Load transfer mechanism and critical length of anchorage zone for anchor bolt

Autoři: Xingliang Xu aff001;  Suchuan Tian aff001
Působiště autorů: Key Laboratory of Deep Coal Resource Mining, Ministry of Education of China, China University of Mining and Technology, Xuzhou, Jiangsu, China aff001;  Mining Department, Xinjiang Institute of Engineering, Urumqi, Xinjiang Uygur Autonomous Region, China aff002
Vyšlo v časopise: PLoS ONE 15(1)
Kategorie: Research Article
doi: 10.1371/journal.pone.0227539


The length of anchorage zone of an anchor bolt affects the distribution of axial force and shear stress therein. Based on a shear–displacement model, the load distribution of anchor bolts in the elastic deformation stage was analysed. Moreover, the mechanical response of threaded steel anchor bolts with different anchorage lengths was explored through pull-out test and numerical simulation. The results showed that axial force and shear stress were negatively exponentially distributed within the anchorage zone of anchor bolts in which there were the maximum axial force and shear stress at the beginning of the anchorage zone. In the elastic deformation stage of the anchorage, the longer the anchorage length, the more uniformly the shear stress was distributed within the anchorage zone and the larger the ultimate shear stress; however, there was a critical anchorage length, which, when exceeded, the ultimate shear stress remained unchanged. The calculation formula for the critical anchorage length was deduced and a reasonable anchorage length determined. The research result provides an important theoretical basis for rapid design of support parameters for anchor bolts.

Klíčová slova:

Deformation – Eigenvalues – Engineering and technology – Laboratory tests – Mechanical properties – Research design – Shear stresses – Simulation and modeling


1. Hsiao FY, Wang CL, Chern JC. Numerical simulation of rock deformation for support design in tunnel intersection area. Tunn Undergr Sp Tech. 2009; 24(1):14–21. https://doi.org/10.1016/j.tust.2008.01.003.

2. Kaiser PK, Cai M. Design of rock support system under rockburst condition. J Rock Mech Geotec Eng. 2012; 4(3):215–227. https://doi.org/CNKI:SUN:JRMG.0.2012-03-005.

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

4. Steen M, Valles JL. Interfacial bond conditions and tress distribution in a two- dimensionally reinforced brittle-matrix composite. Compos Sci Technol. 1998; 58(3–4):313–330. https://doi.org/10.1016/s0266-3538(97)00069-9.

5. Benmokrane B, Chennouf A, Mitri HS. Laboratory evaluation of cement-based grouts and grouted rock anchors. Int J Rock Mech Min. 1995; 32(7):633–642. https://doi.org/10.1016/0148-9062(95)00021-8.

6. Nemcik J, Ma SQ, Aziz N, Ren T, Geng XY. Numerical modelling of failure propagation in fully grouted rock bolts subjected to tensile load. Int J Rock Mech Min. 2014; 71:293–300. https://doi.org/10.1016/j.ijrmms.2014.07.007.

7. Martín LB, Tijani M, Hadj-Hassen F. A new analytical solution to the mechanical behaviour of fully grouted rockbolts subjected to pull-out tests. Constr Build Mater. 2011; 25(2):749–755. https://doi.org/10.1016/j.conbuildmat.2010.07.011.

8. Zhu Y, Wei J, Liao CH. The combined-power model method on determining the bounding length of prestressed anchoring rope. J Wuhan Univ Technol.2005; 08:60–63. https://doi.org/10.3321/j.issn:1671-4431.2005.08.018.

9. Zhang JR, Tang BF. Hyperbolic function model to analyze load transfer mechanism on bolts. Chinese J Geotec Eng. 2002; 24(2):188–192. https://doi.org/10.3321/j.issn:1000-4548.2002.02.013.

10. Zhu XG, Yang Q. Analyzing and studying factors for determining neutral point position of fully grouted rock bolt. Rock Soil Mech. 2009; 11:3386–3392. https://doi.org/10.1201/b10528-151.

11. Jiang ZX. A Gauss curve model on shear stress along anchoring section of anchoring rope of extensional force type. Chinese J Geotec Eng. 2001;23(6):659–662. https://doi.org/10.3321/j.issn:1000-4548.2001.06.010.

12. Štefaňák J, MičaL, Chalmovský J, Leiter A, Tichý P. Full-scale Testing of Ground Anchors in Neogene Clay. Procedia Eng. 2017; 17:1129–1136. https://doi.org/10.1016/j.proeng.2017.02.170.

