Design methodology for permanent complex structures: Secondary lini...
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Document type: Technical Paper
Author: Eleanor Sillerico Mayta MSc, Jose Suarez Diaz MSc CEng MICE, Richard Brierley, ICE Publishing
Publication Date: 09/07/2018
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Crossrail Contract C121’s scope is the design of the SCL (sprayed concrete lining) permanent structures of
five new underground stations (Liverpool St, Whitechapel, Tottenham Court Road, Bond Street and
Farringdon), shafts and three crossovers. Mott MacDonald was appointed to carry out this work. This paper
describes the design methodology of complex permanent structures (secondary linings), particularly
junctions between platform tunnels and cross passages, junctions between shafts and cross passages and
also a combination of all of them.
The paper describes the different junction structures that are usually found in a tunnelling project and
explains the main design parameters such as ground conditions, geometry, boundary conditions, etc.
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The paper also provides an extensive explanation of the modelling process of 3D complex junction models
in FEM software, describing the main challenges to be faced and, how to apply different loads (ground
pressures, water pore pressure, surcharge, etc) and how these loads are transferred from the primary lining
to the secondary lining in the long term. Moreover, the paper describes how to evaluate the structural
behaviour of the lining in different types of junctions, the interpretation of results, and finally, the structural
design, based on the standards of both RILEM [6] and Eurocode 2.0 [4], including the contribution the steel
fibres and the need of additional reinforcement.
Finally, this paper also includes the design requirements and detailing of additional reinforcement if the SFR
is unable to cope with the forces due to the tension status of different zones of these junctions. The
approach for rebar detailing described in this paper is a forthright methodology using these junctions’ 3D
models in combination with Eurocode 2 [4] standards and own designer’s recommendations.
Mott MacDonald was appointed to undertake the design package C121 for the design of all Sprayed
Concrete Lining (SCL) tunnels for the Crossrail project. All types of junctions’ design is one of the most
complex SCL structures into this design package.
Tunnel sections have been designed in 2D and 3D for both primary linings and secondary linings. These
designs have been carried out using a numerical modelling software (FLAC) for the temporary case, and a
FEM structural software (STAAD), for the permanent case, once a calibration process between both
software have been done. However, junctions present more complexity than a single tunnel section and a
plain strain analysis is not enough to assess their structural behaviour. The 3D modelling methodology is the
most reliable method to accurately assess the impact of a child (smaller diameter) tunnel opening in a
parent tunnel (larger diameter).
This design methodology has been undertaken for both secondary lining sprayed and cast concrete in all
SCL stations. Design methodology is in accordance with the following standards: RILEM [6] and Eurocode 2
[4]
. The aim of the methodology is to evaluate the structural behaviour of the most critical cases, according
to the ground properties, depth, geometry and boundary conditions of the following types of junctions in all
SCL tunnels:
Single junctions: Platform tunnels to cross passages. Figure 1
Single junctions: Access passage to shafts, for both top opening and bottom opening. Figure 2
Double junctions type 1: concourse tunnels to cross passages. Figure 3
Double junctions type 2: concourse tunnels to cross passages and headwall. Figure 4
Double junctions type 3: wraparound where platform tunnels are the child tunnel. Figure 5
Double junctions type 4 (Twin openings): Launch Chamber to ventilation ducts. Figure 6
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Figure 1 – Platform tunnel to cross passage
Figure 2 – Shaft to tunnel
Figure 3 – Concourse tunnel to cross
passages with headwall
Figure 4 – Concourse tunnel to cross passages
Figure 5 – Wraparounds
Figure 6 – Twin Openings
The design methodology of permanent complex structures like junctions comprises the following stages:
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3D FEM modelling process:
Meshing: Challenges of the geometrical assembling (meshing size) of complex structures.
Soil – structure interaction element: Design of the boundary conditions of the 3D model.
Material properties.
Loading conditions: loads and load combinations as per Eurocode 0 [9] and Eurocode 1 [10].
