Structural design verifications, structural analysis of tunnels - Tunnel Engineering: Basics and Additional Services for Design and Construction - page 109

3.6 The application of the finite element method in tunnelling

Due to its flexible discretisation potential, the finite element method has become very
significant in tunnelling. The first successful tests were for very shallow tunnels, a field
in which the interaction of shotcrete and soil is still relatively insignificant. The next step
was the consideration of the stress relaxation ahead of the drive for the simulation of
three-dimensional load-bearing. Since it is not possible to make any statement about the
magnitude of the stress relaxation in 2D models, even when the geomechanical parameters
from the modulus of elasticity to the failure criteria are fully known, this was dealt with
from the start by incorporating measurements of displacement. This process is still normal
practice today.
As a result of the mathematical modelling of deep tunnels, the simulation of the interac-
tion between support and ground and the simulation of the advance of the tunnel have now
become particularly significant [51]. The basic procedure is not new and is described in
the references [16, 64, 66, 139, 160].

There follows a description of three FEM applications based on [186].

3.6.1 “Step-by-Step” technique
The basic idea of this method is to simulate the construction process as the tunnel ad-
vances in many steps, which approximate to the procedure in practice.
The procedure for the step-by-step simulation of a tunnel drive is illustrated in Fig. 3-12
through the example of a top heading advance with an idealised cross-section. Starting
from the primary state, in which the calculated section is only loaded by the self-weight
of the rock mass (γ F ), the advance of the top heading is simulated. For the 1 st construction
state, it is assumed that the top heading is excavated in one step along a greater length and
the shotcrete support is installed simultaneously. The support is not installed right up to the
temporary face; there remains an unsupported length of tunnel, whose length equals the
round length. The face is driven forward by this distance in the following working steps.
The entire length of the top heading excavated and supported in the first step is selected
according to the length stated above, after the three-dimensional influence of driving the
advance has subsided to about 1.5 to 2 d.
The simulation is achieved by assigning the excavated element the stiffness 0, meaning
that this element can no longer transfer stress.

3.6.2 Iteration process
This method makes the assumption that the alteration of the loading on the ground and
the shotcrete lining repeats with each advance of the tunnel with the same construction
process. The tunnel has an axis running parallel to the ground surface and uniform ground
with time-dependent stress-strain behaviour in the direction of advance. The state of dis-
placement and stress around the face, which no longer changes with further advance and
is achieved by stepwise simulation of the tunnel advance with the step-by-step method, is
calculated using an iteration procedure.