Skip to main content
SpringerLink
Log in

Analytical and numerical simulations to investigate effective parameters on pre-tensioned rockbolt behavior in rock slopes

  • Original Paper
  • Published:
Bulletin of Engineering Geology and the Environment Aims and scope Submit manuscript

Abstract

Pre-tensioning of rockbolts is permitted to ensure better confinement between bedding rock slopes. The resulting shear adherence between layers is then increased, and a resistance against the rock block’s movement is developed. This paper develops a simple analytical approach to better understand the performance of pre-tensioned grouted rockbolts in bedding rock slopes. The force method approach and the deformation compatibility principles are used to model the contribution of developed axial and shear bolt forces at the intersection between the bolt and the joint plane to evaluate the behavior of the rockbolt in the elastic state. The effects of the pre-tension, the joint roughness, bolt inclination with respect to the joint plane, and rock strength are investigated, and the influence of the bolt contribution to preventing rock layer sliding is discussed. Furthermore, a 3D numerical approach is used to study the bolt performance in a plastic state. The results show that when the bolt is completely perpendicular to the discontinuity, the lower bolt contribution is generated. The pre-tensioning and joint roughness caused an improvement in resistance at the joint due to the utilization of the bolt axial capacity. Besides, the pre-tensioned rockbolt will be more useful for high-strength rock slopes.

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
Table 4
Fig. 17
Fig. 18

Similar content being viewed by others

Abbreviations

2lp :

The deflecting length of the bolt

A :

The cross-sectional area of the bolt

fy :

The yield strength of the bolt

T :

The pre-tensioned load

No :

The axial force acting in the bolt at the intersection between the bolt and the joint plane

Qo :

The shear force acting in the bolt at the intersection between the bolt and the joint plane

X1, X2, X3:

The axial force, shear force, and bending moment acting at the beam end

\({\sigma }_{c}\) :

The uniaxial compressive strength of the rock/grout

\({\Delta }_{1},{\Delta }_{2},{\Delta }_{3}\) :

The axial displacement, shear displacement, and rotation angle at beam end

\({\delta }_{ij}\) :

The displacement of the primary structure due to unit primary unknowns

E :

The Young’s modulus of the bolt

G :

The shear modulus of the bolt

μ :

The Poisson’s ratio of the bolt

I :

The moment of inertia of the bolt

κ :

The shearing-shape coefficient of the bolt

qo :

The maximal collection degree of the compressive load

u, v :

The opening and shear displacements

i :

The dilation angle of the joint

K :

The bolt coefficient

α :

The angle of the bolt with respect to the joint plane

r :

The rockbolt cross section radius

\({\phi }_{r}\) :

The residual friction angle of the joint plane

JRC :

The joint roughness coefficient

JCS :

The compressive strength of the rock at the fracture surface

sl, st :

The longitudinal and transverse distances of bolts in a block

\({\sigma }_{n}\) :

The effective normal stress

R Q,R N,R T :

The contributions to support force against sliding along the joint provided by the shear, axial, and pre-tensioned forces in the bolt at the intersection between the bolt and the joint plane, respectively

γ :

The mass density

db :

The diameter of the bolt steel

N q(x),Q q(x),M q(x):

The axial force, the shear force, and bending moment equations, respectively

References

  • Aziz N, Craig P, Mirzaghorbanali A, Nemcik J (2016) Factors influencing the quality of encapsulation in rock bolting. Rock Mech Rock Eng 49(8):3189–3203

    Article  Google Scholar 

  • Barton N (1973) Review of a new shear-strength criterion for rock joints. Eng Geol 7(4):287–332

    Article  Google Scholar 

  • Barton N, Bandis S, Bakhtar K (1985) Strength, deformation and conductivity coupling of rock joints. Int J Rock Mech Min Sci Geomech Abstr 22(3):121–140

    Article  Google Scholar 

  • Barton N, Choubey V (1977) The shear strength of rock joints in theory and practice. Rock Mech 10(1–2):1–54

    Article  Google Scholar 

  • Bi J, Luo X, Zhang H, Shen H (2019) Stability analysis of complex rock slopes reinforced with prestressed anchor cables and anti-shear cavities. Bull Eng Geol Environ 78(3):2027–2039

    Article  Google Scholar 

  • Bjurstrom S (1974) Shear strength of hard rock joints reinforced by grouted untensioned bolts. Proc 3rd Cong ISRM Denver 2:1194–1199

  • Cao C, Nemcik J, Aziz N, Ren T (2013) Analytical study of steel bolt profile and its influence on bolt load transfer. Int J Rock Mech Min Sci 60:188–195

    Article  Google Scholar 

  • Chen N et al (2018) Shear behavior of rough rock joints reinforced by bolts. Int J Geomech 18(1):0401713

    Article  Google Scholar 

  • Deb D, Das KC (2011) Enriched finite element procedures for analyzing decoupled bolts installed in rock mass. Int J Numer Anal Methods Geomech 35(15):1636–1655

