1756
Proceedings of the 18
th
International Conference on Soil Mechanics and Geotechnical Engineering, Paris 2013
Three distinct soil layers were encountered. A fill layer extends
three meters from ground surface. The fill layer consisted of
asphalt, broken red bricks, and stones. A natural deposit of stiff
overconsolidated silty clay layer under the fill layer is varied from 4
m to 10 m. This deposit includes occasional sand and silt partings.
Beneath the silty clay layers, the silty sandy layer extends from 0.25
m to 1.0 m. Beneath the silty sand layers, the sandy layer extends
down to the bedrock.
Soil parameters were derived from in-situ and laboratory tests. The
main Geotechnical parameters used in the 2-D FEA are presented in
Table 1. The circular tunnel lining consists of seven segments and
one key. The length of the ring is 1.5 m long. The thickness of
tunnel lining is 400 mm. The characteristics of the tunnel lining are
tabulated in Table 2 (NAT, 1993, 1999, 2010).
4
TUNNEL PERFORMANCE UNDER VARIUOS PARAMETERS
The stress and the strength parameters of loose, medium, dense, and
very dense sand are considered in the FEA (Duncan et al., 1980).
The soil parameters required to model performance of tunnel
system are presented in Table 3 (Duncan et al., 1980).
Diameter of tunnel is varied from 5 m, 7.5 m, 10 m, and 12.5 m.
The tunnel is located at different types of cohesionless soils (loose
sand, medium sand, dense sand, and very dense sand). The
numerical analysis is carried out using the drain analysis as the
tunnel passes through sand layer. The variation of soil modulus
(E
s
) with confining pressure is related to effective pressure based on
Janbu’s empirical equation (Janbu, 1963) as presented in Eq. (1).
The different soil parameters (m, n) are selected to simulate the
behavior of different soil types (Duncan et al., 1980).
n
a
a
s
P
mP E
3
(1)
Where; the modulus number (m) and the exponent number (n) are
both pure numbers, P
a
is the atmospheric pressure expressed in
appropriate units, and σ
3
is effective confining pressure.
The surface displacements (surface settlement) are estimated using
empirical equation developed by Peck and Schmidt (1969) as
presented in Eq. (2). The surface displacement trough is calculated
by the normal Gaussian probability curve as shown in Fig. 3.
S= S
max
exp
2
2
2
i
x
(2)
where; S is surface displacement, S
max
is maximum surface
settlement at the point above tunnel centerline, x is distance from
tunnel centerline in transverse direction, and
i
is horizontal distance
from tunnel centerline to point of inflection of settlement trough.
Based on the case study involving medium sand, S
max
is recorded in
the field. For loose sand, dense sand, and very dense sand, S
max
is
estimated using the 2-D finite element analysis. Attwell el at.
(1986) proposed (i) parameter included in the SDE as presented in
Eq. 3.
n
R
Z
R
i
2
= 1, n=1 (3)
Where; Z is overburden depth from ground surface to C.L of tunnel,
R is radius of tunnel, and
and n are constant parameters.
5 SOIL-TUNNEL PERFORMANCE
The case study is located along the Greater Cairo Metro Line 2, as
shown in Fig. 1. The 2-D finite element model is used to predict
the performance of the metro tunnel. The overburden depth from
ground surface to crown of the metro tunnel is 18 m. The computed
values are compared with the field measurements so as to
understand the behavior of the metro tunnel system. This
comparison is used to assess the accuracy of the numerical model,
as shown in Fig. 4. The comparison shows that there is a good
agreement between the computed and measured results.
The stress changes in soil around the metro tunnel system due to
tunneling are also investigated to study detailed tunnel system
behavior. For the metro tunnel, the soil stress analysis has been
undergone four steps of change. These steps correspond to the
construction of the metro tunnel. The loading steps are simulated
using the 2-D FEA. First, the initial principal stresses are computed
with the absence of the metro tunnel. Second, the excavation of the
tunnel is modeled by means of the finite element method. The
metro tunnel excavation is simulated by the removal of those
elements inside the boundary of the tunnel surface to be exposed by
the excavation. Third, the movements and stress changes induced in
the soil media are calculated. Fourth, the calculated changes in
stresses are then added to the initial stresses computed from the first
step to determine the combined stresses resulting from the metro
tunnel construction. The calculated vertical effective stress around
the metro tunnel is also illustrated in Fig. 5.
Based on the good agreement between the computed and measured
values, one can proceed to use the 2-D numerical model to explore
other aspects of the tunnel system performance under the tunnel
construction. In fact, the proposed model can help to predict the
surface displacement at the different sandy soils.
6 SURFACE DISPLACEMENT DUE TO TUNEELING
The surface displacement profile above a tunnel with diameter 9.48
meters are calculated and plotted in Fig. 6 to Fig. 9 using the SDE.
The FEA is also conducted to determine the surface displacements
due to tunneling in different sandy soils (loose sand, medium sand,
dense sand, and very dense sand) based on different ground losses
(V
L
). The average values of the different sandy soil parameters
adopted in the finite element analysis are summarized in Table 3
(Duncan et al., 1980). The volume loss is considered in this study.
The volume loss is the ratio of the difference between the excavated
soil volume and the tunnel volume over the excavate soil volume.
The volume loss of 3 % is adopted in this study (El-Nahhass, 1999).
Based on the FEA, the surface displacements along the centerline of
the metro tunnel for different sandy soil types are presented in Fig.
6 to Fig. 9. However, the results obtained by the SDE are examined
with those obtained by the FEA.
In the case of loose sand, the surface displacement profiles obtained
by both the FEA and the SDE are shown in Fig. 6. The comparison
shows that the surface displacements obtained by the finite element
analysis are higher than those calculated by the surface
displacement equation. However beyond 20 m from the centerline
of the tunnel, the surface displacement calculated by the FEA does
not agree with this calculated by the SDE. The result reveals that
the surface settlement profile obtained by the SDE does not agree
well with those obtained the FEA.
In the case of medium sand, the surface displacement profiles
obtained by both the FEA and the SDE are shown in Fig. 7. The
comparison shows that the surface displacements obtained by the
FEA are higher than those calculated by the SDE. However beyond
20 m from the centerline of the tunnel, the surface displacement
calculated by the FEA has different shape than this calculated by
the SDE. The result reveals that the surface settlement profile
obtained by the SDE does not agree well with those obtained the
FEA.
Fig. 8 shows the comparison between the results obtained by the
FEA with those obtained by the SDE for dense sand. The
comparison indicates that the surface displacement profile
computed by the FEA has the same trend as the surface
displacement profile calculated by the SDE. It is also observed that
the surface displacements calculated by the FEA are larger than
those calculated by the SDE in the region beyond 20 m from the
centerline of the tunnel. In the region between the centerline of the
tunnel and 20 m from centerline of the tunnel, the surface
displacements calculated by the FEA is the same as those calculated
by the SDE. Generally, the results obtained by the FEA agree well
with those obtained by the SDE.
Fig. 9 also shows the comparison between the results obtained by
the FEA with those obtained by the SDE for dense sand. The
comparison again shows that the surface displacement profile
computed by the FEA has the same trend as the surface
displacement profile calculated by the SDE. It is also observed that
the surface displacements calculated by the FEA are larger than
those calculated by surface displacement equation in the region
