Three-Dimensional Face Stability Analysis of Deep and Shallow Tunnels in Rock Masses
Publication: International Journal of Geomechanics
Volume 21, Issue 10
Abstract
Face stability is a critical issue in the stability analysis of tunnels, especially in soft soils and crushed rock masses. In this paper, considering two three-dimensional collapse mechanisms, upper-bound solutions are presented for determining the face pressure of deep and shallow tunnels excavated in rock masses. The Hoek–Brown failure criterion was considered for the rock mass surrounding the tunnel. The proposed upper-bound formulations were compared with three-dimensional finite-element simulations and also with centrifuge test results available in the literature. The obtained results showed that the face pressure decreases with increasing σci, mi, and geological strength index. Besides, increasing the tunnel diameter and the rock mass density led to an increase in the face pressure, where for larger tunnels, the effect of the density became more pronounced. Finally, some charts were presented to specify the range of applicability of the concepts of deep and shallow tunnels. The results obtained from these charts demonstrated that the reduction in the Hoek–Brown parameters of the rock mass results in spreading the collapse mechanism from the tunnel face to the ground surface.
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Data Availability Statement
Some or all data, models, or codes that support the findings of this study are available from the corresponding author upon reasonable request (MATLAB codes and Excel source files).
Notation
The following symbols are used in this paper:
- Ai and Ai+1
- base area of the ith and (i + 1)th elliptical cones;
- C
- height of the tunnel cover;
- ci and ci,i+1
- tangential cohesions corresponding to ϕi and ϕi,i+1, respectively;
- ct
- tangential cohesion corresponding to ϕt;
- D
- disturbance coefficient;
- d
- diameter of the tunnel;
- mb
- value of the Hoek–Brown constant, m for rock masses;
- mi
- value of m for intact rocks;
- s and a
- Hoek–Brown constants that depend upon the characteristics of rock masses;
- Si
- lateral area of the ith sliding block;
- Ui
- absolute velocity of the ith sliding block;
- Ur(i) or Ui,i+1
- relative velocity between the ith and (i + 1)th sliding blocks;
- Vi
- volume of the ith sliding block;
- ϕi
- tangential friction angle along the lateral surface of the ith elliptical cone;
- ϕi,i+1
- relative tangential friction angle between the ith and (i + 1)th sliding blocks;
- ϕt
- tangential friction angle;
- γ
- unit weight of rock masses;
- and
- major and minor effective principal stresses at failure, respectively;
- σci
- uniaxial compressive strength of intact rocks;
- σp
- tunnel face pressure;
- σs
- surcharge applied to the ground surface; and
- ψi
- angle between the absolute velocity of the ith sliding block and the vertical direction.
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International Journal of Geomechanics
Volume 21 • Issue 10 • October 2021
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Oct 27, 2020
Accepted: May 24, 2021
Published online: Aug 6, 2021
Published in print: Oct 1, 2021
Discussion open until: Jan 6, 2022
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