Effect of Geometric Parameters and Construction Sequence on Ground Settlement of Offset Arrangement Twin Tunnels
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geosciences
Article
Effect of Geometric Parameters and Construction Sequence on
Ground Settlement of Offset Arrangement Twin Tunnels
Md Shariful Islam and Magued Iskander *
Department of Civil and Urban Engineering, Tandon School of Engineering, New York University,
Brooklyn, NY 11201, USA; msi247@nyu.edu
* Correspondence: Iskander@nyu.edu
Abstract: A parametric study that examines the ground surface settlement due to the excavation of
shallow offset arrangement twin tunnels is presented. Offset arrangement tunnels are those that
run parallel to each other, but at different elevations. The study focuses on the influence of both the
construction sequence and various geometric parameters on the induced soil settlement. A series
of three-dimensional finite element analyses was carried out to investigate the settlement behavior
and interactions between offset arrangement twin tunnels excavated in clay using a simplified
mechanized excavation method. Analyses were carried out for three cover-to-diameter (C/D) ratios,
three possible construction sequences, five angular relative positions, and five angular spacings. In
addition, settlement data were also investigated by varying horizontal and vertical spacings while
keeping the angular spacing constant. The total settlement of the excavated twin tunnels and the
settlement induced solely by the new second tunnel are both presented, and special attention was
paid to identifying the dominant geometric parameters. The observed data trends from this study
are generally consistent with the limited data available in the literature. This study confirmed a
few perceived behaviors. First, angular relative position better describes the settlement behavior
in comparison to angular spacing. Second, the effect of the vertical distance is noticeably more
Citation: Islam, M.S.; Iskander, M.
Effect of Geometric Parameters and
significant than that of the horizontal distance between the two tunnels. Third, excavation of the
Construction Sequence on Ground lower tunnel at first induces higher total ground settlement than when the upper tunnel is excavated
Settlement of Offset Arrangement first or when both tunnels are excavated concurrently. Fourth, settlement due to the construction
Twin Tunnels. Geosciences 2022, 12, 41. of the newer tunnel decreases with the increase in the cover depth. In addition, two design charts
https://doi.org/10.3390/ have been proposed to calculate the settlement induced from a new second tunnel excavation and
geosciences12010041 the eccentricity of the maximum total settlement relative to the center of the new tunnel.
Academic Editors: Mohamed Shahin
and Jesus Martinez-Frias
Keywords: cover-to-diameter ratio; settlement; three-dimensional numerical analysis; angular spac-
ing; angular relative position; construction sequence
Received: 2 December 2021
Accepted: 10 January 2022
Published: 14 January 2022
Publisher’s Note: MDPI stays neutral 1. Introduction
with regard to jurisdictional claims in The demand for reliable and environmentally sustainable infrastructure in major
published maps and institutional affil- urban centers increasingly requires the construction of twin tunnels, where two or more
iations.
new tunnels are often constructed near to each other. The same demands often result in
building new tunnels near or parallel to existing tunnels. Shallow twin tunnel construction,
particularly in soft ground, has the potential to cause deleterious ground settlements that
may damage existing buildings and sub-surface infrastructure located within the influence
Copyright: © 2022 by the authors.
Licensee MDPI, Basel, Switzerland.
zone. Choi and Lee [1] investigated the influence of the size of an existing tunnel and the
This article is an open access article
distance between tunnel centers, among other factors, on the structural behavior of the
distributed under the terms and
existing and new tunnels by quantifying the displacement and crack propagation during
conditions of the Creative Commons the excavation of a new tunnel constructed near an existing tunnel. As expected, they
Attribution (CC BY) license (https:// found that the displacements decreased and stabilized as the distance between the tunnel
creativecommons.org/licenses/by/ centers increased, depending on the size of the existing tunnel.
4.0/).
Geosciences 2022, 12, 41. https://doi.org/10.3390/geosciences12010041 https://www.mdpi.com/journal/geosciences
Geosciences 2022, 12, 41 2 of 30
Twin tunnels are constructed in many configurations that differ in terms of geometric
position. Offset arrangement twin tunnels run parallel to each other, but at differing
elevations while maintaining their horizontal distance as shown in Figure 1. Due to their
offset positioning in both horizontal and vertical directions, offset arrangement twin tunnels
offer flexibility compared to other twin tunnel geometries in dense developed areas where
Geosciences 2022, 12, x FOR PEER REVIEW 3 of 34
there is other sub-surface infrastructure that must be bypassed. For any twin tunnel
excavation, the main challenges include evaluation and control of ground settlements,
stability of the excavation front, as well as deformations, loads, and stresses in the lining.
influenced
Ground by the tunnel
movement geometry
is a complex and soil conditions,
three-dimensional but also
problem thatbyis construction details.
not only influenced
Forthe
by offset arrangement
tunnel geometry and twinsoiltunnels, the but
conditions, excavations are undertaken
also by construction details.at For
different
offset
arrangement
elevations; thus,twinthe
tunnels, the excavations
interactions can haveareunanticipated
undertaken atinfluences
different elevations;
on surface thus,and
the interactions
subsurface can haveinunanticipated
settlements addition to theinfluences on surface and
stress distributions andsubsurface settlements
deformations of the
in addition
tunnel to Interaction
lining. the stress distributions
between twoand deformations
tunnels of the
and induced tunnel
ground lining. Interaction
settlements for offset
between
arrangementtwo tunnels and induced
excavation are not ground
well settlements
understood,for offset arrangement
considering that excavation
not many
are not well understood,
investigations have beenconsidering
done, be that not many
it field investigations
observations, have experiments,
laboratory been done, beor it
field observations,
numerical analyses.laboratory experiments, or numerical analyses.
Figure 1. Offset arrangement twin tunnels. (a) Lower tunnel is excavated first, and (b) upper tunnel
is excavated
is excavated first.
first.
