PRACTICAL DESIGN OF SHIELD TUNNEL LINING

PRACTICAL DESIGN OF SHIELD TUNNEL LINING

1 INTRODUCTION The present study considers an irrigation tunnel which involves tunneling with tunnel boring

machine(TBM) and consists of segmental concrete lining. The tunnel is located in Madhya

Pradesh state of India. At a certain stretch along the alignment of the tunnel, there is an

operational railway track. Apart from other loads tunnel lining is also subjected to dynamic

train loads.

The TBM driven tunnels are segmented because of the ground

conditions and are constructed mainly from reinforced concrete segments. The excavation

of the ground and the placement of the segments are carried out by Tunnel Boring Machine

itself. Between the segments, longitudinal and circumferential joints are situated.

The general layout plan of the region is shown below:

2 BASICS OF CONCRETE SEGMENTS IN TBM DRIVEN TUNNELS This para is included in the article to understand the concept of segmental

concrete lining installed when tunnels are excavated using tunnel boring machines.

The segmental concrete elements are prefabricated within tight

tolerances. The dimensions of a segment are chosen to be as large as possible, resulting

in a minimum number of segments per ring, with the aim of optimizing the speed at which

the tunnel boring machine advances. Also the available space for transport and placement

of the segments, as well as the maximum possible extension of the jacks, determine the

dimensions of the segments.

The thickness of the concrete segments is determined by the global

structural behavior of the lining and the magnitude and configuration of the applied jack

forces coming from the TBM. The concrete segments are positioned in stretched bond. In

this configuration there is no ongoing joint in axial direction. If a strong interaction between

rings is present, bending moments in segment joints are transferred to segments in

adjacent rings. This way the rotation of segment joints is limited. Following are the

components of segmental concrete lining.

In case of considered irrigation Tunnel, 7 segments per ring are used,

subdivided in 4 normal segments, 2 counter segments and 1 key segment. The key

segment is placed near the top of a ring. The key element is wedge shaped (tapered) and

smaller which makes its placement easier.

The concrete segments are prefabricated and lightly reinforced to withstand bending

moments and splitting forces. These forces not only occur during the normal operation but

also during transport and placement. Additional reinforcement is put on places where jack

forces are introduced, handle and bolt holes are located and around dowels.

2.1 SEGMENTS PROFILE

The segmental lining type system for the considered irrigation tunnel is specified as follows:

- Parallel ring segmental lining system, thickness 30 cm

- Composed of 7 segments per ring. 4 normal segments, 2 counter segments and 1 key

segment

- dowel connectors (tapered guiding rods of dia. 26mm/30mm) in the ring joint

- Bolts (special connectors) for radial joints

The width of one segmental ring is 1.6m. Tunnel cross section is shown below:

3 GEOLOGY / GROUND CONDITIONS Following figure illustrates the geology of the region where railway line is crossing over the

tunnel.

There are complex changes of rock/soil types along the length of tunnel. Conservatively,

soil consisting of clay/Moorum/gravels considered in the analysis. Water table exist almost

up to the surface level.

In the absence of field tests, geotechnical properties surrounding strata have been

estimated based on different available literature. Changes in geotechnical properties will

result in change in analysis results. Following parameters are considered for the

surrounding strata of tunnel lining:

Soil Properties

Density (kN/m3) 22(saturated)/12(submerged)

E(Youngs) (MPa) 200

Internal angle of

friction,

Degrees 30

Cohesion (MPa) .05

Poison’s ratio, 0.3

4 SEGMENTAL LINING PROPERTIES The following materials are to be used for the segments of the TBM tunnel.

RCC and Grout Concrete Grade: M50

Young’s modulus of concrete = 5000√fck = 5000x√50 = 35355.34 N/mm2

Poisson’s ratio of concrete, = 0.2

The reinforcement for the segments is of Fe 500 grade conforming to Indian standard IS

1786: 2008.

Allowable direct compressive stress = 12 N/mm2 as per table 21 of Indian standard IS

456:2000

Allowable bending stress = 16 N/mm2 as per table 21 of IS 456:2000

5 STRUCTURAL ANALYSIS

5.1 STATIC 2D ANALYSIS

Static 2D analysis has been carried out for evaluating the stresses in segmental lining

when it is subjected to combination of maximum static loads. Refer para - 7 for 2D analysis

of concrete segmental lining. 2 dimensional modelling of segmental profile has been carried

out in STAAD pro software.

