IJARE151191422736200

15 Advances in Railway Engineering, An International Journal
Vol.3/ No.1/ Winter and Spring 2015
Numerical Investigation on Effects of Deep Excavations’ Posi-
tion on Existing Metro Tunnels in Urban Areas
H. Abbasi*1
; H. Katebi2
, M. Hajialilue Bonab3
1
M.Sc. in Geotechnical Civil Engineering, University of Tabriz, Tabriz, Iran
2
Associated Professor, Department of Civil Engineering, University of Tabriz, Tabriz, Iran,
katebi@tabrizu.ac.ir
3
Associated Professor, Department of Civil Engineering, University of Tabriz, Tabriz, Iran
Received: 21.02.2015 Accepted: 05.10.2015
Abstract:
Nowadays deep excavations are needed for construction of foundation of high rise buildings, providing space for
parking and etc. In some cases deep excavations may be constructed in the vicinity of the subway tunnels and causes
unpredicted extra displacements and internal forces in tunnel lining of tunnels which were not designed for them and
consequently affect serviceability of tunnel. Therefore in order to avoid structural damages, comprehensive studies
should be carried out when the excavation is located in adjacent of tunnel and necessary precautions should be ad-
opted. In this paper 2D FDM software FLAC 2D was used for modeling and investigating the effects of excavations
on existing tunnels in sand layer. In this analysis it is assumed that the cross section of tunnel is circular and tunnel
exists before deep excavation and also stress relaxation in the soil body around tunnel was taken into account before
installation of tunnel lining. In this study different locations of excavation with respect to the tunnel were taken into
account and effects of excavation on induced displacements and changes of internal forces of tunnel lining have been
studied. Diaphragm wall is used for retaining of excavation and in the analyses Mohr- Coulomb constitutive model is
used for soil body. The results of 2D numerical analyses show that when tunnel is located in the outside of the excava-
tion, because of the shielding effect of the diaphragm wall, excavation has less effect on tunnel in comparison with the
tunnel which is located below the excavation.
Keywords: Deep Excavation, Tunnel, Numerical Modeling, Finite Difference Method.
* Corresponding Author

16Advances in Railway Engineering, An International Journal
1. Introduction
Deep excavation is an important issue in geotechnical
civil engineering, for example, in the construction of
foundation or basement of a high rise building, subways
or mass rapid transit systems, etc. It is inevitable to use
deep excavation. Economic development and urbaniza-
tion make excavations go deeper and larger and some-
times they are carried out in difficult soils. These con-
ditions usually aren’t discussed in general engineering
courses and require advanced analysis such as numerical
methods (Ou, 2006).In order to investigate the effects of
deep excavations on existing tunnels, many researches
have been performed. In some cases researchers have
compared field monitoring results with numerical analy-
sis results and some others only have carried out numeri-
cal simulations.Sharma et al. (2001) have investigated a
deep and large excavation in the vicinity of twin MRT
tunnels in Singapore using CRISP finite element soft-
ware. Also a monitoring system was used for monitoring
displacement of tunnels. Results showed that in general,
computed displacements are larger than measured values
but trends are quite similar. Dolezalova (2001) carried out
a research to investigate effects of deep excavation for
an office block on the underlying tunnel complex using
2D finite element software CRISP. It was reported that
deep excavations have not considerable effect on some
tunnel but in some cases decrease of cracking resistance
and watertightness in tunnel lining was predicted. Also
field measurements was carried out during construction
of deep excavation and a good agreement was reported
between results of numerical analysis and filed monitor-
ing results. Chang et al. (2001) have studied the response
of Taipei Rapid Transit System (TRTS) tunnel to adjacent
excavation. In the study, it is reported that a section of
tunnel in the Panchiao Line was damaged as a result of
adjacent excavation. Also, Cracks had appeared in rein-
forced concrete segments, the concrete slab on the invert
was displaced and detached from the segment. Hu et al.
(2003) have presented the design and construction of a
deep excavation that was located above and beside the
Shanghai Metro tunnels. The paper has discussed some
controlling measures for soil and tunnel deformation. The
measures included concrete diaphragm wall, pumping
consolidation, soil- cement mix pile system and rational
excavation procedures.
Karki (2006) has carried out parametric study on the
effects of deep excavation on circular tunnels in fine-
grained soils using 2D finite element software Plaxis
based on Tan Tock Seng Hospital (TTSH) excavation
project in Singapore. The excavation was close to MRT
twin tunnels. In this study the effect of Young’s modu-
lus and undrained shear strength of soil and also stiff-
ness of diaphragm wall and tunnel lining as parameters
of displacements and internal forces of tunnel was inves-
tigated. Zheng and Wei (2008) have carried out numerical
analyses on influence of pit excavation on existing tun-
nel using 2D finite element software ABAQUS. Modi-
fied cam-clay model was used for modeling silty clay
soil. Result showed that for tunnels located outside the
wall, it experiences more slight distortion during exca-
vation. Chen et al. (2011) have carried out a numerical
study on the movement of existing tunnel due to deep
excavation in Shanghai. In the study, 2D finite element
software, ABAQUS, is used to simulate the behavior of
soft clay with considering nonlinearity of soil. The in-
fluence of some factor, including the excavation proce-
dure and installation of resistance piles are investigated.
Also, the results of numerical analysis are compared with
the results of field measurements. As a result of study,
constructing of small pits close to the tunnel can reduce
the influence of large pit excavation. Huang et al. (2011)
have carried out a parametric study on the influence of
deep excavation on nearby existing tunnels in soft soil of
Shanghai using 3D finite element software Plaxis-GiD.
Results revealed that the influence of excavation on the
underlying tunnel is significant in a distance which is
about five times the excavation width measured along the
tunnel axis. Ding et al. (2012) studied the affection of
foundation pit excavation on metro tunnel using 3D finite
element analysis software MIDASGTS. In this research
induced displacements and internal force of tunnel lining
due to deep excavation was investigated and reported that
effect of excavation on tunnel is not considerable when
distance between excavation and tunnel in more than 4
times of tunnel diameter.
2. Characterization of deformation of the
tunnel lining
Deep excavations adjacent to existing structures such as
tunnels, raft foundations or pile foundations, are highly

complex soil-structure-interaction problem because of
the many different construction processes involved and
highly variable ground conditions. It is often difficult to
visualize the mechanism of ground deformation around
the deep excavation as well as around the existing struc-
tures (Karki, 2006).
Depending on the relative position of deep excavation
and tunnel, response of tunnel to ground movement will
be different. Fig. 1 shows the response of tunnel to the
movement of surrounding ground when the excavation is
located beside and above the tunnel.
When the excavation is located beside the tunnel, retain-
ing wall and the soil behind the wall move towards the
excavation pit and consequently cause the tunnel lining
moves towards the excavation.
The movement of tunnel is accompanied by horizontal
unloading so the horizontal stress at tunnel spring be-
comes smaller and results in distortion of tunnel lining.
Similarly vertical movements and unloading is occurred
when the excavation pit is constructed above the tunnel.
During excavation, vertical unloading is occurred in the
bottom of pit and causes the bottom of excavation to
heave.
Consequently soil and tunnel under excavation move
upward and circular cross section of tunnel distorted to
oval-shaped.