Addenbrooke[2][2]
Addenbrooke reported
reported that arrangement
that offset offset arrangement tunnels characteristics
tunnels demonstrate demonstrate
of both side-by-side
characteristics of both andside-by-side
piggyback tunnels. However,
and piggyback it is important
tunnels. However, to it
distinguish
is important offset
to
arrangement twin tunnels from both side-by-side (horizontally
distinguish offset arrangement twin tunnels from both side-by-side (horizontally aligned) aligned) and piggyback
(vertically
and piggybackaligned) twin tunnels
(vertically as closely
aligned) twinaligned
tunnels side-by-side
as closelyand piggyback
aligned tunnels often
side-by-side and
benefit
piggyback from the reinforcing
tunnels often benefit effect of the
from thefirst tunnel [3].
reinforcing Fang
effect et al.
of the [4]tunnel
first found [3]. thatFang
newly et
constructed
al. [4] foundoffsetthat arrangement
newly constructed tunnelsoffset
in a greenfield
arrangement site demonstrated twice as much
tunnels in a greenfield site
settlement
demonstrated thantwice
a set ofasnewly
muchconstructed
settlementpiggyback
than a settunnels.
of newly Similarly, Standing
constructed et al. [5]
piggyback
reported
tunnels. Similarly, Standing et al. [5] reported larger volume loss for the new with
larger volume loss for the new offset arrangement upper tunnel together offseta
bigger trough width and maximum settlement offset towards
arrangement upper tunnel together with a bigger trough width and maximum settlement the first tunnel excavated
at St. James
offset towards Park,
theLondon.
first tunnelConversely,
excavatedNyren [6] reported
at St. James no offsetConversely,
Park, London. in the position of the
Nyren [6]
maximum settlement above the second tunnel driven, at the same
reported no offset in the position of the maximum settlement above the second tunnel driven,location.
at theAvailable studies summarized by Islam and Iskander [3] shed some light on the effect
same location.
of angular spacing
Available studies (i.e.,summarized
the diagonalbydistance
Islam and between
Iskandertwo[3] tunnels)
shed someandlight
the construction
on the effect
sequence
of angular spacing (i.e., the diagonal distance between two tunnels) and the discrete
on induced ground settlements. However, the findings remain and
construction
unclear due to (i) lack of data for many geometric and field conditions
sequence on induced ground settlements. However, the findings remain discrete and and (ii) the compared
data are gathered
unclear due to (i)from lackstudies
of data employing
for manydifferent
geometricfieldand
conditions, tunnelling
field conditions processes,
and (ii) the
geometric dimensions, and study methodologies, making it difficult
compared data are gathered from studies employing different field conditions, tunnelling to properly compare
the results and
processes, infer the
geometric governing phenomena.
dimensions, For example, the
and study methodologies, effect ofit cover
making depth
difficult to
on the induced
properly compare settlement
the results andanditsinfer
behavior is not clear,
the governing and it is also
phenomena. not clear the
For example, whether
effect
variation in horizontal distance impacts ground settlement generation more or the variation
of cover depth on the induced settlement and its behavior is not clear, and it is also not
in the vertical distance. Similarly, available studies do not provide conclusive information
clear whether variation in horizontal distance impacts ground settlement generation more
related to concurrent excavation of offset arrangement tunnels and how it differs from
or the variation in the vertical distance. Similarly, available studies do not provide
staggered excavation. Chehade and Shahrour [7] presented numerical results for two offset
conclusive information related to concurrent excavation of offset arrangement tunnels
geometries varying the distance in the horizontal direction while keeping the distance
and how it differs from staggered excavation. Chehade and Shahrour [7] presented
numerical results for two offset geometries varying the distance in the horizontal direction
while keeping the distance in the vertical direction and cover depth constant. In their
study, they observed that the construction of the lower tunnel at first leads to higher soil
settlement than that induced when the upper tunnel is first excavated. However,
Geosciences 2022, 12, 41 3 of 30
in the vertical direction and cover depth constant. In their study, they observed that the
construction of the lower tunnel at first leads to higher soil settlement than that induced
Geosciences 2022, 12, x FOR PEER REVIEW
when the upper tunnel is first excavated. However, concurrent excavation of both tunnels 4 of 34
was not studied. Thus, there is a compelling need to investigate the three-dimensional (3D)
effects of the construction sequence to understand the interactive behavior between offset
arrangement tunnels
Interactions during
between construction.
closely spaced tunnels were studied in the past using a variety
of approaches including physical spaced
Interactions between closely model tunnels wereobservations,
tests, field studied in theempirical/analytical
past using a variety
of approaches including physical model tests, field observations, empirical/analytical
methods, and finite element modelling. Among these, finite element modelling is more
methods, and
convenient for finite element
conducting modelling.
parametric AmongInthese,
studies. finite element
this work, a series modelling is more
of systematic 3D
convenient for conducting parametric studies. In this work, a series of
coupled finite element analyses (FEA) were carried out to investigate the interactions systematic 3D
coupled finite element analyses (FEA) were carried out to investigate the interactions
between twin tunnels, which are not aligned in any direction and constructed in clay using
between twin tunnels, which are not aligned in any direction and constructed in clay
a tunnel boring machine (TBM). The scope of this study involves looking at the effects of
using a tunnel boring machine (TBM). The scope of this study involves looking at the
various geometric parameters as well as the effect of three possible construction sequences
effects of various geometric parameters as well as the effect of three possible construction
on observed ground settlements. The numerical TBM model employed is capable of
sequences on observed ground settlements. The numerical TBM model employed is
taking into consideration a large number of processes that take place during tunnel
capable of taking into consideration a large number of processes that take place during
excavation. Attention was paid to the identification of various factors which can affect
tunnel excavation. Attention was paid to the identification of various factors which can
induced settlements and how these factors play a role in defining the magnitude and
affect induced settlements and how these factors play a role in defining the magnitude
position of the maximum settlement. The influence of the tunnel distance in both
and position of the maximum settlement. The influence of the tunnel distance in both
horizontal and vertical direction, as well as angular distance, cover depth, and excavation
horizontal and vertical direction, as well as angular distance, cover depth, and excavation
sequence,
sequence,were
werealso
alsoexplored.
explored.TheTheobjective
objectiveofofthis
thiswork
workisistotoaid
aidininoptimization
optimizationofofboth
both
the relative position of twin tunnels and the construction sequence to yield comparatively
the relative position of twin tunnels and the construction sequence to yield comparatively
low
lowsettlement
settlementwhile
whileexcavating
excavatingoffset
offsetarrangement
arrangementtwin twintunnels.
tunnels.
2.2.Three
ThreeDimensional
DimensionalNumerical
NumericalSimulation
Simulation
Three-dimensional
Three-dimensionalnumerical
numericalinvestigations
investigationswerewereconducted
conductedusing
usingthethefinite
finiteelement
element
program
programMIDAS
MIDASGTS GTSNX NX2019
2019(v2.1)
(v2.1)[8].
[8].AAtunnel
tunnelexcavation
excavationmodel
modelisisdeveloped
developedusingusing
the software, suitable for evaluation of the effects of excavation sequences
the software, suitable for evaluation of the effects of excavation sequences and geometric and geometric
parameters
parameterson onthe
theground
groundsettlements
settlementsinduced
inducedby bythe
theexcavation.
excavation.The Thesoftware
softwareallows
allows
step-by-step
step-by-stepanalysis
analysisofofexcavation,
excavation,application
applicationofofloading,
loading,and andother
otherfactors
factorsthat
thataffect
affect
the
theprocess
processofoftunneling.
tunneling.The Theprogram
programsupports
supportsvarious
varioussoilsoilcharacteristics,
characteristics,loading
loadingandand
boundary conditions,and
boundary conditions, and analytical
analytical methodologies
methodologies to simulate
to simulate real tunnelling
real tunnelling operations.
operations.