5.2 3D FEM ANALYSIS

A 3 dimensional finite element model has been created in MIDAS FEA software to evaluate

construction stage stresses induced in segmental lining. The surrounding ground is defined

by Mohr-Coulomb composite properties.

Refer para-8 and para-9 for stage wise modelling and analysis.

A dynamic analysis has also been carried out considering wave motions generated in

ground by high-speed train passages.

The simulated wave motions in ground were interpreted for train moving loads traveling at a

maximum speed of 150 km per hour. Refer para-10 for dynamic analysis details.

5.3 JOINT SIMULATION

Between the segments of the lining are (plastic) joints. These joints are

modelled as interface elements in MIDAS 3D model.

Bulk modulus(G) and shear modulus(K) of concrete can be evaluated as :

G = 35355.34/(2 x (1+0.2)) = 14731.39 N/mm2

K = 35355.34/(3 x (1-0.2)) = 14731.39 N/mm2

The apparent stiffness of interface zone in normal direction can be expressed as:

Where zmin is the smallest width of an adjoining zone in normal direction as shown below:

Element of 1m size considered to evaluate stiffness moduli.

Therefore normal and shear stiffness modulus of interface element =

(14731.39+4x14731.39/3)/1 = 34373.25 N/mm3 = 3.43 x 1013 N/m3

6 LOADS The tunnel will be subjected to following loads.

6.1 DEAD LOAD

Self-weight of segmental lining is incorporated in the analysis with the input density of

25kN/m3 in the software.

6.2 EXTERNAL WATER PRESSURE

Water table exists almost up to the surface level. Water head at the top of overt is about

15m and bottom of invert it is about 25m. Hence, linearly varying external pressure from

150kN/m2 at the top to 250kN/m2 at the bottom of segmental lining has been applied.

6.3 INTERNAL WATER PRESSURE

The internal water pressure at any point of time during operations shall not exceed the

external pressure. Since internal water pressure will only balance external pressure on

lining, it is not considered in the analysis.

6.4 SOIL PRESSURE

Overburden height = 15m above crown. Since soil is submerged, density of 12 kN/m3 has

been considered. Water pressure is applied separately.

Weight of over burden varies from 12 x 15 = 180 kN/m2 at the top to 12 x (15+4.9) = 238.8

kN/m2 at the springing level.

The horizontal earth pressure is assumed to be a uniformly varying load that increases with

increasing depth. It is derived from the weight multiplied by the coefficient of lateral earth

pressure (). The horizontal ground pressure should be the uniformly varying load acting on

the centroid of lining from the crown to the bottom.

The value of coefficient of lateral earth pressure to be used in the design calculation should

be between the value of coefficient of lateral earth pressure at rest and the one of

coefficient of active lateral earth pressure.

From following equation for evaluating earth pressure

Considering value of as 0.7,

qe1 = 0.7 x (180 + 12 x 0.3/2) = 127.26 kN/m2

qe2 = 0.7 x (180 + 12 x (2 x 4.9 – 0.3/2)) = 207.06 kN/m2

6.5 GROUTING

The grouting pressure of 200 kN/m2 has been considered.

6.6 SURCHARGE PRESSURE

The surcharge pressure of 10kN/m2 has been considered on surface.

6.7 TRAIN DYNAMIC LOADS

Train loads corresponding to standard Indian 25t loading as per clause 2.3 of IRS Bridge

rules, has been used for broad gauge loading. Following axle-load configuration is used in

the analysis.

Thus live load per wheel is 245.2/2 = 122.6 kN and is applied as point load on nodes of

modelled track. Dynamics of a moving train has been simulated in the 3D FEM model

considering maximum train velocity of 150 kM/hr. Variation of the wagon normal force with

time in the direction of moving train has been determined and applied on the numerical

model as a point load.

The situation of axle force in the schematic plan of train wagons and movement direction of

the train and the normal force variation of wagon wheels are depicted in following figure.

