Skip to main content
SpringerLink
Log in

Simulating the effect of disc erosion in TBM disc cutters by a semi-infinite DDM

  • Original Paper
  • Published:
Arabian Journal of Geosciences Aims and scope Submit manuscript

Abstract

Underground excavation in rocks can be accomplished in several steps. The cutting action of mechanical tools such as disc cutters used in tunnel boring machines (TBM) is one of the most basic steps. Indentation of TBM disc cutters into the rock can produce rock chips in different scales. This phenomenon involves the production of micro cracks, their propagating, and coalescing process to form macro cracks. The present research focuses on the concepts of linear elastic fracture mechanics (LEFM) and maximum tangential stress criterion to investigate the micro crack propagation and its direction of growth in rocks underneath the TBM disc cutters. A modified higher order semi-infinite displacement discontinuity method (HSDDM) with third order displacement discontinuity elements (cubic elements) is used to estimate the stress intensity factor in the fractured rocks underneath a single disc cutter. To reduce the errors caused by stress and displacement singularities near the crack tip, three special crack tip elements have been implemented in the HSDDM2D computer code. TBM disc cutters will be eroded after a period of working. Therefore, the numerical simulation of eroded and not eroded discs has been proposed in this study. To simulate the eroded disc, four small elements have been modeled to generate the curvature of the cutter tip, which in turn reduces the cutting efficiency and increases required specific energy for a typical disc cutter.

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

Similar content being viewed by others

References

  • Acaroglu O, Ozdemir L, Asbury B (2008) A fuzzy logic model to predict specific energy requirement for TBM performance prediction. Tunn Undergr Space Technol 23:600–608. doi:10.1016/j.tust.2007.11.003

    Article  Google Scholar 

  • Backers T (2004) Fracture toughness determination and micromechanics of rock under Mode I and Mode II loading. Ph.D. Thesis University of Potsdam, Germany

    Google Scholar 

  • Balci C (2009) Correlation of rock cutting tests with field performance of a TBM in highly fractured rock formations: a case study in Kozyatagi-Kadikoy metro tunnel, Turkey. Tunn Undergr Space Technol 24:423–435. doi:10.1016/j.tust.2008.12.001

    Article  Google Scholar 

  • Behnia M, Goshtasbi K, Marji MF, Golshani A (2013) Numerical simulation of crack propagation in layered formations. Arab J Geosci. doi:10.1007/s12517-013-0885-6

    Google Scholar 

  • Bilgin N, Feridunoglu C, Tumac D, Cinar M, Palakci Y, Gunduz O, Ozyol L (2005) The performance of a full face tunnel boring machine (TBM) in Tarabya (Istanbul). In: Proceedings, 31st ITA-AITES World Tunnel Congress, pp. 821–826

  • Bilgin N, Demircin MA, Copur H, Balci C, Tuncdemir H, Akcin N (2006) Dominant rock properties affecting the performance of conical picks and the comparison of some experimental and theoretical results. Int J Rock Mech Min Sci 43:139–156. doi:10.1016/j.ijrmms.2005.04.009

    Article  Google Scholar 

  • Bilgin N, Kopur H, Balci C (2012) Effects of replacing disc cutters with chisel tools on performance of a TBM in difficult ground conditions. Tunn Undergr Space Technol 27:41–51. doi:10.1016/j.tust.2011.06.006

    Article  Google Scholar 

  • Bowie OL (1973) Solutions of plane crack problems by mapping techniques. In: G.C. Sih, Editor, Mechanics of Fracture, Noordhoff International Publishing Leyden

  • Broek D (1989) The practical use of fracture mechanics, 4th edn. Kluwer Academic Publishers, Netherland

    Book  Google Scholar 

  • Chang SH, Choi SW, Bae GJ, Jeon S (2006) Performance prediction of TBM disc cutting on granitic rock by the linear cutting test. Tunn Undergr Space Technol 21:271–271. doi:10.1016/j.tust.2005.12.131

    Article  Google Scholar 

  • Chen JT, Hong HK (1996) Dual boundary integral equations for exterior problems. Eng Anal Bound Elem 16:333–340

    Article  Google Scholar 

  • Chen JT, Hong HK (1999) Review of dual boundary element methods with emphasis on hyper singular integrals and divergent series. Appl Mech Rev ASME 52:17–33

    Article  Google Scholar 

  • Chen JT, Wong FC (1997) Analytical derivations for one-dimensional eigen problems using dual BEM and MRM. Eng Anal Bound Elem 20:25–33