The plan viewTheofplan view of
the offset the offset arrangement
arrangement twin tunnels
twin tunnels excavation andexcavation
typical crossandsection
typicalof
the 3D
cross model
section ofof twin
the 3D tunnels
model of excavation
twin tunnelsemployed is illustrated
excavation employed in Figure 2. Twenty-seven
is illustrated in Figure
2.numerical models
Twenty-seven encompassing
numerical modelsnine geometriesnine
encompassing andgeometries
three construction
and three sequences were
construction
carried out
sequences as shown
were carriedinout
Table 1.
as shown in Table 1.
(a) (b)
Figure
Figure2.
2. Typical (a)plan
Typical (a) plan view,
view, andand (b) cross-section
(b) cross-section of the of thearrangement
offset offset arrangement twinexcavation
twin tunnels tunnels
excavation sequence used in the study (not to scale).
sequence used in the study (not to scale).
Table 1. Geometries of twin tunnels used in the finite element analyses.
Horizontal Vertical Angular
Cover Angular Relative
ID Distance, x Distance, y Spacing, Q
Depth, C Position, ϴ
(D) (D) (D)
1 1.0 1.5 1.5 2.12 45
2 1.5 1.5 1.5 2.12 45
Geosciences 2022, 12, 41 4 of 30
Table 1. Geometries of twin tunnels used in the finite element analyses.
Horizontal Vertical Angular Angular
Cover
ID Distance, x Distance, y Spacing, Q Relative
Depth, C
(D) (D) (D) Position, θ
1 1.0 1.5 1.5 2.12 45
2 1.5 1.5 1.5 2.12 45
3 2.0 1.5 1.5 2.12 45
4 1.0 2.0 2.0 2.83 45
5 1.0 2.0 1.5 2.50 36.87
6 1.0 1.25 1.25 1.77 45
7 1.0 1.5 2.0 2.50 53.13
8 1.0 1.25 2.0 2.36 58
9 1.0 2.0 1.25 2.36 32
2.1. Constitutive Model Parameters
Geotechnical parameters of the clay used in this numerical parametric study were
assumed as representative of the properties of the silty clay layer, which was encountered
during excavation of the north route transit tunnel of Shanghai Railway transportation
line 11 and reported by Zhang and Huang [9]. The behavior of clay used in this study is
described using a constitutive model similar to that used by Addenbrooke and Potts [10],
Galli et al. [11] and Ieronymaki et al. [12], among others, where the Mohr–Coulomb model
is employed to simulate clay behavior. The Mohr–Coulomb failure criterion is not fully
able to reproduce certain aspects of clay behavior particularly during unloading, including
tunnel excavation. Nevertheless, it was chosen in this study due to its simplicity and
the parametric nature of the work where various configurations of twin tunnel geometric
parameters as well as tunnel excavation depth were compared to each other.
To accommodate the increase in the strength of the clay with depth the soil was
represented using a combination of cohesion and an angle of internal friction. An angle of
friction of 15◦ was selected, which effectively corresponds to a c/σ(Z) ratio of 0.27, where c is
cohesion, and σ(Z) is the effective vertical overburden stress, both at the location of interest.
c/σ(Z) has been found to be useful for describing the increase in strength with depth in
thick clay deposits [13,14]. A value of 0.27 is consistent with a normally consolidated
clay having a plasticity index (PI) of approximately 40, or a lightly over-consolidated low
plasticity clay having a PI of 20. Within the Mohr–Coulomb model, the soil stiffness is
considered constant in the elastic zone until the stress state reaches the plastic zone of
failure. To accommodate the increase in stiffness with depth Young’s modulus of the soil
was increased with depth following Janbu [15] relation presented in Equation (1).
σ(Z)
ES ( Z ) = E0 ( ) (1)
Pre f
where Es denotes Young’s modulus of the soil, and σ is the mean stress due to the soil
self-weight, which is determined using Equation (2).
(
(1+2K0 )γZ
Z ≥ Z0
σ(Z) = 3 (2)
σ ( Z0 ) Z < Z0
where Z denotes depth, γ is soil unit weight, Pref is a reference pressure (100 kPa), E0
designates the Young’s modulus when σ = Pref , and Z0 is the thickness of the surface soil
layer, which is assumed to have a constant stiffness. K0 is the coefficient of lateral earth
pressure at rest, which is calculated from Jaky’s [16] equation as (1 − sin φ).
Geosciences 2022, 12, 41 5 of 30
The magnitude of settlement induced from a tunnel excavation in an FEA study largely
depends on the modulus of elasticity assumed for the top layer of the soil. Settlement
analysis for a single tunnel has been performed for three different moduli of elasticity, and
the observed settlements are plotted in Figure 3. It shows that an increase in modulus of
elasticity for the top soil layer can noticeably decrease induced settlement. A modulus
Geosciences 2022, 12, x FOR PEER REVIEW
of elasticity of E0 = 2000 kN/m2 was selected to amplify the observed settlement 6inofthe 34
context of a parametric study. The modulus of elasticity was increased with depth at a rate
of 1500 kN/m3 per meter. The initial stresses also include a hydrostatic pore water pressure
profile
pressurefrom a water
profile fromtable located
a water 2 mlocated
table below the
2 mground
belowsurface, as shown
the ground in Figure
surface, 2. Soil
as shown in
layers
Figurein2. all
Soilanalyses are
layers in allmodeled
analysesinare
terms of undrained
modeled in terms conditions.
of undrained conditions.
Figure 3. Effect
Figure 3. Effect of
ofYoung’s
Young’smodulus
modulusofofelasticity onon
elasticity tunnelling induced
tunnelling ground
induced settlement
ground (initial
settlement E0
(initial
E0 shown).
shown).
The behavior of the segmental tunnel lining has been assumed to be isotropic elastic
and is modelled
modelled as aa drained
drained material.
material. The thickness of the lining modelled in this study
is equal to 0.25 m.
equal to 0.25 m. The properties of both the soil and the lining used in this study are
summarized in Table
summarized in Table 2. 2.
Table2.2. Material
Table Material parameters
parametersadopted
adoptedin
inthe
thefinite
finiteelement
elementanalyses.
analyses.