Suppose that at t = 0 s, in the origin of Cartesian plane, axel force of the first wheel of the

first train wagon is F1 pace between adjacent wheels of the wagon t1 = X/V, it is possible to

assume that the normal force of wagon wheels is continuous and is equal to F1; i.e. in the

interval (0, t1) the first wheel pair of the first train wagon applies a normal force of F1 on the

rail. After t1, the normal force of first pair of wagon wheels was disappeared until t2, so that

the value of normal axel force in the interval (t1, t2) is zero (see Fig. above) t2 is the

beginning time of applying normal force by the second wheel pair of the first wagon. Then

the value of normal axel force in the interval [t2, t3] is F1. From t3 to t4, the normal force of

wagon wheels is disappeared. In fact t4 is the time of one complete cycle of train force.

Therefore the normal force of other train wagons can be calculated in a similar procedure.

The function of dynamic train force with time in the interval [0, t4] is presented as:

Force-time history can easily be generated from MIDAS software. Following graph shows

the force-time history of train wheels as obtained from MIDAS.

This load is applied as dynamic nodal loads in Finite element model.

7 TWO DIMENSIONAL STATIC ANALYSIS

7.1 STAAD MODEL

9.5m dia. tunnel lining modelled in STAAD

Beam moments are released at longitudinal joint locations to simulate inter-segment interface.

Inclined support with compression only springs are assigned to each node.

Beam numbering is shown below:

Beam moments are released at longitudinal joint locations to simulate inter-segment interface(see

release icons at beam nos. 7,44,37,31,25,19 and 13). Inclined supports directing towards tunnel

center with compression only springs are assigned to each node.

7.2 DESIGN LOAD

1. Self-Weight of Lining Self-weight automatically incorporated in STAAD Pro for modelled geometry corresponding to respective input densities. 2. Contact Grout Pressure = 200.00 kN/m2 3. External Water Pressure

The lining will be subjected to external pressure. For design purpose, 100% of external

water pressure assumed to be act over the lining. Water table exists almost upto the

surface level. Water head at the top of overt is about 15m to bottom of invert is about 25m

At tunnel overt = 150 kN/m2

At Middle tunnel = 200 kN/m2

At crown of tunnel = 250 kN/m2

4. Soil Load

Overburden height = 15 m

Submerged Unit Weight of soil = 12 kN/m3

Soil weight at tunnel crown = 180 kN/m2

Soil weight at springing level = 238.8 kN/m2

Lateral soil pressure

At tunnel overt = 127.26 kN/m2

At Middle tunnel = 207.06 kN/m2

5. Train Load

Tunnel is at a depth of 15m from surface. So, the influence of the train load will be

distributed and it will act as uniform pressure load on the top half of the tunnel.

Load of each wheel = 122.625 kN

Number of wheels = 24

Total wheel load = 2943 kN

Depth of tunnel top from surface = 15 m

Influence angle = 45 degree

Length of influence area = 61 m

Breadth of influence area = 31.7 m

Train load on tunnel overt = 1.5227 kN/m2

On conservative side, the total train load is considered as 3 kN/m2

7.3 SUPPORT SPRING STIFFNESS Spring stiffness for unit length of tunnel lining is worked out based on para 9-4 ,chapter 9

of EM-1110-2-2901(freely available on internet for download).

Radial Spring Stiffness, Kr = Er b Φ / (1+ µr)

Tangential spring stiffness, Kt = Kr / (G.Er)

= 0.5* Kr / (1+ µr)

where,

Modulus of Deformation of Rock = 200.00 N/mm2

Width of element under consideration, b = 1000.0 mm

Length of outer member in STAAD model, l = 0.99 m

Inner radius of Tunnel, ri = 4.60 m

Lining Thickness = 0.30 m

Outer radius of Tunnel, ro = 4.90 m

Angle subtended by the element in Radians (Φ = l/r) = 0.20 Radians

Poisson's ratio of Rock, µr = 0.30

Kr = 31178 kN/m

Say 31178 kN/m

DESIGN OF EACH SEGMENT

7.4 INDUCED FORCES COMBINATION OF ALL LOADS

Bending Moment distribution considering combination of all loads Comressive axial force distribution Maximum axial force = 5880 kN