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

14. Akisanya AR, Ivanović A. Debonding along the fixed anchor length of a ground anchorage. Eng Struct. 2014; 74:23–31. https://doi.org/10.1016/j.engstruct.2014.05.013.

15. Zeng XM, Lin DL, Li SM, Zuo K, Xu XH, Du NB. Comprehensive research of critical anchorage length problem of rod anchorage structure. Chinese J Rock Mech Eng. 2009; 28(S2):3609–3625. https://doi.org/10.3321/j.issn:1000-6915.2009.z2.046.

16. Huang MH, Zhao MH, Chan CF. Influence of anchorage length on stress in bolt and its critical value calculation. Rock Soil Mech. 2018; 39(11):4033–4041+4062. https://doi.org/10.16285/j.rsm.2017.0475.

17. Kılıc A, Yasar E, Celik AG. Effect of grout properties on the pull-out load capacity of fully grouted rock bolt. Tunn Undergr Sp Tech. 2002; 17(4):355–362. https://doi.org/10.1016/S0886-7798(02)00038-X.

18. Tistel J, Grimstad G, Eiksund G. Testing and modeling of cyclically loaded rock anchors. J Rock Mech Geotec Eng. 2017; 9(6):1010–1030. https://doi.org/10.1016/j.jrmge.2017.07.005.

19. Oh BH, Kim SH. Realistic models for local bond stress-slip of reinforced concrete under repeated loading. J Struct Eng. 2007;133(2):216–24. https://doi.org/10.1061/(ASCE)0733-9445(2007)133:2(216).

20. Thenevin I, Blanco-Martín L, Hadj-Hassen F, Schleifer J, Lubosik Z, Wrana A. Laboratory pull-out tests on fully grouted rock bolts and cable bolts: Results and lessons learned. J Rock Mech Geotec Eng. 2017; 9(5):843–855. https://doi.org/CNKI:SUN:JRMG.0.2017-05-007.

21. Long Z, Zhao MH, Zhang EX, Liu JL. A simplified method for calculating critical anchorage length of bolt. Rock Soil Mech. 2010;31(9):2991–2995. https://doi.org/CNKI:SUN:YTLX.0.2010-09-060.

22. Zhang J. Sahng YQ, Ye B. Analytical calculations of critical anchorage length of bolts. Chinese J Rock Mech Eng. 2005; 24(7):1134–1138. https://doi.org/CNKI:SUN:YSLX.0.2005-07-008.

23. Liu YH, Yuan Y. Experimental research on anchorage performance of full-thread gfrp bonding anchor bolts. Chinese J Rock Mech Eng. 2010; 29(02):394–400. http://www.rockmech.org/CN/Y2010/V29/I02/394.

24. Ito F, Nakahara F, Kawano R, Kang S, Obara Y. Visualization of failure in a pull-out test of cable bolts using X-ray CT. Constr Build Mater. 2001; 15(5–6):263–270. https://doi.org/10.1016/s0950-0618(00)00075-1.

25. Assaad JJ, Gerges N. Styrene-butadiene rubber modified cementitious grouts for embedding anchors in humid environments. Tunn Undergr Sp Tech. 2019; 84:317–325. https://doi.org/10.1016/j.tust.2018.11.035.

26. Cai Y, ESAKI T, Jiang YJ. An analytical model to predict axial load in grouted rock bolt for soft rock tunneling. Tunn Undergr Sp Tech. 2004, 19:607–618. https://doi.org/10.1016/j.tust.2004.02.129.

27. Kang HP, Cui QL, Hu B, Wu ZG. Analysis on anchorage performances and affecting factors of resin bolts. J China Coal Soc. 2014,39(1):1–10. https://doi.org/10.13225/j.cnki.jccs.2013.1919.

28. You CA, Zhan YB, Liu QY, Sun LL, Wang KB. Analysis of interfacial slip mesomechanics in anchorage section of prestressed anchor cable. Chinese J Rock Mech Eng. 2009; 28(10):1976–1985. https://doi.org/10.3321/j.issn:1000-6915.2009.10.003.

29. Li HZ, Li XH. Determination of rational anchorage length of bolt based on slip-debonding failure mode of interface. Rock Soil Mech. 2017; 38(11):3106–3112. https://doi.org/10.16285/j.rsm.2017.11.004.

30. Wang HT, Wang Q, Wang FQ, Li SC, Wang DC, Ren YX, et al. Mechanical effect analysis of bolts in roadway under different anchoring lengths and its application. J China Coal Soc., 2015; 40(3):509–515. https://doi.org/10.13225/j.cnki.jccs.2014.0582.

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2020 Číslo 1