Skip to main content
SpringerLink
Log in

Development of a Unified Rock Bolt Model in Discontinuous Deformation Analysis

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

Abstract

In this paper, a unified rock bolt model is proposed and incorporated into the two-dimensional discontinuous deformation analysis. In the model, the bolt shank is discretized into a finite number of (modified) Euler–Bernoulli beam elements with the degrees of freedom represented at the end nodes, while the face plate is treated as solid blocks. The rock mass and the bolt shank deform independently, but interact with each other through a few anchored points. The interactions between the rock mass and the face plate are handled via general contact algorithm. Different types of rock bolts (e.g., Expansion Shell, fully grouted rebar, Split Set, cone bolt, Roofex, Garford and D-bolt) can be realized by specifying the corresponding constitutive model for the tangential behavior of the anchored points. Four failure modes, namely tensile failure and shear failure of the bolt shank, debonding along the bolt/rock interface and loss of the face plate, are available in the analysis procedure. The performance of a typical conventional rock bolt (fully grouted rebar) and a typical energy-absorbing rock bolt (D-bolt) under the scenarios of suspending loosened blocks and rock dilation is investigated using the proposed model. The reliability of the proposed model is verified by comparing the simulation results with theoretical predictions and experimental observations. The proposed model could be used to reveal the mechanism of each type of rock bolt in realistic scenarios and to provide a numerical way for presenting the detailed profile about the behavior of bolts, in particular at intermediate loading stages.

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
Fig. 16

Similar content being viewed by others

References

  • An XM, Ma GW, Cai YC, Zhu HH (2011) A new way to treat material discontinuities in the numerical manifold method. Comput Meth Appl Mech Eng 200(47–48):3296–3308. doi:10.1016/j.cma.2011.08.004

    Article  Google Scholar 

  • Bao HR, Zhao ZY (2012) The vertex-to-vertex contact analysis in the two-dimensional discontinuous deformation analysis. Adv Eng Softw 45(1):1–10. doi:10.1016/j.advengsoft.2011.09.010

    Article  Google Scholar 

  • Bao HR, Zhao ZY (2013) Modeling brittle fracture with the nodal-based discontinuous deformation analysis. Int J Comput Methods. doi:10.1142/S0219876213500400

    Google Scholar 

  • Bao HR, Hatzor Yossef H, Huang X (2012) A new viscous boundary condition in the two-dimensional discontinuous deformation analysis method for wave propagation problems. Rock Mech Rock Eng 45(5):919–928. doi:10.1007/s00603-012-0245-y

    Google Scholar 

  • Cai Y, Esaki T, Jiang YJ (2004) An analytical model to predict axial load in grouted rock bolt for soft rock tunnelling. Tunn Undergr Space Technol 19(6):607–618. doi:10.1016/j.tust.2004.02.129

    Article  Google Scholar 

  • Chang CT (1995) Nonlinear dynamic discontinuous deformation analysis with finite element meshed block system. Ph.D. Thesis. University of California, Berkeley

  • Charette F, Plouffe M (2007) Roofex: results of laboratory testing of a new concept of yieldable tendon. In: Potvin Y (eds) Deep mining 07, proceeding of the 4th international seminar on deep and high stress mining. Australian Centre for Geomechanics, Perth, pp 395–404

  • Chen Y (2014) Experimental study and stress analysis of rock bolt anchorage performance. J Rock Mech Geotech Eng 6(5):428–437. doi:10.1016/j.jrmge.2014.06.002

    Article  Google Scholar 

  • Chen Y, Li CC (2015a) Performance of fully encapsulated rebar bolts and D-Bolts under combined pull-and-shear loading. Tunn Undergr Space Technol 45:99–106. doi:10.1016/j.tust.2014.09.008

    Article  Google Scholar 

  • Chen Y, Li CC (2015b) Influences of loading condition and rock strength to the performance of rock bolts. Geotech Test J 38(2):208–218. doi:10.1520/GTJ20140033

    Article  Google Scholar 

  • Cho N, Martin CD, Sego DC, Christiansson R (2004) Modelling dilation in brittle rocks. In: Proceeding of the 6th North America rock mechanics symposium (NARMS), Houston, Texas, USA

  • Gu J, Zhao ZY (2009) Considerations of the discontinuous deformation analysis on wave propagation problems. Int J Numer Anal Meth Geomech 33(12):1449–1465. doi:10.1002/nag.772

    Article  Google Scholar 

  • Hatzor YH, Wainshtein I, Mazor DB (2010) Stability of shallow karstic caverns in blocky rock masses. Int J Rock Mech Min Sci 47(8):1289–1303. doi:10.1016/j.ijrmms.2010.09.014

    Article  Google Scholar 

  • He L, Ma GW (2010) Development of 3D numerical manifold method. Int J Comput Methods 7(1):107–129. doi:10.1142/S0219876210002088