7.5 REINFORCEMENT CALCULATIONS IN SEGMENT

Most critical member is element no. 28

Characteristic strength of concrete (fck) = 50.00 N/mm2

Characteristic strength of steel (fy) = 500.00 N/mm2

Thickness of the section = 300.00 mm

Clear cover (CC) = 50.00 mm

Initially assumed dia of Bar (φ) = 32.00 mm

Effective Thickness (d =D-CC-φ/2) = 234.00 mm

Factored Bending Moment, Mu=1.5*Mfem = 113.54 kN-m

Mu/fckbd2 = 0.04

Axial force acting induced in the section, Pu = 5879000 N

Pu/fckbd = 0.5024783

From Chart 38 of SP 16 “Design Aids for reinforced concrete to Indian Standard IS 456”

considering d'/d=0.2, pst/fck = 0.02

Min. % of steel (pst) = 1 %

Area of steel required, Ast, reqd=pst*b*d = 2340 mm2

Total reinforcement required in 1.6m width = 3744 mm2

Half of this reinforcement on each face i.e = 1872.00 mm2

18nos 12dia. bars on each face may be provided

Area of reinforcement = 2035.75 mm2

8 3 DIMENSIONAL MIDAS MODELING Step-1 Create a plane surface of segmental lining and excavation profile

Inner dia. = 9.2m

Segment outer dia. = 9.8m

Excavation dia. = 10.14m

1. 10.14m dia. soil to be excavated

2. 0.17m thick grouting area behind segmental lining

3. 0.3m thick segmental lining with inner dia. 9.2m and outer dia. 9.8m

Step-2 Create a plane surface for ground profile with adequate dimensions

Step-3 Extrude all surfaces, 40m out of the plane

Step-4 Create Rail Line

1. Rail track with c/c spacing of 1.73m between 2 rails of one track and 3.17m clear spacing

between two tracks

2. Provide obliquity to Rail tracks as per site condition(53o from horizontal)

3. Create surfaces along the along the rail lines sweeping them in the entire depth of modelled

ground

Step-5 Divide ground solid with track surfaces

Step-6 Divide excavation solid, grout solid and precast segments in 1.6m interval

Excavation solids, grout solids and segments are divided in 25 elements.

Step-7 Auto mesh all the solids with mapped size of 1m in hexahedron elements

Step-8 Rename all the mesh sets in right sequence of excavation so that it is easy to define relevant elements for construction stage analysis

Step-9 Apply self-weight

Step-10 Apply hydraulic pressure driving the cutting wheel into the soil

Apply HP drilling pressure of 200 kN/m2 on excavation profiles 3,5,7,9,11,13,15,17,19,21,23 and 25(HP1 to HP12)

Step-11 Apply Jack thrust pressure on lining segments

It is presumed main thrust provided by all cylinders delivers a nominal force of 40000 kN.

Jacking pressure on segment circumference = 40000/( x 9.5 x 0.3) = 4467.5 kN/m2 say 4500

kN/m2.

Apply Jack Thrust pressure of 4500 kN/m2 on segment profiles 2,4,6,8,12,14,16,18,20,22 and 24(J1 to J12)

Step-12 Apply external water pressure corresponding to water table on lining elements

Apply water pressure of 150 kN/m2 on top and 250 kN/m2 on the bottom of lining elements (WPS1

to WPS25)

Step-13 Apply ground surcharge of 10 kN/m2

Step-14 Apply maximum Static train loads on each track

Step-15 Create interface elements between segments

Step-16 Apply grout pressure on lining elements

Grout pressure (GP1 to GP 25)

Step-17 Apply Boundary conditions for static stage wise analysis

Earth pressure shall automatically be incorporated in finite model as mohr-columb properties are

assigned to the soil.

9 CONSTRUCTION STAGE WISE 3 DIMENSIONAL ANALYSIS Construction stage analysis reults in terms of deformations and major principal stresses are

described in this para.

Post analysis notations for results FROM MIDAS

+ve stresses are tensile and –ve are compressive. Material non linearity not considered in stage

wise analysis conservatively. Practically, young’s modulus of stressed soil around segmental lining

will increase with each stage and there will not be any significant settlement after few stages of

excavation. However, in the present analysis linear soil properties are considered. Deformations are

transferred to next stage with modelled structure is constantly subjected to maximum static loads in

each stage.

Stage-0 Original ground with static train load and surcharge on the surface

(Massless soil considered in this stage)

Maximum deformation and major principal stress distribution in ground obtained from MIDAS

analysis for this stage are shown below:

Stage-1 Excavation from RD 0 to RD 3.2 in modelled topography

For stability of excavated profile, soil pressure shall be balanced from driving side.

