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Analysis of Deformation Characteristics of Fully Grouted Rock Bolts Under Pull-and-Shear Loading

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Abstract

A new analytical approach able to predict the mechanical behavior of fully grouted rock bolts subjected to pull-and-shear load is been proposed. The elastic theory of a semi-infinite length beam and approximate differential equation of the deflection curve (elastic and elastoplastic) are employed to analyze the lateral behavior of a bolt under surrounding rock pressures. Bolt axial behavior is based on a realistic tri-linear bond-slip model with residual bond strength at the grout–bolt interface. According to the Tresca yield criterion, important failure parameters such as shear displacement, tangent direction, tensile displacement, and tensile force can be determined via the analytical approach while the shear force and other basic parameters are provided. Results of the proposed analytical approach for 0°, 20°, 40°, 60°, and 90° displacing angles correlate well with experimental test results. Parametric analysis of both the rock and bolt mechanical behavior are also carried out using this new analytical approach.

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(after Li and Stillborg 1999)

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(after Ren et al. 2010)

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Abbreviations

D b :

Bolt diameter

D tot :

Total displacement

E :

Young’s modulus in the elastic stage of bolt

E 1 :

Young’s modulus in the hardening stage of bolt

F tot :

Total force

L i :

Elongation due to bending deformation

L t :

Elongation due to joint aperture

L r :

Elongation due to bolt rotation

M e :

Elastic limit bending moment

M s :

Plastic limit bending moment

M 0 :

Bend moment

m, n, A, B, C1, C2, D1, D2, U, Ue :

Some constants

N 0 :

Pull-out load applied on the bolt

N 1 :

Maximum shear stress in case the interface remains elastic

N 2 :

Minimum shear stress in case the interface appears debonding

N 3 :

Yield force of bolt

Q 0 :

Shear load applied on the bolt

q u :

Rock resistant pressure

S p :

Peak shear strength at the bolt–rock interface

\(S_{\text{p}}^{\prime }\) :

Shear strength at the bolt–rock interface when N0 is known

S r :

Residual shear strength at the bolt–rock interface

y 0 :

Bolt deflection

y e :

Bolt deflection when the host rock reached bearing capacity

ω Sr/Sp :

The ratio of the residual shear strength to the peak shear strength

φ :

The displacing angle

θ 0 :

Rotation angle of bolt

τb (x):

The shear stress at the interface of bolt and grout

σb (x):

The axial stress of the bolt

ε (x):

The strain of the bolt

δ L :

The elongation of bolts

Δ:

The length of partially decoupled with the residual shear strength increasing to the peak strength

\(\Delta^{\prime}\) :

The length of partially decoupled with the residual shear strength increasing to the peak strength when N0 is known

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Acknowledgements

The authors would like to acknowledge the financial support for the research: Project (51604299) and (41672298) supported by the National Natural Science Foundation of China.

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Authors and Affiliations

  1. School of Resources and Safety Engineering, Central South University, No.932 Lushan South Road, Changsha, 410006, Hunan, China

    Yu Chen, Guanping Wen & Jianhua Hu

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  1. Yu Chen
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  2. Guanping Wen
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  3. Jianhua Hu
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Correspondence to Guanping Wen.

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Chen, Y., Wen, G. & Hu, J. Analysis of Deformation Characteristics of Fully Grouted Rock Bolts Under Pull-and-Shear Loading. Rock Mech Rock Eng 53, 2981–2993 (2020). https://doi.org/10.1007/s00603-020-02108-0

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