

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图 10 椭球形落石的整体形状变化范围

Figure 10. Variation of the overall shape of the ellipsoid falling rocks

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图 11 无量纲冲击因子与无量纲侵入深度之间的相关性

Figure 11. Correlation between dimensionless impact factors and penetration depths

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图 12 不同形状落石无量纲侵入深度的拟合曲线

Figure 12. Fitting curves of the dimensionless penetration depths of the blocks

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表 1 球形落石冲击砂垫层试验工况

Table 1. Conditions of impact test by spherical falling rocks

编号	m/kg	v₀/（m·s⁻¹）	H/m	d/m	I	λ	z_m/d
S-01	10	4.43	1.00	0.12	1.73	5.22	1.45
S-02	10	6.26	2.00	0.12	3.47	5.22	1.88
S-03	10	8.85	4.00	0.12	6.93	5.22	2.67
S-04	10	13.28	9.00	0.12	15.60	5.22	3.46
S-05	50	4.43	1.00	0.25	0.96	2.89	1.00
S-06	50	6.26	2.00	0.25	1.92	2.89	1.15
S-07	50	8.85	4.00	0.25	3.83	2.89	1.47
S-08	50	13.28	9.00	0.25	8.63	2.89	1.84
S-09	100	4.43	1.00	0.36	0.64	1.93	0.71
S-10	100	6.26	2.00	0.36	1.28	1.93	0.76
S-11	100	8.85	4.00	0.36	2.57	1.93	1.06
S-12	100	13.28	9.00	0.36	5.78	1.93	1.17

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表 2 锥形落石冲击砂垫层试验工况

Table 2. Conditions of impact test by conical falling rocks

编号	m/kg	v₀/（m·s⁻¹）	H/m	d/m	I	λ	z_m/d
C-01	10	4.40	1.00	0.12	1.73	5.22	1.89
C-02	10	6.30	2.00	0.12	3.47	5.22	2.00
C-03	10	8.90	4.00	0.12	6.93	5.22	2.75
C-04	50	2.40	0.30	0.25	0.29	2.89	0.76
C-05	50	6.30	2.00	0.25	1.92	2.89	1.06
C-06	50	8.90	4.00	0.25	3.83	2.89	1.27
C-07	50	13.30	9.00	0.25	8.63	2.89	1.59
C-08	50	17.10	15.00	0.25	14.38	2.89	2.16

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表 3 平头落石冲击砂垫层试验工况

Table 3. Conditions of impact test by flat falling rocks

编号	m/kg	v₀/（m·s⁻¹）	H/m	d/m	I	λ	z_m/d
F-01	50	4.40	1.00	0.25	0.96	2.89	0.52
F-02	50	6.30	2.00	0.25	1.92	2.89	0.68
F-03	50	8.90	4.00	0.25	3.83	2.89	0.86
F-04	50	13.30	9.00	0.25	8.63	2.89	1.06
F-05	50	6.30	2.00	0.30	1.11	1.67	0.37
F-06	50	13.30	9.00	0.30	4.99	1.67	0.68

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表 4 无量纲冲击因子之间及与侵入深度的相关性

Table 4. Correlation between dimensionless impact factors and penetration depths

冲击因子	I	λ	z_m/d
I	1.00	0.24	0.71
λ	0.24	1.00	0.77
z_m/d	0.71	0.77	1.00

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表 5 不同形状落石3种拟合公式的拟合参数比较

Table 5. Comparison of parameters of three fitting formulas for falling rocks with different shapes

落石形状	z_m/d=Aλ ln(1+CI/λ)拟合参数
落石形状	A	C
球形	0.18	11.67
锥形	0.12	47.64
平头	0.10	15.09

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