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Analytical Modelling of Load–Displacement Performance of Cable Bolts Incorporating Cracking Propagation

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Abstract

The application of cable bolts tends to increase in both underground mining operations and civil tunnel excavations have given its outstanding performance to support the excavation surface and hence minimise the hazards and risk of failure in the field. Understanding the mechanical behaviour of cable bolts under axial loading subjected to different field environment from analytical perspective is essential and economic for selecting the most appropriate cable bolt for a specific scenario and also the ground support system design. This study develops a novel analytical model coupling the crack propagation in the grout annulus to capture the load–displacement performance of cable bolts under axial loading. The majority of the input parameters associated with mechanic properties of the cable bolt and grout are readily determinable by laboratory tests. Additionally, the model simulates the ongoing varying conditions of the confinement to the grouted cable bolt during the pull-out test based on the proposed crack propagation equation, leading to a more realistic reflection of the field conditions. Finally, the capability of the proposed model to simulate the performance of cable bolts under axial loading is demonstrated by validating against experimental results in the literature.

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References

  • Aziz N, Heeman K, Nemcik J, Mayer S (2014) Shear strength properties of Hilti plain and indented strand cable bolts. In: Coal Operators’ Conference, Wollongong, pp 156–162

  • Benmokrane B, Chennouf A, Mitri HS (1995) Laboratory evaluation of cement-based grouts and grouted rock anchors. Int J Rock Mech Min Sci 32(7):633–642

    Article  Google Scholar 

  • Blanco Martín L, Tijani M, Hadj-Hassen F (2011) A new analytical solution to the mechanical behaviour of fully grouted rockbolts subjected to pull-out tests. Constr Build Mater 25(2):749–755

    Article  Google Scholar 

  • Blanco Martín L, Tijani M, Hadj-Hassen F, Noiret A (2013) Assessment of the bolt-grout interface behaviour of fully grouted rockbolts from laboratory experiments under axial loads. Int J Rock Mech Min Sci 63:50–61. https://doi.org/10.1016/j.ijrmms.2013.06.007

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Chen J, Saydam S, Hagan PC (2015) An analytical model of the load transfer behavior of fully grouted cable bolts. Constr Build Mater 101(1):1006–1015

    Article  Google Scholar 

  • Chen J, Hagan P, Saydam S (2016) Load transfer behavior of fully grouted cable bolts reinforced in weak rocks under tensile loading conditions. Geotech Test J 39(2):252–263

    Google Scholar 

  • Clifford B, Kent L, Altounyan P, Bigby D (2001) Systems used in coal mining development in long tendon reinforcement. In: Peng SS, Mark C, A.Khair. W (eds) 20th International conference on ground control in mining, Morgantown, West Virginia, U.S., 2001. Dept. of Mining Engineering, College of Engineering and Mineral Resources, West Virginia University

  • Farmer IW (1975) Stress distribution along a resin grouted rock anchor. Int J Rock Mech Min Sci Geomech Abstr 12(11):347–351. https://doi.org/10.1016/0148-9062(75)90168-0

    Article  Google Scholar 

  • Fuller PG, Cox RHT (1975) Mechanics of load transfer from steel tendons to cement based grout. In: Fifth Australian conference on the mechanics of structure and materials, Melbourne, Australia, pp 189–203

  • Hassani FP, Mitri HS, Khan UH, Rajaie H (1992) Experimental and numerical studies of the cable bolt support systems. In: MaCreath Ka (ed) Rock support in mining and underground construction, Rotterdam. Balkema, Rotterdam, pp 411–417

    Google Scholar 

  • Hutchinson DJ, Diederichs MS (1996) Cablebolting in underground mines. BiTech Publishers Ltd, Richmond

    Google Scholar 

  • Hyett AJ, Bawden WF, Reichert RD (1992) The effect of rock mass confinement on the bond strength of fully grouted cable bolts. Int J Rock Mech Min Sci 29(5):503–524

    Article  Google Scholar 

  • Hyett AJ, Bawden WF, Macsporran GR, Moosavi M (1995) A constituitive law for bond failure of fully grouted cable bolts using a modified hoek cell. Int J Numer Anal Meth Geomech 32(1):11–36

    Google Scholar 

  • Jeremic ML, Delaire GJP (1983) Failure mechanics of cable bolt systems. CIM Bull 76(856):66–71

    Google Scholar 

  • Kent L, Bigby D (2001) Performance tests for stranded ground reinforcement in mines. Rock Mechanics Technology Ltd, Colegate, Norwich

    Google Scholar 

  • Ladanyi B (1967) Expansion of cavities in brittle media. Int J Rock Mech Min Sci Geomech Abstr 4(3):301–328. https://doi.org/10.1016/0148-9062(67)90013-7