    Article  Google Scholar 

  • Chen JT, Lin TW, Chen IL, Lee YJ (2005a) Fictitious frequency for the exterior Helmholtz equation subject to the mixed-type boundary condition using BEM. Mech Res Commun 32:75–92. doi:10.1016/j.mechrescom.2004.03.009

    Article  Google Scholar 

  • Chen JT, Chen IL, Lee YJ (2005b) Eigen solutions of multiply-connected membranes using method of fundamental solution. Eng Anal Bound Elem 29:166–174. doi:10.1016/j.enganabound.2004.10.005

    Article  Google Scholar 

  • 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 25:230–244. doi:10.1016/j.tust.2009.11.007

    Article  Google Scholar 

  • Crouch SL, Starfield AM (1983) Boundary element methods in solid mechanics. Allen and Unwin, London

    Google Scholar 

  • De Bremaecker J-C, Ferris MC, Ralph D (2000) Compressional fractures considered as contact problems and mixed complementarity problems. Eng Fract Mech 66:287–303. doi:10.1016/S0013-7944(00)00022-9

    Article  Google Scholar 

  • Erdogan F, Sih GC (1963) On the crack extension in plates under loading and transverse shear. J Fluids Eng 85:519–527. doi:10.1115/1.3656897

    Google Scholar 

  • Fowell RJ, Chen JF (1990) The third chevron-notch rock fracture specimen—the cracked chevron-notched Brazilian disk. In: Proceedings, 31st US Symposium on Rock Mechanics, pp. 295–302

  • 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 44:238–246. doi:10.1016/j.ijrmms.2006.07.007

    Article  Google Scholar 

  • Gong QM, Zhao J (2009) Development of a rock mass characteristics model for TBM penetration rate prediction. Int J Rock Mech Min Sci 46:8–18

    Article  Google Scholar 

  • Gong QM, Jiao YY, Zhao J (2006) Numerical simulation of the effects of joint spacing on rock fragmentation by TBM cutters. Tunn Undergr Space Technol 21:46–55. doi:10.1016/j.ijrmms.2008.03.003

    Article  Google Scholar 

  • Haeri H, Shahriar K, Marji MF, Moarefvand P (2013a) Simulating the bluntness of TBM disc cutters in rocks using an indirect boundary element method, 13th International Conference on Fracture June 16–21, Beijing, China

  • Haeri H, Shahriar K, Fatehi Marji M, Moarefvand P (2013b) A coupled numerical-experimental study of the breakage process of brittle substances. Arab J Geosci. doi:10.1007/s12517-013-1165-1

    Google Scholar 

  • Haeri H, Shahriar K, Fatehi Marji M, Moarefvand P (2014a) On the HDD analysis of micro cracks initiation, propagation and coalescence in brittle substances. Arab J Geosci. doi:10.1007/s12517-014-1290-5

    Google Scholar 

  • Haeri H, Shahriar K, Fatehi Marji M, Moarefvand P (2014b) An experimental and numerical study of crack propagation and cracks coalescence in the pre-cracked rock-like disc specimens under compression. Int J Rock Mech Min Sci 67:20–28. doi:10.1016/j.ijmms.2014.01.008

    Google Scholar 

  • Haeri H, Shahriar K, Fatehi Marji M, Moarefvand P (2014c) On the strength and crack propagation process of the pre-cracked rock-like specimens under uniaxial compression. Strength Mater 46:140–152. doi:10.1007/s11223-014-9525-y

    Article  Google Scholar 

  • Hong HK, Chen JT (1988) Generality and special cases of dual integral equations of elasticity. J Chin Soc Mech Eng 9:1–9

    Google Scholar 

  • Hussian MA, Pu EL, Underwood JH (1974) Strain energy release rate for a crack under combined mode I and mode II. In: Fracture analysis, ASTM STP 560. American Society for Testing and Materials, pp. 2–28

  • Ingraffea AR (1983) In: Rossmanith HP (ed) Numerical modeling of fracture propagation, rock fracture mechanics. Springer Verlagwien, New York, pp 151–208

    Google Scholar 

  • 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 39:491–505. doi:10.1016/S1365-1609(02)00043-6

    Article  Google Scholar 

  • Marji MF (2013) On the use of power series solution method in the crack analysis of brittle materials by indirect boundary element method. Eng Fract Mech 98:365–382. doi:10.1016/j.engfracmech.2012.11.015