TBM operator shall ensure the stability during operation. TBM cutting wheel and shield shall have

enough strength to bear the surrounding pressures.

Once excavation is carried out, 2 segments of 1.6m length each has been considered to be installed.

Active Load cases in this stage: GP1, GP2, WPS1, WPS2, self-weight, surface surcharge and

static train load

Deformation In segmental lining:

Principal stress distribution in segmental lining:

Stage-2 Drilling on soil face at RD 3.2 in modelled topography

Active Load cases in this stage: GP1, GP2, WPS1, WPS2, HP1, self-weight, surface surcharge

and static train load

Remarks: Drilling pressure (HP1) on surface profile of excavation element-3 included

Deformation In segmental lining:

Principal stress distribution in segmental lining:

Stage-3 Excavation and segment installation from RD 3.2 to RD 6.4 in modelled topography

Active Load cases in this stage : GP1,GP2,GP3,GP4,WPS1,WPS2,WPS3,WPS4,HP2,J1,self-weight,surface surcharge and static

train load

Remarks: Drilling pressure (HP2) on surface profile of excavation element-5 and jacking pressure

J1 on segmental lining-2 included apart from all loads on segmental lining from 1 to 4.

Deformation in segmental lining:

Principal stress distribution:


Active Load cases in this stage : GP1 to GP6, WPS1 to WPS6, HP3, J2, self-weight, surface surcharge and static train load


J2 on segmental lining-4 included apart from all loads on segmental lining from 1 to 6.


Principal stress distribution:


Active Load cases in this stage GP1 to GP8, WPS1 to WPS8, HP4, J3, self-weight, surface surcharge and static train load


(J3) on segmental lining-6 included apart from all loads on segmental lining from 1 to 8.


Principal stresses in segmental lining:

































Remarks: Drilling pressure (HP10) on surface profile of excavation element- 21 and jacking

pressure (J9) on segmental lining-18 included apart from all loads on segmental lining from 1 to 20.
















Active Load cases in this stage : GP1 to GP25, WPS1 to WPS25, J12, self-weight, surface surcharge and static train load

Remarks: Jacking pressure (J12) on segmental lining-24 included apart from all loads on segmental

lining from 1 to 25.



Main reinforcement Calculations

Maximum stress is in 3rd segment .

Locallised stress in bottom most segment

Average tensile stress in the element = 0.5 x (5.68516 + 2.5) = 4.09258 N/mm2

Permisible tensile strength of steel = 0.55 x Fe500 = 275 N/mm2

Total reinforcement required for this stress = 4.09258 x 300 x 1000 / 275 = 4464.633 mm2 per m

Half of this reinforcement to be provided on each face i.e. = 4464.633/2 = 2232.316 mm2

For 1.6m width, reinforcement required = 1.6 x 2232.316 = 3571.706 mm2

Provide circumfrential reinforcement of 18 nos 16mm dia. bars on each face.

Provided reinforcement = 3618mm2.

10 DYNAMIC ANALYSIS In this finite element model, wave propagation induced by moving train as a force history is

applied on the surface at the location of rail track and ground vibrations are obtained from

the numerical modeling. The crown of segmental tunnel lining is located just about 15m

below the existing railway track, so it is very important to evaluate ground vibration and its

effect on concrete tunnel lining. Trains running on both the tracks and in opposite directions

at a speed of 150 km/hr have been simulated in the model. Analysis has been carried out

with load time interval of 0.03 sec with total time of 30 sec. The geology is mainly dominant

by clay/moorum/gravel soil and tunnel boring machine has been used for construction of

tunnel. Although Mohr–Coulomb constitutive modeling is used for assigning surrounding

earth properties, the dynamic analysis requires only the elastic model as the dynamic wave

produced by the moving train cannot excite large deformation in the soil media, so

deformation is limited in the elastic range.

In this model wave propagation induced by moving train as a force history is applied on the

rail road and ground vibrations are obtained from the numerical modeling.

Initially Eigenvalue analysis is carried out to analyze dynamic property of structure itself. It

is also called Free Vibration Analysis. This determines the damping matrix which will be

used in time history analysis by calculating natural period values of first and second period

modes, in which mass participation rates are high. Result from Eigenvalue analysis is not

the final result. Our final purpose is to evaluate the ground behavior and stresses induced

in segmental lining. This step is just to obtain the value needed in further analysis.