Assessment of outputs of the 3D model.
Structural design as per RILEM [6] and Eurocode 2 [4].
Detailing of rebar as per Eurocode 2 [4].
All these parts of the design methodology are thoroughly explained in this paper to understand the benefits
of this approach in the design of complex permanent structures and show a method to assess the structural
behaviour of these junctions in their various configurations.
Furthermore, assessment of the most critical junctions in accordance with the ground properties, levels and
geometry of tunnels, and boundary conditions of junctions are also presented in the paper.
Junctions are structural elements in tunnels that are formed by the connection between a main tunnel with a
larger dimension called “parent tunnel” and a second tunnel with smaller diameter called “child tunnel”. The
main junctions are set up between platform tunnels and cross passages, and between concourse tunnels
and cross passages. There are also other junctions such as concourse tunnels and shafts in which
openings can be placed either at the crown or invert (such as for sumps and ventilation adits).
The secondary lining in junctions is defined by contraction joints that are located between 4 to 8 meters from
the opening centre line in parent tunnels, and between 1 to 2 meters in child tunnels. Junctions can be
either designed in sprayed concrete and cast in situ concrete with or without Steel Fibre Reinforced
Concrete (SFRC). Since the primary lining is not a waterproofing element, contraction joints of the
secondary lining might become potential zones of leakage thus, to guarantee the watertight conditions, all
contraction joints are designed with water-barriers and re-injectable grout tubes along the joint in radial and
axial direction.
As there are several junctions in each Crossrail Station and most of them present similar geometric
characteristics, a selection of the most representative junctions are presented. This exercise has been done
based on the following significant factors (i.e. the deepest one, the one with the biggest aspect ratio, the one
with the higher pore water pressure, etc):
Ground conditions
Depth of Junctions
Geometry
Boundary conditions
Geometrical properties of tunnels of different types of junctions designed with this methodology (described
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in this paper on sections 3 to 5) are detailed in table 1:
Table 1 – Geometry of Junctions
Parent
Child
tunnel
tunnel
secondary
secondary
lining
lining
thickness
thickness
(mm)
(mm)
0.7
350
300
4.50
0.84
300
275
9.95
7.50
0.75
250
250
6.0
4.05
0.7
250
250
8.95
7.0 (VD5) &
6.0 (VD4)
0.78
(VD5) –
0.7 (VD4)
300
300 (VD5) &
250 (VD4)
Parent tunnel
Child tunnel
diameter at
diameter at
tunnel axis
tunnel axis
level
level
(m)
(m)
Single junction
– STW1 – VA1
(FAR)
9.60
6.85
Double
junctions
(Type 2) –
AP6a to
AP10a&b (LIS)
5.35
Type of
junction
Aspect
ratio
Wraparounds
(Type 3) – PTE
to CP6
(LIS)
CH7 to shaft
(LIS)
LCE to VD4 &
VD5 (Type 4)
(LIS)
STAAD.Pro v8i is a structural analysis and design program that is based on the Finite Element Method. It
can efficiently generate finite element geometry for complex structures with openings such as junctions in
tunnels. The modelling process and analysis carried out using STAAD.Pro provided the results of the
analyses in terms of the predicted axial and shear forces, bending moment and deformation of the
secondary lining under long-term conditions.
Since the modelling process in STAAD is a complex task, the best way of understanding this process is
thoroughly detailing the structural modelling process that has been utilised by C121 for the Crossrail Project.
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The geometric construction of 3D models for tunnel junctions is the most time-consuming part of this
methodology. For Finite Element (FE) models the Designer selects the appropriate mesh sizes to achieve
the following:
Accurate geometrical representation of the behaviour of the selected junction.
Finer mesh sizing at points of isolated loads to achieve accurate output.
Coarser mesh at zones where construction is unlikely to change the stress conditions prior to the
construction of the junction.
The required level of numerical accuracy i.e. the fineness of the mesh (see figure 7).
