基于摩擦与变形耗能的滚石切向恢复系数影响因素

黄福有; 张路青; 周剑; 马显东

doi:10.3799/dqkx.2022.369

基于摩擦与变形耗能的滚石切向恢复系数影响因素

doi: 10.3799/dqkx.2022.369

黄福有^{1, 2, ,},
张路青¹,
周剑³,
马显东^{1, 2}

1.
中国科学院地质与地球物理研究所页岩气与地质工程重点实验室北京 100029
2.
中国科学院大学地球与行星科学学院, 北京 100049
3.
北京工业大学城市与工程安全减灾教育部重点实验室北京 100124

基金项目:

国家重点研发计划项目 2019YFC1509703

第二次青藏高原综合科学考察研究资助项目 2019QZKK0904

中国科学院重点部署项目 KFZD-SW430

国家自然科学基金项目 41972287

详细信息

作者简介:
黄福有（1994-），男，硕士研究生，主要从事地质工程和地质灾害方面的研究工.ORCID：0000-0003-2444-5488.E-mail：huangfuyou@mail.iggcas.ac.cn

中图分类号: P642.21
计量
- 文章访问数: 560
- HTML全文浏览量: 336
- PDF下载量: 27
- 被引次数: 0
出版历程
- 收稿日期: 2022-06-29
- 网络出版日期: 2023-01-10
- 刊出日期: 2022-12-25

Influence Factors of Tangential Restitution Coefficient of Rolling Stone Based on Friction and Deformation Energy Dissipation

Huang Fuyou^{1, 2
,
,},
Zhang Luqing¹,
Zhou Jian³,
Ma Xiandong^{1, 2}

1.
Key Laboratory of Shale Gas and Geoengineering, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China
2.
College of Earth and Planetary Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
3.
Key Laboratory of Urban Security and Disaster Engineering of Ministry of Education, Beijing University of Technology, Beijing 100124, China

摘要

摘要:
切向恢复系数是滚石碰撞回弹的重要控制参数，目前的理论公式不能完全反映其作用机制，这是滚石动力学研究的一个难点问题.为此，根据滚石不同的回弹状态，提出基于入射角度变化的切向力模型；进一步，以切向接触理论和动能定理为基础，考虑碰撞过程中切向的摩擦耗能与变形耗能，推导了切向恢复系数的理论公式；最后研究入射速度、入射角、被撞击物体的变形模量对切向恢复系数的影响.结果表明：滚动回弹的切向恢复系数主要受切向变形量的影响；滑动回弹时，入射速度对切向恢复系数的影响参数为
\begin{document}$ {v}^{\frac{1}{20}} $\end{document}
，切向恢复系数随着其增加而缓慢减少；入射角度对切向恢复系数的影响参数为
$ \frac{\mathrm{c}\mathrm{o}{\mathrm{s}}^{\frac{1}{20}}{\beta }_{i}}{\mathrm{t}\mathrm{a}\mathrm{n}{\beta }_{i}} $
，切向恢复系数随其增加而增大；被撞击物体的变形模量对切向恢复系数的影响参数为
$ {E}_{2}^{-\frac{5}{8}} $
，切向恢复系数随其增加而增加.基于摩擦与变形耗能的切向恢复系数计算公式为滚石的碰撞回弹过程提供了新的计算模型.
- 滚石 /
- 斜碰撞 /
- 切向恢复系数 /
- 能量损失 /
- 影响因素 /
- 工程地质
Abstract:
The tangential restitution coefficient is an important control parameter for the rebound of the rolling stone, and the current theoretical formula can not fully reflect its mechanism. Firstly, according to the different rebound states of the rolling stone, a tangential force model based on the change of incident angle is proposed. Further considering the tangential friction energy dissipation and deformation energy dissipation in the collision process, the theoretical formula of tangential restitution coefficient is derived based on tangential contact theory and kinetic energy theorem. Finally, the influence of various factors on the tangential restitution coefficient is studied. The results show that the tangential restitution coefficient of rolling rebound is mainly affected by tangential deformation. When the rolling stone slips, the influence parameter of incident velocity on the tangential restitution coefficient is
\begin{document}$ {v}^{\frac{1}{20}} $\end{document}
, and the tangential restitution coefficient decreases slowly as it increases, while the influence parameter of incident angle on tangential restitution coefficient is
$ \frac{\mathrm{c}\mathrm{o}{\mathrm{s}}^{\frac{1}{20}}{\beta }_{i}}{\mathrm{t}\mathrm{a}\mathrm{n}{\beta }_{i}} $
, and the tangential restitution coefficient increases with its increase, the influence parameter of the deformation modulus of the impacted object on the tangential restitution coefficient is
$ {E}_{2}^{-\frac{5}{8}} $
, and the tangential restitution coefficient increases with its increase. The tangential recovery coefficient based on friction and deformation energy dissipation provides a new computational model for the collision process of rolling stone.
- rolling stone /
- oblique collision /
- tangential restitution coefficient /
- energy loss /
- influence factor /
- engineering geology

