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An Analytical Model for Fully Grouted Rockbolts with Consideration of the Pre- and Post-yielding Behavior

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Abstract

For rockbolts subjected to tensile loads, there exists a unique local slip–strain relationship as well as a unique bond–slip relationship between rockbolts and rock mass. An analytical model is presented in this study for fully grouted rockbolts under tension, based on the slip–strain relationship of rockbolts. This analytical model takes into account the trilinear bond–slip relationship and the pre- and post-yielding characteristics of the rockbolt material. The reliability and accuracy of the proposed analytical model are verified by experimental pullout tests. Verification studies show that the proposed model is capable of representing the strain and stress distributions of the rockbolts, and the overall load–displacement relationships of rockbolts before and after yielding. Additionally, the model has successfully captured the decoupling mechanism at the bolt–rock interface.

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Abbreviations

\(\varepsilon_{\text{y}}\) :

Bolt yield strain

\(\varepsilon_{\text{sh}}\) :

Strain at the onset of hardening phase

\(f_{\text{u}}\) :

Yield and tensile strengths of the bolt

\(f_{\text{y}}\) :

Tensile strengths of the bolt

\(\sigma_{\text{y}}\) :

Bolt yield strength

\(\tau\) :

Shear stress at bolt–rock interface

S:

Relative slip between the bolt and rock

\(\tau_{\text{f}}\) :

Peak shear bond stress at the bolt–rock interface

\(\tau_{\text{r}}\) :

Residual shear stress at the bolt–rock interface

\(s_{\text{n}}\) :

Non-dimensional (normalized) slip

\(S\) :

Local slip of the bolt

D :

Bolt diameter

\(\varepsilon_{\text{s}}\) :

Bolt axial strain

\(f_{c}^{\prime }\) :

Concrete compressive strength

\(l_{\text{seg}}\) :

Segment length of the bolt

\(E_{\text{b}}\) :

Bolt’s Young’s modulus

\(E_{\text{e}}\) :

Young’s modulus in the elastic stage

\(E_{\text{r}}\) :

Young’s modulus in the hardening stage

\(\tau (n)\) :

Interfacial shear bond stress between the nth and (n − 1)th bolt segments

\(\varepsilon_{n}\) :

Strain for the nth segment

P :

Pullout load applied on the bolt

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Acknowledgements

This work was supported by the Open Fund of State Key Laboratory of Geohazard Prevention and Geoenviroment Protection under Grant No. SKLGP2017K007.

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Authors and Affiliations

  1. Key Laboratory of Transportation Tunnel Engineering, Ministry of Education, School of Civil Engineering, Southwest Jiaotong University, Chengdu, 610031, China

    Shuqi Ma

  2. School of Civil and Environmental Engineering, Nanyang Technological University, Singapore, 639798, Singapore

    Shuqi Ma, Zhiye Zhao & Wen Nie

  3. State Key Laboratory of Geohazard Prevention and Geoenvironment Protection, Chengdu University of Technology, Chengdu, 610059, People’s Republic of China

    Shuqi Ma & Xing Zhu

Authors
  1. Shuqi Ma
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  2. Zhiye Zhao
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  3. Wen Nie
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  4. Xing Zhu
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Correspondence to Wen Nie.

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Ma, S., Zhao, Z., Nie, W. et al. An Analytical Model for Fully Grouted Rockbolts with Consideration of the Pre- and Post-yielding Behavior. Rock Mech Rock Eng 50, 3019–3028 (2017). https://doi.org/10.1007/s00603-017-1272-5

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  • DOI: https://doi.org/10.1007/s00603-017-1272-5

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