Material Parameters
Material Parameters ClayClay
Soil Soil Lining Segment
Lining Segment
Unit
Unit weight (kN/m3 )3)
weight(kN/m 18.0 18.0 24.0 24.0
Saturated density 3 20.0 20.0 25.2 25.2
Saturated density(kN/m
(kN/m)3)
Initial Void ratio, e 0.5 -
Initial Void ratio, 0e0 0.5 -
Coefficient of permeability (m/s) 1e-5 -
Coefficient of permeability
K0 (m/s) 0.74121e-5 1 -
K0 E (kN/m )
Elastic modulus, 2 0.7412
2000 + 1500 z1 2.1e7 1
Undrained
Elastic poisson’s
modulus, ratio, ν2)
E (kN/m 0.495+ 1500 z 1
2000 - 2.1e7
◦)
Undrained poisson’s(ratio,
Friction Angle, ϕ ν 15 0.495 - -
Cohesion, c (kN/m2 ) 25 -
Friction Angle, φ
Drainage conditions
(°) Undrained
15 Drained
-
1 z, depthCohesion, c (kN/m2)
below the ground surface (in meters).
25 -
Drainage conditions Undrained Drained
1z, depth
2.2. Finitebelow the Mesh
Element ground surface
and Initial(in meters).
Ground Conditions
A 3D isometric view of the finite element mesh of the twin offset arrangement tunnels
2.2. Finite Element Mesh and Initial Ground Conditions
(ID# 1) is presented in Figure 4. In order to minimize boundary effects, the length of the
meshAin3D isometric
the view
lateral (x) of the finite
direction element
extends 6.0Dmesh
fromof thespringlines
the twin offsetof
arrangement tunnels
both tunnels. The
(ID# 1) is presented in Figure 4. In order to minimize boundary effects, the length
depth of the mesh also extends 6.0D below the lowest tunnel invert to the model boundary, of the
mesh in the lateral (x) direction extends 6.0D from the springlines of both tunnels. The
depth of the mesh also extends 6.0D below the lowest tunnel invert to the model
boundary, which exceeds five times the excavation depth, as suggested by Li et al. [17].
The distance between the two tunnels in both x and y directions as well as the distance of
the upper tunnel crown to the surface are variable due to the parametric nature of the
Geosciences 2022, 12, x FOR PEER REVIEW 6 of 33
Geosciences 2022, 12, 41 6 of 30
depth of the mesh also extends 6.0D below the lowest tunnel invert to the model bound-
which exceeds
ary, which five times
exceeds five the excavation
times depth, as
the excavation suggested
depth, by Li et al.
as suggested by [17].
Li etThe distance
al. [17]. The
between
distance between the two tunnels in both x and y directions as well as the distanceupper
the two tunnels in both x and y directions as well as the distance of the of the
tunnel
upper crown
tunnel to the surface
crown are variable
to the surface due to the
are variable dueparametric nature of
to the parametric the work.
nature of the work.
(a) (b)
Figure4.4.Mesh
Figure Meshininthe
theFEM
FEMtwin
twintunnel
tunnelmodel
model(ID
(ID#1).
#1).(a)
(a)Perspective
Perspectiveview
viewof
ofthe
themesh
meshof
ofthe
theentire
entire
model, and (b) zoomed view of the mesh around the twin tunnels.
model, and (b) zoomed view of the mesh around the twin tunnels.
The soil
The soilwas
wasmodeled
modeledusing using aahybrid
hybridmesher
mesherto toincrease
increaseaccuracy
accuracywhile
whilethe
thetunnel
tunnel
lining was
lining was modeled
modeled using
using aa six-node
six-nodeelastic
elasticplate
plateelement.
element.WhileWhilemeshing,
meshing,thethe
tunnel
tunnelex-
cavation was
excavation wasmeshed
meshedfirst
firstfollowed
followedby bymeshing
meshing ofof the remaining soil mass.mass. Mesh
Mesh sizes
sizes
usedin
used inthis
thisstudy
studyare
are0.5
0.5mmandand 2.0
2.0 m,
m, respectively,
respectively,forforthe
theexcavated
excavatedtunnels
tunnelsandandthethesoil
soil
mass. “Match adjacent faces” command was employed, which effectively
mass. “Match adjacent faces” command was employed, which effectively reduces the mesh reduces the
mesh
size sizethe
near near the tunnel,
tunnel, to increase
to increase the numerical
the numerical accuracy accuracy
near the near the tunnel
tunnel face. face.
The tunnel
The tunnel linings were constrained
constrainedto tomove
movewith
withthe thesurrounding
surrounding soils, and
soils, andthethe
ef-
fect ofofthe
effect theinstallation
installationprocedure
procedure waswasignored.
ignored.As As
for for
thethe
boundary
boundaryconditions, the the
conditions, dis-
placements were
displacements setset
were to zero in the
to zero three
in the directions
three at the
directions bottom
at the of the
bottom of mesh withwith
the mesh no hor-
no
izontal or or
horizontal vertical movements
vertical movementspermitted.
permitted.Movements
Movementsin intwo
two horizontal directions were
horizontal directions were
restrained,
restrained,andandonly
onlyvertical
verticalmovement
movementwas wasallowed
allowedon onthe
thefour
fourside
sideboundaries.
boundaries.
2.3.
2.3. Tunnel
TunnelGeometry
GeometryandandExcavation
ExcavationMechanism
Mechanism
The
The TBM shield used in the FEA models
TBM shield used in the FEA models ofof this
this study
study has
has been
been modelled
modelled using
using aa
simplified
simplified geometry and is cylindrical in shape instead of an actual cone-shaped shield.
geometry and is cylindrical in shape instead of an actual cone-shaped shield.
Most
Mostof ofthe
themain
mainoperational
operationalelements
elementsofofa mechanized
a mechanized excavation
excavationhave been
have beensimulated in
simulated
this model, including the face pressure applied on the shield excavation face
in this model, including the face pressure applied on the shield excavation face and the and the jack
thrust. Face pressure
jack thrust. has been
Face pressure has estimated depending
been estimated on theon
depending horizontal stress induced
the horizontal in the
stress induced
ground in front of the tunnel face following the methodology presented
in the ground in front of the tunnel face following the methodology presented by Anag-by Anagnostou
and Kovari
nostou and[18], where
Kovari face
[18], pressure
where facehas been modelled
pressure has beenby applyingby
modelled a pressure
applyingdistribution
a pressure
to the excavation face. The distribution of the jack thrust has been assumed
distribution to the excavation face. The distribution of the jack thrust has been to be assumed
uniform
around the perimeter of the tunnel lining segment. The jacking forces adopted in this study
to be uniform around the perimeter of the tunnel lining segment. The jacking forces
are based on the theoretical method proposed by Rijke [19]. The shield external pressure
adopted in this study are based on the theoretical method proposed by Rijke [19]. The
and segment external pressure were applied around the shield excavation face.