    Article  Google Scholar 

  • He L, An XM, Zhao ZY (2015) Fully grouted rock bolts: an analytical investigation. Rock Mech Rock Eng 48(3):1181–1196. doi:10.1007/s00603-014-0610-0

    Article  Google Scholar 

  • Hsiung SM (2001) Discontinuous deformation analysis (DDA) with nth order polynomial displacement functions. In: Proceedings of the 38th US rock mechanics symposium, Washington DC, pp 1437–1444

  • Huang ZP, Broch E, Lu M (2002) Cavern roof stability-mechanism of arching and stabilization by rockbolting. Tunn Undergr Space Technol 17(3):249–261. doi:10.1016/S0886-7798(02)00010-X

    Article  Google Scholar 

  • Industrial Fasteners Institute (2003) Inch fastener standards—7th edition

  • Itasca (2004) UDEC-universal distinct element code, version 4.0. Itasca Consulting Group, Minneapolis

  • Itasca (2007) 3DEC-3-dimensional Distinct Element Code, Version 4.1. Itasca Consulting Group, Minneapolis

  • Ivanović A, Neilson RD (2009) Modelling of debonding along the fixed anchor length. Int J Rock Mech Min Sci 46(4):699–707. doi:10.1016/j.ijrmms.2008.09.008

    Article  Google Scholar 

  • Jager AJ (1992) Two new support units for the control of rockburst damage. In: Proceedings of the international symposium on rock support, Sudbury, Ontario, Canada, 16–19 June, pp 621–631

  • Jalalifar H (2006) A new approach in determining the load transfer mechanism in fully grouted bolts. Ph.D. Thesis. University of Wollongong

  • Jalalifar and Naj (2010) Experimental and 3D numerical simulation of reinforced shear joints. Rock Mech Rock Eng 43(1):95–103. doi:10.1007/s00603-009-0031-7

    Article  Google Scholar 

  • Jiao YY, Zhang XL, Zhao J, Liu QS (2007) Viscous boundary of DDA for modeling stress wave propagation in jointed rock. Int J Rock Mech Min Sci 44(7):1070–1076. doi:10.1016/j.ijrmms.2007.03.001

    Article  Google Scholar 

  • Jing LR, Ma Y, Fang ZL (2001) Modeling of fluid flow and solid deformation of fractured rocks with discontinuous deformation analysis (DDA) method. Int J Rock Mech Min Sci 38(3):343–355. doi:10.1016/S1365-1609(01)00005-3

    Article  Google Scholar 

  • Kim YI, Amadei B, Pan E (1999) Modeling the effect of water, excavation sequence and rock reinforcement with discontinuous deformation analysis. Int J Rock Mech Min Sci 36(7):949–970. doi:10.1016/S0148-9062(99)00046-7

    Article  Google Scholar 

  • Koo CY, Chern JC (1996) The development of DDA with third order displacement function. In: Proceedings of the first international forum on discontinuous deformation analysis (DDA) and simulations of discontinuous media, TSI Press, San Antonio, Texas, pp 342–349

  • Koyama T, Nishiyama S, Yang M, Ohnishi Y (2011) Modeling the interaction between fluid flow and particle movement with discontinuous deformation analysis (DDA) method. Int J Numer Anal Methods Geomech 35(1):1–20. doi:10.1002/nag.890

    Article  Google Scholar 

  • Li CC (2010) A new energy-absorbing bolt for rock support in high stress rock masses. Int J Rock Mech Min Sci 47(3):396–404. doi:10.1016/j.ijrmms.2010.01.005

    Article  Google Scholar 

  • Li CC (2011) Chapter 18. Rock support for underground excavations subjected to dynamic loads and failure. In: Zhou Y, Zhao J (eds) Advances in rock dynamics and applications. CRC Press, Boca Rotan, pp 483–506

    Chapter  Google Scholar 

  • Li CC, Doucet C (2012) Performance of D-bolts under dynamic loading. Rock Mech Rock Eng 45(2):193–204. doi:10.1007/s00603-011-0202-1

    Article  Google Scholar 

  • Li C, Håkansson U (1999) Performance of the Swellex bolt in hard and soft rocks. In: Proceedings of the international conference on rock support and reinforcement practice in mining, Balkema, pp 103–108

  • Li C, Stillborg B (1999) Analytical models for rock bolts. Int J Rock Mech Min Sci 36(8):1013–1029. doi:10.1016/S1365-1609(99)00064-7

    Article  Google Scholar 

  • Lin CT, Amadei B, Jung J, Dwyer J (1996) Extensions of discontinuous deformation analysis for jointed rock masses. Int J Rock Mech Min Sci 33(7):671–694. doi:10.1016/0148-9062(96)00016-2

    Article  Google Scholar 

  • Ma GW, An XM, Zhang HH, Li LX (2009) Modeling complex crack problems using the numerical manifold method. Int J Fract 156(1):21–35. doi:10.1007/s10704-009-9342-7