HTML全文

图 1 滚石运动过程示意图

Fig. 1. Movement process of rockfall

下载: 全尺寸图片幻灯片

图 2 斜碰撞瞬时示意图

Fig. 2. Schematic diagram of instantaneous oblique collision

下载: 全尺寸图片幻灯片

图 3 切向力与入射角的关系

Fig. 3. The relationship between tangential force and incident angle

下载: 全尺寸图片幻灯片

图 4 冲击力与入射角的关系

Fig. 4. The relationship between impact force and incident angle

下载: 全尺寸图片幻灯片

图 5 滚石切向荷载-变形曲线

Fig. 5. Tangential force-displacement curves of rolling stone

下载: 全尺寸图片幻灯片

图 6 不同入射速度下的切向恢复系数

Fig. 6. Tangential restitution coefficients at different incident velocities

下载: 全尺寸图片幻灯片

图 7 不同入射速度下切向恢复系数变化曲线

Fig. 7. Variation of restitution coefficient at different incident velocities

下载: 全尺寸图片幻灯片

图 8 不同入射角下的切向恢复系数

Fig. 8. Tangential restitution coefficient at different incident angles

下载: 全尺寸图片幻灯片

图 9 不同入射角下的恢复系数($ v= $20 m/s)

Fig. 9. Variation of coefficient of restitution under different incident angles($ v= $20 m/s)

下载: 全尺寸图片幻灯片

图 10 不同入射角下的耗能比例系数S

Fig. 10. The energy dissipation proportional coefficient S at different incident angles

下载: 全尺寸图片幻灯片

图 11 恢复系数随$ {E}_{2} $/$ {E}_{1} $变化曲线

Fig. 11. Variation of coefficient of restitution under different ratios of $ {E}_{2} $/$ {E}_{1} $

下载: 全尺寸图片幻灯片

表 1 滚石冲击计算参数

Table 1. Calculation parameters of rock fall impact

滚石				防护物体
变形模量$ {E}_{1} $(GPa)	泊松比 $ {\mu }_{1} $	半径R(m)	密度 ρ(kg· m^－3)	变形模量$ {E}_{2} $(GPa)	泊松比 $ {\mu }_{2} $	摩擦系数 $ f $
40	0.2	0.5	2 500	30	0.2	0.5

下载: 导出CSV

表 2 $ {\mathit{\beta }}_{\mathit{i}} $=1°时不同入射速度碰撞特征量统计

Table 2. Collision typical parameters quantity statistics under different incidence speeds($ {\beta }_{i} $=1°)

