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.
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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
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The authors received financial support from the University of Tabriz.
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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
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DOI: https://doi.org/10.1007/s10064-021-02563-1