    Article  Google Scholar 

  • Deb D, Das KC (2014) A new doubly enriched finite element for modelling grouted bolt crossed by rock joint. Int J Rock Mech Min Sci 70:47–58

    Article  Google Scholar 

  • Dight PM (1982) Improvements to the stability of rock walls in open pit mines. Monash University, Melbourne

    Google Scholar 

  • Ferrero AM (1995) The shear strength of reinforced rock joints. Int J Rock Mech Min Sci Geomech Abstr 32(6):595–605

    Article  Google Scholar 

  • Grasselli G (2005) 3D behaviour of bolted rock joints: experimental and numerical study. Int J Rock Mech Min Sci 42(1):13–24

    Article  Google Scholar 

  • Hutchinson D, Falmagne V (2000) Observational design of underground cable bolt support systems utilizing instrumentation. Bull Eng Geol Environ 58(3):227–241

    Article  Google Scholar 

  • Hibbeler RC (2012) Structural analysis, 8th edn. Pearson Prentice Hall, New Jersey, p 375

    Google Scholar 

  • Jalalifar H, Aziz N (2010a) Analytical behaviour of bolt–joint intersection under lateral loading conditions. Rock Mech Rock Eng 43(1):89–94

    Article  Google Scholar 

  • Jalalifar H, Aziz N (2010b) Experimental and 3D numerical simulation of reinforced shear joints. Rock Mech Rock Eng 43(1):95–103

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Li C, Wu J, Wang J, Li X (2016) Layout and length optimization of anchor cables for reinforcing rock wedges. Bull Eng Geol Environ 75(4):1399–1412

    Article  Google Scholar 

  • Liu C, Li Y (2017) Analytical study of the mechanical behavior of fully grouted bolts in bedding rock slopes. Rock Mech Rock Eng 50(9):2413–2423

    Article  Google Scholar 

  • Liu C, Li Y (2020) Predicting the shear resistance contribution of passive fully grouted bolts to jointed rock. Int J Geomech 20(2):04019174

    Article  Google Scholar 

  • Martín LB, 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

    Article  Google Scholar 

  • Mohammadi M, Hossaini MF, Bagloo H (2017) Rock bolt supporting factor: rock bolting capability of rock mass. Bull Eng Geol Environ 76(1):231–239

    Article  Google Scholar 

  • Nemcik J, Ma S, Aziz N, Ren T, Geng X (2014) Numerical modelling of failure propagation in fully grouted rock bolts subjected to tensile load. Int J Rock Mech Min Sci 71:293–300

    Article  Google Scholar 

  • Oreste P, Cravero M (2008) An analysis of the action of dowels on the stabilization of rock blocks on underground excavation walls. Rock Mech Rock Eng 41(6):835–868

    Article  Google Scholar 

  • Pellet F, Egger P (1996) Analytical model for the mechanical behaviour of bolted rock joints subjected to shearing. Rock Mech Rock Eng 29(2):73–97

    Article  Google Scholar 

  • Ranjbarnia M, Fahimifar A, Oreste P (2016a) Practical method for the design of pretensioned fully grouted rockbolts in tunnels. Int J Geomech 16(1):04015012

    Article  Google Scholar 

  • Ranjbarnia M, Oreste P, Fahimifar A, Arya A (2016b) Analytical-numerical solution for stress distribution around tunnel reinforced by radial fully grouted rockbolts. Int J Numer Anal Methods Geomech 40(13):1844–1862

    Article  Google Scholar 

  • Saadat M, Taheri A (2020) A numerical study to investigate the influence of surface roughness and boundary condition on the shear behaviour of rock joints. Bull Eng Geol Environ 79(5):2483–2498

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Wang F, Liu C, Gong Z (2014) Mechanisms of bolt support for bedding rock slopes. Chin J Rock Mech Eng 33(7):1465–1470

    Google Scholar 

  • Wyllie DC, Mah C (2014) Rock slope engineering. CRC Press, Boca Raton

    Google Scholar 

  • Xiurun G, Jianwu L (1988) Study on the shear resistance behaviour of bolted rock joints. Chin J Geotech Eng 1:001

    Google Scholar 

Download references

Funding

The authors received financial support from the University of Tabriz.

Author information

Authors and Affiliations

  1. Department of Geotechnical Engineering, Faculty of Civil Engineering, University of Tabriz, Tabriz, Iran

    Masoud Ranjbarnia & Mir Mahdi Rashedi

  2. Antea Group, Antony, France

    Daniel Dias

  3. Grenoble Alpes University, Laboratory 3SR, 38401, Grenoble Cedex 9, France

    Daniel Dias

Authors
  1. Masoud Ranjbarnia
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mir Mahdi Rashedi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Daniel Dias
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Masoud Ranjbarnia.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ranjbarnia, M., Rashedi, M.M. & Dias, D. Analytical and numerical simulations to investigate effective parameters on pre-tensioned rockbolt behavior in rock slopes. Bull Eng Geol Environ 81, 74 (2022). https://doi.org/10.1007/s10064-021-02563-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10064-021-02563-1

Keywords

Search

Navigation