So the effect of deep excavation on tunnel is taken into
account in two aspects:
1- Displacements of tunnel lining
2- Distortion of tunnel lining
In the current study, only the influence of deep excava-
tion on displacements of tunnel lining was investigated
in uniform sand soils layer.
the relative position of deep excavation and tunnel, response of tunnel to ground movement will be
1 shows the response of tunnel to the movement of surrounding ground when the excavation is located
ve the tunnel.
vation is located beside the tunnel, retaining wall and the soil behind the wall move towards the
and consequently cause the tunnel lining moves towards the excavation. The movement of tunnel is
y horizontal unloading so the horizontal stress at tunnel spring becomes smaller and results in distortion
. Similarly vertical movements and unloading is occurred when the excavation pit is constructed above
ing excavation, vertical unloading is occurred in the bottom of pit and causes the bottom of excavation
equently soil and tunnel under excavation move upward and circular cross section of tunnel distorted
deep excavation on tunnel is taken into account in two aspects:
cements of tunnel lining
tion of tunnel lining
study, only the influence of deep excavation on displacements of tunnel lining was investigated in
oils layer.
Fig 1. Displacement and distortion of tunnel lining due to adjacent excavation.
ion’s Code of Practice for Railway Protection does not allow the construction work in close distance
hat can displace the tunnels by more than 15 mm. According to codes in order to safe operation of
, allowable deformations of existing tunnel are specified and includes (Sharma et al., 2001):
solute displacement of tunnel should be less than 20 mm;
ave displacement of tunnel invert should be less than 15 mm;
Fig 1. Displacement and distortion of tunnel lining
due to adjacent excavation.
MRT Corporation’s Code of Practice for Railway Pro-
tection does not allow the construction work in close
distance of the tunnels that can displace the tunnels by
more than 15 mm. According to codes in order to safe
operation of subway tunnels, allowable deformations of
existing tunnel are specified and includes (Sharma et al.,
2001):
1- the absolute displacement of tunnel should be less than
20 mm;
2- the heave displacement of tunnel invert should be less
than 15 mm;
3- The distortion ratio should be less than 1/2500.
So it is important to control the displacements of tunnel
lining and deformation of surrounding soil mass in con-
struction phase of excavation.
3. Materials and soil parameters
3.1. Constitutive model for soil
In the analysis, in order to model the soil, Mohr- Cou-
lomb constitutive model is adopted.
This model is an elastic- perfectly plastic model and in
general, soil modeled with Mohr- Coulomb model be-
haves linearly in elastic range.
This does not present realistic behavior of soil, neverthe-
less it is a simple model that has been used most widely
over the past years.
Mohr- Coulomb model includes five parameters: two of
them (Young’s modulus, E and Poisson’s ratio, ) define
stress- strain behavior of soil. There are two strength pa-
rameters that define failure criteria (cohesion, C and the
friction angle, ) and also a parameter (dilation angle,) that
is used for modeling the volume changes in the shearing
(Ti et al., 2009).
3.2. Soil parameters
Soil used in numerical modeling was Berlin sand and pa-
rameters for that are presented in Table 1.
where is the Coefficient of lateral earth pressure at rest
and is estimated by following relation known as Jaky’s
relation:
K0 = 1 − sinφ (1)
In the literature Poisson’s ratio for Berlin sand has not been presented an
medium dense sand according to Table 2.
Table 1. Berlin sand parameters (Schweig
Soil type
𝛄𝛄
𝐊𝐊𝐊𝐊 𝐦𝐦𝟑𝟑⁄
𝛄𝛄𝐬𝐬𝐬𝐬𝐬𝐬
𝛗𝛗
𝐂𝐂
𝐊𝐊𝐊𝐊 𝐦𝐦𝟐𝟐⁄
Medium
19 20 35 0
(1)
In the literature Poisson’s ratio for Berlin sand has not
been presented and Poisson’s ratio is assumed for me-
dium dense sand according to Table 2.

Table 1. Berlin sand parameters (Schweiger, 2002)
4
= 1 − sinφ (1)
the literature Poisson’s ratio for Berlin sand has not been presented and Poisson’s ratio vs = 0.3 is assumed for
dium dense sand according to Table 2.
Soil type
𝛄𝛄
𝛗𝛗
𝐂𝐂
𝛙𝛙 𝐊𝐊𝟎𝟎 𝐯𝐯𝐬𝐬
Medium
dense sand
19 20 35 0 5 0.426 0.3
Table 2. Poisson’s ratio for granular soil (Das, 2008)
Soil type Range of Poisson’s ratio
Loose sand 0.2- 0.4
Medium dense sand 0.25- 0.4
Dense sand 0.3- 0.45
Silty sand 0.2- 0.4
Sand and gravel 0.15- 0.35
e dilation angle was determined by the following expression:
≈ φ − 30 (2)
ere φ is the internal friction angle of granular soil (Khoiri, 2013).
riable Young’s modulus with respect to depth is assigned for uniform Berlin sand according to following relations
chweiger, 2002):
Es = 20000√Z (KPa) for 0 < Z < 20m
Es = 60000√Z (KPa) for Z > 20m
ere Z is depth below surface.
3. Diaphragm wall and tunnel lining parameters
e diaphragm wall as a retaining system is used for stability of excavation pit. The thickness of the diaphragm wall
0.80 m and its depth is 25 m. Table 3. shows required parameters for numerical modeling of wall. The wall’s
rameters are adopted from an excavation project in Berlin that presented for studying and research purpose
chweiger, 2002).
Also, the dimensions and geometric properties of tunnel in current study are selected based on 2nd
Line of Tabriz
etro Tunnel properties. This Subway line is designed as a single tunnel and constructing by tunnel boring machine
BM).
It is assumed that cross section of tunnel is circular and the radius of excavated Tunnel equals 5m. Table 4. shows
e parameters of tunnel lining.
The wall and tunnel lining is modeled by beam element.
4.Model parameter for soil- structure interaction
4
ature Poisson’s ratio for Berlin sand has not been presented and Poisson’s ratio vs = 0.3 is assumed for
ense sand according to Table 2.
Soil type
𝛄𝛄
𝛗𝛗
𝐂𝐂
Medium
dense sand
19 20 35 0 5 0.426 0.3
Loose sand 0.2- 0.4
Silty sand 0.2- 0.4
n angle was determined by the following expression:
30 (2)
the internal friction angle of granular soil (Khoiri, 2013).
Young’s modulus with respect to depth is assigned for uniform Berlin sand according to following relations
r, 2002):
Es = 20000√Z (KPa) for 0 < Z < 20m
Es = 60000√Z (KPa) for Z > 20m
depth below surface.
phragm wall and tunnel lining parameters
ragm wall as a retaining system is used for stability of excavation pit. The thickness of the diaphragm wall
and its depth is 25 m. Table 3. shows required parameters for numerical modeling of wall. The wall’s
are adopted from an excavation project in Berlin that presented for studying and research purpose
r, 2002).
the dimensions and geometric properties of tunnel in current study are selected based on 2nd
Line of Tabriz
nel properties. This Subway line is designed as a single tunnel and constructing by tunnel boring machine
ssumed that cross section of tunnel is circular and the radius of excavated Tunnel equals 5m. Table 4. shows
eters of tunnel lining.
wall and tunnel lining is modeled by beam element.
el parameter for soil- structure interaction
The dilation angle was determined by the following ex-
pression:
4
In the literature Poisson’s ratio for Berlin sand has not been presented and Poisson’s ratio vs = 0.3 is assumed for
medium dense sand according to Table 2.
Soil type
𝛄𝛄
𝛗𝛗
𝐂𝐂
Medium
dense sand
19 20 35 0 5 0.426 0.3
Loose sand 0.2- 0.4
Silty sand 0.2- 0.4
The dilation angle was determined by the following expression:
ψ ≈ φ − 30 (2)
where φ is the internal friction angle of granular soil (Khoiri, 2013).
