1774
Proceedings of the 18
th
International Conference on Soil Mechanics and Geotechnical Engineering, Paris 2013
Figure 2. Circular tunnel device.
aluminum rods, having diameters of 1.6 and 3.0 mm mixed with
a ratio of 3:2 in weight, is used as ground material. The unit
weight of the aluminum rods mass is 20.4kN/m
3
, and the length
is 50 mm. The mass of aluminum rods are stacked up to a
prescribed height after setting single tunnel device or twin
tunnels devices according to the purpose of the experiments.
The initial ground is made in such a way that the earth pressure
becomes similar to the earth pressure at rest adjusting the block
of aluminum set at the bottom of the apparatus. The tunnel
excavation is simulated by controlling the shrinkage of the
tunnel device. The resulting surface settlement of the ground is
measured using a laser type displacement transducer.
Photographs are taken during the experiments for the
determination of ground movements with a program based on
the technique of Particle Image Velocimetry (PIV).
To simulate building loads strip foundation and pile
foundation are used. The dead loads are applied on the top of
the raft before performing tunnel excavation and are kept fixed
throughout the test. Depending on the foundation types and the
length of the piles different values of dead load are applied on
the ground surface, which is around 1/3 of the ultimate bearing
capacity. The model tests have been conducted for four kinds of
overburden ratio,
D/B
, where
D
is the depth from the ground
surface to the top of the tunnel and
B
(10cm) is the width of the
tunnel. As the width of the tunnel is 10cm, the depth of 40cm
corresponds to 40m in prototype scale. Therefore, the soil cover
of
D/B
=4.0 represents the tunneling in deep underground. In the
case of the tunneling in deep underground pile foundation, of
different pile lengths, is used to consider building loads.
Figure 3. Different positions of twin tunnels.
3 DESCRIPTION OF NUMERICAL ANALYSES
Figure 4 shows a typical mesh used in the finite element
analyses. Isoparametric 4-noded elements are used in the mesh.
Both vertical sides of the mesh are free in the vertical direction,
and the bottom face is kept fixed. To simulate the tunnel
excavation, negative volumetric strain in the tunnel elements is
applied which corresponds the amount of radial shrinkage of the
tunnel. This is an important simulation technique to consider
free movements of the tunnel. Analyses are carried out with the
same conditions of the model tests. Two-dimensional finite
element anlyses are carried out with FEMtij-2D using the
subloading
t
ij
model (Nakai and Hinokio, 2004). Model
parameters for the aluminum rod mass are shown in Table 1.
The parameters are fundamentally the same as those of the Cam
clay model except the parameter
a,
which is responsible for the
influence of density and confining pressure. The parameter
represents the shape of yield surface. The parameters can easily
be obtained from traditional laboratory tests. Figure 5 shows the
results of the biaxial tests for the mass of aluminum rods used in
the model tests. From the stress-strain behavior of the element
tests simulated with subloading
t
ij
model, it is noticed that this
model can express the dependency of stiffness, strength and
dilatancy on the density as well as on the confining pressure.
The initial stresses of the ground are calculated by simulating
the self-weight consolidation applying body forces starting from
a negligible confining pressure. In the case of the building loads,
the ground is initially formed under geostatic condition, and
then concentrated load is applied at the middle node of the
foundation.
Figure 4. Typical finite element mesh for twin tunnel analyses.
Figure 5.
Stress-strain-dilatancy relation of aluminum rods mass
.
Table 1. Parameters of soil materials
_______________________________________
Parameters
Value
_______________________________________
0.0080
0.0040
N
(
e
NC
at p=98kPa & q=
0
kPa
)
0.30
R
CS
=(
1
/
3
)
CS(comp.)
1.80
1.20
e
0.20
a
1300
_______________________________________
4 RESULTS AND DISCUSSIONS
4.1
Twin Tunnels Excavations
Figure 6 illustrates the surface settlement profiles for both
preceding (1
st
) tunnel and following (2
nd
) tunnel excavation in
the case where the 2
nd
tunnel is constructed directly underneath
the 1
st
tunnel and at a distance of S
T1
=1.0B. The soil cover of
the preceding tunnel
D/B
=2.0. The vertical axis represents
surface settlement, while the abscissa shows the distance from
the center of the tunnel. A wider settlement trough and larger
settlement are observed due to the excavation of the 2
nd
tunnel
as can be expected. The maximum surface settlement occurs in
the centerline above the tunnel crown as the preceding tunnel
moves towards the following tunnel excavation. The preceding
tunnel moves towards the following tunnel when it is
constructed below the level of the preceding tunnel at any
direction and at a certain range. When the following tunnel sits
in the same elevation of the preceding tunnel the maximum
surface settlement does not change significantly except its range
which becomes wider compare to a single tunneling. The
numerical analyses capture well the settlement troughs of the
model tests.
1 2 3 4 5 6 7 8 9
• •
1
=const.
• •
d
• • • • • •
stressratio,
• •
1
/
• •
2
1
2
3
• •
v
• • • • • •
0
0.2
0.4
-0.2
-0.4
-0.6
-0.8
-1.0
3.5
observed(
• •
1
=19.6kPa)
caclulated(
• •
1
=19.6kPa)
calculated(
• •
1
=0.2kpa)
1 2 3 4 5 6 7 8 9
• •
d
• • • • • •
stressratio
• •
1
/
• •
2
1
2
3
• •
v
• • • • • •
0
0.2
0.4
-0.2
-0.4
-0.6
-0.8
-1.0
observed(
• •
2
=19.6kPa)
caclulated(
• •
2
=19.6kPa)
calculated(
• •
2
=0.2kpa)
• •
2
=const.
3.5
(a)
(b)
2