    Article  Google Scholar 

  • Marji MF (2014) Numerical analysis of quasi-static crack branching in brittle solids by a modified displacement discontinuity method. Int J Solids Struct 51:1716–1736. doi:10.1016/j.ijsolstr.2014.01.022

    Article  Google Scholar 

  • Marji MF, Hosseini-Nasab H, Kohsary AH (2006) On the uses of special crack tip elements in numerical fracture mechanics. Int J Solids Struct 43:1669–1692. doi:10.1016/j.ijsolstr.2005.04.042

    Article  Google Scholar 

  • Marji MF, Hosseini-nasab H, Hosseinmorsgedy A (2009) Numerical modeling of the mechanism of crack propagation in rocks under TBM disc cutters. J Mech Mater Struct 2:439–457

    Google Scholar 

  • Melin S (1986) When does a crack grow under mode II condition? Int J Fract 30:103–114. doi:10.1007/BF00034020

    Google Scholar 

  • Nilsen B, Ozdemir L (1993) Hard rock tunnel boring prediction and field performance. In: Proceedings, rapid excavation and tunneling Conference (RETC), pp. 833–852

  • Park KI, Chang SH, Choi SW, Jeon S (2006) Prediction of the optimum cutting condition of TBM disc cutter in Korean granite by the linear cutting test. In: Proceedings, Korean Society for Rock Mechanics Conference, pp. 217–236. (in Korean)

  • Rostami J, Ozdemir L (1993) A new model for performance prediction of hard rock TBMs. In: Proceedings, rapid excavation and tunneling Conference (RETC), pp. 793–809

  • Roxborough FF, Philips HR (1975) Rock excavation by disc cutter. Int J Rock Mech Min Sci Geomech Abstr 12:361–366

    Article  Google Scholar 

  • Sanford RJ (2003) Principles of fracture mechanics, pearson education, hIC., Upper Saddle River, New Jersey. pp.1-15

  • Scavia C (1990) Fracture mechanics approach to stability analysis of crack slopes. Eng Fract Mech 35:889–910

    Article  Google Scholar 

  • Shao JF, Rudnicki JW (2000) A micro crack-based continuous damage model for brittle geomaterials. Mech Mater 32:607–619. doi:10.1016/S0167-6636(00)00024-7

    Article  Google Scholar 

  • Shen B, Stephansson O (1994) Modification of the G-criterion for crack propagation subjected to compression. Eng Fract Mech 47:177–189. doi:10.1016/0013-7944(94)90219-4

    Article  Google Scholar 

  • Shou KJ, Crouch SL (1995) A higher order displacement discontinuity method for analysis of crack problems. Int J Rock Mech Min Sci Geomech Abstr 32:49–55. doi:10.1016/0148-9062(94)00016-V

    Article  Google Scholar 

  • Sih GC (1974) Strain-energy–density factor applied to mixed mode crack problems. Int J Fract 10:305–321. doi:10.1007/BF00035493

    Article  Google Scholar 

  • Uga Y, Sakoi K, Sugiyama S, Kondo Y, Nishimura K, Ono H (1986) Development of new tunnel boring machine with slurry transport system–penetration efficiency of disc cutters. Kawasaki Heavy Industry Report 91, 1–8 (in Japanese). 21 (3–4), 271

  • Whittaker BN, Singh RN, Sun G (1992) Rock fracture mechanics, principles, design and applications. Elsevier, Netherlands

    Google Scholar 

  • Zhao J, Gong QM, Eisenstein Z (2007) Tunneling through a frequently changing and mixed ground: a case history in Singapore. Tunn Undergr Space Technol 22:388–400. doi:10.1016/j.tust.2006.10.002

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mining Engineering, Bafgh Branch, Islamic Azad University, Bafgh, Iran

    Hadi Haeri

  2. Mine exploitation Engineering Department, Faculty of Mining and Metallurgy, Institution of Engineering, Yazd University, Yazd, Iran

    Mohammad Fatehi Marji

  3. Department of Mining and Metallurgical Engineering, Amirkabir University of Technology, Tehran, Iran

    Kourosh Shahriar

Authors
  1. Hadi Haeri
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mohammad Fatehi Marji
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Kourosh Shahriar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hadi Haeri.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Haeri, H., Marji, M.F. & Shahriar, K. Simulating the effect of disc erosion in TBM disc cutters by a semi-infinite DDM. Arab J Geosci 8, 3915–3927 (2015). https://doi.org/10.1007/s12517-014-1489-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12517-014-1489-5

Keywords

Search

Navigation