the Full Text Article in PDF format

Design Considerations for Bored Tunnels at Close Proximity
Dazhi Wen, John Poh, Yang Wah Ng
Land Transport Authority, Singapore
ABSTRACT
In the various stages of the Circle Line (CCL) in Singapore, civil engineers constantly face the
challenge to achieve the optimum alignment through heavily built-up areas. Both construction risks
and site constraints have to be taken into account when selecting the alignment. In CCL Stage 3, the
twin bored tunnels are aligned with a minimum separation of 2.3m in order to avoid tunnelling directly
under buildings. This paper describes in detail the design considerations for the pre-cast reinforced
concrete segmental lining for the bored tunnels of CCL Stage 3. The effect of the second tunnel
construction on the first tunnel is examined. The methodology for evaluating the additional loading on
the first tunnel lining due to the second tunnel construction is also presented
1. INTRODUCTION
The proposed Circle Line Stage 3 (CCL3) is a medium capacity rail system. It continues from Circle
Line Stage 2 network from Bartley station. After leaving Bartley station the tunnels pass under an area
of private residential houses at Lorong Gambir and St. Gabriel’s Secondary School before entering the
Serangoon public housing estates and Serangoon Station. The tunnels continue to travel under
Serangoon area and then enter Lorong Chuan station, after which they pass under the CTE and arrive
at the Bishan station. Leaving Bishan station, the tunnels will be under the private residential area of
Jalan Binchang and Pemimpin Drive before reaching the last station of CCL3 at Marymount station.
Altogether there are five underground stations connected by tunnels. The total length is approximately
5.7km. In order to avoid underpinning of the residential houses and high-rise residential flats, the twin
bored tunnels have to be aligned at very close distance of less than one tunnel diameter. The tunnels at
Lorong Gambir are the closest with a minimum clearance of 2.3m, see Figure 1.
Serangoon Ave. 1
St. Gambriel’s
Secondary
School
Minimum clearance
between tunnels: 2.3m
Gambir Walk
To Serangoon station
Figure 1. Tunnels at Lorong Gambir
F19 1

Figure 2 shows the general arrangement of the segments. The pre-cast reinforced concrete segmental
linings are designed by the LTA in-house team. The internal diameter of the tunnels is 5.8 metres
defined by space requirements. The thickness of the lining is designed to be 275mm. A segment length
of 1.4m is adopted. Each ring consists of five ordinary segments plus a key segment. Curved bolts are
designed for both the radial and circumferential joints. A composite hydrophilic and elastomeric
gasket is specified on the drawing. The rings have a maximum taper of 40mm. The radial joints are
convex to convex joints. This type of joints allows some articulation to take place. Because the radial
joints are staggered from ring to ring, the lining is considered in the normal load combinations as a
continuous ring. The circumferential joints are flat joints.
Figure 2. General arrangement of tunnel segments
The concrete for the segments is specified to be grade 60 concrete with a 28-day compressive strength
of 60 N/mm 2 . Silica fume is required in the concrete mix under the contract to reduce the permeability
and the chlorite diffusion rate of the segments. The extrados of the segments is also required to be
coated with epoxy.
2. DESIGN OF REINFORCED CONCRETE SEGMENTAL LINING
2.1 Design concept
It has been well established that tunnel lining in soft ground will redistribute the ground loading. The
ground loading acting on a circular tunnel lining can be divided into two components: the uniform
distributed radial component and the distortional component. The uniform distributed radial
component will only produce hoop thrust and the lining will deform in the radial direction with the
shape of the ring remaining circular. The distortional component will produce bending moments in the
lining, and the crown and invert will be squatted (move inwards) and at the axial level the lining will
move outwards, Figure 3. The soil pressure at the crown and invert will be reduced as a result of the
inward movement and the soil pressure at the axial level will be increased due to the outward
movement of the lining. The redistribution of ground pressure around the ring and the lining
deformation will continue until a balance is achieved. The stability of the tunnel lined by concrete
segments thus depends on a continuous support / pressure around ring. Any cavity in the space
between the tunnel lining and the ground will result in excessive distortional loading on the lining and
may subject the ring to undergo excessive distortion, causing unacceptable cracking of the segments.
F19 2

