d
u
e
t
o
s
w
e
l
li
n
g
(
c
m
)
ds
0.0
1
10
St
r
ain
100
Pressure (kPa)
dewd
Suggested swelling pressure (kPa) vs Strain
1000
0.5
1.0
1.5
2.0
2.5
3.0
3.5 %
%
%
%
%
%
%
%
-400
-600
-200
0
-1000
-1200
0.0
5
-5
10
-10
10
-15
10
-20
10
-25
5
10
15
20
25
Stresses vs. Depth at the tunnel's centerline
Stresses change that
causes swelling
Initial stress (kPa)
Stresses change that
causes swelling
Tunnel
excavation
-800
Final stress (kPa)
Swelling pressure (kPa)
0
200
400
600
800
1000
1200
1400
1600
1800
2000
Max. axial force
[kN/m]
Max. bending moment
[kN.m/m]
Max. shear force
[kN/m]
Without considering swelling
Considering swelling
0
1
2
3
4
5
10-
8-
6-
4-
2-
0
2
4
6
8
10
D
i
s
p
l
a
ce
m
e
n
t
Distance from the centerline of the tunnel axis (m)
Depth (m)
Pressure (kPa)
Calculating swelling effect on tunnel lining
We modelled the tunnel construction using a plane strain finite
element model and considering the excavation stages, the
installation of the temporary support, the placement of the final
lining, as well as the soil-structure interaction. In this model, we
applied prescribed displacements at the bottom of the invert to
represent the swelling effect. Accordingly, the resulting forces
and bending moments inside the lining at the final stage of the
construction were computed.
Figure 2 illustrates an example of calculating the swelling deformation at the tunnel's centerline. We also
calculated the displacements at sections 2 m, 4 m and 6.4 m away from the centerline.
Figure 2
The prescribed displacement at one specific section of the invert was determined using the analytical method
explained below and shown on Figure 2 :
· The mean initial stress and the stress decrease further to the tunnel excavation are plotted versus depth.
· The depth of influence of swelling below the invert is determined from the area between the initial stress and
the final stress, limited by the swelling pressure (Wittke-Gatterman, 1998).
· The swelling strain is then obtained by integrating the strain with depth as suggested by Kiehl (1990).
35
A cure for swelling
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