CROSS CONNECTIONS - The Westerschelde Tunnel: Approaching Limits - page 188

Fig. 13.5
Diagrammatic
representation of 'New
Austrian Tunnelling
Method (NATM)'

23,300 mm

Tunnel tube
west

Tunnel tube
east

Freeze-pipe

Freeze-pipe

Longitudinal cross section

lining by means of formwork being the final structure. After this has hard-
ened, the freezing can be halted.

Calculating method

The frozen soil, the outer lining as well as the inner lining were considered
in the design calculations as independent loadbearing structures: each one
had to separately be able to bear the full load. The stresses in the frozen soil
are calculated by means of a three-dimensional finite elements model. This
has taken into consideration the temperature-dependent properties of the
frozen ground regarding the elasticity as well as the maximum strength.
The cross-sections of both the outer lining and the inner lining are calculated
as monolithic single-ringed bar charts according to the principles of the
'Emphelungen für Tunnel im Lockergestein, 1980' (ETL), in which the ring is
loaded by water and ground pressures and supported by radially acting soil
springs. In the strength calculation for the outer lining of shotcrete a reduc-
tion of 50 mm on the wall thickness has been used. It has been assumed that
the first 50 mm of the outer lining - which lies directly against the frozen soil
- could not or could barely harden as a result of the low temperature.
Besides, the elasticity modulus has also been reduced to 50%.This reduction
was necessary because the concrete was loaded sooner as a result of creep
by the frozen soil, than the 28 days which is always taken into account.
In both the construction and the final phase, the deformations and the forces
(bending moments and coupling forces) in the tunnel tube at the location of
the cross connection, are calculated with an extension of the model which is
used for the normal tunnel cross-section. The model for the usual tunnel
cross section, a two-ringed framework analysis with rotation joints between
the segments of a ring and translation springs between the rings, was
extended to a 4-ringed model in which, aside from the cross connection ring,
on both sides another 2 1 ⁄ 2 (

5 metres) rings were modelled. In this model the
deviating stiffness of the steel segments was also included .
Assuming the stresses and couples that are already present as a result of
the load which is normally present, the so-called nil-situation, then a semi-
phased calculation was carried out in which the result of the previous phase
formed the input for the following phase. The following phases were con-
secutively calculated to the nil-situation:
- applying of the stiffening beams;
- changed bedding as a result of the freezing of the soil;
- falling away of bedding and load as a result of the excavation of the cross
connection;
- fixing of the deformation at the positioning of the applied inner and outer
lining;
- applying a changed bedding as a result of the thawing of the soil.