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21.3.4 Stability Analyses, Assumptions and Computation Steps
The computation section used for the stability analyses could be selected much smaller
than the computation section for the seepage flow analysis because the influence of a
tunnel excavation on stresses and deformations in the rock mass from experience is
limited to a smaller area (Fig. 21.28, Section 10.4). Also, for the stability analyses the
vertical plane through the tunnel axis was assumed to be a plane of symmetry. The FE-
mesh and the selected boundary conditions are represented in Fig. 21.29, and Fig. 21.30
shows a detail of this FE-mesh.
Figure 21.29
Stability analyses, FE-mesh and boundary conditions (Wittke et al. 2006)
The stresses in the shield not only depend on the applied loads and the thickness of the
shield skin but also on the stiffenings mounted within the shield. Therefore at least the
most important stiffenings needed to be considered in the analyses.
The inner and outer rings of the steel-girder construction of the shield were discre-
tized by means of isoparametric elements (Figs. 21.30 and 21.31, left, cf. Section
10.3.1). The stiffenings in between consist of three plates that are assembled like an
I-girder (Fig. 21.31). Such stiffening enables the transmission of a normal thrust N
t
,
of a bending moment M
s
and of shear forces S
r
and S
t
. The indices r, s and t refer
to the local coordinates of isoparametric elements defined in Wittke (2000). In the
analyses, the three plates are modeled with four truss elements (Section 10.3.2). The
cross-sectional areas of the truss elements were selected in such a way that their sum
in the plane of the local coordinates r and s is equal to the sum of the cross-sec-
tional areas of the stiffening members in the corresponding plane (r-s plane). Thus,
the transmission of normal thrust N
t
by the stiffening was simulated correctly by
the truss elements. Furthermore, the truss elements 1, which are directed parallel to
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