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An estimation model for the fragmentation properties of brittle rock block due to the impacts against an obstruction

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Abstract

Mountain hazards with large masses of rock blocks in motion–such as rock falls, avalanches and landslides–threaten human lives and structures. Dynamic fragmentation is a common phenomenon during the movement process of rock blocks in rock avalanche, due to the high velocity and impacts against obstructions. In view of the energy consumption theory for brittle rock fragmentation proposed by Bond, which relates energy to size reduction, a theoretical model is proposed to estimate the average fragment size for a moving rock block when it impacts against an obstruction. Then, different forms of motion are studied, with various drop heights and slope angles for the moving rock block. The calculated results reveal that the average fragment size decreases as the drop height increases, whether for free-fall or for a sliding or rolling rock block, and the decline in size is rapid for low heights and slow for increasing heights in the corresponding curves. Moreover, the average fragment size also decreases as the slope angle increases for a sliding rock block. In addition, a rolling rock block has a higher degree of fragmentation than a sliding rock block, even for the same slope angle and block volume. Finally, to compare with others’ results, the approximate number of fragments is estimated for each calculated example, and the results show that the proposed model is applicable to a relatively isotropic moving rock block.

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References

  • Asteriou P, Saroglou H, Tsiambaos G (2012) Geotechnical and kinematic parameters affecting the coefficients of restitution for rock fall analysis. International Journal of Rock Mechanics and Mining Sciences 54: 103–113. DOI: 10.1016/j.ijrmms.2012. 05.029

    Article  Google Scholar 

  • Azzoni A, Rossi PP, Drigo E, et al. (1992) In situ observations of rockfalls analysis parameters. In: Proceedings of the 6th International Symposium on landslides, Christchurch. pp 307–314.

    Google Scholar 

  • Balaz P (2008) Mechanochemistry in nanoscience and minerals engineering. Berlin: Springer Science and Business Media. DOI: 10.1007/978-3-540-74855-7

    Google Scholar 

  • Bond FC (1952) The third theory of comminution. Transactions AIME 193: 484–494. DOI: 10.1016/j.mineng.2006.01.007

    Google Scholar 

  • Bond FC (1960) Crushing and grinding calculations. Canadian Mining and Metallurgical Bulletin 47: 466–472.

    Google Scholar 

  • Bowman ET, Take WA, Rait KL, Hann C (2012) Physical models of rock avalanche spreading behaviour with dynamic fragmentation. Canadian Geotechnical Journal 49: 460–476. DOI: 10.1139/t2012-007

    Article  Google Scholar 

  • Broili L (1973) In situ tests for the study of rockfall. Geologia applicata e Idrogeologia (Applied Geology and Hydrogeology) 8: 105–111.

    Google Scholar 

  • Chau KT, Wong RHC, Wu JJ (2002) Coefficient of restitution and rotational motions of rockfall impacts. International Journal of Rock Mechanics and Mining Sciences 39: 69–77. DOI: 10.1016/S1365-1609(02)00016-3

    Article  Google Scholar 

  • Crosta GB, Frattini P, Imposimato S, Agliardi F (2006) Modeling vegetation and fragmentation effects on rockfalls. Geophysical Research Abstracts 8: 76–94.

    Google Scholar 

  • Chandar KR, Deo SN, Baliga AJ (2016) Prediction of Bond's work index from field measurable rock properties. International Journal of Mineral Processing 157: 134–144. DOI: 10.1016/j.minpro.2016.10.006

    Article  Google Scholar 

  • Cherepanov GP (1979) Mechanics of brittle fracture. New York: McGraw-Hill.

    Google Scholar 

  • Dai F, Xia K, Zheng H, Wang YX (2011) Determination of dynamic rock mode-I fracture parameters using cracked chevron notched semi-circular bend specimen. Engineering Fracture Mechanics 78: 2633–2644. DOI: 10.1016/j. engfracmech.2011.06.022

    Article  Google Scholar 

  • De Blasio FV (2011) Dynamical stress in force chains of granular media traveling on a bumpy terrain and the fragmentation of rock avalanches. Acta Mechanica 221: 375–382. DOI: 10.1007/s00707-011-0504-0

    Article  Google Scholar 

  • De Blasio FV, Crosta GB (2014) Simple physical model for the fragmentation of rock avalanches. Acta Mechanica 225: 243–252. DOI: 10.1007/s00707-013-0942-y

    Article  Google Scholar 

  • Dorren LK (2003) A review of rockfall mechanics and modelling approaches. Progress in Physical Geography 27(1): 69–87. DOI: 10.1191/0309133303pp359ra