Variable Young’s modulus with respect to depth is assigned for uniform Berlin sand according to following relations
(Schweiger, 2002):
Es = 20000√Z (KPa) for 0 < Z < 20m
Es = 60000√Z (KPa) for Z > 20m
where Z is depth below surface.
3.3. Diaphragm wall and tunnel lining parameters
The diaphragm wall as a retaining system is used for stability of excavation pit. The thickness of the diaphragm wall
is 0.80 m and its depth is 25 m. Table 3. shows required parameters for numerical modeling of wall. The wall’s
parameters are adopted from an excavation project in Berlin that presented for studying and research purpose
(Schweiger, 2002).
Also, the dimensions and geometric properties of tunnel in current study are selected based on 2nd
Line of Tabriz
Metro Tunnel properties. This Subway line is designed as a single tunnel and constructing by tunnel boring machine
(TBM).
It is assumed that cross section of tunnel is circular and the radius of excavated Tunnel equals 5m. Table 4. shows
the parameters of tunnel lining.
The wall and tunnel lining is modeled by beam element.
3.4.Model parameter for soil- structure interaction
(2)
where is the internal friction angle of granular soil (Kho-
iri, 2013).
Variable Young’s modulus with respect to depth is as-
signed for uniform Berlin sand according to following
relations (Schweiger, 2002):
4
Poisson’s ratio for Berlin sand has not been presented and Poisson’s ratio vs = 0.3 is assumed for
sand according to Table 2.
Soil type
𝛄𝛄
𝛗𝛗
𝐂𝐂
Medium
dense sand
19 20 35 0 5 0.426 0.3
Loose sand 0.2- 0.4
Silty sand 0.2- 0.4
gle was determined by the following expression:
(2)
nternal friction angle of granular soil (Khoiri, 2013).
’s modulus with respect to depth is assigned for uniform Berlin sand according to following relations
02):
Es = 20000√Z (KPa) for 0 < Z < 20m
Es = 60000√Z (KPa) for Z > 20m
h below surface.
gm wall and tunnel lining parameters
wall as a retaining system is used for stability of excavation pit. The thickness of the diaphragm wall
ts depth is 25 m. Table 3. shows required parameters for numerical modeling of wall. The wall’s
adopted from an excavation project in Berlin that presented for studying and research purpose
02).
imensions and geometric properties of tunnel in current study are selected based on 2nd
Line of Tabriz
roperties. This Subway line is designed as a single tunnel and constructing by tunnel boring machine
ed that cross section of tunnel is circular and the radius of excavated Tunnel equals 5m. Table 4. shows
of tunnel lining.
nd tunnel lining is modeled by beam element.
arameter for soil- structure interaction
where Z is depth below surface.
3.3. Diaphragm wall and tunnel lining parameters
The diaphragm wall as a retaining system is used for stabil-
ity of excavation pit. The thickness of the diaphragm wall
is 0.80 m and its depth is 25 m. Table 3. shows required
parameters for numerical modeling of wall.The wall’s pa-
rameters are adopted from an excavation project in Berlin
that presented for studying and research purpose (Schwei-
ger, 2002).Also, the dimensions and geometric properties
of tunnel in current study are selected based on 2nd
Line of
Tabriz Metro Tunnel properties. This Subway line is de-
signed as a single tunnel and constructing by tunnel boring
machine (TBM).It is assumed that cross section of tunnel
is circular and the radius of excavated Tunnel equals 5m.
Table 4. shows the parameters of tunnel lining.The wall
and tunnel lining is modeled by beam element.
3.4. Model parameter for soil- structure interaction
There are several instances in geomechanics in which it is
desirable to represent planes on which sliding or separa-
tion can occur. Separation between either tunnel lining
and surrounded soil or diaphragm wall and soil are such
a good examples. In these case, interface element is ap-
plied for connection between soil and structure.FLAC
provides interfaces that are characterized by coulomb
sliding and/or tensile separation. Interfaces have the
properties of shear strength (S), normal stiffness (kn
) and
shear stiffness (ks
), and tensile strength (T) (Itasca, 2000).
It is considerable that for cohesionless soils T=0 and S is
specified as a function of interface friction angle ().In this
study, it is assumed that for medium-dense sand against
concrete, (Green et al., 2008) A schematic of interface
element is presented in Fig 2.
There are several instances in geomechanics in which it is desirable to represent planes on which sliding or
can occur. Separation between either tunnel lining and surrounded soil or diaphragm wall and soil are su
examples. In these case, interface element is applied for connection between soil and structure.
FLAC provides interfaces that are characterized by coulomb sliding and/or tensile separation. Interface
properties of shear strength (S), normal stiffness (kn) and shear stiffness (ks), and tensile strength (T) (Itasca
is considerable that for cohesionless soils T=0 and S is specified as a function of interface friction angle (𝜑𝜑𝑖𝑖
𝛿𝛿). In this study, it is assumed that for medium-dense sand against concrete, 𝛿𝛿 = 31(Green et al., 2008) A
of interface element is presented in Fig 2.
Fig 2. Schematic of finite difference interface element (Green et al., 2008)
As a rule-of-thumb, it should be set to 10 times of the equivalent stiffness of the stiffest neighboring zo
2000).
𝐾𝐾𝑛𝑛 = 10 (max [
𝐾𝐾+
4
3
𝐺𝐺
∆𝑧𝑧 𝑚𝑚𝑚𝑚 𝑚𝑚
]) (3)
In the equation (3), K and G are the bulk and shear modulus of soil and according to Fig. 3, ∆𝑧𝑧𝑚𝑚𝑚𝑚𝑚𝑚 is th
width of zone in the normal direction of interface surface.
Fig 3. Zone dimension used in stiffness calculation
The properties of interface element are presented in table 5.
3.5. Struts parameters
The most types of wall alone can rarely resist earth pressure and additional bracing systems are required.
horizontal struts in front of retaining walls to resist the earth pressure on the back of walls is called t
excavation method (Ou, 2006). Struts are one of several bracing systems.
In the numerical modeling of this study the diaphragm wall is supported by 4 levels of w-section steel
4.5 m horizontal spacing. Parameters for steel section used for struts are presented in table 6. Contact poin
strut and diaphragm wall were not rigid and a pin connection is defined to permit free rotation in the c
between strut and wall.
Fig 2. Schematic of finite difference interface element
(Green et al., 2008)
As a rule-of-thumb, it should be set to 10 times of the
equivalent stiffness of the stiffest neighboring zone (Itas-
ca, 2000).
There are several instances in geomechanics in which it is desirable to
can occur. Separation between either tunnel lining and surrounded s
examples. In these case, interface element is applied for connection b
FLAC provides interfaces that are characterized by coulomb slid
properties of shear strength (S), normal stiffness (kn) and shear stiffne
is considerable that for cohesionless soils T=0 and S is specified as a
𝛿𝛿). In this study, it is assumed that for medium-dense sand against co
Fig 2. Schematic of finite difference interface el
As a rule-of-thumb, it should be set to 10 times of the equivalent
2000).
𝐾𝐾+
4
3
𝐺𝐺
]) (3)
In the equation (3), K and G are the bulk and shear modulus of s
Fig 3. Zone dimension used in stif
The most types of wall alone can rarely resist earth pressure and ad
horizontal struts in front of retaining walls to resist the earth pres
excavation method (Ou, 2006). Struts are one of several bracing syst
(3)
In the equation (3), K and G are the bulk and shear modu-
lus of soil and according to Fig. 3, is the smallest width
of zone in the normal direction of interface surface.
