Civil Engineering Reference
In-Depth Information
Figure 25.8
Settlement profile above a tunnel in soft ground.
Ground loss at the tunnel causes a settlement trough at the surface, as shown in
Fig. 25.8. The settlements are greatest directly above the tunnel axis and become smaller
away from it as shown. The shape of the settlement trough is often approximated by
a normal probability or Gaussian distribution curve given by
S
m
e
−
x
2
S
=
(25.5)
2
i
2
where
S
m
is the maximum settlement above the tunnel axis,
x
is the distance measured
away from the centre line and
i
is the distance to the point of inflection where the
curvature changes and the slope of the ground surface is greatest. The volume of the
settlement trough (per unit length along the tunnel)
V
s
is
=
(
V
s
2
π)
iS
m
(25.6)
If the soil is undrained then
V
s
≈
V
t
. The values of
i
depend principally on the
depth of the tunnel and to a lesser extent on whether the soil is coarse-grained or fine-
grained. Figures 25.9(a) and (b) show that
i
increases from
i
1
to
i
2
as the tunnel depth
increases from
z
1
to
z
2
but, for a given ground loss the maximum settlement decreases
from
S
m
1
to
S
m
2
. From Fig. 25.9(c) the value of
i
increases approximately linearly with
z
and
V
e
−
≈
i
kz
(25.7)
For most cases you can take
k
0.5 for fine-
grained soils. If you make an assumption about the percentage ground loss you can
use the above relationships to calculate the profile of surface settlement above a tunnel
in soft ground.
=
0.35 for coarse-grained soils and
k
=