shield external pressure and segment external pressure were applied around the shield
Grouting pressure behind the shield tail was also simulated. Grouting pressure
excavation face.
has been estimated based on the ground overburden pressure at the crown of excavated
Grouting pressure behind the shield tail was also simulated. Grouting pressure has
tunnels [20]. The grout was simulated using a uniform pressure distribution, which was
been estimated based on the ground overburden pressure at the crown of excavated tun-
applied in between the cylindrical surface of the excavated ground and the external surface
nels [20]. The grout was simulated using a uniform pressure distribution, which was ap-
of the tunnel lining segment. The grout was assumed to harden beyond the length of
plied in between the cylindrical surface of the excavated ground and the external surface
one lining segment ring (0.25D or 1.0 m in this study) and was simulated by means of an
of the tunnel lining segment. The grout was assumed to harden beyond the length of one
isotropic elastic material having an elastic modulus, Egrout of 1e4 kN/m2 and, Poisson’s
ratio, νgrout = 0.22 [20].
Geosciences 2022, 12, 41 7 of 30
Geosciences 2022, 12, x FOR PEER REVIEW 8 of 34
To simplify the model and to minimize the computational time the weight of the
components of a mechanized tunnelling process were not considered, including the weight
of the shield
machine. Thismachine and the
was justified byweight of the back-up
the parametric naturetrain behind
of the the shield
comparison. Themachine.
effect ofThis
this
was justifiedisby
assumption the parametric
believed to be minornature of context
in the the comparison. The effect
of a comparative of this assumption
parametric study. The
is believed
pressure to be minor
parameters usedin in
thethis
context
studyof fora analysis
comparative
ID #3parametric study.inThe
are summarized pressure
Table 3. The
parameters used in this study for analysis ID #3 are summarized in
analysis and the parametric study are sensitive to the pressure parameters employed,Table 3. The analysis
and
and
thusthe
theparametric
simulations study
are are sensitive to the
representative pressure
of the parameters
indicated employed,
parameters and areand thus the
useful for
simulations
comparison are of representative of the indicated
geometric properties. parameters
If tunnels and arewith
are installed useful for comparison
TBMs employing
of geometric
different properties.
operating If tunnelsthe
parameters, aremagnitude
installed with TBMs employing
of geometric different
inferences outlinedoperating
herein
parameters, the magnitude of geometric inferences outlined herein
may not necessarily hold. In particular, variation in pressure parameters during twinmay not necessarily
hold. In particular,
tunneling variation
will impact in pressureofparameters
the magnitude settlementduring twinrelative
obtained tunneling will parametric
to the impact the
magnitude of settlement
simulations presented herein. obtained relative to the parametric simulations presented herein.
Table 3. Pressure
Table 3. Pressure parameters
parameters used
used in
inthe
thefinite
finiteelement
elementanalyses
analysesto
tomodel
modelTBM
TBMexcavation.
excavation.
Pressure Parameters
Pressure Parameters Magnitude
Magnitude
FaceFace support
support pressure
pressure 2
180 kN/m
180 kN/m 2
Jack Jack
thrustthrust 4500 4500 2
kN/mkN/m2
Shield external pressure 50 kN/m 2
Shield external pressure 50 kN/m2
Segment external pressure 1000 kN/m2
Segment external pressure 1000 kN/m 2
The tunnel construction
construction process is is modelled
modelled using
using aa step-by-step
step-by-step approach.
approach. Each
excavation step corresponds to an advancement of the tunnel face of 1.0 m (equivalent to
0.25D), which
which is followed
followed by installation
installation ofof a lining ring. The influence of the tunnel length
advancement
advancement without any support (i.e., lining
without any support (i.e., lining segment),
segment), in in other
other words,
words, unsupported
unsupported
excavation
excavation length (UEL), has been evaluated for a single tunnel, and it
length (UEL), has been evaluated for a single tunnel, and it is
is evident
evident from
from
Figure
Figure 55 that
that UEL
UEL has
has significant
significant impact
impact on on induced
induced ground
ground settlement.
settlement. The
The higher
higher the
the
UEL,
UEL, the
the higher
higher the
the induced
induced settlement
settlement is. Thus, to
is. Thus, to minimize
minimize the the impact
impact resulting
resulting from
from
longer
longer UELs,
UELs, aa low
low UEL
UEL of
of 0.25D
0.25D has
has been
been used
used throughout
throughout this
this study.
study.
Figure 5. Effect of unsupported excavation length (UEL) on tunnelling
tunnelling induced
induced ground
ground settlement.
settlement.
The diameter of the excavated tunnel also has a significant impact on the induced induced
settlement. Settlements induced by a single tunnel for four different diameters are plotted
in Figure 6, and it is observed
observed that
that the
the larger
larger the
the tunnel
tunnel diameter,
diameter, the
the larger
larger the
the settlement.
settlement.
Larger tunnels require much larger models with resulted resulted in
in longer
longer computational
computational time
when doing stage analysis. Therefore, a circular tunnel having a relatively small diameter
of
of 4.0
4.0mmhas
hasbeen
beenmodelled in this
modelled in study to reduce
this study computation
to reduce time andtime
computation to allow
and relatively
to allow
relatively more stages and low UEL in the excavation, which resulted in increased
accuracy of a finite element (FE) model.
Geosciences 2022, 12, 41 8 of 30
Geosciences 2022, 12, x FOR PEER REVIEW 9 of 34
more stages and low UEL in the excavation, which resulted in increased accuracy of a finite
element (FE) model.
Figure 6.
Figure 6. Effect
Effect of
of tunnel
tunnel diameter
diameter on
on tunnelling
tunnelling induced
induced ground
ground settlement.
settlement.
Three
Three excavation
excavationsequences
sequences were modelled
were modelled as follows:
as follows:(i) excavation of the of
(i) excavation firstthe
tunnel
first
(left
tunneland(left
lower) andand thenand
lower) excavation of the second
then excavation of thetunnel
second(right and (right
tunnel upper),and (ii) upper),
excavation (ii)
of the first tunnel
excavation of the first(right and upper)
tunnel (right andandupper)
then excavation of the second
and then excavation of thetunnel
second (left and
tunnel
lower),
(left andand (iii) concurrent
lower), excavationexcavation
and (iii) concurrent of both lower left tunnel
of both lower and upper right
left tunnel tunnel.right
and upper For
cases (i) and (ii), successive excavation of the new second tunnel
tunnel. For cases (i) and (ii), successive excavation of the new second tunnel followed thatfollowed that of the first
tunnel aftertunnel
of the first it reachedafterits full assigned
it reached its fulllength in the
assigned model,
length which
in the was which
model, taken as was 20taken
m (5
times
as 20 the
m (5tunnel
timesdiameter)
the tunnelindiameter)
all models. inThus, excavation
all models. Thus,ofexcavation
the first tunnel
of the proceeded
first tunnel in
20 stages followed
proceeded in 20 stages by 20followed
stages forbythe
20second
stages tunnel. Groundtunnel.
for the second conditions at theconditions
Ground end of each at
stage were employed as initial conditions for the next stage.
the end of each stage were employed as initial conditions for the next stage.