There are several instances in geomechanics in which it is desirable to represent planes on which sliding or se
can occur. Separation between either tunnel lining and surrounded soil or diaphragm wall and soil are such
examples. In these case, interface element is applied for connection between soil and structure.
FLAC provides interfaces that are characterized by coulomb sliding and/or tensile separation. Interfaces
properties of shear strength (S), normal stiffness (kn) and shear stiffness (ks), and tensile strength (T) (Itasca,
is considerable that for cohesionless soils T=0 and S is specified as a function of interface friction angle (𝜑𝜑𝑖𝑖 𝑖𝑖𝑖𝑖
𝛿𝛿). In this study, it is assumed that for medium-dense sand against concrete, 𝛿𝛿 = 31(Green et al., 2008) A sc
Fig 2. Schematic of finite difference interface element (Green et al., 2008)
As a rule-of-thumb, it should be set to 10 times of the equivalent stiffness of the stiffest neighboring zone
2000).
𝐾𝐾+
4
3
𝐺𝐺
]) (3)
In the equation (3), K and G are the bulk and shear modulus of soil and according to Fig. 3, ∆𝑧𝑧𝑚𝑚𝑚𝑚𝑚𝑚 is the
The most types of wall alone can rarely resist earth pressure and additional bracing systems are required. I
horizontal struts in front of retaining walls to resist the earth pressure on the back of walls is called th
excavation method (Ou, 2006). Struts are one of several bracing systems.
In the numerical modeling of this study the diaphragm wall is supported by 4 levels of w-section steel st
4.5 m horizontal spacing. Parameters for steel section used for struts are presented in table 6. Contact point
strut and diaphragm wall were not rigid and a pin connection is defined to permit free rotation in the co
between strut and wall.
The most types of wall alone can rarely resist earth pres-

sure and additional bracing systems are required. Install-
ing horizontal struts in front of retaining walls to resist
the earth pressure on the back of walls is called the braced
excavation method (Ou, 2006). Struts are one of several
bracing systems.In the numerical modeling of this study
the diaphragm wall is supported by 4 levels of w-section
steel struts with 4.5 m horizontal spacing. Parameters
for steel section used for struts are presented in table 6.
Contact point between strut and diaphragm wall were not
rigid and a pin connection is defined to permit free rota-
tion in the connection between strut and wall.
Table 3. Concrete diaphragm wall parameters
(Schweiger, 2002)Table 3. Concrete diaphragm wall parameters (Schweiger, 2002)
𝐄𝐄, 𝐊𝐊𝐊𝐊 𝐦𝐦𝟐𝟐⁄ 𝐀𝐀 , 𝐦𝐦𝟐𝟐 𝐈𝐈, 𝐦𝐦𝟒𝟒 𝐭𝐭, 𝐦𝐦 𝐯𝐯 𝐰𝐰, 𝐊𝐊𝐊𝐊 𝐦𝐦/𝐦𝐦⁄
3.00×107
0.80 0.04267 0.80 0.15 24
Table 4. Tunnel precast concrete lining parameters (Katebi and Sa’adeyn, 2010)
𝐄𝐄, 𝐊𝐊𝐊𝐊 𝐦𝐦𝟐𝟐⁄ 𝐀𝐀 , 𝐦𝐦𝟐𝟐
𝐈𝐈, 𝐦𝐦𝟒𝟒 𝐭𝐭, 𝐦𝐦 𝐯𝐯 𝐰𝐰, 𝐊𝐊𝐊𝐊 𝐦𝐦/𝐦𝐦⁄ 𝐑𝐑, 𝐦𝐦
3.15×107
0.35 0.00357 0.35 0.15 8.4 5
Table 5. Soil- structure interaction parameters
Interface 𝑲𝑲𝒏𝒏 , 𝑷𝑷𝑷𝑷
𝒎𝒎⁄ 𝑲𝑲𝒔𝒔 , 𝑷𝑷𝑷𝑷
𝒎𝒎⁄ 𝝋𝝋𝒊𝒊𝒊𝒊𝒊𝒊𝒊𝒊𝒊𝒊𝒊𝒊𝒊𝒊𝒊𝒊𝒊𝒊
Tunnel 4.85×109
4.85×108
31
Wall 4.04×109
4.04×108
31
Table 6. Steel struts parameters, H 400× 400 Profile (Ou, 2006)
𝐄𝐄, 𝐊𝐊𝐊𝐊 𝐦𝐦𝟐𝟐⁄ 𝐀𝐀 , 𝐦𝐦𝟐𝟐 𝐈𝐈𝐱𝐱,𝐜𝐜 𝐜𝐜𝟒𝟒 𝛒𝛒,𝐊𝐊𝐊𝐊 𝐦𝐦𝟑𝟑⁄
2.10×108
218.69 66621 7850
Table 7. Excavation’s dimensions in last studies
Researcher
Excavation
width, m
Excavation
depth, m
Tunnel
diameter, m
Sharma (2001) 140 15 6
Dolazelova (2001) 30 13 8-12
Karki (2006) 20 12 6
Zheng (2008) 40 8 6
Huang (2011) 10 11 6.2, 11
odification for wall and lining stiffness
hragm wall and tunnel lining is simulated with elastic beam elements. In FLAC 2D structural element logic
Table 4. Tunnel precast concrete lining parameters
(Katebi and Sa’adeyn, 2010)
Table 3. Concrete diaphragm wall parameters (Schweiger, 2002)
3.00×107
0.80 0.04267 0.80 0.15 24
3.15×107
0.35 0.00357 0.35 0.15 8.4 5
𝒎𝒎⁄ 𝝋𝝋𝒊𝒊𝒊𝒊𝒊𝒊𝒊𝒊𝒊𝒊𝒊𝒊𝒊𝒊𝒊𝒊𝒊𝒊
Tunnel 4.85×109
4.85×108
31
Wall 4.04×109
4.04×108
31
𝐄𝐄, 𝐊𝐊𝐊𝐊 𝐦𝐦𝟐𝟐⁄ 𝐀𝐀 , 𝐦𝐦𝟐𝟐 𝐈𝐈𝐱𝐱,𝐜𝐜 𝐜𝐜𝟒𝟒 𝛒𝛒,𝐊𝐊𝐊𝐊 𝐦𝐦𝟑𝟑⁄
2.10×108
218.69 66621 7850
Researcher
Excavation
width, m
Excavation
depth, m
Tunnel
diameter, m
Sharma (2001) 140 15 6
Dolazelova (2001) 30 13 8-12
Karki (2006) 20 12 6
Zheng (2008) 40 8 6
Huang (2011) 10 11 6.2, 11
6. Modification for wall and lining stiffness
e diaphragm wall and tunnel lining is simulated with elastic beam elements. In FLAC 2D structural element logic
𝐈𝐈, 𝐦𝐦𝟒𝟒 𝐭𝐭, 𝐦𝐦 𝐯𝐯 𝐰𝐰, 𝐊𝐊𝐊𝐊 𝐦𝐦/𝐦𝐦⁄
3.00×107
0.80 0.04267 0.80 0.15 24
3.15×107
0.35 0.00357 0.35 0.15 8.4 5
𝒎𝒎⁄ 𝝋𝝋𝒊𝒊 𝒊𝒊𝒊𝒊𝒊𝒊𝒊𝒊𝒊𝒊𝒊𝒊𝒊𝒊𝒊𝒊
Tunnel 4.85×109
4.85×108
31
Wall 4.04×109
4.04×108
31
𝐈𝐈𝐱𝐱,𝐜𝐜𝐜𝐜𝟒𝟒
𝛒𝛒,𝐊𝐊𝐊𝐊 𝐦𝐦𝟑𝟑⁄
2.10×108
218.69 66621 7850
Researcher
Excavation
width, m
Excavation
depth, m
Tunnel
diameter, m
Sharma (2001) 140 15 6
Dolazelova (2001) 30 13 8-12
Karki (2006) 20 12 6
Zheng (2008) 40 8 6
Huang (2011) 10 11 6.2, 11
ation for wall and lining stiffness
wall and tunnel lining is simulated with elastic beam elements. In FLAC 2D structural element logic
Table 6. Steel struts parameters, H 400× 400 Profile
(Ou, 2006)
𝐈𝐈, 𝐦𝐦𝟒𝟒 𝐭𝐭, 𝐦𝐦 𝐯𝐯 𝐰𝐰, 𝐊𝐊𝐊𝐊 𝐦𝐦/𝐦𝐦⁄
3.00×107
0.80 0.04267 0.80 0.15 24
3.15×107
0.35 0.00357 0.35 0.15 8.4 5
Tunnel 4.85×109
4.85×108
31
Wall 4.04×109
4.04×108
31
𝐈𝐈𝐱𝐱,𝐜𝐜𝐜𝐜𝟒𝟒
𝛒𝛒,𝐊𝐊𝐊𝐊 𝐦𝐦𝟑𝟑⁄
2.10×108
218.69 66621 7850
Researcher
Excavation
width, m
Excavation
depth, m
Tunnel
diameter, m
Sharma (2001) 140 15 6
Dolazelova (2001) 30 13 8-12
Karki (2006) 20 12 6
Zheng (2008) 40 8 6
Huang (2011) 10 11 6.2, 11
ation for wall and lining stiffness
3.00×107
0.80 0.04267 0.80 0.15 24
3.15×107
0.35 0.00357 0.35 0.15 8.4 5
Tunnel 4.85×109
4.85×108
31
Wall 4.04×109
4.04×108
31
𝐄𝐄, 𝐊𝐊𝐊𝐊 𝐦𝐦𝟐𝟐⁄ 𝐀𝐀 , 𝐦𝐦𝟐𝟐 𝐈𝐈𝐱𝐱,𝐜𝐜𝐜𝐜𝟒𝟒 𝛒𝛒,𝐊𝐊𝐊𝐊 𝐦𝐦𝟑𝟑⁄
2.10×108
218.69 66621 7850
Researcher
Excavation
width, m
Excavation
depth, m
Tunnel
diameter, m
Sharma (2001) 140 15 6