Following Eigenvalue results are obtained from MIDAS FEA analysis:

5% damping has been considered for complete system.

After Eigen value analysis, some modifications need to be done in model to prepare

necessary conditions for dynamic analysis. These changes include conversion of boundary

condition to viscose, applying dynamic train load as a function with time and defining the

dynamic damping for the complete system.

Lysmer and Kuhlemeyer (1969) proposed the concept of viscose boundary in tractions

(dashpots) to absorb incident waves. The dashpots are attached to the boundary in the

normal and shear directions and thus the reflection of outward propagating waves back into

the model is prevented.

To define viscose boundary,calculate and input damper value about x, y, z direction

according to ground material. Formulas to calculate Damper value are shown below.

Considering unit weight of 12 kN/m3 , = 0.3 and E = 200000kN/m2

Elastic modulus

Volume Shear Unit Poisson’s P wave S wave

modulus modulus weight ratio E λ G W

Cp Cs

(kN/m2) (kN/m2) (kN/m2) (kN/m3) (kN·sec/m3) (kN·sec/m3)

200000 115384.6 76923.08 12 0.3 573.8765 306.7499

Multiplying the Cp, Cs (kN•sec/m^3 units) by the cross-section area eventually leads to the spring

stiffness of the viscous boundary element in kN•sec/m units. This is automatically carried out in

MIDAS FEA by assigning surface springs with these parameters. Results of the analysis are

shown below.

Maximum deformation in model due to dynamic train loads

Deformations are considerably less. There is no resonance.

11 SPREADING FORCE IN SEGMENT LONGITUDINAL JOINTS The longitudinal joints shall be checked for the maximum compressive forces with respect to

concrete stress and required spreading reinforcement. These are calculated as per Fritz

Leonhardt model.

Transverse tensile forces are given as:

Where Nd,max is the maximum axial load.

Maximum normal force(as observed in static analysis) = 5880 kN

Maximum normal Force N 5880 kN

Spreading Force,Zd = 0.3Nd(1-a/d)

With a/d =~ 2/3

Zd 588kN say 600kN

Total area required Req. As 600 x 1000/275 = 2181 mm2

Area of steel already provided 3618mm2, hence no extra

reinforcement is required

12 SPLITTING REINFORCEMENT FOR JACK FORCES IN THE RING JOINT Splitting reinforcement in the ring joint is required to transfer the jack forces during construction.

Following jack data is considered here:

No. of jack cylinders = 16 (presumed)

Total Jack forces = 40000 kN/16 jack

Force on each cylinder = 2500 kN/jack

Pressed area on segment = 30cm x 20cm

Estimation of splitting reinforcement in radial direction

Poperation = 2500 kN

Force will be dipersed as shown below:

A1 = b1xd1 , b1 = 30cm and d1 = 20cm

A1 = 0.3 x 0.2 = 0.06 m2

A = b2 x d2; b2 = lsegment/3 = 1600/3 = 533.33mm ; d2 = 250mm(conservatively)

A = 0.533 x 0.25 = .13325mm2

Concrete compressive stress = 50 x sqrt(A/A1) = 50 x sqrt(0.13325/0.06) = 74.5 N/mm2 > 16N/mm2

Estimation of splitting reinforcement

Zs = 0.25 x 2500 x (1-0.2/0.3) = 208.33 kN/ jack

Req As = 208.33 x 1000 / 275 = 757.6 mm2/jack

Longitudinal reinforcement parallel to tunnel axis

4 bars of 10mm dia. longitudinal reinforcement + 3 nos 2 legged 10mm dia. stirrups to be provided at

each jack location. Width of jack pad is 300mm.

314.16 + 471.24 = 785.4 mm2/jack

Provide 10mm dia. – 16nos longitudinal reinforcement + 2 legged 10mm dia. @ 100 c/c on

circunfrential eges of segment which will catter to the above reinforcement.

Estimation of splitting reinforcement in tangential direction

Estimation of reinforcement for force Zy

Considering d = 1.65m

a = 300mm

Zy = 0.09(1-0.9(300/1650)^2) x 2500

=218.3 kN

As,y = 218*1000/275 = 792.72mm2

Estimation of reinforcement for force,Zsi and Zsa

The value of dsi and dsa shall be utilize to estimate tension force Zsi and Zsa

The terms dsi and dsa are the lengths of the jack load transfer area of the previously built ring.

