Page 47 - Numerical Analysis and Modelling in Geomechanics

28 A.A.JAVADI
(3) Other losses (including air locks, drainage, and ventilation)

This can be stated as:

(2.1)

The third item can be estimated from the size of the air lock, the pressure and the
frequency of use. However, it is not significant compared with face losses
occurring in open ground or losses from the tunnel perimeter walls.
The main factors influencing the air losses from the tunnel face and perimeter
walls are the permeability of shotcrete (in cases where it is used as a temporary or
permanent lining) and the ground (which is in turn a function of degree of
saturation of soil). The permeability of shotcrete varies as it cures, so this time-
dependency should be taken into account when analysing the air losses in a
tunnel where shotcrete is used as a primary or permanent support.

Permeability of the ground to air
Water permeability of the ground can be determined by in situ, laboratory or
theoretical methods, of which in-situ tests are more reliable due to the erratic
1
nature of soils. The permeability of a soil to air can be related to its permeability
to water using a relationship of the type shown in Figure 2.1.
As compressed air flows through the ground, the groundwater is driven back
and a region around the tunnel face becomes unsaturated. The permeability of
unsaturated soils to air is a function of many parameters such as type of the soil,
relative density, pressure gradient, viscosity of air and water, particle size
distribution and degree of saturation. Therefore, the possible relationship would
be very complex. At present there is no clear relationship expressing the
dependence of the permeability of unsaturated soils to all the above parameters.
In this study, the following simple relationship between the permeability of soils
to air and to water has been used which considers the dependence of permeability
on viscosity and density of the flowing fluid: k /k =η /η , where η is dynamic
a
w
a
w
viscosity, which is the ratio of the kinematic viscosity of the fluid to its density.
The viscosity of a flowing fluid varies with changing temperature. Therefore,
the ratio of the air permeability to the water permeability of soil is a function of
temperature. Figure 2.1 shows the variation of the ratio of air permeability to
water permeability with temperature. At 10° C ambient temperature, i.e., the
assumed average temperature in the ground, this ratio is approximately equal to
70, i.e.,
(2.2)

where k a is the permeability of dry soil to air and k w is the permeability of
saturated soil to water at a temperature of 10° C. The use of this factor of 70 is a