Rock Mechanics and Rock Engineering

, Volume 45, Issue 5, pp 837–849 | Cite as

A Study of Optimal Rock-Cutting Conditions for Hard Rock TBM Using the Discrete Element Method

Original Paper


The efficiency of TBM performance affected by the specific s/p (s: spacing and p: penetration) ratio of the disc cutter is a research issue in demand. This article presents a multi-indentation simulation using discrete element method (DEM) analysis to study the optimal rock-cutting phenomena in terms of the interaction of the s/p ratio with intact rock properties. The multi-indentation simulation attempts to represent a linear cutting machine (LCM) test, which is a full-scale test for evaluating the optimal rock-cutting condition and measuring required reaction forces based on the intact rock condition in general practice. A governing equation relating mechanical rock properties with geometric characteristics for the optimal rock-cutting condition is derived by the numerical simulation, and its performance is evaluated with the result of the laboratory LCM tests. The results of simulations and real LCM tests show that the effective rock-cutting condition corresponding to the minimum specific energy can be estimated by an optimized s/p ratio, which, in turn, is linearly proportional to the square of the material brittleness, B 2, and cutter tip width, t (i.e., s/p = cB 2 t, where c is coefficient). The limitation of the numerical simulation associated with the sample preparation is also discussed.


LCM DEM Multi-indentation s/p ratio TBM Brittleness 

List of symbols


Contact area of indenter


Total crack areas


Internal crack angle




Constant coefficient

\( \tilde{D} \)

Average diameter of assemblage


Arbitrary position angle


Young’s modulus


Young’s modulus for plane strain


Crack-related force


Peak load of indenter


Strain energy release rate for mode I


Fracture toughness for mode I


Normal stiffness


Shear stiffness


Friction coefficient


Poisson’s ratio


Penetration of disc cutter


Contact angle between disc and rock sample

\( \dot{\theta } \)

Angular velocity


Material hardness


Unit length


Number of debonded particles


Chipping radius


Spacing of disc cutter


Compressive strength


Tensile strength


Tip width of disc cutter


Normal bonding


Shear bonding


Shear strength


Total energy


Strain energy


Friction energy


Tangential velocity


x Component of tangential velocity


y Component of tangential velocity


  1. Cho N, Martin CD, Sego DC (2007) A clumped particle model for rock. Int J Rock Mech Min Sci 44:997–1010Google Scholar
  2. Cho JW, Jeon S, Yu SH, Chang SH (2010) Optimum spacing of TBM disc cutters: a numerical simulation using the three-dimensional dynamic fracturing method. Tunn Undergr Space Technol 25:230–244CrossRefGoogle Scholar
  3. Cook NGW, Hood M, Tsai F (1984) Observations of crack growth in hard rock loaded by an indenter. Int J Rock Mech Min Sci Geomech Abstr 21:97–107CrossRefGoogle Scholar
  4. Diederich MS (2000) Instability of hard rock masses: the role of tensile damage and relaxation. PhD thesis, University of WaterlooGoogle Scholar
  5. Gertsch R, Gertsch L, Rostami J (2007) Disc cutting tests in Colorado red granite: implications for TBM performance prediction. Int J Rock Mech Min Sci 44:238–246CrossRefGoogle Scholar
  6. Gong QM, Jiao YY, Zhao J (2006a) Numerical modeling of the effects of joint spacing on rock fragmentation by TBM cutters. Tunn Undergr Space Technol 21:46–55CrossRefGoogle Scholar
  7. Gong QM, Zhao J, Hefny AM (2006b) Numerical simulation of rock fragmentation process induced by two TBM cutters and cutter spacing optimization. Tunn Undergr Space Technol 21:263CrossRefGoogle Scholar
  8. Griffith AA (1921) The Phenomena of rupture and flow in solids. Philos Trans Roy Soc Lond Ser A Containing Papers Math Phys Character 221:163–198Google Scholar
  9. Huang H (1999) Discrete element modeling of tool-rock interaction. Ph.D thesis, University of MinnesotaGoogle Scholar
  10. Itasca Consulting Group Inc (1999) PFC2D Particle flow code computer manualsGoogle Scholar
  11. Lama RD, Vutukuri VS (1978) Handbook on mechanical properties of rocks (Testing techniques and results—volume II). Trans tech publicationsGoogle Scholar
  12. Lawn BR, Marshall DB (1979) Hardness, toughness and brittleness: an indentation analysis. J Ceram Soc 62(78):347–350CrossRefGoogle Scholar
  13. Lawn BR, Swain MV (1975) Microfracture beneath point indentations in brittle solids. J Mat Sci 10:113–122CrossRefGoogle Scholar
  14. Liu HY, Kou SQ, Lindqvist PA, Tang CA (2002) Numerical simulation of the rock fragmentation process induced by indenters. Int J Rock Mech Min Sci 39:491–505CrossRefGoogle Scholar
  15. Moon T, Nakagawa M, Berger J (2007) Measurement of fracture toughness using the distinct element method. Int J Rock Mech Min Sci 44:449–456CrossRefGoogle Scholar
  16. Potyondy DO, Cundall PA (2004) A bonded-particle model for rock. Int J Rock Mech Min Sci 41:1329–1364CrossRefGoogle Scholar
  17. Potyondy DO, Cundall PA, Lee CA (1996) Modelling rock using bonded assemblies of circular particles. In: 2nd North American Rock Mechanics symposium 1937–1944Google Scholar
  18. Rostami J, Ozdemir L (1993) A new model for performance prediction of hard rock TBMs. Proc RETC Boston, MA, pp 793–809Google Scholar
  19. Roxborough FF, Phillips HR (1975) Rock excavation by disc cutter. Int J Rock Mech Min Sci Geomech Abstr 12:361–366CrossRefGoogle Scholar
  20. Snowdon RA, Ryley MD, Temporal J (1982) A study of disc cutting in selected British rocks. Int J Rock Mech Min Sci Geomech Abstr 19:107–121Google Scholar
  21. Swain MV, Lawn BR (1976) Indentation fracture in brittle rocks and glasses. Int J Rock Mech Min Sci Geomech Abstr 13:311–319CrossRefGoogle Scholar
  22. Teale R (1965) The concept of specific energy in rock drilling. Int J Rock Mech Min Sci Geomech Abstr 2:57–73CrossRefGoogle Scholar
  23. Yarema S, Krestin GS (1966) Determination of the modulus of cohesion of brittle materials by compressive tests on disc specimens containing cracks. Soviet Materials Sci 2(1):7–10CrossRefGoogle Scholar
  24. Yoon J (2007) Application of experimental design and optimization to PFC model calibration in uniaxial compression simulation. Int J Rock Mech Min Sci 44:871–889CrossRefGoogle Scholar
  25. Zhang ZX (2002) An empirical relation between mode I fracture toughness and the tensile strength of rock. Int J Rock Mech Min Sci 39:401–406CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.PB Geotechnical and Tunneling, Parsons Brinckerhoff Inc.New YorkUSA

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