The
The numerical
numerical simulation
simulation ofofeacheachmodel
modelhas hasbeenbeenrepeated
repeated forfor
three
threedifferent
differentse-
quences of excavation and settlement results have been
sequences of excavation and settlement results have been extracted as follows: extracted as follows:
(a) Case (i)
(a) Case (i) and
and(ii):
(ii):Settlement
Settlementmagnitude
magnitude has been
has been extracted
extracted at the completion
at the completion of the offirst
the
tunnel excavation and at the end of the second tunnel excavation.
first tunnel excavation and at the end of the second tunnel excavation. The difference The difference of
these two settlement magnitudes is the settlement induced
of these two settlement magnitudes is the settlement induced by the new second by the new second tunnel
excavation.
tunnel excavation.
(b) Case (iii):
(b) Case (iii): Settlement
Settlement magnitude
magnitude has has been
been extracted
extracted at at the
the completion
completion of of concurrent
concurrent
twin tunnel excavation. This settlement magnitude
twin tunnel excavation. This settlement magnitude can be compared can be compared against combined
against
settlement obtained at the end of twin tunnels excavation for
combined settlement obtained at the end of twin tunnels excavation for cases (i) and cases (i) and (ii).
(ii). Validation
2.4. Model
The settlement
2.4. Model Validation data obtained from this study are validated against data available
in the literature and the data in Figure 7 show good agreement. While comparing the
data Thefromsettlement data obtained
various studies, from this
the similarities ofstudy are validated
geometric parameters, against data available
i.e., cover depth and in
the literature and the data in Figure 7 show good agreement. While
angular spacing between two offset arrangement tunnels, were taken in account to conduct comparing the data
afrom
validvarious
comparison.studies,
FEMthe similarities
analysis resultsofaregeometric
comparedparameters,
in Figure 7a to i.e.,previously
cover depth and
reported
angular spacing between two offset arrangement tunnels, were
centrifuge experiments [21] in clay and FE analysis [7] in sand. FEA analysis results are taken in account to
conduct a valid comparison. FEM analysis results are compared in Figure
also compared in Figure 7b with a reported field observation [22] in stiff boulder clay on 7a to previously
reported
the Singaporecentrifuge experiments
Mass Rapid Transit.[21] in clay
It can andfrom
be seen FE analysis
Figure 7a [7]that
in sand.
offset FEA analysis
arrangement
results are also compared in Figure 7b with a reported field
twin tunnels of cover-to-diameter (C/D) ratio of 2.0 (for the upper tunnel) and angularobservation [22] in stiff
boulder clay on the Singapore Mass Rapid Transit. It can be seen
spacing (Q) of 2.12 employed in this work yields similar settlements to those reportedfrom Figure 7a that offset
by
arrangement twin tunnels of cover-to-diameter (C/D) ratio of 2.0
Divall [21]. However, settlement for offset arrangement twin tunnels of C/D ratio of 2.0 (for the upper tunnel)
and the
(for angular
upperspacing
tunnel)(Q)
andofangular
2.12 employed
spacing in of this
2.83work
in thisyields
studysimilar
varies settlements to those
from the settlement
reported by
observed by Divall
Chehade [21].and
However,
Shahrour settlement
[7] in sand,for whereas
offset arrangement
this study is twin tunnels in
performed of clay
C/D
ratio of 2.0 (for the upper tunnel) and angular spacing of 2.83 in this study varies from the
settlement observed by Chehade and Shahrour [7] in sand, whereas this study is
performed in clay soil. In addition, it can be seen from Figure 7b that offset arrangement
Geosciences 2022, 12, 41 9 of 30
Geosciences 2022, 12, x FOR PEER REVIEW 10 of 34
soil. In addition, it can be seen from Figure 7b that offset arrangement twin tunnels of
twin ratio
C//D tunnels of C//D
of 2.0 ratio ofspacing
and angular 2.0 and (Q)
angular spacing
of 2.04 (Q) of 2.04
show similar show
results for similar results for
field observations
field observations
compared compared
with numerical withThese
analysis. numerical
resultsanalysis. These
suggest that the results suggest
developed modelthat
canthe
be
developed
used model can be used with confidence.
with confidence.
Figure 7.7.Model
Figure Model validation:
validation: (a) comparison
(a) comparison betweenbetween normalized
normalized total settlement
total settlement of offset
of offset arrangement
arrangement twin tunnels observed in this study and in similar published studies, (b) comparison
twin tunnels observed in this study and in similar published studies, (b) comparison of field observed
of field observed settlement data with FEM analyses for two offset arrangement twin tunnels.
settlement data with FEM analyses for two offset arrangement twin tunnels.
3. Interpretation
3. Interpretation of Results and
of Results and Discussions
Discussions
Ground displacements
Ground displacements perpendicular
perpendicular to to the
the tunnels’
tunnels’ axes
axes atat the
the end
end of
of the
the simulated
simulated
excavation stages were extracted from the FEA model at the section coinciding with the
tunnel face (y == 0 m). m). The
The influence
influence of the model boundary conditions on the tunnel
behavior at this section is believed to be negligible based on prior studies presented by Do
et al. [23].
The behavior of twin tunnels during the excavation process of a new tunnel in the
presence of an existing tunnel, and when both tunnels are excavated concurrently, is
explored through
explored throughaaseriesseriesofofexcavation
excavationstages.
stages.First,
First,settlement
settlement induced
induced after
after excavation
excavation of
the first
of the tunnel
first tunnelis is
presented.
presented. Next,
Next,settlement
settlementinduced
inducedafterafterthetheexcavation
excavationof of the
the second
tunnel is also presented. Third, the combined settlement of both tunnels is presented for
the case of staggered excavations. Finally, the combined settlement when both tunnels are
excavated concurrently is also presented. The effect of various geometric parameters and
excavation sequences on the computed settlement settlement areare investigated.
investigated.
