Civil Engineering Reference
In-Depth Information
MODELLING THE LINING
As mentioned previously, in 2-D the analysis does not recognize the 3-D
support from the lining already installed behind the face, into which the
stresses arch. So called wished-in-place lining occurring in a single increment
in the analysis is common, for example when using the volume loss or
convergence-confinement approaches. There are two ways of modelling
the lining using solid element or shell elements. Solid elements are standard
elements used for representing most materials within finite element meshes
and hence there are a wide range of constitutive models available for these
elements. However, solid elements have the problem that the element shape
can be an issue (defined by the aspect ratio of length to width). Linings
are relatively thin in relation to the tunnel diameter and therefore a large
number of elements are required to maintain acceptable aspect ratios. Shell
elements in contrast have zero thickness and curved shell elements can be
used to model tunnel linings. This removes the problem of aspect ratio and
allows more flexibility with respect to the mesh definition. There are many
issues to consider when modelling tunnel linings, particularly segmental
linings, and the reader is encouraged to read more detailed literature on
this subject, for example Potts and Zdavkovic (2001).
3.6.3 Modelling the tunnel construction in 3-D
3-D numerical analyses allow the possibility of modelling the tunnel
operation more realistically, particularly the behaviour of the ground ahead
of the tunnel face and the 3-D arching effects that occur around the tunnel
face. Although these analyses are more costly in terms of computation time,
it is still not possible to model accurately every aspect of the tunnel
construction in detail and assumptions are still required. However, modern
software packages do offer the possibility of doing this type of analysis
with relative ease. It must be remembered, however, that it is important to
understand what you are doing and to consider the limitations and
assumptions that are made in these analyses. Figure 3.9 shows an example
of a finite element 3-D mesh.
An example of three-dimensional numerical modelling was reported by
Ng
et al.
(2004) who carried out a series of three-dimensional finite element
analyses to investigate multiple tunnel interactions for sprayed concrete
lined tunnels in stiff clay using ABAQUS
®
. In parallel, Lee and Ng (2005)
studied the effects of tunnels on an existing loaded pile using three-
dimensional finite element modelling, again using ABAQUS
®
. Bloodworth
(2002), following on from previous work by Burd
et al.
(2000), conducted
a detailed study to investigate the effects of new tunnelling on existing
structures in 2-D and 3-D. This work highlights many of the issues
associated with simulating both the tunnelling operation and the realistic
modelling of, in this case, the buildings at the ground surface. The numerical