Deformed ring
Deformed
ring
Figure 3. Tunnel lining subjected to uniform distributed loading and distortional loading
Various design methods are available for segmental lining design. The Design Criteria of the Land
Transport Authority (LTA) of Singapore accept the methods of continuum model by Muir Wood
(1975) modified by Curtis (1976), bedded beam model by Duddeck et al (1982) or the finite element
method. The lining for the CCL3 bored tunnel is designed using the continuum model. The method
assumes that the lining deforms in an elliptical shape and the ground is an elastic continuum. The hoop
thrust and moment induced by the soil-structure interaction are evaluated accordingly.
2.2 Design analyses
The tunnels are to be constructed through soft ground with a tunnel boring machine (TBM). The
vertical pressure applied to the lining is thus the full overburden pressure. Distortional loading is
derived by using the appropriate K-factor in Curtis formulae according to the soil condition at the
tunnel location. The following K-factors are used in accordance with the LTA Design Criteria:
Table 1. K-factor
Soil Type
K
Estuarine, Marine and Fluvial Clays 0.75
Beach Sands, Old Alluvium, Completely Weathered Granite, Fluvial Sands 0.5
Completely Weathered Sedimentary Rocks 0.4
Moderately to Highly Weathered Sedimentary or Granite Rocks 0.3
A uniform surcharge of 75 kN/m 2 is considered in the design. The design ground water table is taken
at both the ground surface (upper limit) and 3m (lower limit) below the surface.
The design assumes that the segments in the permanent condition are short columns subject to
combined hoop thrust and bending moment. Both ultimate limit state (ULS) and serviceability limit
state (SLS) are checked. Ultimate limit state design ensures that the load bearing capacity of the lining
is not exceeded while serviceability limit state design checks both the crack-width and deformation of
the lining. The following factors are used in the limit state design:
• Ultimate limit state: Load factor for overburden and water pressure = 1.4
Load factor for surcharge = 1.6
F19 3

• Serviceability limit state: Load factor for overburden, surcharge and water pressure = 1.0
The overburden, surcharge and water pressure are assumed as loads on the tunnel, and the effects of
ground arching around the tunnel are neglected for tunnels in soft ground. For reinforcement design
for both the ULS and SLS, the thrust and moment are obtained assuming a continuous lining with full
section moment of inertia and short-term Young's modulus for the concrete. This is to obtain the
maximum moment in the ring. For deflection checking the Young's modulus of the concrete is
reduced by 50% to account for concrete creep. The moment of inertia of the segment is also reduced
based on the recommendation by Muir Wood (1975) that:
I = I j +I f (4/n) 2
where I j is the moment of inertia of the joint (I j = 0), n is the total number of segments in a ring and I f
is the full moment of inertia before reduction. This is to obtain the maximum deflection in the ring.
The design analyses have been carried out for sections where the tunnels are expected to experience a
maximum and minimum overburden pressure and where the tunnels transverses different soil strata.
The load combinations are listed in Table 2.
Table 2. Load combinations
LOAD
COMBINATIONS
Load Factor = 1.4
and 1.6
ULS
SLS
(crack width)
SLS
(deflection)
1 2 3 4 5 6 7 8 9 10 11 12
√ √ √ √ √
Load Factor = 1.0 √ √ √ √ √ √ √
75kN/m 2 Uniform
Surcharge
Water Table at
Ground Surface
Water Table 3m
Below Ground
Surface
Full Section Moment
of Inertia
Reduced Section
Moment of Inertia
Short Term Concrete
Young's Modulus
Long Term Concrete
Young's Modulus
Additional Distortion
of 15mm on
Diameter
√ √ √ √ √ √ √ √
√ √ √ √ √
√ √ √ √ √ √ √
√ √ √ √ √ √ √ √
√ √ √ √
√ √ √ √ √ √ √ √
√ √ √ √
√
√
F19 4

2.3 Effect of the second tunnel construction on the first tunnel
Typically for twin bored tunnels, the second tunnel drive will be some distance behind the first tunnel
drive. If there is adequate clearance between the two tunnels, the effect of the second tunnel
construction on the erected segmental lining of the first tunnel is negligible. The rule of thumb is that
the clearance between the two tunnels should not be less than one tunnel diameter. If the clearance
between the tunnels is less than one tunnel diameter, the design should make allowance in the lining of
the first tunnel for the effect of the second tunnel construction.
Ground movement due to the second tunnel construction will cause additional movements to the first
tunnel besides that due to the ground loading. The additional movements will result in additional
distortion, which is the difference of the movements of the first tunnel at two diametrically opposite
points, such as at points a and b, where point a is closest to and point b is the furthest from the second
tunnel, see Figure 4. Correspondingly there will also be an additional distortion between the crown
and invert of the tunnel. For design purpose, it is necessary to establish the maximum additional
distortion to compute the maximum additional moment that the lining will be subjected to. The
maximum distortion will take place across the diameter along the line connected by the centres of the
two tunnels, i.e. points a and b in Figure 4. This maximum distortion can be calculated based on the
theory of elasticity by using the volume loss due to the construction of the second tunnel.
y
p
Second
tunnel
r o
x
a
First
tunnel
b
Figure 4. Two tunnels at close proximity
Assuming that the ground is a homogeneous, isotropic, linearly elastic mass, the radial movement of
the ground at a radial distance r from the centre of the second tunnel can be derived based on the
theory of elasticity as follows:
u = u o r o /r (1)
The volume loss during tunnelling can be expressed as:
Vs = {πr o 2 - π( r o - u o ) 2 }/ πr o
2
(2)
Equation (2) gives:
u o = r o {1-√(1-Vs)} (3)
F19 5

