Skip to main content
SpringerLink
Log in

A Numerical Based Approach to Calculate Ore Dilution Rates Using Rolling Resistance Model and Upside-Down Drop Shape Theory

  • Original Paper
  • Published:
Rock Mechanics and Rock Engineering Aims and scope Submit manuscript

Abstract

The chief characteristic of the caving mining method is that caved ores, surrounded by overlying rocks, are drawn from the drawpoint. And the ultimate objective of investigating the draw problems is to forecast the ore loss and dilution. In this paper, the rolling resistance model in the Particle Flow Code was used to simulate the effect of actual shape of different materials flowing towards a drawpoint under the near-field condition and improve the computational efficiency at the same time. The reliability of the rolling resistance model was validated against experimental results, and the new empirical equations were deduced for calculation of the ore dilution rates based on the upside-down drop shape theory (UDDS theory). Within the precision and range of values considered in this paper, the results show that when the height of IEZ is in the range of 30–80 m, the particle size, the drawpoint size and the column height have no significant influence on the (isolated extraction zone) IEZ’s shape and maximal width. And regardless of near-field gravity flow with one or two granular materials, the shape of IEZ was coincident with the upside-down drop shape.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

References

  • Ai J, Chen JF, Rotter JM et al (2011) Assessment of rolling resistance models in discrete element simulations. Powder Technol 206(3):269–282

    Google Scholar 

  • Alford CG (1978) Computer simulation models of the gravity flow of ore in sublevel caving. Master Thesis, University of Melbourne, Melbourne

  • Brown ET (2003) Block caving geomechanics. Brisbane: Julius Kruttschnitt Mineral Research Centre. University of Queensland, St Lucia

    Google Scholar 

  • Castro RL (2006) Study of the mechanisms of gravity flow for block caving. Ph.D Thesis, University of Queensland, Brisbane

  • Chang CS, Liao CL (1990) Constitutive relation for a particulate medium with effect of particle rotation. Int J Solids Struct 26(4):437–453

    Google Scholar 

  • Durda DD, Movshovitz N, Richardson DC et al (2011) Experimental determination of the coefficient of restitution for meter-scale granite spheres. Icarus 211(1):849–855

    Google Scholar 

  • Elmo D, Rogers S, Dorador L (2014) An FEM-DEM numerical approach to simulate secondary fragmentation. In: Proceedings of the 14th Int. Conference of IACMAG. Kyoto, pp 1623–1629

  • Fröström J (1970) Examination of equivalent model materials for development and design of sublevel caving. Master of Science thesis, Royal Institute of Technology, Stockholm (in Swedish)

  • Grima AP, Wypych PW (2011) Discrete element simulations of granular pile formation: method for calibrating discrete element models. Eng Comput 28(3):314–339

    Google Scholar 

  • Hancock WR (2013) Gravity flow of rock in caving mines: numerical modeling of isolated, interactive and non-ideal draw. Ph.D Thesis, University of Queensland, Brisbane

  • Huang J, Da Silva MV, Krabbenhoft K (2013) Three-dimensional granular contact dynamics with rolling resistance. Comput Geotech 49:289–298

    Google Scholar 

  • Itasca Consulting Group (2016) PFC2D (particle flow code in 2 dimensions) user’s guide in PFC2D version 5.0. Itasca Consulting Group Inc, Minnersota

    Google Scholar 

  • Jiang MJ, Yu HS, Harris D (2005) A novel discrete model for granular material incorporating rolling. Comput Geotech 32(5):340–357

    Google Scholar 

  • Jiang MJ, Shen ZF, Wang JF (2015) A novel three-dimensional contact model for granulates incorporating rolling and twisting resistances. Comput Geotech 65:147–163

    Google Scholar 

  • Jin AB, Sun H, Ma GW et al (2016) A study on the draw laws of caved ore and rock using the discrete element method. Comput Geotech 80:59–70

    Google Scholar 

  • Jin AB, Sun H, Wu SC et al (2017) Confirmation of the upside-down drop shape theory in gravity flow and development of a new empirical equation to calculate the shape. Int J Rock Mech Min Sci 92:91–98

    Google Scholar 

  • Kawaguchi T, Tanaka T, Tsuji Y et al (1992) Numerical simulation of fluidized bed using the discrete element method (the case of spouting bed). JSME(B) 58(551):2119–2125

