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Stability of a Rock Block in a Tunnel Roof Under Constant Normal Stiffness Conditions

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Abbreviations

\(b\) :

Width of rock block

\(c\) :

Constant relating to calculate boundary normal stiffness

\(c_{0} ,c_{1} ,c_{2}\) :

Empirical constants defining joint dilation rate

\(F\) :

Support force

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

Young’s modulus of rock mass

\(i\) :

Dilation angle

\({\text{JRC}}\) :

Joint roughness coefficient

\({\text{JCS}}\) :

Compressive strength of joint surface

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

Normal stiffness at an external boundary

\(K\) :

Ratio of horizontal stress to vertical stress

\(k_{\text{ni}}\) :

Initial normal stiffness of joint

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

Shear stiffness of joint

\(L\) :

Length of rock block

\(M\) :

Damage coefficient

\(N_{0}\) :

Initial normal force

\(p\) :

Vertical stress component

\(R\) :

Radius of tunnel

\(r\) :

Radial distance of the point from the centre of opening

\(S_{0}\) :

Initial shear force

\(V_{\text{m}}\) :

Maximum joint closure

\(W\) :

Weight of rock block

\(z\) :

Depth below surface

\(\dot{v}\) :

Dilation rate

\(\dot{v}_{\text{peak}}\) :

Peak dilation rate

\(\alpha ,\beta ,\lambda\) :

Components relating to shear stress-shear displacement equation

\(\theta\) :

Polar angle with respect to horizontal axis \(x\)

\(\psi\) :

Polar angle with respect to vertical axis \(y\)

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

Unit weight of rock mass

\(\delta_{\text{h}}\) :

Shear displacement

\(\delta_{\text{h - peak}}\) :

Shear displacement at peak stress ratio

\(\sigma\) :

Normal stress

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

Normal stress at shear displacement \(\delta_{\text{h}}\)

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

Initial normal stress (at \(\delta_{\text{h}} = 0\))

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

Radial stress component

\(\sigma_{{{\text{r}}\theta }}\) :

Shear stress component

\(\sigma_{\theta \theta }\) :

Tangential stress component

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

Mobilised shear stress

\(\tau\) :

Shear stress

\(\bar{\tau }\) :

Average shear stress along the vertical joints

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

Basic friction angle of joint

\(\phi_{\text{mob}}\) :

Mobilised friction angle

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Acknowledgments

The authors would like to thank the Australian Research Council (ARC) Linkage Project for the financial support of the lead author’s doctoral studies.

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Authors and Affiliations

  1. Faculty of Engineering and Information Sciences, Centre for Geomechanics and Railway Engineering, University of Wollongong, Wollongong, NSW, 2522, Australia

    Sivanathan Thirukumaran & Buddhima Indraratna

  2. Golder Associates Pty Ltd, PO Box 1734, Milton, QLD, 4064, Australia

    E. T. Brown

  3. Laurentian University, Sudbury, ON, Canada

    Peter K. Kaiser

Authors
  1. Sivanathan Thirukumaran
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  2. Buddhima Indraratna
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  3. E. T. Brown
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  4. Peter K. Kaiser
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Corresponding author

Correspondence to Buddhima Indraratna.

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Thirukumaran, S., Indraratna, B., Brown, E.T. et al. Stability of a Rock Block in a Tunnel Roof Under Constant Normal Stiffness Conditions. Rock Mech Rock Eng 49, 1587–1593 (2016). https://doi.org/10.1007/s00603-015-0770-6

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  • DOI: https://doi.org/10.1007/s00603-015-0770-6

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