Design Considerations for Bored Tunnels at Close Proximity

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

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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/mm2. 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.

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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/m2 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:

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Load factor for overburden and water pressure = 1.4 Load factor for surcharge = 1.6

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 = Ij+If(4/n)2 where Ij is the moment of inertia of the joint (Ij = 0), n is the total number of segments in a ring and If 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

SLS (crack width)

ULS 1

2

3

4

5

√

√

√

√

√

Load Factor = 1.0 75kN/m2 Uniform Surcharge Water Table at Ground Surface

√ √

√

√

7

8

9

10

11

12

√

√

√

√

√

√

√

√

√

√

√

√ √

√

√

√

√

√

√

√

√

√ √

√

√

√

√

Reduced Section Moment of Inertia Short Term Concrete Young's Modulus

6

√

√

Water Table 3m Below Ground Surface Full Section Moment of Inertia

√

√

√

√

√

SLS (deflection)

√

√

√

√

√

√

√

√

√

√

Long Term Concrete Young's Modulus

√

√

Additional Distortion of 15mm on Diameter

√

√

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√

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 ro

x

Second tunnel

a

b First tunnel

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 = uoro /r

(1)

The volume loss during tunnelling can be expressed as: Vs = {πro2- π( ro - uo )2}/ πro2

(2)

Equation (2) gives: uo = ro{1-√(1-Vs)}

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(3)

5

Using equation (1) and (3): At point a, ua = uoro /ra, where ra is the distance of point a to the centre of the second tunnel. At point b, ub = uoro /rb, where ra is the distance of point a to the centre of the second tunnel. The maximum diametrical distortion, δd is defined as δd = ua - ub The radial distortion is given by: δr = δd /2

(4)

Morgan (1961) showed that the bending moment due to distortion over radius is given by: M = (3EIδr)/ ro2

(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

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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 9000

fcu = 60 N/mm2 h = 275 mm b = 1000 mm

8000

N (kN)

7000 6000 5000

Ground Loading

4000 3000

Spare Capacity

Ground Loading Ground Loading +1% Volume Loss

2000 1000 0 0

50

100

150

200

250

300

350

400

M (kNm)

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 1D Once daily

1D

L

1D

Every 6 hours or every ring progress

3D Once daily

whichever is

Legend: L = length of TBM shield, D = Excavated tunnel diameter Figure 6. Convergence monitoring scheme with reading frequency

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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.

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