    Article  Google Scholar 

  • Maclaughlin M, Sitar N, Doolin D, Abbot T (2001) Investigation of slope-stability kinematics using discontinuous deformation analysis. Int J Rock Mech Min Sci 38(5):753–762. doi:10.1016/S1365-1609(01)00038-7

    Article  Google Scholar 

  • Moosavi M, Grayeli R (2006) A model for cable bolt-rock mass interaction: integration with discontinuous deformation analysis (DDA) algorithm. Int J Rock Mech Min Sci 43(4):661–670. doi:10.1016/j.ijrmms.2005.11.002

    Article  Google Scholar 

  • Nie W, Zhao ZY, Ning YJ, Sun P (2014) Development of rock bolt elements in two-dimensional discontinuous deformation analysis. Rock Mech Rock Eng 47(6):2157–2170. doi:10.1007/s00603-013-0525-1

    Article  Google Scholar 

  • Shi GH (1988) Discontinuous deformation analysis—a new numerical model for the static and dynamics of block systems. Ph.D. Thesis. University of California, Berkeley

  • Shi GH (1992). Manifold method of material analysis. In: Transactions of the conference on applied mathematics and computing, Minneapolis: Minnesota. pp 57–76

  • Shyu K (1993) Nodal-based discontinuous deformation analysis. Ph.D. Thesis. University of California, Berkeley

  • Spang K, Egger P (1990) Action of fully-grouted bolts in jointed rock and factors of influence. Rock Mech Rock Eng 23(3):201–229. doi:10.1007/BF01022954

    Article  Google Scholar 

  • Varden R, Lachenicht R, Player J, Thompson A, Villaescusa E (2008) Development and implementation of the Garford Dynamic Bolt at the Kanowna Belle Mine. In: 10th Underground operators’ conference, Launceston, Australia, p 19

  • Wang MC (2003) Finite element method. Tsinghua University Press, Beijing (In Chinese)

    Google Scholar 

  • Windsor CR (1997) Rock reinforcement systems. Int J Rock Mech Min Sci 34(6):919–951. doi:10.1016/S1365-1609(97)80004-4

    Article  Google Scholar 

  • Wu JH (2010) Seismic landslide simulations in discontinuous deformation analysis. Comput Geotech 37(5):594–601. doi:10.1016/j.compgeo.2010.03.007

    Article  Google Scholar 

  • Wu JH, Ohnishi Y, Nishiyama S (2004) Simulation of the mechanical behavior of inclined jointed rock masses during tunnel construction using discontinuous deformation analysis (DDA). Int J Rock Mech Min Sci 41(5):731–743. doi:10.1016/j.ijrmms.2004.01.010

    Article  Google Scholar 

  • Wu JH, Ohnishi Y, Nishiyama S (2005) A development of the discontinuous deformation analysis for rock fall analysis. Int J Numer Anal Methods Geomech 29(10):971–988. doi:10.1002/nag.429

    Article  Google Scholar 

  • Yazici S, Kaiser P (1992) Bond strength of grouted cable bolts. Int J Rock Mech Min Sci 29(3):279–292. doi:10.1016/0148-9062(92)93661-3

    Article  Google Scholar 

  • Yeung MR, Jiang QH, Sun N (2003) Validation of block theory and three-dimensional discontinuous deformation analysis as wedge stability analysis methods. Int J Rock Mech Min Sci 40(2):265–275. doi:10.1016/S1365-1609(02)00137-5

    Article  Google Scholar 

  • Zhao ZY, Zhang Y, Bao HR (2011) Tunnel blasting simulations by the discontinuous deformation analysis. Int J Comput Methods 8(2):277–292. doi:10.1142/S0219876211002599

    Article  Google Scholar 

Download references

Acknowledgements

This study is supported partially by supported by “the Fundamental Research Funds for the Central Universities, China,” and the National Natural Science Foundation of China (Grant Nos. 11402070, 41372266). These supports are gratefully acknowledged.

Author information

Authors and Affiliations

  1. School of Civil Engineering, Southeast University, Nanjing, 210096, China

    L. He & J. Zhao

  2. School of Civil and Environmental Engineering, Nanyang Technological University, Singapore, 639798, Singapore

    X. M. An & Z. Y. Zhao

  3. NJU-ECE Institute for Underground Space and Geo-environment School of Earth Sciences and Engineering, Nanjing University, Nanjing, 210093, China

    X. B. Zhao

  4. Monash University – Southeast University Joint Research Institute, Suzhou, 215123, China

    J. Zhao

Authors
  1. L. He
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. X. M. An
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. X. B. Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Z. Y. Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. J. Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to L. He.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

He, L., An, X.M., Zhao, X.B. et al. Development of a Unified Rock Bolt Model in Discontinuous Deformation Analysis. Rock Mech Rock Eng 51, 827–847 (2018). https://doi.org/10.1007/s00603-017-1341-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00603-017-1341-9

Keywords

Search

Navigation