Dolazelova (2001) 30 13 8-12
Karki (2006) 20 12 6
Zheng (2008) 40 8 6
Huang (2011) 10 11 6.2, 11
dification for wall and lining stiffness
ragm wall and tunnel lining is simulated with elastic beam elements. In FLAC 2D structural element logic
3.6. Modification for wall and lining stiffness
The diaphragm wall and tunnel lining is simulated with
elastic beam elements. In FLAC 2D structural element
logic is based on plane- stress formulation but this struc-
ture is continuous in the direction perpendicular to analy-
sis plan, so elastic modulus of concrete wall and tunnel
lining needs modification to correspond to the plane-
strain model using following expression:
6
3.6. Modification for wall and lining stiffness
The diaphragm wall and tunnel lining is simulated with elastic beam eleme
is based on plane- stress formulation but this structure is continuous in the d
elastic modulus of concrete wall and tunnel lining needs modification to c
following expression:
EPlane strain =
E
1−υ2 (4)
where υ is the poisson’s ration of structural element (Green, 2008; Itasca
modification shouldn’t be applied for steel struts elements.
4. Finite difference method analysis
Numerical methods provide strong tools for predicting the behavior of so
engineering problems. In this study two- dimensional plane strain and Fini
for assessment of effects of deep excavations on existing tunnels.
(4)
where υ is the poisson’s ration of structural element
(Green, 2008; Itasca, 2000). It is remarkable that men-
tioned modification shouldn’t be applied for steel struts
elements.
4. Finite difference method analysis
Numerical methods provide strong tools for predicting
the behavior of soil and structures and solving geotechni-
cal engineering problems. In this study two- dimensional
plane strain and Finite difference program FLAC 2D are
used for assessment of effects of deep excavations on ex-
isting tunnels.
4.1. Modeling procedure
According to Fig. 4 process of numerical simulation for
parametric studies was carried out in 10 following steps:
1- Insitue str ess (K0
=1-sin)
2- Stepping to initial equilibrium state and reset displace-
ments to zero
3- Excavation of tunnel and 20% stress relaxation in tun-
nel boundary
4- Installation of tunnel lining and 100% stress relaxation
in tunnel boundary and reset displacements to zero
5- Activate diaphragm wall (wished- in- place) and set
displacements to zero
6- Excavate to depth of 3 m and construct the 1st
level of
strut
7- Excavate to depth of 6 m and construct the 2nd
level
of strut
8- Excavate to depth of 9 m and construct the 3rd
level
of strut
9- Excavate to depth of 12 m and construct the 4th
level
of strut
10- Excavate to depth of 15 m.
It is remarkable that in numerical simulation it is assumed
that the tunnel is constructed using tunnel boring machine
and the soils inside the tunnel are removed in one stage.
So before installation of lining some stress relaxation

(20%~ 30%) in tunnel boundaries is occurred (Mirzamo-
hammadi, 2010). An evaluation of numerical installa-
tion procedures for closed face shield tunnelling based
on ground response cure (GRC) indicates that in contrast
to open face tunnelling a relatively small stress reduc-
tion of around 20–30% is required (Moller and Vermeer,
2008). For simulation of stress relaxation in FLAC 2D
first tunnel boundary gridpoints are identified by fixing
in x- and y- direction and then x- and y- reaction forces
are recovered. Recovered reaction forces are reduced in
20% and after removing previous fixity conditions, 80%
reaction forces are applied to tunnel boundary gridpoints
in opposite direction and finally tunnel lining is installed
and complete relaxation is allowed (100% relaxation) to
develop loads in the lining (Itasca, 2000).
7
4.1. Modeling procedure
According to Fig. 4 process of numerical simulation for parametric studies was carried out in 10 following steps:
1) Insitue stress (K0=1-sinφ)
2) Stepping to initial equilibrium state and reset displacements to zero
3) Excavation of tunnel and 20% stress relaxation in tunnel boundary
4) Installation of tunnel lining and 100% stress relaxation in tunnel boundary and reset displacements to zero
5) Activate diaphragm wall (wished- in- place) and set displacements to zero
6) Excavate to depth of 3 m and construct the 1st
level of strut
7) Excavate to depth of 6 m and construct the 2nd
level of strut
8) Excavate to depth of 9 m and construct the 3rd
level of strut
9) Excavate to depth of 12 m and construct the 4th
level of strut
10) Excavate to depth of 15 m.
It is remarkable that in numerical simulation it is assumed that the tunnel is constructed using tunnel boring machine
and the soils inside the tunnel are removed in one stage. So before installation of lining some stress relaxation (20%~
30%) in tunnel boundaries is occurred (Mirzamohammadi, 2010). An evaluation of numerical installation procedures
for closed face shield tunnelling based on ground response cure (GRC) indicates that in contrast to open face tunnelling
a relatively small stress reduction of around 20–30% is required (Moller and Vermeer, 2008). For simulation of stress
relaxation in FLAC 2D first tunnel boundary gridpoints are identified by fixing in x- and y- direction and then x- and
y- reaction forces are recovered. Recovered reaction forces are reduced in 20% and after removing previous fixity
conditions, 80% reaction forces are applied to tunnel boundary gridpoints in opposite direction and finally tunnel
lining is installed and complete relaxation is allowed (100% relaxation) to develop loads in the lining (Itasca, 2000).