(m· s^-1)$ v $	$ {t}_{1} $ (ms)	$ T $ (ms)	$ {F}_{N\mathrm{m}\mathrm{a}\mathrm{x}}/ $ $ MN $	$ {F}_{T\mathrm{m}\mathrm{a}\mathrm{x}}/ $ $ MN $	恢复系数
(m· s^-1)$ v $	$ {t}_{1} $ (ms)	$ T $ (ms)	$ {F}_{N\mathrm{m}\mathrm{a}\mathrm{x}}/ $ $ MN $	$ {F}_{T\mathrm{m}\mathrm{a}\mathrm{x}}/ $ $ MN $	$ {e}_{n} $	$ {e}_{t} $
10	1.456	3.058	12.264	0.183	0.622	0.743
15	1.343	2.849	19.95	0.299	0.562	0.675
20	1.267	2.711	28.175	0.423	0.523	0.631
25	1.212	2.609	36.825	0.552	0.495	0.599
30	1.170	2.527	45.832	0.687	0.473	0.573
35	1.133	2.461	55.145	0.826	0.455	0.553
40	1.104	2.405	64.728	0.971	0.439	0.536

下载: 导出CSV

表 3 $ {\mathit{\beta }}_{\mathit{i}} $=60°时不同入射速度碰撞特征量统计

Table 3. Collision typical parameters quantity statistics under different incidence speeds($ {\beta }_{i} $=60°)

(m· s^-1)$ v $	$ {t}_{1} $ (ms)	$ T $ (ms)	$ {F}_{N\mathrm{m}\mathrm{a}\mathrm{x}}/ $ $ MN $	$ {F}_{T\mathrm{m}\mathrm{a}\mathrm{x}}/ $ $ MN $	恢复系数
(m· s^-1)$ v $	$ {t}_{1} $ (ms)	$ T $ (ms)	$ {F}_{N\mathrm{m}\mathrm{a}\mathrm{x}}/ $ $ MN $	$ {F}_{T\mathrm{m}\mathrm{a}\mathrm{x}}/ $ $ MN $	$ {e}_{n} $	$ {e}_{t} $
10	1.669	3.443	5.403	2.701	0.738	0.509
15	1.539	3.209	8.789	4.394	0.667	0.501
20	1.453	3.052	12.412	6.206	0.621	0.491
25	1.389	2.936	16.224	8.112	0.587	0.487
30	1.340	2.844	20.191	10.095	0.561	0.484
35	1.299	2.769	24.294	12.147	0.540	0.481
40	1.265	2.706	28.516	14.258	0.522	0.476

下载: 导出CSV

表 4 不同入射角度碰撞特征量统计($ \mathit{v}= $20 m/s)

Table 4. Collision typical parameters quantity statistics under different incident angles($ v= $20 m/s)

$ {\beta }_{i} $ (°)	$ {t}_{1} $ (ms)	$ T $ (ms)	$ {F}_{N\mathrm{m}\mathrm{a}\mathrm{x}}/ $ $ MN $	$ {F}_{T\mathrm{m}\mathrm{a}\mathrm{x}}/ $ $ MN $	恢复系数
$ {\beta }_{i} $ (°)	$ {t}_{1} $ (ms)	$ T $ (ms)	$ {F}_{N\mathrm{m}\mathrm{a}\mathrm{x}}/ $ $ MN $	$ {F}_{T\mathrm{m}\mathrm{a}\mathrm{x}}/ $ $ MN $	$ {e}_{n} $	$ {e}_{t} $
1	1.267	2.708	28.345	0.438	0.523	0.631
10	1.269	2.710	28.004	4.340	0.524	0.524
20	1.281	2.735	26.476	8.472	0.530	0.419
30	1.302	2.774	23.994	11.997	0.541	0.382
45	1.356	2.874	18.810	9.405	0.569	0.193
60	1.453	3.052	12.412	6.206	0.620	0.491
75	1.658	3.423	5.623	2.811	0.731	0.745
89	2.358	4.825	0.221	0.111	0.829	0.907