Using equation (1) and (3):
At point a, u a = u o r o /r a , where r a is the distance of point a to the centre of the second tunnel.
At point b, u b = u o r o /r b , where r a is the distance of point a to the centre of the second tunnel.
The maximum diametrical distortion, δ d is defined as δ d = u a - u b
The radial distortion is given by:
δ r = δ d /2 (4)
Morgan (1961) showed that the bending moment due to distortion over radius is given by:
M = (3EIδ r )/ r o
2
(5)
Based on equations (4) and (5), the additional distortional moment in the first tunnel lining due to the
second tunnel construction can be calculated. The total bending moments for structural design of the
segments are superimposed by adding the additional distortional moment to the moment due to ground
loading, assuming the hoop thrust remains unchanged.
3. ALLOWABLE ADDITIONAL DISTORTION FOR CONSTRUCTION
The method outlined in Section 2.3 above can be used to make allowance in the design of the tunnel
lining to cater for the effect of the second tunnel construction on the first tunnel. However, it is
difficult to monitor such effect during construction as the method relies on the prompt assessment of
the volume loss generated by the second tunnel construction. This back analysis of the volume loss is
typically not readily available at the time of tunnel construction. It is thus not practicable to use
volume loss as a controlling parameter during construction. In order to overcome this shortcoming, it
is proposed to use the conventional convergence monitoring as a means to ensure that the additional
distortion of the first tunnel due to the second tunnel construction is within the capacity of the lining of
the first tunnel.
Additional analyses have been carried out in the design of CCL3 tunnel lining to determine the
allowable additional diametrical distortion for construction. This allowable diametrical distortion is
not only for the effect of second tunnel construction, but also for the effects of all other construction
activities, for example cross passage construction. In the analyses, it has been assumed that the ring
has a reduced moment of inertia as recommended by Muir Wood (1975). The following steps are
taken to determine the allowable diametrical distortion for construction:
• The hoop thrust and moment under the ground loading and surcharge are calculated based on the
method described by Muir Wood (1975) and modified by Curtis (1976);
• The spare moment capacity is taken as the difference between the ultimate capacity based on the
reinforcement provided and the calculated moment due to the ground loading and surcharge. Both
ULS and SLS are checked and the lesser of the two is taken as the spare moment capacity that the
ring has for construction.
• This spare moment capacity is converted into radial distortion with the use of Equation (10). This
distortion multiplied by two is thus the allowable diametrical distortion for construction.
Assuming the allowable diametrical distortion will be fully developed during construction, the ring is
checked for the capacity of 15mm distortion allowed for long term due to adjacent future unknown
F19 6

development. Again, the additional moment that will be generated in the lining due to the 15mm
diametric distortion is computed by using Equation (10).
The above procedures are illustrated by the N-M interaction diagram in Figure 5 for the ultimate limit
state. For serviceability limit state (crack width checking), similar approach can be adopted.
10000
N (kN)
9000
8000
7000
6000
5000
4000
3000
2000
1000
0
Ground
Loading
Spare
Capacity
0 50 100 150 200 250 300 350 400
M (kNm)
f cu = 60 N/mm 2
h = 275 mm
b = 1000 mm
Ground Loading
Ground Loading +1%
Volume Loss
Figure 5. Moment – Hoop Thrust interaction diagram for reinforcement ratio of 1.19%.
4. MONITORING REQUIREMENTS
The proposed monitoring scheme is shown in Figure 6. The convergence monitoring can be made by
extensometers and the measurement should be able to determine the diametrical distortion of the
lining. The required monitoring frequency for each ring in the first tunnel will depend on the position
of the TBM of the second tunnel.
Direction of advance
TBM
2nd Tunnel
1st Tunnel
1 D 1 D L 1 D 3 D
Once daily
Every 6 hours or every ring
progress whichever is
Once daily
Legend: L = length of TBM shield, D = Excavated tunnel diameter
Figure 6. Convergence monitoring scheme with reading frequency
F19 7

5. CONCLUSIONS
The design methodology is presented for the design of the tunnel linings for CCL3 bored tunnels. A
method has been proposed to make allowance in the tunnel lining design to cater for the effect of the
second tunnel construction on the first tunnel if the two tunnels are aligned at closer than one tunnel
diameter apart. Procedures are developed to derive the additional distortional capacity of tunnel
linings. This capacity can be monitored during construction by the conventional tunnel convergence
monitoring using taper extensometers. As the monitoring is relatively simple and fast, the results will
enable the engineer to assess whether the capacity of the lining is exceeded during construction.
6. REFERENCES
Curtis, D.J., 1976. Discussion, Geotechnique 26, 231 – 237
Duddeck, H. and Erdmann, J., 1982. Structural design models for tunnels, Tunnelling’82, International
Symposium organised by Institution of Mining and Metallurgy.
Morgan, H.D., 1961. A contribution to the analysis of stress in a circular tunnel, Geotechnique 11, 37
– 46
Muir Wood, A.M., 1975. The circular tunnel in elastic ground, Geotechnique 25, No. 1, 115 – 127.
F19 8