Figure 7 – 3D model mesh for a double junction
Concrete properties to model the secondary lining in junctions have been used in accordance with both
specifications KT20 SCL[1] and KF10[2] Cast in situ concrete and paragraph 4.6.4 of the SCL Numerical
Modelling Guidelines, Rev 9.0[3]:
Concrete Grade: C32/40 at 90 days
Density: 2500 kg/m³
Poisson ratio: 0.2
Young’s modulus: 17 GPa
Coefficient of thermal expansion: alpha: 10-5 K-1
The interaction between soil and the structure is established through springs-beams attached to every node
of the plates that form the 3D model. The radial beam-springs act in compression only as compressive
stresses are transferred between the tunnel and the surrounding mass. The stiffness Ki [kN/m/m] of the
radial spring at node “i” is determined by using the following equation:
(1)
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where ‘Esi’ (kN/m²) is the modulus of elasticity of the soil surrounding the tunnel at that certain node, ‘Ri’ (m)
is the radius of the lining at the given node, while Si (m) is the surface associated with the node of the
element in circumferential direction along which the spring is operating.
Figure 8 – Spring beams model
Ending supports have to be implemented in the model. These represent the contraction joints by means of
stiff springs acting in compression only along the tunnel axis. This support condition is applied at both
endings of the parent tunnel and the ending of the child tunnel in their respective directions.
Figure 9 – Spring supports in PTW to CP3a single Junction, Liverpool Street
Self-weight is applied on the whole structure except for the spring beams representing soil as these are not
structural elements of the model.
The earth pressure acting on the secondary lining is determined in accordance with the results of FLAC
analysis for the long term (120 years). The radial contact pressure on the interface between primary and
secondary lining consists of both ‘active’ and ‘passive’ load (bedding reaction from deformation of the tunnel
lining).
The principle is illustrated in Figure 10 by the total (i.e., active + passive) ground pressure (hatched line) and
its active load (solid bold line). In a spring-beam model, only the ‘active’ part of the ground pressure load
should be applied onto the secondary lining. The ‘passive’ part of the ground load is provided automatically
by the springs.
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This structural model in STAAD withstands the shared ground load between primary & secondary linings
and the full pore water pressure in long term conditions (up 120 years), the temperature loads (winter and
summer), drying shrinkage and finally a surcharge of 75 kPa applied on the surface.
Figure 10 – Total and ‘active’ ground load
This model also considers a sharing ground load effect between the primary and secondary lining working
as a composite support.
The ground load is applied perpendicular to the surface above axis level and linearly decreases from crown
to the invert where the pressure is nil. The following example, junction STW1-VA1 at Farringdon, illustrates
the ground load distribution along the lining (see Figure 11).
Figure 11 – Earth pressure profile
The ULS (ultimate limit state) and SLS (service limit state) water pressure is depth-dependant and is taken
from the water pressure profile for each station. To illustrate this load a template in junction CP5/6
Wraparound at Liverpool Street is shown in Figure 12 and Figure 13.
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Figure 12 – Pore water pressure variation with depth
Figure 13 – Pore water pressures at CP5/6 wraparound
Shrinkage is determined according to Eurocode 2 where strains are a combination of drying and
autogenous shrinkages.
Shrinkage depends on concrete parameters and lining thickness and it is simulated as a change in
temperature. The following shrinkage values (considered as temperature increments ΔT) have been applied
as follows depending on the different thicknesses of secondary lining elements:
Table 2 – Shrinkage values
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Thickness (mm)
ε (10-4)
ΔT ( C)
300
2.90
24.2
500
2.80
23.1
800
2.60
21.3
1200
2.30
19.0
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In addition to the concrete temperature at the time of installation, the following temperatures at tunnel level
have been defined for the analysis of the secondary lining.