下载: 导出CSV

表 5 不同被撞击物体变形模量碰撞特征量

Table 5. Collision typical parameters quantity statistics under deformation modulus of different objects impacted($ v= $20 m/s, $ {\beta }_{i}= $60°)

E₂ (MPa)	$ {t}_{1} $ (ms)	$ T $ (ms)	$ {F}_{N\mathrm{m}\mathrm{a}\mathrm{x}}/ $ $ MN $	$ {F}_{T\mathrm{m}\mathrm{a}\mathrm{x}}/ $ $ MN $	恢复系数
E₂ (MPa)	$ {t}_{1} $ (ms)	$ T $ (ms)	$ {F}_{N\mathrm{m}\mathrm{a}\mathrm{x}}/ $ $ MN $	$ {F}_{T\mathrm{m}\mathrm{a}\mathrm{x}}/ $ $ MN $	$ {e}_{n} $	$ {e}_{t} $
10	28.578	69.193	0.631	0.315	0.173	0.352
50	15.018	35.519	1.201	0.601	0.211	0.389
100	11.387	26.663	1.584	0.792	0.230	0.405
200	8.638	20.024	2.088	1.044	0.251	0.421
500	6.005	13.736	3.002	1.501	0.283	0.441
1 000	4.574	10.353	3.943	1.972	0.311	0.455
10 000	1.971	4.278	9.151	4.575	0.457	0.483
40 000	1.453	3.052	12.412	6.206	0.621	0.563

下载: 导出CSV

参考文献(54)

