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Effect of Contributing Parameters on the Behaviour of a Bolted Rock Joint Subjected to Combined Pull-and-Shear Loading: A DEM Approach

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Abstract

The mechanical performance of fully grouted rock bolts is essential in the stability of underground excavations in jointed rock masses. This research implements a new cohesive contact model in distinct element codes (PFC2D) to investigate the fracturing response of rock-like and grout material, as well as the bolt–grout interface. The results are compared in detail with experimental observations. The proposed modelling approach, used in conjunction with the distinct element method (DEM), successfully predicted the behaviour of grout failure and the bolt–grout interface’s shear response. We then developed a novel numerical, stepwise pull-and-shear test (SPST) scheme to further analyse the mechanical behaviour of bolted rock joints subjected to simultaneous pull–shear loading. The cohesive DEM framework proposed in this paper was used to carry out the SPST scheme numerically. The mechanism involved in enhancing the shear strength of bolted rock joint was determined by monitoring the \( \sigma_{\text{n}}^{\text{i}} \) and its corresponding contact chain force network during the pull-out test. The influence of pretension stress, the rig angle of the bolt profile, and the constant normal stiffness (CNS) condition are assessed systematically. In particular, the pretension stress magnitude at which the synthetic rock bolting system exhibits the highest shear resistance is identified. The findings from this research highlight the sensitivity of bolted rock joints to the simultaneous pull-and-shear loading, boundary conditions, and bolt–grout interface configurations.

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Abbreviations

CCM:

Cohesive contact model

CNL:

Constant normal load

CNS:

Constant normal stiffness

CSJM:

Cohesive smooth-joint model

DEM:

Distinct element method

DLL:

Dynamic link library

JRC:

Joint roughness coefficient

SJM:

Smooth joint model

SPST:

Stepwise pull-and-shear test

\( \varvec{u}^{\text{p}} \) :

Relative displacement

\( \varvec{u}^{\text{e}} \) :

Relative elastic displacement

\( \varvec{u}^{\text{p}} \) :

Relative plastic displacement

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

Contact normal stress

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

Contact shear stress

\( k_{\text{n}}^{0} \) :

Contact normal stiffness

\( k_{\text{s}}^{0} \) :

Contact shear stiffness

\( u_{\text{n}}^{\text{p}} \) :

Total normal plastic displacement

\( u_{\text{s}}^{\text{p}} \) :

Total shear plastic displacement

\( F \) :

Yield function

\( C \) :

Cohesion of contact

\( C^{0} \) :

Initial cohesive of contact

\( \mu \) :

Friction coefficient of contact

\( \kappa \) :

Softening parameter

\( u^{\text{p}} \) :

Accumulated plastic displacement of contact

\( D \) :

Damage parameter

\( G \) :

Plastic potential

\( \beta \) :

Dilation coefficient of contact

\( d\lambda \) :

Plastic multiplier

\( \sigma_{\text{n}}^{\text{trial}} \) :

Trial normal stress of contact

\( \sigma_{\text{s}}^{\text{trial}} \) :

Trial shear stress of contact

\( F^{\text{trial}} \) :

Trial yield function

\( \bar{A} \) :

Cross-sectional area of contact

\( \bar{R} \) :

Radius of DEM particle

\( \overline{{E_{\text{c}} }} \) :

Elastic modulus of contact

\( L \) :

Contact length

\( k^{*} \) :

Normal-to-shear stiffness ratio of contact

υ:

Poisson’s ratio

\( r_{ \hbox{max} } \) :

Maximum radius of DEM particle

\( r_{ \hbox{min} } \) :

Minimum radius of DEM particle

\( \alpha \) :

Rib angle

\( \bar{E}_{c,CCM} \) :

CCM elastic modulus

\( C_{\text{CCM}}^{0} \) :

CCM initial cohesion

\( \mu_{\text{CCM}} \) :

CCM friction coefficient

\( \beta_{\text{CCM}} \) :

CCM dilation coefficient

\( k_{\text{CCM}}^{*} \) :

CCM normal-to-shear stiffness ratio

\( \kappa_{\text{CCM}} \) :

CCM-softening parameter

\( D_{\text{CCM}} \) :

CCM damage parameter

\( k_{\text{n}}^{\text{sj}} \) :

Normal stiffness of SJM contact

\( k_{\text{s}}^{\text{sj}} \) :

Shear stiffness of SJM contact

\( \mu^{\text{sj}} \) :

Friction coefficient of SJM contact

\( k_{\text{s,CSJM}}^{0} \) :

CSJM shear stiffness

\( k_{\text{n,CSJM}}^{0} \) :

CSJM normal stiffness

\( C_{\text{CSJM}}^{0} \) :

CSJM initial cohesion

\( \mu_{\text{CSJM}} \) :

CSJM friction coefficient

\( \beta_{\text{CSJM}} \) :

CSJM dilation coefficient

\( \kappa_{\text{CSJM}} \) :

CSJM-softening parameter

\( D_{\text{CSJM}} \) :

CSJM damage parameter

\( \lambda \) :

Wavelength of idealised rock joint

\( \sigma_{\text{n}}^{0} \) :

Applied normal stress in CNL direct shear test

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

Rock compressive strength

\( \sigma_{\text{n}}^{\text{i}} \) :

Induced normal stress on rock joint interface

\( {\text{d}}\sigma_{\text{n}} \) :

Change in the normal stress during CNS direct shear test

\( k^{\text{cns}} \) :

CNS stiffness

\( {\text{d}}\delta_{\text{n}} \) :

Change in the normal displacement of rock joint

\( \sigma_{\text{n}}^{\text{u}} \) :

Updated normal stress in CNS direct shear test

\( \sigma_{\text{n}}^{\text{total}} \) :

Applied normal stress in pull-and-shear test

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Acknowledgements

The cohesive model employed in this study was formulated based on a generic framework by Giang D. Nguyen (University of Adelaide) and Ha H. Bui (Monash University), with Giang D. Nguyen’s help in the development and revision of the model. The first author thanks Mr Sacha Emam from Itasca Consulting group for his invaluable help and comments during implementation and verification of the model in PFC software. The comments from Dr. David O. Potyondy from Itasca Consulting group are highly appreciated. The authors also acknowledge the assistance of professional editor Leticia Mooney in preparation of this paper.

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Authors and Affiliations

  1. School of Civil, Environmental and Mining Engineering, The University of Adelaide, Adelaide, Australia

    Mahdi Saadat & Abbas Taheri

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  1. Mahdi Saadat
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  2. Abbas Taheri
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Correspondence to Mahdi Saadat.

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Saadat, M., Taheri, A. Effect of Contributing Parameters on the Behaviour of a Bolted Rock Joint Subjected to Combined Pull-and-Shear Loading: A DEM Approach. Rock Mech Rock Eng 53, 383–409 (2020). https://doi.org/10.1007/s00603-019-01921-6

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  • DOI: https://doi.org/10.1007/s00603-019-01921-6

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