Table 3 – Absolute design temperatures
Face
Summer temperature (° C)
Winter temperature (° C)
Extrados (far face)
25
10
Intrados (near face)
30
15
The load combinations are defined as per BS EN 1990:2002 (Eurocode 0) Basis of structural design.
The ULS and SLS load combinations and applied factors as described in Numerical Modelling Guidelines[3]
are presented in this section (see Table 4, Table 5 and Table 6).
Table 4 – Loads and related load factors used in the model
ID
Load type
Description
I
Self-weight
γG = 1.40 (ULS) / γG = 1.00 (SLS)
II
Ground (earth) pressure
γG = 1.40 (ULS) / γG = 1.00 (SLS) (vertical and
horizontal ground loading including surcharges)
III
Water pressure ULS
γG = 1.40
IV
Water pressure SLS
γG = 1.00
V
Traction Load
γG = 1.40 (not included in the analysis)
VI
Shrinkage strain
γG = 1.40 (ULS) / γG = 1.00 (SLS)
Combination factor ψ0 = 0.6
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γQ = 1.50 (ULS) / γQ = 1.00 (SLS)
Summer temperature
Combination factor ψ0 = 0.6
VIII
γQ = 1.50 (ULS) / γQ = 1.00 (SLS)
Winter temperature
Combination factor ψ0 = 0.6
NB: γG is the partial factor for permanent actions, γQ is the partial factor for variable actions,
Table 5 – ULS combinations and applied factors (partial and combination factors)
Load
I
II
III
IV
V
VI
VII
VIII
Combination
1
1.4
–
–
–
–
1.40 x
0.6
–
1.50 x
0.6
2
1.4
–
–
–
–
1.40 x
0.6
1.50 x
0.6
–
3
1.4
–
1.4
–
–
1.40 x
0.6
–
1.50 x
0.6
4
1.4
–
1.4
–
–
1.40 x
0.6
1.50 x
0.6
–
5
1.4
1.4
–
–
–
1.40 x
0.6
–
1.50 x
0.6
6
1.4
1.4
–
–
–
1.40 x
0.6
1.50 x
0.6
–
7
1.4
1.4
1.4
–
–
1.40 x
0.6
–
1.50 x
0.6
8
1.4
1.4
1.4
–
–
1.40 x
0.6
1.50 x
0.6
–
Table 6 – SLS combinations and applied factors (partial and combination factors)
Load
I
II
III
IV
V
VI
VII
VIII
Combination
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1
1.00
–
–
–
–
1.00 x
0.6
–
1.00 x
0.6
2
1.00
–
–
–
–
1.00 x
0.6
1.00 x
0.6
–
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3
1.00
–
–
1.00
–
1.00 x
0.6
–
1.00 x
0.6
4
1.00
–
–
1.00
–
1.00 x
0.6
1.00 x
0.6
–
5
1.00
1.00
–
–
–
1.00 x
0.6
–
1.00 x
0.6
6
1.00
1.00
–
–
–
1.00 x
0.6
1.00 x
0.6
–
7
1.00
1.00
–
1.00
–
1.00 x
0.6
–
1.00 x
0.6
8
1.00
1.00
–
1.00
–
1.00 x
0.6
1.00 x
0.6
–
Resultant features of the analysis in STAAD are based on the matrix displacement method. In the matrix
analysis of structures by the displacement method, the structure is first idealized into an assembly of
discrete structural components (plates) as the loads are applied in the form of distributed loads on the
element surfaces or as concentrated loads at the joints (as described above).
STAAD calculates member stresses specified at intermediate sections as well as at the start and end joints.
These stresses include:
Axial stress (Si)
Bending-y stress (Mi)
Shear stresses (SQi) and
Combined stress (Top Combined SX & SY and Bottom combines SX & SY) which is the sum of axial-i
and bending-i stresses.
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Figure 14 – Stresses and Moments on Plate Elements
STAAD also generates force envelopes of the member forces FX (axial force), FY (Shear-y), and MZ
(bending moment) for any number of intermediate sections (see Figure 14).