Fig 4. Details of construction and modeling procedure.
4.2. Modeling assumptions
Some assumptions were made in numerical modeling as following:
1) Because this paper only investigates the effects of deep excavation on tunnel so all displacements developed
in soil and structural elements due to tunneling and wall construction and displacement due to gravitational
loading set to zero before deep excavation.
2) Tunnel lining and diaphragm wall is modeled as wished- in- place, i.e. the deformations of ground during
installation of lining and construction of wall are neglected.
3) Linear elastic behavior was assumed for steel struts, concrete diaphragm wall and precast concrete tunnel
lining.
4) The mesh size is assumed 1 m× 1 m.
5) The analyses are carried out without the presence of groundwater.
Fig 4. Details of construction and modeling procedure.
4.2. Modeling assumptions
Some assumptions were made in numerical modeling as
following:
1- Because this paper only investigates the effects of deep
excavation on tunnel so all displacements developed in
soil and structural elements due to tunneling and wall
construction and displacement due to gravitational load-
ing set to zero before deep excavation.
2- Tunnel lining and diaphragm wall is modeled as
wished- in- place, i.e. the deformations of ground dur-
ing installation of lining and construction of wall are ne-
glected.
3- Linear elastic behavior was assumed for steel struts, con-
crete diaphragm wall and precast concrete tunnel lining.
4- The mesh size is assumed 1 m× 1 m.
5- The analyses are carried out without the presence of
groundwater.
6- It is assumed that in the modeling of tunnel lining seg-
ments there is no joint between segments and beam ele-
ments are considered as continues beam.
4.3. Verification
Finally, numerical results from this research were com-
pared with the results of Karki, R (2006) and Sharma J. S.
(2001) to verify the present numerical model. The results
of the FDM-analyses were in good conformity with these
results.
5. Parametric study
In order to assess the effects of deep excavation on tun-
nel, 27 different positions of tunnel with respect to deep
excavation was investigated and displacements of tunnel
lining due to excavation was obtained. Fig. 5 shows typi-
cal positions of tunnel with respect to deep excavation
where excavation width (we
) is equal 40m, (he
) is the ex-
cavation depth that equals 15m and tunnel radius (R) is
assumed 5m. The selected Dimensions for excavation’s
width and depth in this study are based on an average deal
of width and depth of excavations that are mentioned in
studied papers in introduction (Table 7).The parameters
for studies include horizontal distance between tunnel
center point and excavation centerline (dh
) that is varied
from 0 to 40m and vertical distance between tunnel crown
and diaphragm wall (dv
) that is varied from 2m to 10m.
Figs. 6, 7 Show the induced vertical displacements in
crown and invert of tunnel, respectively due to adjacent
excavation for different dh
and dv
. It can be seen that
maximum vertical displacement in tunnel lining occurred
in a position which tunnel is located between two dia-
phragm walls. When tunnel is located outside of excava-
tion pit, vertical displacements are considerably reduced.
Reduction in vertical displacement is occurred because
diaphragm wall acts as a shield for tunnel and controls
its deformation and displacement.According to results,
the induced vertical displacement of crown and invert of
tunnel due to above excavation reduced with increase of
tunnel buried depth. In reality the displacement of tunnel
lining depends on deformation of soil around it and with
increasing of depth, the effects of loading and unload-
ing on tunnel reduce and consequently tunnel lining dis-
places less in comparison with the tunnel which is close
to excavation bottom.

10
Fig 6. Vertical displacement of tunnel crown.
Fig 7. Vertical displacement of tunnel invert.
Fig 8. Horizontal displacement of tunnel crown.
Fig 6. Vertical d
isplacement of tunnel crown.
10
Fig 8. Horizontal displacement of tunnel crown.
10
Fig 8. Horizontal displacement of tunnel crown.Fig 8. Horizontal displacement of tunnel crown.
11
Fig 9. Horizontal displacement of tunnel invert.
Fig. 8 shows induced horizontal displacements of tunnel lining at the crown due to adjacent excavation. Results show
that when dh equals zero, i.e. when center point of tunnel and excavation center line coincide, because of symmetry in
geometry and symmetrical unloading in horizontal direction on tunnel crown, no displacement occurs in crown. Then
with increasing dh, horizontal displacements of tunnel crown increase and when tunnel is located under the diaphragm
wall, maximum horizontal displacement is occurred. In the outside of the excavation pit with increasing of dh,
horizontal displacements decrease. The cause of this reduction is the shielding effect of diaphragm wall on tunnel and
soil behind the wall.
According to Fig. 6, when tunnel is located between excavation centerline and diaphragm wall, with increasing of
buried depth of tunnel, horizontal displacements of crown decrease. But in the outside of pit the trend is reversible,
i.e. in outside of the pit with increasing tunnel depth, the horizontal displacements of tunnel crown increase, because
with increasing depth, tunnel distances from shielding effect area of diaphragm wall and can displaces easily in
horizontal direction.
Fig. 9 shows horizontal displacement of tunnel invert. With comparing Figs. 8, 9, it can be seen that horizontal
displacements of tunnel invert are similar to crown’s, when tunnel is located between pit centerline and diaphragm
wall. But in the tunnel invert trend of results for positions which tunnel is located in outside of pit are different from
crown, i.e. with increasing tunnel depth, the horizontal displacements of invert are reduced either when the tunnel is
located inside or outside of the excavation. Because, with increasing the depth of tunnel invert, it gets away from the
area in which more horizontal displacements are occurred.
Results of the study and comparison between computed displacements and allowable displacements show that
considerable displacement is induced in tunnel lining due to adjacent excavation but does not violated from allowable
displacement.
The investigation of effects of construction of deep excavation adjacent to existing tunnel is a complex soil-structure
interaction problem and the amount of displacements of soil and tunnel depend on many factors such as soil stiffness,
thickness of tunnel lining and diaphragm wall and etc. So in some cases displacements may be violate allowable
displacement. So, for detailed investigation of effects of excavations on existing tunnels further analyses should be
carried out.
6. Effects of excavation on the internal forces of tunnel lining
Fig. 10 shows the induced shear and axial forces and also bending moment on the tunnel lining due to surrounding
soil and other loading on it. As mentioned before, because of deep excavation adjacent to existing tunnel, the stresses
of soil around tunnel are disturbed and therefore results in changes in the internal forces of tunnel lining.
In order to determine the loading capacity of structural members that are subjected to axial force and bending moment,
the interaction curves are used. So, in order to investigate the effects of excavation on the internal forces of adjacent
tunnel, the interaction curve for lining section should be calculated and drawn.
Fig 9. Horizontal displacement of tunnel invert.
Fig. 8 shows induced horizontal displacements of tunnel
lining at the crown due to adjacent excavation. Results
show that when dh
equals zero, i.e.
when center point of tunnel and excavation center line
coincide, because of symmetry in geometry and symmet-
rical unloading in horizontal direction on tunnel crown,
no displacement occurs in crown. Then with increasing
dh
, horizontal displacements of tunnel crown increase and
when tunnel is located under the diaphragm wall, maxi-
mum horizontal displacement is occurred.
In the outside of the excavation pit with increasing of dh
,
horizontal displacements decrease.
