Abstract
The bolt anchoring force is closely related to the shear properties of the anchor interface. The shear stress distribution of full-length grouted bolts is analyzed based on the stress-strain relationship among the bolt, grout, rock mass and bond interface, considering the shear properties of the grout and contact interface bonding behavior. In this case, the interfacial shear stress of the grout and rock mass and the bolt axial force are obtained under pull-out and normal working conditions. The results show that the peak shear stress of the interface with the shear deformation of the bond interface is significantly lower than that without it when the pull-out force is applied. When designing bolt parameters of grade IV and V rock mass, the relative deformation between the rock mass and anchor should be considered, with a “unimodal” to “bimodal” shear stress distribution. In the case of a low elastic modulus of rock masses, both the shear stress concentration and distribution range are obvious, and the neutral point is near the bolt head. As the elastic modulus increases, the shear stress concentration and distribution range are reduced, and the neutral point moves towards the distal end. As a result, the optimum length of full-length grouted bolts can be determined by in-situ pull-out tests and decreases with the increased elastic modulus of the rock mass.
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27 June 2023
An Erratum to this paper has been published: https://doi.org/10.1007/s11629-023-7910-3
Abbreviations
- Variables:
-
Explanatory
- (x, y, z):
-
Cartesian coordinate
- τ,τ max,τ r :
-
The shear stress, maximum shear stress, and residual shear stress at the contact interface
- τ 1,τ 2 :
-
The shear stress of the first and second interface
- δ, δ m :
-
The shear strain and maximum shear strain at the contact interface
- δ 1, δ 2, γ :
-
The shear strain of the first and second interface and grout
- K 1, K 2, G b :
-
The shear modulus of the first and second interface and grout
- D 1, D 2 :
-
The diameter of the bolt and borehole
- G r, E r, µ r :
-
The shear modulus, elastic modulus and Poisson’s ratio of rock mass
- E a :
-
The elastic modulus of bolts
- F, F r, σ :
-
The drawing force, additional force and stress of bolts
- u r :
-
The displacement of the rock mass
- ε a, ε r :
-
The strain of the bolt and rock mass
- ε r1, ε r2 :
-
The rock mass strain generated by drawing force and the actual working condition [Eqs. (8), (27)]
- L :
-
The length of bolts
- P :
-
The in-situ stress
- β :
-
The lining influence coefficient [Eq. (26)]
- r, r o :
-
The radius of the rock mass and tunnel
- A, B, C 1, C 2, t :
-
The coefficient related to the rock mass characteristic and boundary [Eqs. (13), (14), (17), (25), (34)]
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Acknowledgements
The research reported in this manuscript is funded by the Natural Science Foundation of China (Grants Nos. 52179113, 42207199, 41831278). The authors wish to acknowledge Professor of CHEN Weizhong, Institute of Rock and Soil Mechanics, for his help in interpreting the significance of the results of this study.
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Zhu, Zd., Shu, Xy., Li, Z. et al. Stress analysis of full-length grouted bolt under shear deformation of anchor interface. J. Mt. Sci. 19, 3286–3301 (2022). https://doi.org/10.1007/s11629-022-7566-4
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DOI: https://doi.org/10.1007/s11629-022-7566-4