    Article  Google Scholar 

  • Ladanyi B, Archambault G (1969) Simulation of shear behavior of a jointed rock mass. In: The 11th US symposium on rock mechanics (USRMS), Berkeley, California. American Rock Mechanics Association, Berkerley, pp 12-40

  • Li C, Stillborg B (1999) Analytical models for rock bolts. Int J Rock Mech Min Sci 36(8):1013–1029

    Article  Google Scholar 

  • Li Y, Oh J, Mitra R, Hebblewhite B (2016) A constitutive model for a laboratory rock joint with multi-scale asperity degradation. Comput Geotech 72:143–151

    Article  Google Scholar 

  • Li D, Masoumi H, Saydam S, Hagan PC (2017) A constitutive model for load-displacement performance of modified cable bolts. Tunn Undergr Space Technol 68:95–105

    Article  Google Scholar 

  • Li D, Masoumi H, Saydam S, Hagan PC (2018a) Mechanical characterisation of modified cable bolts under axial loading: an extensive parametric study. Rock Mech Rock Eng 51(9):2895–2910

    Article  Google Scholar 

  • Li D, Masoumi H, Saydam S, Hagan PC, Asadizadeh M (2018b) Parametric study of fully grouted cable bolts subjected to axial loading. Can Geotech J 56(10):1514–1525

    Article  Google Scholar 

  • Li D, Masoumi H, Hagan PC, Saydam S (2019a) Experimental and analytical study on the mechanical behaviour of cable bolts subjected to axial loading and constant normal stiffness. Int J Rock Mech Min Sci 113:83–91

    Article  Google Scholar 

  • Li Y, Tang C, Li D, Wu C (2019b) A new shear strength criterion of three-dimensional rock joints. Rock Mech Rock Eng 53:1477–1483. https://doi.org/10.1007/s00603-019-01976-5

    Article  Google Scholar 

  • Li D, Li Y, Asadizadeh M, Masoumi H, Hagan P, Saydam P (2020) Assessing the mechanical performance of different cable bolts based on design of experiments techniques and analysis of variance. Int J Rock Mech Min Sci 130:104307

    Article  Google Scholar 

  • Ma S, Nemcik J, Aziz N, Zhang Z (2014) Analytical model for rock bolts reaching free end slip. Constr Build Mater 57:30–37. https://doi.org/10.1016/j.conbuildmat.2014.01.057

    Article  Google Scholar 

  • Moosavi M (1997) Load distribution along fully groutedd cable bolts based on constituitive models obtained from modified Hoek cells. PhD thesis, Queen’s University

  • Popov EP (1978) Mechanics of material. Prentice-Hall, Englewood Cliffs

    Google Scholar 

  • Price D (2008) Engineering geology principles and practice. Springer, Berlin Heidelberg

    Google Scholar 

  • Queener CA, Smith TC, Mitchell WL (1965) Transient wear of machine parts. Wear 8(5):391–400. https://doi.org/10.1016/0043-1648(65)90170-5

    Article  Google Scholar 

  • Ren FF, Yang ZJ, Chen JF, Chen WW (2010) An analytical analysis of the full-range behaviour of grouted rockbolts based on a tri-linear bond-slip model. Constr Build Mater 24(3):361–370

    Article  Google Scholar 

  • Stillborg B (1984) Experimental investigation of steel cables for rock reinforcement in hard rock. PhD thesis, Lulea University of Technology

  • Thenevin I, Blanco-Martín L, Hadj-Hassen F, Schleifer J, Lubosik Z, Wrana A (2017) Laboratory pull-out tests on fully grouted rock bolts and cable bolts: results and lessons learned. J Rock Mech Geotech Eng 9(5):843–855

    Article  Google Scholar 

  • Wu Z, Yang S, Zheng J, Hu X (2010) Analytical solution for the pull-out response of FRP rods embedded in steel tubes filled with cement grout. Mater Struct 43(5):597–609. https://doi.org/10.1617/s11527-009-9515-x

    Article  Google Scholar 

  • Yazici S, Kaiser PK (1992) Bond strength of grouted cable bolts. Int J Rock Mech Min Sci 29(3):279–292

    Article  Google Scholar 

  • Yuan H, Teng JG, Seracino R, Wu ZS, Yao J (2004) Full-range behavior of FRP-to-concrete bonded joints. Eng Struct 26(5):553–565. https://doi.org/10.1016/j.engstruct.2003.11.006

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the Australian Coal Association Research Program (ACARP 29019 and 29022) and National Science Foundation of China (Grant Numbers: 51774112, 51525402, 51874069 and 51761135102) for supporting this research.

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Correspondence to Yingchun Li.

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Li, D., Li, Y. & Zhu, W. Analytical Modelling of Load–Displacement Performance of Cable Bolts Incorporating Cracking Propagation. Rock Mech Rock Eng 53, 3471–3483 (2020). https://doi.org/10.1007/s00603-020-02123-1

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  • DOI: https://doi.org/10.1007/s00603-020-02123-1

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