These values depend upon the size, arrangement and properties of the choosen hard timber plates.

In current calculations we assume dimensions of hard timber base plates as b x I = 150mm x

250mm. Find further below a schematic arrangement of the timber plates on a typical segment for

jack force transfer.

The values of dsi and dsa are estimated as follows:

dsi = 25 x 2 + 15 = 65cm

dsa = 25+7.5 = 32.5cm

Zsi = 0.25 x P(1-a/dsi)

=0.25 x 2500x(1-300/650)= 336.5385 kN

As,si = 336.54 x 1000/275 = 1223.78 mm2

Zsa = 0.25 x P(1-b/dsa) = 0.25 x 2500 x (1- 200/325) = 240.385kN

As,sa = 240.385 x 1000/275 = 874.12 mm2

13 JOINT CONNECTIONS

13.1 GASKET CEILING The gaskets placed between lining segments in TBM-bored tunnels are a vital component in

ensuring a long and useful life for the tunnel by protecting the lining and the tunnel interior from

ingress of groundwater, and other material, under pressure. Most sealing gaskets for tunnel lining

segments are made from extruded EPDM rubber. A section through the gasket shows a cell

structure of apertures that allows, by design, the gasket to be compressed in a known way as the

segments are installed and pushed together during installation of a lining ring. Generally the larger

the gasket structure, the greater the groundwater pressures that can be handled, but much depends

on the quality of manufacture and materials.Typical installed gasket in between segments is shown

below:

13.2 CAM-POCKET COUPLING IN CIRCUMFRENTIAL JOINT Tunnels in poor ground conditions are designed to be as rigid as possible. To achieve this, the

segmental rings are coupled at the circumferential joints using cam-pocket couplings. cam-pocket

arrangement is segments are shown below:

Provided circumfrential CAM-pocket arrangement in considered tunnel:

13.3 BOLTS

The purpose of bolts in segmental lining is only to provide temporary support until the grout annulus

hardens. The bolts are needed for short duration untill the radial joint and circumfrential joint gaskets

are compressed when TBM ram is released.They also assist in segment weight whilst the TBM ram

is removed to install a new segment. Provided bolts in circumfrential and radial joints:

13.4 GUIDING RODS The guiding rods are fixed to each segment so they can mate with the corresponding receiving

recesses of the adjacent segment in the ring, thus assisting the accurate placement of segments

inside the tunnel. Typical guiding rod as installed in segment is shown below:

Provided guiding rod opening in radial joints:

Section through guide rod opening is shown below:

13.5 GROUT HOLES

The lining segments have to be equipped with holes to fill the annular gap with grouting material.

The grout holes should have a mechanism to retain the grouting material in the annular gap like non-

return valves or plugs.For grouting through grout holes in lining segments, the segments are

provided with holes fitted with screwed connection pieces. They are closed during ring build by

plugs. Distinction has to be made between primary and secondary grouting.Primary grouting is to

fascilitate the bedding of segments in order to keep settlements during excavation as low as

possible. Secondary grouting is carried out to fill remaining cavities around the tunnel. Conventially,

the presence of voids within the grout are detected by drilling cast-in holes along the crown of the

completed TBM tunnel. These cast-in holes are blind grout hole which are not drilled through the

entire segment.

Provided grout holes:

Refernces

1. O. Arnau, C. Molins Experimental and analytical study of the structural response of segmental tunnel linings based on an in situ loading test. Part 2: numerical simulation

Tunnelling and Underground Space Technology, 26 (6) (2011), pp. 778–788

2. O. Arnau, C. Molins Three dimensional structure response of segmental tunnel linings

Engineering Structures, 44 (2012), pp. 210–221

3. N. Do, D. Dias, P. Oreste, I. Djeran-Maigre 2D numerical investigation of segmental tunnel lining behavior

4. F. Gruebl Segmental ring design: new challenges with high tunnel diameter

5. ITA Working Group No. 2 Guidelines for the design of shield tunnel lining

Tunnelling and Underground Space Technology, 15 (3) (2000), pp. 303–331

Documents

PRACTICAL DESIGN OF SHIELD TUNNEL LINING