    Article  Google Scholar 

  • Ghorbani Z, Masoumi AA, Hemmat A (2010) Specific energy consumption for reducing the size of alfalfa chops using a hammer mill. Biosystems Engineering 105(1): 34–40. DOI: 10.1016/j.biosystemseng.2009.09.006

    Article  Google Scholar 

  • Giacomini A, Buzzi O, Renard B, Giani GP (2009) Experimental studies on fragmentation of rock falls on impact with rock surfaces. International Journal of Rock Mechanics and Mining Sciences 46(4): 708–715. DOI: 10.1016/j.ijrmms.2008.09.007

    Article  Google Scholar 

  • Giani GP, Giacomini A, Migliazza M, Segalini A (2004) Experimental and theoretical studies to improve rock fall analysis and protection work design. Rock Mechanics and Rock Engineering 37: 369–389. DOI: 10.1007/s00603-004-0027-2

    Article  Google Scholar 

  • Grady DE, Kipp ME (1987) Dynamic rock fragmentation. Fracture Mechanics of Rock 10: 429–475.

    Article  Google Scholar 

  • Greco OD, Fornaro M, Mancini R, et al. (1981) Indagiine sperimentale sull'abbattimento meccanico delle rocce mediante martelli demolitori di medio peso (Experimental study on the mechanical cutting of rocks by using medium weight of hammer). Bollettino dell Associazione Mineraria Subalpina. pp 88–102.

    Google Scholar 

  • Gupta A, Yan DS (2006) Size reduction and energy requirement. In book: Mineral Processing Design and Operation, Amsterdam, Elsevier. pp 63–98. DOI: 10.1016/B978-044451636-7/50004-8

    Book  Google Scholar 

  • Guzzetti F, Crosta G, Detti R, et al. (2002) STONE: a computer program for the three-dimensional simulation of rock-falls. Computers & Geosciences 28: 1079–1093. DOI: 10.1016/S0098-3004(02)00025-0

    Article  Google Scholar 

  • Hukki RT (1962) Proposal for a solomonic settlement between the theories of von Rittinger, Kick and Bond. Transaction of American Institute of Mining, Metallurgical, and Petroleum Engineers 223: 403–408

    Google Scholar 

  • Hou TX, Xu Q, Yang XG, et al. (2015a) Experimental study of the fragmentation characteristics of brittle rocks by the effect of a freefall round hammer. International Journal of Fracture 194: 169–185. DOI: 10.1007/s10704-015-0046-x

    Article  Google Scholar 

  • Hou TX, Yang XG, Huang C, et al. (2015b) A calculation method based on impulse theorem to determine the impact force of rockfall on structure. Chinese Journal of Rock Mechanics and Engineering 34: 3116–3122. (In Chinese) DOI: 10.13722/j.cnki.jrme.2013.1912

    Google Scholar 

  • Iqbal MJ, Mohanty B (2007) Experimental calibration of ISRM suggested fracture toughness measurement techniques in selected brittle rocks. Rock Mechanics and Rock Engineering 40: 453–475. DOI: 10.1007/s00603-006-0107-6

    Article  Google Scholar 

  • Jankovic A, Dundar H, Mehta R (2010) Relationships between comminution energy and product size for a magnetite ore. Journal of the South African Institute of Mining and Metallurgy 110: 141–146.

    Google Scholar 

  • Kick F (1885) The Law of Proportional Resistance and Its Applications (Das Gesetz der proportionalen Widerstände und seine Anwendungen). Verlag A. Felix, Leipzig, Germany.

    Google Scholar 

  • Kopp JB, Schmittbuhl J, Noel O, et al. (2014) Fluctuations of the dynamic fracture energy values related to the amount of created fracture surface. Engineering Fracture Mechanics 126: 178–189. DOI: 10.1016/j.engfracmech.2014.05.014

    Article  Google Scholar 

  • Labiouse V, Heidenreich B (2009) Half-scale experimental study of rockfall impacts on sandy slopes. Natural Hazards and Earth System Science 9: 1981–1993. DOI: 10.5194/nhess-9-1981-2009

    Article  Google Scholar 

  • Liu YJ (2003) Study on fluidifying theory of large highspeed rockslide. Chinese Journal of Mechanics and Engineering 22: 170. (In Chinese)

    Google Scholar 

  • Morrell S (2004) An alternative energy–size relationship to that proposed by Bond for the design and optimization of grinding circuits. International Journal of Mineral Processing 74: 133–141. DOI: 10.1016/j.minpro.2003.10.002

    Article  Google Scholar 

  • Mecholsky JJ, Rice RW, Freiman SW (1974) Prediction of fracture energy and flaw size in glasses from mirror size. Journal of the American Ceramic Society 57: 440–443. DOI: 10.1111/j.1151-2916.1974.tb11377.x

    Article  Google Scholar 

  • Paluszny A, Tang XH, Nejati M, Zimmerman RW (2016) A direct fragmentation method with Weibull function distribution of sizes based on finite-and discrete element simulations. International Journal of Solids and Structures 80: 38–51. DOI: 10.1016/j.ijsolstr.2015.10.019

    Article  Google Scholar 

  • Refahi A, Rezai B, Mohandesi JA (2007) Use of rock mechanical properties to predict the Bond crushing index. Minerals Engineering 20: 662–669. DOI: 10.1016/j.mineng.2006.12.015

    Article  Google Scholar 

  • Rittinger PR (1867) Lehrbuch der Aufbereitungskunde. Berlin: Ernst und Korn. pp 17–19.