The cause of this reduction is the shielding effect of dia-
phragm wall on tunnel and soil behind the wall. Accord-
ing to Fig. 6, when tunnel is located between excavation
centerline and diaphragm wall, with increasing of buried
depth of tunnel, horizontal displacements of crown de-
crease. But in the outside of pit the trend is reversible, i.e.
in outside of the pit with increasing tunnel depth, the hor-
izontal displacements of tunnel crown increase, because
with increasing depth, tunnel distances from shielding
effect area of diaphragm wall and can displaces easily
in horizontal direction.Fig. 9 shows horizontal displace-
8
6) It is assumed that in the modeling of tunnel lining segments there is no joint between segments and beam
elements are considered as continues beam.
4.3 Verification
Finally, numerical results from this research were compared with the results of Karki, R (2006) and Sharma J. S.
(2001) to verify the present numerical model. The results of the FDM-analyses were in good conformity with these
results.
5. Parametric study
In order to assess the effects of deep excavation on tunnel, 27 different positions of tunnel with respect to deep
excavation was investigated and displacements of tunnel lining due to excavation was obtained. Fig. 5 shows typical
positions of tunnel with respect to deep excavation where excavation width (we) is equal 40m, (he) is the excavation
depth that equals 15m and tunnel radius (R) is assumed 5m. The selected Dimensions for excavation’s width and depth
in this study are based on an average deal of width and depth of excavations that are mentioned in studied papers in
introduction (Table 7).
The parameters for studies include horizontal distance between tunnel center point and excavation centerline (dh) that
is varied from 0 to 40m and vertical distance between tunnel crown and diaphragm wall (dv) that is varied from 2m to
10m.
Figs. 6, 7 Show the induced vertical displacements in crown and invert of tunnel, respectively due to adjacent
excavation for different dh and dv. It can be seen that maximum vertical displacement in tunnel lining occurred in a
position which tunnel is located between two diaphragm walls. When tunnel is located outside of excavation pit,
vertical displacements are considerably reduced. Reduction in vertical displacement is occurred because diaphragm
wall acts as a shield for tunnel and controls its deformation and displacement.
According to results, the induced vertical displacement of crown and invert of tunnel due to above excavation reduced
with increase of tunnel buried depth. In reality the displacement of tunnel lining depends on deformation of soil around
it and with increasing of depth, the effects of loading and unloading on tunnel reduce and consequently tunnel lining
displaces less in comparison with the tunnel which is close to excavation bottom.
Fig 5. Typical positions of tunnel with respect to excavation pit.Fig 5. Typical positions of tunnel with respect to excavation pit.

ment of tunnel invert. With comparing Figs. 8, 9, it can
be seen that horizontal displacements of tunnel invert are
similar to crown’s, when tunnel is located between pit
centerline and diaphragm wall. But in the tunnel invert
trend of results for positions which tunnel is located in
outside of pit are different from crown, i.e. with increas-
ing tunnel depth, the horizontal displacements of invert
are reduced either when the tunnel is located inside or
outside of the excavation.
Because, with increasing the depth of tunnel invert, it
gets away from the area in which more horizontal dis-
placements are occurred.
Results of the study and comparison between computed
displacements and allowable displacements show that
considerable displacement is induced in tunnel lining due
to adjacent excavation but does not violated from allow-
able displacement.
The investigation of effects of construction of deep exca-
vation adjacent to existing tunnel is a complex soil-struc-
ture interaction problem and the amount of displacements
of soil and tunnel depend on many factors such as soil
stiffness, thickness of tunnel lining and diaphragm wall
and etc. So in some cases displacements may be violate
allowable displacement. So, for detailed investigation of
effects of excavations on existing tunnels further analy-
ses should be carried out.
6. Effects of excavation on the internal forces
of tunnel lining
Fig. 10 shows the induced shear and axial forces and also
bending moment on the tunnel lining due to surround-
ing soil and other loading on it. As mentioned before, be-
cause of deep excavation adjacent to existing tunnel, the
stresses of soil around tunnel are disturbed and therefore
results in changes in the internal forces of tunnel lining.
In order to determine the loading capacity of structural
members that are subjected to axial force and bending
moment, the interaction curves are used. So, in order to
investigate the effects of excavation on the internal forces
of adjacent tunnel, the interaction curve for lining sec-
tion should be calculated and drawn.Figs. 11, 12 Show
the precast reinforcement concrete for tunnel lining and
its interaction curve, respectively.
In order to study the effect of excavation on tunnel, the
horizontal distance between tunnel center and excavation
center (dh
), is assumed to be 0, 10, 20, 30 and 40 meters.
Also it is assumed that the tunnel is located 2 meters be-
low the wall.
For different positions of tunnel, axial force and bending
moment in the lining were calculated before deep exca-
vation and after excavation to depth -15.00 meters and
results are illustrated in Figs. 13-17.It can be seen from
results that the maximum changes and effects on the in-
ternal forces of tunnel lining are occurred, when tunnel
is located between excavation centerline and diaphragm
wall.
12
Figs. 11, 12 Show the precast reinforcement concrete for tunnel lining and its interaction curve, respectively.
In order to study the effect of excavation on tunnel, the horizontal distance between tunnel center and exc
center (dh), is assumed to be 0, 10, 20, 30 and 40 meters. Also it is assumed that the tunnel is located 2 meter
the wall.
For different positions of tunnel, axial force and bending moment in the lining were calculated before deep exc
and after excavation to depth -15.00 meters and results are illustrated in Figs. 13-17.
It can be seen from results that the maximum changes and effects on the internal forces of tunnel lining are o
when tunnel is located between excavation centerline and diaphragm wall.
Fig 10. Induced forces and moment in tunnel lining (Hashash et al., 2001).
Fig 11. Tunnel lining section (Ghasempour, 2008).
Fig 12. Interaction curve for tunnel lining section.
Fig 10. Induced forces and moment in tunnel lining
(Hashash et al., 2001).
Figs. 11, 12 Show the precast reinforcement concrete for tunnel lining and its interaction curve, respe
In order to study the effect of excavation on tunnel, the horizontal distance between tunnel center
center (dh), is assumed to be 0, 10, 20, 30 and 40 meters. Also it is assumed that the tunnel is located
the wall.
For different positions of tunnel, axial force and bending moment in the lining were calculated before
It can be seen from results that the maximum changes and effects on the internal forces of tunnel lini
Fig 12. Interaction curve for tunnel lining section.
12
Figs. 11, 12 Show the precast reinforcement concrete for tunnel lining and its interaction curve, respectively.
In order to study the effect of excavation on tunnel, the horizontal distance between tunnel center and exc
center (dh), is assumed to be 0, 10, 20, 30 and 40 meters. Also it is assumed that the tunnel is located 2 meter
the wall.
For different positions of tunnel, axial force and bending moment in the lining were calculated before deep exc
It can be seen from results that the maximum changes and effects on the internal forces of tunnel lining are o
Fig 12. Interaction curve for tunnel lining section.Fig 12. Interaction curve for tunnel lining section.

13
Fig 13. Bending moment and axial force in tunnel lining before and after excavation for dv=2 m, dh=0 m.
Fig 13. Bending moment and axial force in tunnel lining before and after excavation for dv
=2 m, dh
=0 m.
13
Fig 14. Bending moment and axial force in tunnel lining before and after excavation for dv=2 m, dh=10 m.Fig 14. Bending moment and axial force in tunnel lining before and after excavation for dv
=2 m, dh
=10 m.