Azzoni, A., de Freitas, M. H., 1995. Experimentally Gained Parameters, Decisive for Rock Fall Analysis. Rock Mechanics and Rock Engineering, 28(2): 111-124. https://doi.org/10.1007/bf01020064
Brizmer, V., Kligerman, Y., Etsion, I., 2006. The Effect of Contact Conditions and Material Properties on the Elasticity Terminus of a Spherical Contact. International Journal of Solids and Structures, 43(18): 5736-5749.
Buzzi, O., Giacomini, A., Spadari, M., 2012. Laboratory Investigation on High Values of Restitution Coefficients. Rock Mechanics and Rock Engineering, 45(1): 35-43. https://doi.org/10.1007/s00603-011-0183-0
Cagnoli, B., Manga, M., 2003. Pumice-Pumice Collisions and the Effect of the Impact Angle—Art. No. 1636. Geophysical Research Letters, 30(12): 1636.
Chau, K., Wong, R., Wu, J., 2002. Coefficient of Restitution and Rotational Motions of Rockfall Impacts. International Journal of Rock Mechanics and Mining Sciences, 39(1): 69-77. doi: 10.1016/S1365-1609(02)00016-3
Chen, Y. L., 2013. Influence of Key Factors on Trajectories of Rockfalls. Chinese Journal of Geotechnical Engineering, 35(Suppl. 2): 191-196(in Chinese with English abstract).
Chen, Y. Q., Wang, Q. C., 2018. Correction Calculation of Impact Force of Rockfall Based on Hertz Contact Theory and Thornton Elastoplasticity Hypothesis. Science Technology and Engineering, 18(13): 37-41(in Chinese with English abstract). doi: 10.3969/j.issn.1671-1815.2018.13.006
Day, R. W., 1997. Case Studies of Rockfall in Soft versus Hard Rock. Environmental and Engineering Geoscience, 3(1): 133-140.
Dussauge, C., Grasso, J., Helmstetter, A., 2003. Statistical Analysis of Rockfall Volume Distributions: Implications for Rockfall Dynamics. Journal of Geophysical Research: Solid Earth, 108(B6): ETG2-1-ETG2-11.
Giani, G. P., Giacomini, A., Migliazza, M., et al., 2004. Experimental and Theoretical Studies to Improve Rock Fall Analysis and Protection Work Design. Rock Mechanics and Rock Engineering, 37(5): 369-389. https://doi.org/10.1007/s00603-004-0027-2
He, S. M., Wu, Y., Li, X. P., 2009. Research on Restitution Coefficient of Rock Fall. Rock and Soil Mechanics, 30(3): 623-627(in Chinese with English abstract).
He, S. M., Zhuang, W. L., Zhang, X., et al., 2013. Research on Rockfall Impact Prevention of Chediguan Bridge Pier, Duwen Road. Chinese Journal of Rock Mechanics and Engineering, 32(Suppl. 2): 3421-3427(in Chinese with English abstract).
Hu, X. L., Tang, H. M., Zhu, L. X., 2011. Collapse Mode and Mechanism of High Magmatite Rock Slope in Wenchuan Epicentral Area. Earth Science, 36(6): 1149-1154(in Chinese with English abstract).
Kharaz, A., Gorham, D., Salman, A., 2001. An Experimental Study of the Elastic Rebound of Spheres. Powder Technology, 120(3): 281–291. doi: 10.1016/S0032-5910(01)00283-2
Labiouse, V., Heidenreich, B., 2009. Half-Scale Experimental Study of Rockfall Impacts on Sandy Slopes. Natural Hazards and Earth System Science, 9(104): 1981-1993.
Liu, X. F., Zhao, Y. Q., Wang, X. R., et al., 2022. Current Status and Prospects of Research on Fatigue Damage and Failure Precursors of Rocks. Earth Science, 47(6): 2190-2198(in Chinese with English abstract).
Liu, Y. J., 2002. Study on Fluidifying Theory of Large Highspeed Rockslide (Dissertation). Southwest Jiaotong University, Chengdu(in Chinese with English abstract).
Luo, G., Cheng, Q. G., Shen, W. G., et al., 2022. Research Status and Development Trend of the High-Altitude Extremely-Energetic Rockfalls. Earth Science, 47(3): 913-934(in Chinese with English abstract).
Lü, Q., Sun, H. Y., Zhai, S. K., et al., 2003. Evaluation Models of Rockfall Trajectory. Journal of Natural Disasters, 12(2): 79-84 (in Chinese with English abstract). doi: 10.3969/j.issn.1004-4574.2003.02.014
Maw, N., Barber, J. R., Fawcett, J. N., 1976. The Oblique Impact of Elastic Spheres. Wear, 38(1): 101-114. doi: 10.1016/0043-1648(76)90201-5
Mangwandi, C., Cheong, Y., Adams, M., et al., 2007. The Coefficient of Restitution of Different Representative Types of Granules. Chemical Engineering Science, 62(1): 437-450.
Mei, X. F., Hu, X. W., Luo, G., et al., 2019. A Study on the Coefficient of Restitution and Peak Impact of Rockfall Based on the Elastic-Plastic Theory. Journal of Vibration and Shock, 38(8): 14-20(in Chinese with English abstract).
Mindlin, R. D., 1949. Compliance of Elastic Bodies in Contact. Journal of Applied Mechanics, 16(3): 259-268. doi: 10.1115/1.4009973
Qin, Z. Y., Lu, Q. S., 2006. Analysis of Impact Process Model Based on Restitution Coefficient. Journal of Dynamics and Control, (4): 294-298(in Chinese with English abstract). doi: 10.3969/j.issn.1672-6553.2006.04.002