The magnitude of calculated settlement in this study is generally high and, in many
cases, resulted in volume loss over over 1%. Tunnels excavated with EPB or slurry shield
1%. Tunnels
machines
machines where all tunnel operations parameters are
where all tunnel operations parameters are simulated
simulated doesdoes not
not typically
typically exceed
exceed
1%
1% of volume loss. This difference could be attributed to the soft nature of the
of volume loss. This difference could be attributed to the soft nature of the soil,
soil, which
which
is
is also
also evident
evident from
from thethe studies
studies performed
performed by by Addenbrooke
Addenbrooke and and Potts
Potts [10]
[10] and
and Chapman
Chapman
et al. [24]
et al. [24] in
inundrained
undrainedclays. clays.Their
Theirwork
work showed
showed a larger
a larger volume
volume lossloss ratio
ratio caused
caused by
by the
the excavation of the second tunnel. Other reasons include simplification
excavation of the second tunnel. Other reasons include simplification of the shield of the shield
excavation
excavation and and assumption
assumption of of aa low
low stiffness
stiffness for
for the
the top
top soil
soil layer
layer in
in this
this study.
study.
3.1. Effect of Angular Relative Position
3.1. Effect of Angular Relative Position
Hefny et al. [25] describes the geometry of offset arrangement tunnels using the angular
Hefny et al. [25] describes the geometry of offset arrangement tunnels using the
relative position angle, θ, of a new tunnel relative to an existing tunnel. The angle θ is
angular relative position angle, ϴ, of a new tunnel relative to an existing tunnel. The angle
measured between the center-to-center connecting line of two tunnels and the horizontal line
ϴ is measured between the center-to-center connecting line of two tunnels and the
drawn from the center of the lower tunnel (Figure 1). An angle of 90◦ represents a new tunnel
horizontal line drawn from the center of the lower tunnel (Figure 1). An angle of 90°
directly above the crown or below the invert of an existing tunnel (vertically aligned tunnels
represents a new tunnel directly above the crown or below the invert of an existing tunnel
(vertically aligned tunnels or piggyback tunnels), while an angle of 0° represents a new
Geosciences 2022, 12, 41 10 of 30
or piggyback tunnels), while an angle of 0◦ represents a new tunnel located beside and at the
same depth as the existing tunnel (horizontally aligned tunnels or side-by-side twin tunnels).
Settlement of the excavated twin tunnels for all three excavation sequences are plotted
in Figure 8. Five different angular relative positions at a fixed cover-to-diameter ratio
(C/D = 1.0) were considered in this study to investigate the effect of angular relative
position. It is observed that, as the angle between the tunnels increase with respect to the
horizontal axis, the surface soil settlement of the excavated twin tunnels increases for all
construction sequences. This can be explained by the shear strain data presented in Figure 9,
where increasing strain in the crown, invert, and springlines of the lower tunnel are observed
with the increase in the magnitude of angular relative position. The reason for this is that the
higher the magnitude of angular relative position, the more the new second upper tunnel
falls within the influence zone of the lower tunnel. Lower tunnel excavation is the major
contributor of the total settlement induced during excavation of offset arrangement twin
tunnels. The relationship between the maximum observed soil settlement and the angular
relative position is summarized in Figure 8d. The data suggest that a significant increase in
settlement can be anticipated till θ reaches a certain magnitude (53.13◦ in this study),
Geosciences 2022, 12, x FOR PEER REVIEW
and
12 of 34
then the increase slows down. However, since the increase in settlement is common to all
three construction sequences, geometric position is believed to play a larger role.
8. Effect
FigureFigure of angular
8. Effect relative
of angular position
relative on (a–c)
position combined
on (a–c) surface
combined settlement
surface settlement caused
causedbybythe
the
excavation of offset
excavation arrangement
of offset twin twin
arrangement tunnels and and
tunnels (d) maximum total
(d) maximum surface
total settlement
surface settlementofof
the
thetwin
twin
tunnels.
tunnels.Geosciences 2022, 12, 41 11 of 30
Geosciences 2022, 12, x FOR PEER REVIEW 13 of 34
Figure 9. Effect of angular relative position on shear strain in the crown, invert, and springlines of
Figure 9. Effect of angular relative position on shear strain in the crown, invert, and springlines of
twin tunnels at the end of excavation (a–c).
twin tunnels at the end of excavation (a–c).
Settlement from the excavation of a new second tunnel is plotted in Figure 10a,b for
Settlement
both sequences fromthe
when the excavation
lower tunnel isofexcavated
a new second tunnel
first and whenisthe plotted
upperintunnel
Figure is 10a,b for
excavated first. Thus, Figure 10a,b represent settlement induced solely from the tunnel is
both sequences when the lower tunnel is excavated first and when the upper
excavated first.
excavation of new Thus, Figure
upper 10a,band
tunnel represent
from thesettlement induced
excavation of newsolely fromtunnel,
lower the excavation
of new upper
respectively. Thetunnel
observedand from
trend the excavation
of maximum of new
settlement fromlower tunnel, respectively.
the excavation of a new The
second tunnel
observed is summarized
trend of maximum in Figure 10c. Itfrom
settlement is noticed that as the of
the excavation angle between
a new second the tunnel is
tunnels increase
summarized inwith respect
Figure 10c.toItthe horizontal
is noticed axis,
that as the
the surface soil settlement
angle between induced
the tunnels by
increase with
the new second
respect tunnel excavation
to the horizontal axis, thedecreases
surfacewhen the lower tunnel
soil settlement inducedis excavated first.second
by the new The tunnel
reason for this
excavation is that thewhen
decreases higherthethelower
magnitude
tunnelof the angular relative
is excavated first. position,
The reasonthe for
more this is that
the new tunnel falls within the influence zone of the existing tunnel, which provide
the higher the magnitude of the angular relative position, the more the new tunnel falls
reinforcement support to the excavated new tunnel within its influence zone thus the new
within the influence zone of the existing tunnel, which provide reinforcement support to the
tunnel induces low settlement. This observation agrees well with the findings from Divall
excavated new tunnel within its influence zone thus the new tunnel induces low settlement.
This observation agrees well with the findings from Divall [21] and Channabasavaraj and
Visvanath [26]. However, a distinct trend was not observed when the upper tunnel is
excavated first, because the magnitude of observed upheaval when the upper tunnel is
excavated first in undisturbed ground impacts the settlement induced by the lower secondGeosciences 2022, 12, 41 12 of 30
tunnel during its excavation. The high upheaval observed from the excavation of the
shallower upper tunnel likely resulted from the low stiffness at top soil layers, as evident
from Figure 3. Significant heave is not typically observed in in situ or in centrifuge tests.
However, in numerical models, heave results from the use of a uniform modulus over
the entire strain range. The inability of the employed constitutive model to account for
higher stiffness at small strains and its rapid decay with increasing strains, as well as the
dependence of the modulus on the past stress history, contributed to the observed heave.