Fig 15. Bending moment and axial force in tunnel lining before and after excavation for dv=2 m, dh=20 m.Fig 15. Bending moment and axial force in tunnel lining before and after excavation for dv
=2 m, dh
=20 m.

It can be seen from Fig. 18 that the lining segments which
used for tunnel, has high loading capacity against static
loads so the excavation adjacent to tunnel has not consid-
erable effect on the bending moment and axial forces of
lining. However these results have been obtained from
special circumstances and in order to get more exact re-
sults, it is necessary to simulate similar models with dif-
ferent soil stiffness and tunnel depth and also with differ-
ent dimension for excavation pit.
According to Fig. 18 it can be seen that the minimum
changes in internal forces are related to positions that the
tunnel is located in the outside of the excavation pit and
this is due to shieling effect of diaphragm wall. Also the
maximum effect is occurred when the tunnel is located in
the inside area of excavation pit.
14
15
It can be seen from Fig. 18 that the lining segments which used for tunnel, has high loading capacity against static
loads so the excavation adjacent to tunnel has not considerable effect on the bending moment and axial forces of
lining. However these results have been obtained from special circumstances and in order to get more exact results, it
is necessary to simulate similar models with different soil stiffness and tunnel depth and also with different dimension
for excavation pit.
According to Fig. 18 it can be seen that the minimum changes in internal forces are related to positions that the tunnel
is located in the outside of the excavation pit and this is due to shieling effect of diaphragm wall. Also the maximum
effect is occurred when the tunnel is located in the inside area of excavation pit.
=2 m, dh
=30 m.
=2 m, dh
=40 m.

16
parison of internal forces of lining before and after excavation for different positions of tunnel with
respect to the excavation.
16
Fig 18. The comparison of internal forces of lining before and after excavation for different positions of tunnel with
16
arison of internal forces of lining before and after excavation for different positions of tunnel with
16
Fig 18. The comparison of internal forces of lining before and after excavation for different positions of tunnel with
respect to the excavation.Fig 18. The comparison of internal forces of lining
before and after excavation for different positions of
tunnel with respect to the excavation.
7. Conclusions
2D FDM numerical modeling was used in order to in-
vestigate the effects of deep excavations on existing tun-
nel. Based on the study, following results are obtained;
it should be considered that following obtained results
are valid only for specific case in which some simplifier
assumptions (above mentioned) are applied in numerical
simulation.
1) Maximum vertical displacement in crown and
invert of tunnel occurs in position which tunnel is located
in the center of pit excavation.
2) Maximum horizontal displacement in tunnel in-
vert occurs when tunnel is located under the diaphragm
wall.
3) When tunnel is located between two diaphragm
walls, with increase in tunnel depth, horizontal displace-
ments of invert decreases, but in the outside of excava-
tion pit it is reversible.
4) In the outside of the excavation, because of
shielding effect of diaphragm wall, horizontal displace-
ments decrease.
5) Considerable influences can be induced in tun-
nel lining depending on different soil and structures prop-
erties.
6) Maximum changes in bending moment and
axial forces in tunnel lining are occurred when tunnel is
located in inside area of excavation, i.e. between two dia-
phragm walls.
References:
- Abbasi H (2013) "Investigation of effects of deep exca-
vations on tunnel in urban areas", M.Sc. thesis, Univer-
sity of Tabriz, Tabriz, Iran.
- Bolton M D (1986) "The Strength and Dilatancy of
Sands", Geotechnique 36, No. I.65578.
- Chang C T, Sun C W, Duann S W, Hwang R N (2001)
"Response of a Taipei Rapid Transit System (TRTS) tun-
nel to adjacent excavation", Tunnelling and Underground
Space Technology, 16: 151-158.
- Chen J J, Wang J H, Xiang G W, Wen S L, Du Y (2011)
"Numerical Study on the Movement of Existing Tun-

nel Due to Deep Excavation in Shanghai", Geotechnical
Engineering Journal of the SEAGS & AGSSEA Vol. 42
No.3: 30-40.
- Das B M (2008) "Advanced Soil Mechanics", Taylor
& Francis.
- Ding J, Xian Y and Liu T (2012) "Numerical Modeling
of Affection of Foundation Pit Excavation on Metro Tun-
nel", Advanced Materials Research Vols. 368-37: 2562-
2566.
- Dolezalova M (2001) "Tunnel Complex Unloaded by
a Deep Excavation", Computers and Geotechnics 28:
469–493.
- Ghasempour N (2008) "Comparing Stability of Single
and Twin Tunnels- Case Study of Tabriz Urban Railway
Line 2", M.Sc. thesis, University of Tarbiat Modares,
Tehran, Iran.
- Green R A, Olgun C G and Cameron W I (2008) "Re-
sponse and Modeling of Cantilever Retaining Walls Sub-
jected to Seismic Motions", Computer-Aided Civil and
Infrastructure Engineering 23:309–322.
- Hashash Y M A, Hook J J, Schmidt B and Yao J I-C
(2001) "Seismic design and analysis of underground
structures", Tunneling and Underground Space Technol-
ogy, Vol. 16: 247- 293.
- Hu Z F, Yue Z Q, Zhou J, and Tham L G (2003) "Design
and construction of a deep excavation in soft soils adja-
cent to the Shanghai Metro tunnels", Canadian Geotech-
nical Journal, 40:933-948.
- Huang X, Schweiger H F and Huang H (2011) "Influ-
ence of Deep Excavations on Nearby Existing Tunnels",
International Journal of Geomechanics.
- Itasca (2000) "FLAC (Fast LagrangianAnalysis of Con-
tinua) User’s Manuals", Itasca Consulting Group, Min-
neapolis, MN.
- Katebi H and Sa’adeyn M (2010) "Analysis and pre-
diction of ground surface settlement due to tunneling
(Case study: Tabriz 2nd
Line of Metro Tunnel)", Journal
of Transportation Engineering, V4: 67-75.
- Karki R (2006) "Effects of Deep Excavations on Circu-
lar Tunnels in Fine-Grained Soils", MS Thesis. Univer-
sity of Saskatchewan, Canada.
- Khoiri, M. and Ou, C-Y. (2013) "Evaluation of Defor-
mation Parameter for Deep Excavation in Sand Through
Case Histories", Computers and Geotechnics, 47: 57-67.
- Mirzamohammadi mamaghani M (2010) "Investigation
of Seismic behavior of Tabriz 2nd Line Subway Structure
Under Possible Earthquakes", M.Sc. thesis, University of
Tabriz, Tabriz, Iran.
- Moller S C, Vermeer P A (2008) "On numerical simula-
tion of tunnel installation", Tunnelling and Underground
Space Technology 23: 461–475.
- Ou C-Y (2006) "Deep Excavation: Theory and Prac-
tice", Taylor & Francis.
- Schweiger H F (2002) "Results from Numerical Bench-
mark Exercises in Geotechnics", Institute for Soil Me-
chanics and Foundation Engineering. Graz University of
Technology, Austria.
- Sharma, J. S., Hefny, A. M., Zhao, J. and Chan C W
(2001) "Effect of Large Excavation on Deformation of
Adjacent MRT", Tunnelling and Underground Space
Technology 16: 93-98.
- Ti K S, Huat B K, Noorzaei J, Jaafar M S and Sew G S
(2009) "A Review of Basic Soil Constitutive Models for
Geotechnical Application".
- Zheng G and Wei S W (2008) "Numerical Analyses of
Influence of Overlying Pit Excavation on Existing Tun-
nels", J. Cent South Univ. T., 15(2): 69-75.

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