Scheiner, S., Pichler, B., Hellmich, C., et al., 2006. Loading of Soil-Covered Oil and Gas Pipelines Due to Adverse Soil Settlements: Protection against Thermal Dilatation-Induced Wear, Involving Geosynthetics. Computers and Geotechnics, 33(8): 371-380. doi: 10.1016/j.compgeo.2006.08.003
Schwager, T., Becker, V., Pöschel, T., 2008. Coefficient of Tangential Restitution for Viscoelastic Spheres. The European Physical Journal E, Soft Matter, 27(1): 107-114. https://doi.org/10.1140/epje/i2007-10356-3
Seifried, R., Schiehlen, W., Eberhard, P., 2005. Numerical and Experimental Evaluation of the Coefficient of Restitution for Repeated Impacts. International Journal of Impact Engineering, 32(1): 508-524.
Vu-Quoc, L., Lesburg, L., Zhang, X., 2004. An Accurate Tangential Force-Displacement Model for Granular-Flow Simulations: Contacting Spheres with Plastic Deformation, Force-Driven Formulation. Journal of Computational Physics, 196(1): 298-326. https://doi.org/10.1016/j.jcp.2003.10.025
Wang, Y. S., Cheng, W. Q., Liu, J. W., 2022. Forming Process and Mechanisms of Geo-Hazards in Luding Section of the Sichuan-Tibet Railway. Earth Science, 47(3): 950-958(in Chinese with English abstract).
Wu, C. Y., Li, L. Y., Thornton, C., 2003. Rebound Behavior of Spheres for Plastic Impacts. International Journal of Impact Engineering, 28: 929-946. doi: 10.1016/S0734-743X(03)00014-9
Yang, H. Q., Zhou, X. P., 2009. A New Approach to Calculate Trajectory of Rockfall. Rock and Soil Mechanics, 30(11): 3411-3416(in Chinese with English abstract). doi: 10.3969/j.issn.1000-7598.2009.11.032
Ye, S. Q., Gong, S. Q., 2015. Research on Normal Restitution Coefficient of Rockfall Collision by Model Tests. China Railway Science, 36(4): 13-19(in Chinese with English abstract).
Ye, S. Q., Gong, S. Q., Wang, L. F., et al., 2018. Research on Value of Tangential Restitution Coefficient for Rockfall Collision. China Railway Science, 39(1): 8-15(in Chinese with English abstract).
Zhang, L. Q., Yang, Z. F., Xu, B., 2004. Rock Falls and Rock Fall Hazards. Journal of Engineering Geology, 12(3): 225-231 (in Chinese with English abstract). doi: 10.3969/j.issn.1004-9665.2004.03.001
Zhang, G. C., Tang, H. M., Xiang, X., 2012. Characteristic Parameters Theoretical Analysis of Rockfall Impact on Ground. Chinese Journal of Rock Mechanics and Engineering, 31(Suppl. 1): 2839-2846(in Chinese with English abstract).
Zhang, G. C., Xiang, X., Tang, H. M., 2011. Field Test and Numerical Calculation of Restitution Coefficient of Rockfall Collision. Chinese Journal of Rock Mechanics and Engineering, 30(6): 1266-1273(in Chinese with English abstract).
陈颖骐, 王全才, 2018. 基于Hertz弹性理论和Thornton弹塑性假设的滚石冲击力的修正计算. 科学技术与工程, 18(13): 37-41. https://www.cnki.com.cn/Article/CJFDTOTAL-KXJS201813006.htm
陈宇龙, 2013. 滚石运动过程中关键参数的影响分析. 岩土工程学报, 35(增刊2): 191-196. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC2013S2032.htm
何思明, 吴永, 李新坡, 2009. 滚石冲击碰撞恢复系数研究. 岩土力学, 30(3): 623-627. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX200903010.htm
何思明, 庄卫林, 张雄, 等, 2013. 都汶公路彻底关大桥桥墩抗滚石冲击防护研究. 岩石力学与工程学报, 32(增刊2): 3421-3427. https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX2013S2056.htm
胡新丽, 唐辉明, 朱丽霞, 2011. 汶川震中岩浆岩高边坡破坏模式与崩塌机理. 地球科学, 36(6): 1149-1154. doi: 10.3799/dqkx.2011.121
刘新锋, 赵英群, 王晓睿, 等, 2022. 岩石疲劳损伤及破坏前兆研究现状与展望. 地球科学, 47(6): 2190-2198. doi: 10.3799/dqkx.2021.186
刘涌江, 2002. 大型高速岩质滑坡流体化理论研究(博士论文). 成都: 西南交通大学.
罗刚, 程谦恭, 沈位刚, 等, 2022. 高位高能岩崩研究现状与发展趋势. 地球科学, 47(3): 913-934. doi: 10.3799/dqkx.2021.133
吕庆, 孙红月, 翟三扣, 等, 2003. 边坡滚石运动的计算模型. 自然灾害学报, 12(2): 79-84. https://www.cnki.com.cn/Article/CJFDTOTAL-ZRZH200302013.htm
梅雪峰, 胡卸文, 罗刚, 等, 2019. 基于弹塑性理论的落石碰撞恢复系数和峰值冲击力研究. 振动与冲击, 38(8): 14-20. https://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ201908003.htm
秦志英, 陆启韶, 2006. 基于恢复系数的碰撞过程模型分析. 动力学与控制学报, (4): 294-298. https://www.cnki.com.cn/Article/CJFDTOTAL-DLXK200604001.htm
王运生, 程万强, 刘江伟, 2022. 川藏铁路廊道泸定段地质灾害孕育过程及成灾机制. 地球科学, 47(3): 950-958. doi: 10.3799/dqkx.2021.179
杨海清, 周小平, 2009. 边坡落石运动轨迹计算新方法. 岩土力学, 30(11): 3411-3416. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX200911041.htm
叶四桥, 巩尚卿, 2015. 落石碰撞法向恢复系数的模型试验研究. 中国铁道科学, 36(4): 13-19. https://www.cnki.com.cn/Article/CJFDTOTAL-ZGTK201504004.htm
叶四桥, 巩尚卿, 王林峰, 等, 2018. 落石碰撞切向恢复系数的取值研究. 中国铁道科学, 39(1): 8-15. https://www.cnki.com.cn/Article/CJFDTOTAL-ZGTK201801003.htm
张路青, 杨志法, 许兵, 2004. 滚石与滚石灾害. 工程地质学报, 12(3): 225-231. https://www.cnki.com.cn/Article/CJFDTOTAL-GCDZ200403000.htm
章广成, 唐辉明, 向欣, 2012. 冲击地面过程中落石特征参量的理论分析. 岩石力学与工程学报, 31(增刊1): 2839-2846. https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX2012S1030.htm
章广成, 向欣, 唐辉明, 2011. 落石碰撞恢复系数的现场试验与数值计算. 岩石力学与工程学报, 30(6): 1266-1273. https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX201106026.htm

