790
Proceedings of the 18
th
International Conference on Soil Mechanics and Geotechnical Engineering, Paris 2013
analysis often requires excessive computation resources (both
storage and time). During tunnel construction, a volume of soil
squeezing into the opening creates deformations around and
above the tunnel, which cannot be simulated directly in 2D
finite element analysis. Hence, various methods have been
proposed to take account of the stress and strain changes ahead
of the tunnel face when adopting 2D plane strain analyses to
simulate tunnel construction (Karakus 2007).
In this study, a two-dimensional finite element multistep
simulation model for shield-driven tunnel excavation is
presented. The model takes into account all relevant
components of the construction process as separate components
in model (including: soil and ground water, tunnel lining and
tail void grouting). The buildings were simulated by an elastic
beam at the surface of the models. Each surface beam has an
equivalent moment of inertia (I) and thickness (t) representing
the associate building. The surrounding soil above the ground
water level was discretized by 4-node first order fully integrated
continuum elements (CPE4) and the tunnel liner and elastic
beams (representing buildings) simulated as 2-node linear
Timoshenko beam elements. The under groundwater soil and
the grout material are modelled as saturated porous media using
pore pressure elements (CPE4P). The time dependence of the
grout material characteristics due to hydration is modelled in a
simplified manner by employing a time-dependent Young’s
modulus and Poisson’s ratio. The soil behavior is assumed to be
governed by an elastic perfectly-plastic constitutive relation
based on the Mohr–Coulomb criterion with a non-associative
flow rule.
The behavior of lining concrete is assumed to be linearly
elastic with properties which are usual for C45/55 concrete
(E=36000MPa, υ=0.2). For considering decrease of rigidity at
segment joints, a transfer ratio of bending moment is
introduced. This aspect is transferred to numerical analyses with
Correction of the elastic modulus of the ring, according to
modification factor
ζ=0.3
:
Mpa
E
E
CLS
25200
36000
)3.01(
) 1(
c
(1)
Where
E
c
is the virtual modulus of the ring and
E
cls
is the
concrete modulus. During the parametric studies, the geological
features were considered unchanged and similar to the Tabriz
metro line2 site conditions that described later. The ground
water ingress into the tunnels during construction phase is not
considered in this study. The excavation and construction of the
tunnel are simulated in 5 stages. In the first phase, the geostatic
equilibrium achieved and in second step the building is
constructed, but the corresponding deformations are not taken
into account in further steps. In excavation step inside the tunnel
the soil is excavated by de-activating the corresponding volume
elements and allows that the tunnel border moves radialy
accordance with overcutting value. In next step, the lining
installed and grout elements are activated in the fluid state
simultaneous with application of the injection pressure. After
installing step the injection pressure removed and the
mechanical characteristic of grout elements changed to
hardened one. Based on similar projects, under good operative
conditions, time duration of excavation step considered 5400
seconds and the time of lining ring erection considered 900s.
Boundary conditions, element types and mesh density of the
numerical models were selected based on several sensitivity
analyses as not to influence the results. The finite-element mesh
extends to a depth of two times the tunnel diameter (
D
) below
the tunnel spring line and laterally to a distance of 6
D
from the
tunnel centerline. The locations of the lateral and bottom
boundaries are selected so that the presence of the artificial
boundaries does not significantly influence the stress-strain-pore
pressure field in the domain. The modelled domain was 120 m
in width and 45 m in depth, consisting approximately 10,000
nodes and 2,000 elements.
3 CHARACTERISTICS OF TABRIZ METRO LINE 2
Tabriz with 160
km
2
area and the population about 1,600,000 is
one of most populated and important cities in northwestern of
Iran. TURL2 about 22 km in length will connect eastern part of
the city to its western part. This line comprises a single tunnel
which has been constructed using one earth pressure balance
EPB-TBM with a cutting-wheel diameter of 9.49 m and a shield
with external diameter of 9.46 m in front of shield that induce
overcut equal to 1.5 cm in each side of shield. For lining of the
tunnel, 35 cm-thick precast concrete segments with a length of
150 cm are installed just behind the shield.
Geologically, in central part of the route, based on conducted
studies in the corridor of TURL2, soil is mainly silt with low
plasticity (ML) and silty sand (SM) and water table is about 9m
deep. Geotechnical specifications used for soil layers of the
models are presented in Table1. Mechanical properties of tunnel
liner and tail void grout, utilized in the numerical simulations,
are summarized in Table2.
Table1. Geotechnical specifications used for soil layers of the model
ID
Dry
density
(KN/m
3
)
Wet
density
(KN/m
3
)
Elastic
modulus
(kPa)
Cohesion
(kPa)
Internal
friction
angle
Dialation
angle
SM 16.25
20
40000
7
34
3
ML
16.8
20.35
25000
17
25
0
In general the grout pressure value considered 0.5 bar more
than applied face support pressure. Therefore, the required face
pressure for each model calculated and in accordance with
calculated value, the grout pressure adopted for each model.
Table 2. Material properties used in numerical simulations
Material
Unit
weight
(KN/m3)
Compressive
strength
(MPa)
Elastic
modulus
(MPa)
Poisson
ratio
Tunnel liner concrete
25
40
25200
0.2
Tail void grout (fluid)
18
0
5
0.47
Tail void grout (hardened)
18
3
20
0.3
4 PARAMETRIC STUDIES
The effects of building’s geometry, position and weight on
lining loads were studied. Four types of 3, 5, 8 and 10 story
buildings above the center of the tunnel were modelled to apply
the effect of surface buildings weight. For each floor, 10 kN/m2
was considered as weight load. In addition study of geometry
effect on the model turned out to be possible through modelling
of buildings with different width and different distance from
tunnel center. The lining stresses of tunnel bored in coarse
grained sand overlain by soft soil layer are compared to induced
stresses in lining of tunnel in a homogeneous sandy soil. The
values of above parameters have been selected based on Tabriz
metro line 2 data and its urban conditions, as introduced in
Table 3.
Table 3. Factors and their values used in parametric studies
Parameter
Description
Values
Z
0
Tunnel center depth
13.8m ,18.4m, and 23m (according to
C/D=1, C/D=1.5 and C/D=2 respectively)
W
Building weight
30, 50, 80 and 100 (KN/m
2
)
B
Buildings width
10, 15, 20, 30 and 40m
E
Distance between tunnel
and building centers
0, 10, 20, 30 and 40m
L
Edge to edge distance
between buildings
15 m, 20 m, 30m, 40m (corresponding
to width of the streets along the route)