The following is the sign convention for the maximum and minimum values:
FX – A positive value is compression, and negative tension.
FY – A positive value is shear in the positive y-direction, and negative in the negative y-direction.
FZ – Same as above, except in local z-direction.
MZ – A positive moment will mean a moment causing tension at the top of the member. Conversely, a
negative moment will cause tension at the bottom of the member. The top of a member is defined as the
side towards positive local y-axis.
MY – Same as above, except about local z axis.
Access Passage AP6a is a pedestrian tunnel within the Northern Line Link between the Crossrail Liverpool
Street Station and the London Underground Moorgate Station.
AP6a (parent tunnel) is an unusual tunnel since it has a double junction to two other tunnels (child tunnels)
AP10a and AP10b (each of them with different dimensions and shapes), a headwall, a sump and two
service chutes on its crown as per Figure 15.
Figure 15 – Plate model and thickness model representation
The secondary lining thickness and diameter for each tunnel section is listed below as shown in Table 7:
Table 7 – Secondary lining properties
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Tunnel
Diameter
(m)
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Concrete
SFRC – Arch
AP10a Child
Tunnel
4.00
Thickness
(mm)
300
Variable
Cast-In-Situ Invert
250 to 460
AP10b Child
Tunnel
AP6a
SFRC – Arch
275
Cast-In-Situ Invert
225
SFRC – Arch
300
Cast-In-Situ Invert
350
4.50
5.35
Headwall
5.35
SFRC – Arch
250
Sump (AP6a)
1x1
Cast-In-Situ Invert
250
Once the model has been completed in terms of inputs as described in Section 3, it is run and postprocessed. Once the model is run, the post-process stage follows where certain or all load combinations
can be selected as STAAD has calculated deformations, stresses and forces for each one of them.
The first parameter presented in STAAD is the deformed shape which is the calculation of the
displacements at every single node of the model and available for each individual load case and load
combinations in ULS and SLS as shown in Figure 16, Figure 17 and Figure 18.
Figure 16 – Elevation view – Deformed shape under load case SLS 07
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Figure 17 – Top view – Deformed shape under load case SLS 07
Figure 18 – Cross-section – Deformed shape under load case SLS 07
The deformed shapes are used to determine whether the crown or invert of the section is stressed.
STAAD presents the internal forces: axial forces and bending moments along two local axis: X and Y. When
analysing tunnels it is recommended that the local axis x follows the “longitudinal” direction of the tunnel
while local axis y follows the “hoop” direction of the tunnel. The following Figure 19 shows the typical
orientation of the local axis in tunnels:
Figure 19 – Local axis direction to interpret forces and stresses
STAAD presents the axial stresses, bending moments and shear stresses in both directions X (longitudinal)
& Y (hoop). The axial and shear forces can be calculated by multiplying these values by the thickness of the
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element.
The combined normal stresses are calculated as:
Along local X (Figure 20):
(2)
Along local Y (Figure 21):
(3)
Where:
(4)
t is the thickness of the element.
Figure 20 – Top combined stresses SX in X (longitudinal) direction in crown and invert sides
Figure 21 – Top combined stresses SY in Y (hoop) direction in crown and invert sides
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Once the combined stresses have been obtained for every load case and every load combinations and
having determined which of them is the critical case then the structural analysis follows and the calculation
of additional (aside of SFRC) reinforcement if required. These stages will be described in the following
sections.
Steel quantity calculation is done according to Eurocode 2.0
The process of detailing is based on the following standards:
Eurocode 2. BS EN 1992-1-1 [4].
Eurocode 2 BS EN 1992-1- 2 [5].
RILEM TC 162-TDF [6].
CIRIA C660 [7].
BS 8666:2005 [8].