施引文献

资源附件(0)

访问统计

点击查看大图

图(11) / 表(5)

计量

文章访问数: 560
HTML全文浏览量: 336
PDF下载量: 27
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

留言板

基于摩擦与变形耗能的滚石切向恢复系数影响因素

doi: 10.3799/dqkx.2022.369

作者简介:
黄福有（1994-），男，硕士研究生，主要从事地质工程和地质灾害方面的研究工.ORCID：0000-0003-2444-5488.E-mail：huangfuyou@mail.iggcas.ac.cn

计量

Influence Factors of Tangential Restitution Coefficient of Rolling Stone Based on Friction and Deformation Energy Dissipation

计量

目录

留言板

基于摩擦与变形耗能的滚石切向恢复系数影响因素

doi: 10.3799/dqkx.2022.369

作者简介: 黄福有（1994-），男，硕士研究生，主要从事地质工程和地质灾害方面的研究工.ORCID：0000-0003-2444-5488.E-mail：huangfuyou@mail.iggcas.ac.cn

计量

出版历程

Influence Factors of Tangential Restitution Coefficient of Rolling Stone Based on Friction and Deformation Energy Dissipation

计量

出版历程

目录

作者简介:
黄福有（1994-），男，硕士研究生，主要从事地质工程和地质灾害方面的研究工.ORCID：0000-0003-2444-5488.E-mail：huangfuyou@mail.iggcas.ac.cn