Page 75 - Numerical Analysis and Modelling in Geomechanics

56 A.A.JAVADI
pressure can result in a decrease in the soil strength and reduce the stability of
the tunnel.
The results of the tests can be used to predict the change in shear strength of
the ground due to the flow of air in compressed air tunnelling. From the results
of the experiments, it can be seen that for the practical range of changes in the air
pressure, the variation of the shear strength with the stress state variables can be
considered to be linear. The internal air pressure applied in driving tunnels under
compressed air is usually about one atmosphere and because of safety
considerations it is rarely increased beyond two (or at most three) atmospheres.
So the assumption of a planar failure envelope for the Mohr circles is reasonable.
If the equations for the assumed planar stress point envelope for the soil at failure
and the change in the stress state variables are known, then the change in the
shear strength of the soil with change in the air pressure can be predicted.
A planar surface was assumed for the stress point failure envelope and a
surface fitting technique was used to determine the closest fit planar surface to the
results obtained from the laboratory tests. In the equation of the failure surface
(equation (2.12)), p and r were known parameters from the test results (Tables
f
f
2.5, 2.6 and 2.7), and the three unknown parameters d', Ψ' and Ψ b were to be
identified. For the soil specimens tested, the results of the surface fitting analysis
indicated that the following values for the unknown parameters gave the best fit
between the test results and the assumed planar surface:

Therefore, for the soil tested, the equation for the failure envelope will be:

Figure 2.20 shows the planar failure envelope for the soil tested which is the
graphical presentation of equation (2.12).

Conclusion
Selection of an air pressure and supply requirements for tunnelling is currently
based on judgement and empirical formulae. The judgements are overly
simplistic and the formulae do not account for the true behaviour of the materials.
A numerical model has been developed that can predict air losses from a
tunnel driven under compressed air. The model predicts the air losses from the
tunnel face as well as from the perimeter walls.
A relationship has been presented for the time-dependency of the air
permeability of shotcrete and the parameters of this relationship have been