    Google Scholar 

  • Kuchta ME (2002) A revised form of the Bergmark-Ross equation for describing the gravity flow of broken rock. Min Resour Eng 11(4):349–360

    Google Scholar 

  • Kvapil R (1965a) Gravity flow of granular material in hoppers and bins part 1. Int J Rock Mech Min Sci 2:35–41

    Google Scholar 

  • Kvapil R (1965b) Gravity flow of granular material in hoppers and bins part 2. Int J Rock Mech Min Sci 2:277–304

    Google Scholar 

  • Kvapil R, Baeza L, Rosenthal J et al (1989) Block caving at El Teniente mine, Chile. Trans Inst Min Metall A 98:43–56

    Google Scholar 

  • Laubscher D (1994) Cave mining—the state of the art. J S Afr Inst Min Metall 94:279–293

    Google Scholar 

  • Li Q, Feng MX, Zou ZS (2013) Validation and calibration approach for discrete element simulation of burden charging in pre-reduction shaft furnace of COREX process. ISIJ Int 53(8):1365–1371

    Google Scholar 

  • Marano G (1980) The interaction between adjacent draw points in free flowing materials and its application to mining. Chamber Mines J 22:25–32

    Google Scholar 

  • Melo F, Vivanco F, Fuentes C (2009) Calculated isolated extracted and movement zones compared to scaled models for block caving. Int J Rock Mech Min Sci 46(4):731–737

    Google Scholar 

  • Mergili M, Jan-Thomas F, Krenn J et al (2017) Ravaflow v1, an advanced open-source computational framework for the propagation and interaction of two-phase mass flows. Geosci Model Dev 10(2):553–569

    Google Scholar 

  • Mergili M, Emmer A, Juřicová A et al (2018) How well can we simulate complex hydro-geomorphic process chains? The 2012 multi-lake outburst flood in the Santa Cruz Valley (Cordillera Blanca, Perú). Earth Surf Proc Land 43(7):1373–1389

    Google Scholar 

  • Mullins WW (1972) Stochastic theory of particle ow under gravity. J Appl Phys 43(2):665–678

    Google Scholar 

  • Munjiza A (2004) The combined finite-discrete element method. Wiley, London

    Google Scholar 

  • Nedderman RM, Tüzün U (1979) A kinematic model for the ow of granular materials. Powder Technol 22(2):243–253

    Google Scholar 

  • Pierce ME (2009) A model for gravity flow of fragmented rock in block caving mines. Ph.D. Thesis, University of Queensland, Brisbane

  • Pierce ME, Cundall PA (2002) PFC3D modeling of caved rock under draw. In: Proceedings of the 1st international PFC symposium on block and sublevel caving. Gelsenkirchen, pp 211–217

  • Pineda M (2012) Study of the gravity flow mechanisms at Goldex Mine by means of a physical model. Ph.D Thesis, University of Queensland, Brisbane

  • Power G (2004) Modeling granular flow in caving mines: large scale physical models and full scale experiments. Ph.D Thesis, University of Queensland, Brisbane

  • Pudasaini SP (2012) A general two-phase debris flow model. J Geophys Res Earth Surf 117(F3):1–28

    Google Scholar 

  • Pudasaini SP, Krautblatter M (2014) A two-phase mechanical model for rock-ice avalanches. J Geophys Res Earth Surf 119(10):2272–2290

    Google Scholar 

  • Pudasaini SP, Mergili M (2019) A multi-phase mass flow model. Earth Surf J Geophys Res. https://doi.org/10.1029/2019JF005204

    Article  Google Scholar 

  • Rustan A (2000) Gravity flow of broken rock—what is known and unknown. In: Proceedings of mass min. Brisbane, pp 557–567

  • Sakaguchi H, Ozaki E, Igarashi T (1993) Plugging of the flow of granular materials during the discharge from a soil. Int J Mod Phys B 7(9n10):1949–1963

    Google Scholar 

  • Sánchez K, Palma S, Castro RL (2019a) Numerical modelling of water flow through granular material for isolated and simultaneous extractions in block caving. Rock Mech Rock Eng 52(1):133–147

    Google Scholar 

  • Sánchez V, Castro RL, Palma S (2019b) Gravity flow characterization of fine granular material for block caving. Int J Rock Mech Min Sci 114:24–32

    Google Scholar 

  • Sun H, Gao YT, Elmo D et al (2019) A study of gravity flow based on the upside-down drop shape theory and considering rock shape and breakage. Rock Mech Rock Eng 52(3):881–893