The process starts assessing two main results of the calculation:
1. The need of rebar in different zones according to the Moment-Axial design capacity check.
2. Zone under tensile stresses according to the stress contours obtained in the 3D model.
Therefore, if there is a need for reinforcement in some specific areas, these areas are limited to the plotted
contours in the 3D model as is described below in Figure 22:
Figure 22 – Stresses contour on near face
Areas with tensile stresses bigger than approximately 3 N/mm2 (for a 300mm thickness lining) are the
zones where reinforcement is needed. These contours are compared with the tensile strength of the SFRC
which depends on the thickness in each case.
The rebar in these areas is designed for the minimum length of anchorage and lapping as per Eurocode 2.
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Scheduling, dimensioning, bending and cutting of steel are designed following the BS8666 requirements
(see Figure 23).
Figure 23 – Detailing of rebar. Near face at top heading connection
Aside from Eurocode 2 requirements in terms of detailing, the following rules have to be considered for
sprayed lining (SCL) with reinforcement:
No spraying of bars greater than 16 mm diameter at 150 mm centres as encapsulation problems are
much more likely with larger diameter bars. This also applies to groups of bars than when considered
together in terms of diameters and spacing build up to the same concentration of steel. This statement is
exclusively for SCL (with steel fibres).
No spraying is possible through areas that structurally require shear links.
No spraying through two layers of reinforcement.
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In the interface between reinforced cast in situ concrete and reinforced sprayed concrete the overlapping
of the reinforcement in the cast invert with the reinforcement in the sprayed concrete would require
spraying through two layers of reinforcement. This is to be solved by installing the far face reinforcement
and adding positional couplers to the near face so the spraying of only one layer of reinforcement at a
time is undertaken.
Concrete sprayed through reinforcement to be preferably no steel fibre in order to avoid encapsulation.
Lining therefore could be sprayed in alternate layers of steel fibre reinforced concrete and non SFR
concrete.
In this section the assessment of the most critical junctions selected based on ground properties, levels and
geometry of tunnels and boundary conditions of junctions are described:
The assessment is set up considering the following aspects:
Ground conditions, levels and ground water: the parameters of the ground define how the ground loads
are acting on the secondary lining. For instance junctions in London Clay will be withstanding more pore
water pressure than junctions located in the Lambeth Group due to different permeabilities and soil
stiffness.
Junction depth: the level of tunnel axis will determine the ground pressure that will be transferred to the
secondary lining when this load is shared between both linings, primary and secondary, as is set up in
the Numerical Modelling guideline [3]. Deeper junctions will be most critical since more ground pressure
will be acting on the lining.
Geometry: The following geometric factors are important:
Number of child tunnels: single junctions, or double junctions where deflections and tensile stress are
larger.
The ratio between the diameter of the smaller (child) tunnel and larger (parent) tunnel has a
considerable influence on the design and typically varies between 0.4 and 0.8. Tunnel junctions with
larger aspect ratios have been selected since tensile stresses are larger on the crown zone of the
connection on near faces.
The location of the child tunnel opening with regards to the parent tunnel, i.e. this opening can be
located at sides of the parent tunnel forming a typical junction or the openings can be located at
crowns which is the case of shafts connection with cross passages.
Thicknesses of linings are important when junctions are cast in situ in different pours and, thus, the
Early Age Thermal Cracking (EATC) has to be considered in the design.
Boundary conditions: It is important to evaluate the potential impact of a nearby structural element such
as headwalls, sumps and shafts on junctions. Headwalls, for example, have an important impact with
regards to the reinforcement design when located very close (less than 2m) to the openings of child
tunnels.
These factors determine the structural behaviour of selected representative junctions in C121 SCL stations.
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This selection is summarised in the following table (matrix of junction assessment):
Table 8 – Matrix of junction assessment
Typology of
junctions /
Number of
child tunnels
Station
Single junction
FAR(Loading
conditions –
PWP
pressure
bigger at
crown level)
Type of
ground
Tunnel
axis
level –
depth
Pore
water
pressure
(PWP)
Boundary
conditions
Junction
selected /
main
selection
factor
London
clay –
LC3
106
mATD –
20 m
110 KPa
crown to
50 kPa
invert.