    Google Scholar 

  • Song SZ, Kong J, Wang CH, et al. (2006) Analysis of rockfall and its impact on the cut-and-cover tunnel in dynamics. Wuhan University Journal of Natural Sciences 11: 905–909. DOI: 10.1007/BF02830186

    Article  Google Scholar 

  • Vocialta M, Molinari JF (2015) Influence of internal impacts between fragments in dynamic brittle tensile fragmentation. International Journal of Solids and Structures 58: 247–256. DOI: 10.1016/j.ijsolstr.2015.01.008

    Article  Google Scholar 

  • Wang Y, Tonon F (2009) Modeling Lac du Bonnet granite using a discrete element model. International Journal of Rock Mechanics and Mining Sciences 46: 1124–1135. DOI: 10.1016/j.ijrmms.2009.05.008

    Article  Google Scholar 

  • Wang Y, Tonon F (2010) Calibration of a discrete element model for intact rock up to its peak strength. International Journal for Numerical & Analytical Methods in Geomechanics 34: 447–469. DOI: 10.1002/nag.811

    Article  Google Scholar 

  • Wang Y, Tonon F (2011) Discrete element modeling of rock fragmentation upon impact in rock fall analysis. Rock Mechanics and Rock Engineering 44: 23–35. DOI: 10.1007/s00603-010-0110-9

    Article  Google Scholar 

  • Wu F, Wu J, Qi S (2010) Phenomena and theoretical analysis for the failure of brittle rocks. Journal of Rock Mechanics and Geotechnical Engineering 2: 331–337. DOI: 10.3724/SP.J.1235. 2010.00331

    Google Scholar 

  • Wyllie DC (2014) Calibration of rock fall modeling parameters. International Journal of Rock Mechanics and Mining Sciences 67: 170–180. DOI: 10.1016/j.ijrmms.2013.10.002

    Article  Google Scholar 

  • Xie YJ, Wang XH, Hu XZ, Zhu XZ (2015) Fracture-based model of periodic-arrayed indentation for rock cutting. International Journal of Rock Mechanics and Mining Sciences 76: 217–221. DOI: 10.1016/j.ijrmms.2015.03.018

    Article  Google Scholar 

  • Zhang YQ, Lu Y, Hao H (2004) Analysis of fragment size and ejection velocity at high strain rate. International Journal of Mechanical Sciences 46: 27–34. DOI: 10.1016/j.ijmecsci.2004. 03.002

    Article  Google Scholar 

  • Zhang ZX, Kou SQ, Yu J, et al. (1999) Effects of loading rate on rock fracture. International Journal of Rock Mechanics and Mining Sciences 36: 597–611. DOI: 10.1016/S0148-9062(99) 00031-5

    Article  Google Scholar 

Download references

Acknowledgments

This work is supported by the National Natural Science Foundation of China (41472272, 41225011), the Youth Science and Technology Fund of Sichuan Province (2016JQ0011) and the Opening Fund of the State Key Laboratory of Geohazard Prevention and Geoenvironment Protection (Chengdu University of Technology) (SKLGP2013K015).

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Authors and Affiliations

  1. State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu, 610065, China

    Tian-xing Hou & Jia-wen Zhou

  2. State Key Laboratory of Geohazard Prevention and Geoenvironment Protection, Chengdu University of Technology, Chengdu, 610059, China

    Qiang Xu

  3. College of Water Resource and Hydropower, Sichuan University, Chengdu, 610065, China

    Hong-qiang Xie & Nu-wen Xu

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  1. Tian-xing Hou
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  2. Qiang Xu
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  3. Hong-qiang Xie
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Correspondence to Jia-wen Zhou.

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http://orcid.org/0000-0001-5963-791X

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Hou, Tx., Xu, Q., Xie, Hq. et al. An estimation model for the fragmentation properties of brittle rock block due to the impacts against an obstruction. J. Mt. Sci. 14, 1161–1173 (2017). https://doi.org/10.1007/s11629-017-4398-8

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  • DOI: https://doi.org/10.1007/s11629-017-4398-8

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