In this case, when the tunnel is excavated numerically, all soil elements below the invert
arch follow an unloading stress path that is characterized by the same stiffness occurring in
loading, making the computed heave proportional to the depth of the
Geosciences 2022, 12, x FOR PEER REVIEW 15 mesh
of 34 bottom, and
likely higher than what is observed physically.
Figure 10. Effect of angular relative position on (a,b) surface settlement above the new second tunnel
Figure 10. Effect of angular relative position on (a,b) surface settlement above the new second tunnel
and (c) maximum settlement from the excavation of the new second tunnel.
and (c) maximum settlement from the excavation of the new second tunnel.
3.2. Effect of Angular Spacing
Tunnel offset is often described in terms of angular spacing, Q (Figure 1), although it
is a less sensitive measure than the angular relative position, since distance does not
always correlate with influence zone. Settlement from the excavation of a new secondGeosciences 2022, 12, 41 13 of 30
3.2. Effect of Angular Spacing
Tunnel offset is often described in terms of angular spacing, Q (Figure 1), although it is
a less sensitive measure than the angular relative position, since distance does not always
correlate with influence zone. Settlement from the excavation of a new second tunnel is
plotted in Figure 11a,b for two excavation sequences, representing when the lower tunnel
is excavated first and vice versa. Offset arrangement twin tunnels of five different angular
spacings at a fixed cover-to-diameter ratio (C/D = 1.0) were modelled in this study to
investigate the effect of angular spacings. Figure 11a,b represent settlement induced solely
from the excavation of new upper tunnel and from the excavation of new lower tunnel,
respectively. Generally, the larger the angular spacing, the larger the settlement induced
from the excavation of the new lower tunnel when the upper tunnel is excavated first. The
finding is consistent with the observation from numerical studies performed by Chehade
and Shahrour [7] and experiments conducted by Divall [21]. The trough width becomes
wider and deeper as the angular distance increases. The observed trend is summarized in
Figure 11c, where the trend suggests opposite behavior depending on which the tunnel is
excavated first. The smaller the angular spacing, the larger the settlement induced from
the excavation of a new upper tunnel when the lower tunnel is excavated first. However,
there appears to be a threshold represented by approximately Q > 2 where the settlement
induced from the excavation of the new second upper tunnel is markedly less influenced
by prior excavation as seen in Figure 11a.
The combined settlement of the excavated twin tunnels for all three excavation se-
quences are plotted in Figure 12 for the five different angular spacings considered in this
study. Generally, as the angular spacing between the tunnels decreases, the surface soil
settlement of the excavated twin tunnels increases. However, it is not feasible to draw
definitive conclusions, because twin tunnels having a specific angular distance can have
different dimensions in the horizontal and vertical direction, which can exhibit different
settlement behavior, as detailed below.Geosciences
Geosciences 12,12,
2022,
2022, 41 PEER REVIEW
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of of
3430
Figure 11.11.
Figure Effect of of
Effect angular spacing
angular onon
spacing (a,b) surface
(a,b) settlement
surface above
settlement thethe
above new second
new tunnel
second and
tunnel (c)(c)
and
maximum settlement from the excavation of the new second tunnel.
maximum settlement from the excavation of the new second tunnel.Geosciences 2022, 12,
Geosciences 2022, 12, 41
x FOR PEER REVIEW 15 of
18 of 30
34
Figure 12.
Figure 12. Effect
Effect of
of angular
angular spacing
spacing on
on (a–c)
(a–c) combined
combined surface
surface settlement
settlement caused
caused by
by the
the excavation
excavation
of offset arrangement twin tunnels and (d) maximum total surface settlement of the twin tunnels.
of offset arrangement twin tunnels and (d) maximum total surface settlement of the twin tunnels.
3.3. Effect of Horizontal and Vertical Distance
Distance When
When Angular
Angular Spacing
Spacing Is
Is Fixed
Fixed
Angular spacing
Angular spacing is is a direct result
result of the horizontal and vertical distance between two
tunnels. ForFor two
two offset arrangement twin tunnels, the horizontal distance (X) and the the
vertical
vertical distance
distance(Y)(Y) cancan
be different while having
be different the samethe
while having angular
samespacing.
angularTospacing.
understand To
(i) the effect of
understand (i) the horizontal
effect of theand vertical distances
horizontal and vertical between
distancestwobetween
tunnels andtwo (ii) whether
tunnels and
the
(ii) horizontal
whether the or vertical distance
horizontal has significantly
or vertical distance has moresignificantly
impact on the tunnelling
more impactinduced
on the
settlement at a fixed
tunnelling induced angular spacing
settlement at a fixedand at a fixed
angular spacingC/D andratio, several
at a fixed C/D analyses were
ratio, several
performed, and the results are presented in Figures 13 and 14. The
analyses were performed, and the results are presented in Figures 13 and 14. The effect of effect of the horizontal
and vertical distance
the horizontal on surface
and vertical settlement
distance on surface above the new second
settlement above the tunnel
newinsecond
the presence
tunnel ofin
an
theexisting
presencetunnel
of an at a fixedtunnel
existing angularat aspacing is presented
fixed angular spacing in Figure 13. It in
is presented is evident
Figure 13. thatIt
variation
is evidentinthatX and Y has ainsignificant
variation X and Y has effect on induced
a significant settlement,
effect on induced evensettlement,
though angular even
spacing remainsspacing
though angular the same. It canthe
remains besame.
seen from
It can Figure
be seen13bfromthat a decrease
Figure 13b that inaXdecrease
and an
increase in Y significantly increase the induced ground settlement
in X and an increase in Y significantly increase the induced ground settlement of the of the new second tunnel
new
when the upper tunnel is excavated first. The reason is that,
second tunnel when the upper tunnel is excavated first. The reason is that, with an with an increase in vertical
distance,
increase in thevertical
possibility of thethe
distance, existing upperoftunnel
possibility providing
the existing upperstiffness
tunnelinproviding
the soil within the
stiffness
influence zone of the lower tunnel diminishes. On the contrary and
in the soil within the influence zone of the lower tunnel diminishes. On the contrary and as shown in Figure 13a,
decrease
as showninin X Figure
and increase in Y decrease
13a, decrease in X theandinduced
increaseground settlement
in Y decrease theofinduced
the new ground
second
tunnel when the lower tunnel is excavated first. The effect of the
settlement of the new second tunnel when the lower tunnel is excavated first. The effect horizontal and vertical
distance on the total
of the horizontal and surface
vertical settlement
distance oncaused
the total bysurface
two offset arrangement
settlement caused twin
by two tunnels
offsetYou can also read