Contraction
joints all
ends
STW1/VA1
(worst
ground
conditions)
London
Clay –
LC3
79
mATD –
35 m
200 KPa
crown to
240 kPa
invert.
Contraction
joint /
headwall
LS – CH7
to Shaft
(Worst
condition in
shear)
150 KPa
crown to
120 kPa
invert.
Contraction
joints and
headwall
CP1a to
EPW1
(bigger
aspect
ratio)
82
mATD –
32m
180 KPa
crown to
220 kPa
invert.
Headwall
in parent
tunnel, in
other ends,
contraction
joints
AP6a to
AP10a /
AP10b
(loading
conditions
– PWP)
79
mATD –
35m
190 KPa
crown to
250 kPa
invert.
Headwall
in child
tunnel and
contraction
joints in
other ends
CP5 / CP6
to
PTE/PTEW
(thickness
– EATC
impact)
LIV
Shaft to tunnel
(Only with
this sort of
junctions)
88
Double
junction -Type
1
Double
junction –
headwall –
Type 2
Wraparound
(Double
junction type
3)
WHI
(deeper)
LIV – NLL
LIV (thicker
lining)
London
Clay –
LC3
London
Clay –
LC3
London
Clay –
LC3
mATd –
24m
* Geometric properties are described in table 1.
Output: Near Face Stresses Hoop Direction
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Figure 24. Single Junctions: Platform tunnels to cross passages
The model contours with tensile stresses higher than 3 N/mm2 are zones where the most critical tensile
stresses are concentrated. These tensile stresses are bigger than the maximum tensile strength of the
SFRC, thus additional reinforcement is needed on near faces. Furthermore, these contours define the limit
length of reinforcement in terms of detailing to ensure the correct anchorage and lapping.
Output: Shear stresses around the shaft connection
Figure 25. Single junctions: Access passage to Shafts
The shear stresses are localized on the main tunnel where the shaft lining is punching and is governing the
design against shear.
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Figure 26. CH7 to Lift Shaft at Liverpool St Station
Output: Near Face Stresses Longitudinal Direction
Figure 27. Double junctions type 1: concourse tunnels to cross passages
The tensile stresses are concentrated at crown and invert connection between parent and child tunnel, so
reinforcement must be provided on those areas. The bigger the aspect ratio the higher additional
reinforcement is required.
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Figure 28. AP7 to CP1 and CP4 at Liverpool St Station
Output: Near face stresses longitudinal direction
Figure 29. Double junctions type 2: concourse tunnels to cross passages and headwall
This case has stresses concentrated on near face in longitudinal direction. Furthermore, the headwall is
withstanding heavy compression on near face what means tensile stresses will be concentrated radially and
L bars will be needed to be installed on far face.
Figure 30. EPW1 to CP1 at Whitechapel Station
Output: Far face stresses in hoop direction
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Figure 31. Double junctions type 3: wraparound tunnels
These contours show tensile stresses around the headwall in far face what means reinforcement in hoop
direction on far face will be required and heavy compressions on inverts on bottom faces what is a usual
resultant from the pore water pressure loading. Tensile stresses are encountered on top faces of the invert.
Figure 32. PTE to CP6 Wraparound at Liverpool St Station
Outputs: Stresses in hoop direction and far face stresses in longitudinal direction.
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Figure 33. Double junctions type 4: Twin openings
The stresses in hoop show strong compressions between both child tunnels that have been checked
against the maximum compression strength of the SFRC. This concentration of compression stresses is
usual in junctions with two very close child tunnels. Furthermore, there is a concentration of tensile stresses
on the far face in longitudinal direction between both child tunnels (above and below the tunnel axis).
Longitudinal reinforcement is needed to be extended between both child tunnels, and between each child
tunnel and joints located at the ends on the model.