    Google Scholar 

  • Teufelsbauer H, Wang Y, Pudasaini SP et al (2011) DEM simulation of impact force exerted by granular flow on rigid structures. Acta Geotech 6(3):119–133

    Google Scholar 

  • Thomas R, Richter C, André K et al (2019) Development of a standard calibration procedure for the DEM parameters of cohesionless bulk materials-part I: solving the problem of ambiguous parameter combinations. Powder Technol 343:803–812

    Google Scholar 

  • Tian JQ, Liu EL (2018) Effect of particle shape on micro-and mesostructure evolution of granular assemblies under biaxial loading conditions. CR Mecanique 346:1233–1252

    Google Scholar 

  • Verdugo R, Ubilla J (2004) Geotechnical analysis of gravity flow during block caving. In: Proceedings of MassMin 2004. Santiago, pp 195–200

  • Wang CH (1982) Draw theory. Metallurgical Industry Press, Beijing (in Chinese)

    Google Scholar 

  • Wang RX (1986) Mathematical statistics. Xi’an Jiaotong University Press, Xi’an (in Chinese)

    Google Scholar 

  • Wensrich CM, Katterfeld A (2012) Rolling friction as a technique for modeling particle shape in DEM. Powder Technol 217:409–417

    Google Scholar 

  • Wong C, Daniel MC, Rongong JA et al (2009) Energy dissipation prediction of particle dampers. J Sound Vib 319(1):91–118

    Google Scholar 

  • Wu AX, Wu LC, Liu XH et al (2012) Study on structural parameters of sublevel caving. J Cent South Univ (Sci Technol) 43(5):1845–1850 (in Chinese)

    Google Scholar 

  • Xu S, Suorineni FT, An L et al (2017) A study of gravity flow principles of sublevel caving method in dipping narrow veins. Granul Matter 19(4):82

    Google Scholar 

  • Yashar P (2013) Mathematical programming for sequence optimization in block cave mining. Ph.D Thesis, University of Alberta, Edmonton

  • Zhao SW, Nan Z, Zhou XW et al (2017) Particle shape effects on fabric of granular random packing. Powder Technol 310:175–186

    Google Scholar 

  • Zhao SW, Evans TM, Zhou XW (2018) Shear-induced anisotropy of granular materials with rolling resistance and particle shape effects. Int J Solids Struct 150(1):268–281

    Google Scholar 

  • Zhou YC, Wright BD, Yang RY et al (1999) Rolling friction in the dynamic simulation of sandpile formation. Phys A 269(2–4):536–553

    Google Scholar 

Download references

Acknowledgements

The research presented in this paper was supported by the Fundamental Research Funds for the Central Universities (Grant No. FRF-TP-19-026A1) and the National Natural Science Foundation of China (Grant No. 51674015). The authors would like to acknowledge all the reviewers and editors as they contributed greatly to the improvements of the manuscript. The first author would show his appreciation to the China Scholarship Council (CSC) for funding 1-year study at University of British Columbia (UBC) as a joint Ph.D. student.

Author information

Authors and Affiliations

  1. Key Laboratory of Ministry for Efficient Mining and Safety of Metal Mines, University of Science and Technology Beijing, Beijing, China

    Hao Sun, Aibing Jin, Yongtao Gao & Shunchuan Wu

  2. School of Civil and Resource Engineering, University of Science and Technology Beijing, Beijing, China

    Hao Sun, Aibing Jin, Yongtao Gao & Shunchuan Wu

  3. Norman B. Keevil Institute of Mining Engineering, University of British Columbia, Vancouver, Canada

    Davide Elmo

  4. Faculty of Land Resource Engineering, Kunming University of Science and Technology, Kunming, China

    Shunchuan Wu

Authors
  1. Hao Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Aibing Jin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Davide Elmo
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yongtao Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Shunchuan Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Aibing Jin or Shunchuan Wu.

Ethics declarations

Conflict of interest

We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sun, H., Jin, A., Elmo, D. et al. A Numerical Based Approach to Calculate Ore Dilution Rates Using Rolling Resistance Model and Upside-Down Drop Shape Theory. Rock Mech Rock Eng 53, 4639–4652 (2020). https://doi.org/10.1007/s00603-020-02180-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00603-020-02180-6

Keywords

Search

Navigation