Page 57 - Numerical Analysis and Modelling in Geomechanics

38 A.A.JAVADI
corresponding stage, which together with the permeability values of the soil
layers can be used to predict the air losses associated with this section (segment).
The air loss for each segment is re-evaluated in the next excavation stages to
account for the age of the shotcrete. The programme can consider any delay in the
construction process such as holidays or other interruptions.

Parameter identification
In order to numerically simulate the flow of compressed air from the tunnel face
and walls into the ground, it is necessary to develop appropriate constitutive
models of all materials used in the tunnel. The governing equation describing
this problem can be obtained by combining the continuity equation and the
equation of flow. The flow equation can be expressed by Darcy’s (or Pick’s)
law. 1, 11 This model contains a number of material parameters which can ideally
be determined from experiments on material specimens. The most important
material parameters controlling the flow process are the permeability of soil
layers and shotcrete tunnel lining.
The first step in the numerical analysis of the problem will be to collect and
use the appropriate permeability values for soil layers and shotcrete. For
practical purposes, permeability of soil can be assumed to be constant while
permeability of shotcrete is not constant and varies with time during the curing
process. Thus time-dependency of air permeability of shotcrete lining as it cures,
should be taken into consideration and therefore it is very important to establish
a relationship which describes the variation of air permeability of shotcrete tunnel
lining with time. Obviously, any data collected from laboratory tests on small
samples of shotcrete can be unreliable, mainly due to the effect of cracks in the
shotcrete lining.
An alternative way of dealing with this problem, which is more reliable and
economic, can be the use of a parameter identification technique, provided that
some field or experimental data is available. The method is based on finding the
material parameters which when introduced to the geotechnical analysis of the
problem in hand, provide results as close as possible to the field observations or
measurements. The identification problem can then be formulated as an
optimisation problem where the function to be minimised is an error function
that expresses the difference between the numerical simulation results and the field
or experimental data. 13 This method of parameter identification overcomes the
shortcomings of the traditional methods in that it does not necessarily require
homogeneous material behaviour.
The basic assumptions of the material parameter identification method are:

• A constitutive model is available which can simulate the behaviour of the
material.
• An accurate and efficient computational method incorporating the constitutive
model is available to simulate the problem numerically.