Figure 34. LCE to VD4 and VD5 at Liverpool St Station
This paper has presented a method of designing secondary linings considering the contribution primary
lining in sprayed concrete structures with complex geometries. The method was found to have the following
advantages:
The system of calibration between 2D models for soil-structure interaction (FLAC in this case) and more
typical structural design software (STAAD) avoided the need for extensive use of 3D geotechnical
modelling software, which is typically very time consuming.
The standardization of the design method allowed many different geometry schemes to be undertaken
without repeating all modelling from the beginning. With a project as geometrically complex as Crossrail,
with many different cross-passage, ventilation adits and access passage geometries, this allowed a great
number of different junction types to be analysed relatively quickly.
The method allows the benefits of the two programmes used to be utilised to their full. In the case of
FLAC, the design of the primary lining, where SLS states are not of interest, the soil-structure interaction
is key. For the secondary lining, STAAD is able to add load cases such as temperature, shrinkage,
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internal and accidental loads. The SLS load cases can be considered in more detail as they apply to the
secondary lining.
The method allows specific areas of junctions to be identified to ensure that heavy reinforcement, if
needed at all, is limited to stress and bending moment concentrations. This minimises working at height
to fix reinforcement and is extremely important for sprayed linings as the reduction of reinforcement
improves workmanship.
The identification of areas with concentration of stresses is key to whether decide the real need for
additional reinforcement or further analysis. Usually, further analysis is the preferred and is usually done
through:
Allow for plastic hinges to develop and check rotation in both primary and secondary lining. This
allowed reinforcement to be avoided in some areas.
Allow stress concentrations considered to be unrealistic to be smoothed out over immediately
adjacent parts of the structure, e.g. in tight corners around the immediate perimeter of the junction
openings.
In using this method, patterns can be seen in the behaviour of junctions:
The near and far face bending patterns are typically very similar (although with differing magnitudes), as
can be seen by the various displacement plots shown throughout this paper. An exception is egg-shaped
parent tunnels, which can cause the moments immediately around the child tunnel perimeter to change
tension face.
It would likely be possible to define a standard spring stiffness for use in secondary lining models per
project or per set of similar ground conditions and depths, without significant loss of accuracy.
Junctions where the child tunnel approaches on a slope typically require more reinforcement. Along with
tunnels approaching at an oblique angle in plan, these are also significantly more difficult to detail. Such
geometry would be best avoided from a pure tunnelling perspective. However, many other factors rightly
govern the geometry and the method presented here has proven able to cope with such cases. Such
flexibility is invaluable for new stations in dense urban areas.
In general, the reinforcement of the cast-in situ invert slabs was unaffected by the presence of the
opening. In this case, the simpler 2D analysis used for areas remote from the junction usually governed
for the invert reinforcement. Exceptions are openings directly in the invert (e.g. sumps).
Double facing junctions, e.g. those from concourse to cross-passages presented here, cannot generally
be assumed to behave as mirrored single junctions, especially as the aspect ratio child/parent grows.
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[1]
KT20: C121 – SCL Specification Sprayed Concrete Linings
[2]
KF10: C122-M&W Specification – In-situ Concrete
[3]
SCL Numerical Modelling Guidelines (C121 Document)
[4]
Eurocode 2. BS EN 1992-1-1 Design of concrete structures. Part 1.1: General rules.
[5]
Eurocode 2 BS EN 1992-1- 2 Design of concrete structures. Part 1.2: Structural fire design.
[6]
RILEM TC 162-TDF: ‘Test and design methods for steel fibre reinforced concrete’.
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Design methodology for permanent complex structures: Secondary lini...
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[7]
CIRIA C660: Early-age thermal crack control in concrete.
[8]
BS 8666:2005: Scheduling, dimensioning, bending and cutting of steel reinforcement for concrete —
Specification.
[9]
BS EN 1990 Eurocode 0
[10]
BS EN 1991 Eurocode 1
C121 Tunnel Design Lead
C121 Design Manager
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