ACME 2011 Proceedings of the 19 UK National Conference of the ...

Displacements are then back-transformed into the time domain using de Hoog’s efficient numerical
inversion algorithm [4]. A computer program was written using MATLAB to carry out these calculations.
3 RESULTS
The parameters used in the analyses presented here are r0=4.57 m, q1=q2=6.897 MPa, ν=0.2, G1=344.86
MPa, η1=239486.1 MPa Day, G2=3448.6 MPa and η2=47897222.2 MPa Day. Figure 3 compares the
radial displacement of the proposed energy-based solution with other methods. Figure 3(a) shows that in
the plane-strain condition the proposed solution has good agreement with the closed form solution
derived by Fahimifar et al. [2]. Figure 3(b) shows that in the region close to the tunnel face the proposed
analysis yields results that are comparable with FE analysis and field data.
Figure 3: Comparison of radial displacement with: (a) closed form solution; (b) FE analysis and field data
(t=0).
4 CONCLUSION
A 3D approximate solution for the time-dependent convergence of a deeply embedded and unsupported
circular tunnel, driven in a linear viscoelastic rock, was presented. This new approach is comparable with
FE analysis, but is faster. In addition the input to our method is accomplished through a simple text file,
while the geometry and optimal meshing for an FE analysis requires considerable time. Here Burger’s
model has been used to describe rock behaviour, however a wide range of constitutive models can be
incorporated into this analysis. This new method can be used for the initial design of tunnels.
References
(a) (b)
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Numerical and Analytical Methods in Geomechanics, 1, 249-269, 1977.
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tunnels in a visco-elastic Burger’s material under hydrostatic stress field. Tunnelling and Underground Space
Technology, 25(4), 297-304, 2010.
[3] R.E. Goodman, Introduction to Rock Mechanics, 2 nd Edition, Wiley: New York, 1989.
[4] F.R. de Hoog, J.H. Knight, A.N. Stokes. An improved method for numerical inversion of Laplace transforms.
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[5] M. Panet, Le calcul des tunnels par la method convergence-confinement. Presses de l’Ecole Nationale des
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