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Evaluating the application limits of Unreinforced & Steel Fiber Reinforced Concrete (SFRC) for tunnel final linings Ilias Michalis, DEng (NTUA), MSc, DIC Associate Technical Director, Arcadis / Dubai

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Evaluating the application limits of

Unreinforced &

Steel Fiber Reinforced Concrete (SFRC)

for tunnel final linings

Ilias Michalis, DEng (NTUA), MSc, DIC

Associate Technical Director, Arcadis / Dubai

OUTLINE OF THE PRESENTATION

1. Recent tunnel cases with unreinforced and Steel Fiber Reinforced Concrete

tunnel linings

2. Existing Design Codes and Design Recommendations framework

3. Numerical analyses of the unreinforced concrete tunnel linings under static

and seismic loading conditions. T1 & T2 tunnels of Maliakos - Kleidi Motorway

and T26 tunnel of Athens - Patras Motorway in Greece.

4. Numerical analyses of SFRC tunnel linings under static loading conditions.

5. Some critical thoughts about the geostatic loads on to the tunnel final linings.

6. Some critical thoughts about the ground elastic modulus for the design of

tunnel linings

7. Conclusions

The existing design and construction

experiences in tunnelling worldwide

gives the answer:

NO

1. ARE THE CONCEPTS OF

THE UNREINFORCED &

STEEL FIBER REINFORCED

CONCRETE TUNNEL FINAL

LININGS PROHIBITIVE

ONES?

Tunnel Country Type of

tunnel

Completion

time

Length

(km)

Tunnel

section

(m2)

Final lining

thickness

(cm)

Brief

geology

Tradenberg Switzerland Motorway 2009 2 126 40 Mudstones,

Sandstones,

Clay marls

Grouft Tunnel Luxembourg Motorway 2010 3 96 Marls,

Sandstones

Gotthard -

Base Tunnel

Switzerland Railway On going 25 65 30 - 40 Gneiss

Loetschberg

Tunnel

Switzerland Railway 2008 35

Schwarzer berg

Tunnel

Germany Motorway 2004 1 102 30 - 40 Gypsum

CTRL 104 North

Downs Tunnel

U.K. Railway 2002 3 103 35 - 40 Chalk

RECENT TUNNELS WITH UNREINFORCED CONCRETE

TUNNEL FINAL LININGS

Tunnel Country Type of

tunnel

Completion

time

Length

(km)

Tunnel

section

(m2)

Final lining

thickness

(cm)

Brief

geology

Aesch Tunnel Switzerland Motorway 2.3 135 35 - 40 Molasse rocks

Rennsteigtunnel Germany Motorway 2001 8 80 - 120 30 Sandstones,

Siltstones,

Conglomerates

Tempi Tunnel T1 Greece Motorway 2014 1.8 120 45 Marbles and

Amphobolites

Tempi Tunnel T2 Greece Motorway 2014 6 120 45 Amphibolites

Marbles with

phyllites

intercalations

Panagopoula

Tunnel T26

Greece Motorway On going 4 100 40 Limestones,

Cherts and

Conglomerates

RECENT TUNNELS WITH UNREINFORCED CONCRETE

TUNNEL FINAL LININGS

Tunnel Country Type of

tunnel

Completion

time

Length

(km)

Tunnel

section

(m2)

Final lining

thickness

(cm)

Brief

geology

CTRL

(Connection to

St. Pancras Station)

U.K. Railway 2004 2 40.2 35 London Clay

Oenzberg Tunnel Switzerland Railway 2003 3.16 102.7 40 Molasse

Hofoldinger Stollen tunnel Germany Hydraulic 2004 17.5 8.6 18 Hard

Conglomerates

STEP

(Strategic Tunnel

enhancement Programme)

U.A.E (Abu

Dhabi)

Hydraulic 2012 15.6 31.2 28 Claystones &

Mudstones

Siltstones

Gypsum

Barcelona Metro

(Line 9) - Can Zam stretch

Spain Railway 2003 3.9 93.3 35 Granodiorites

RECENT TUNNELS WITH STEEL FIBER REINFORCED CONCRETE

TUNNEL FINAL LININGS

Tunnel Country Type of

tunnel

Completion

time

Length

(km)

Tunnel

section

(m2)

Final lining

thickness

(cm)

Brief

geology

Sao Paulo Metro (Line 4) Brazil Railway 2009 1.2 55.4 35 Weathered

Gneiss

Clem Jones Tunnel Australia Motorway 2010 4.8 102 40 Volcanic Ash

Metamorphic

rocks

Gold Coast

Desalination Tunnels

Australia Hydraulic 2008 (planned) 4.2 9.1 30 Sandstones &

Mudstones

RECENT TUNNELS WITH STEEL REINFORCED CONCRETE

TUNNEL FINAL LININGS

Unreinforced concrete tunnel linings were

successfully constructed for tunnels of large

cross sections and in different ground conditions.

Rennsteig tunnel presently is the longest

Motorway tunnel in Germany (length ~ 8km).

Tempi Tunnel T2 presently is the longest Motorway tunnel in the Balkans region (length ~

6km).

In CTRL 104 North Downs Tunnel, the unreinforced lining is considered as a real “value

engineering” solution resulted to £10m savings in

the budget and completion time 5 months ahead of the Project’s schedule.

https://www.db-international.de

Steel fiber reinforced concrete tunnel final linings

have been successfully constructed mainly in

railway tunnels of cross sections between 40m2 to 90m2.

Thickness of the Steel fiber reinforced concrete

tunnel final linings in railway tunnels varied between 35cm 45cm.

Barcelona Line 9. “Mixed” concept of steel fibers

and traditional steel reinforcement was applied.

Clem Jones Tunnel currently is the longest

motorway tunnel in Australia (4.8 km).

STEP is the first application of the steel reinforced concrete concept in segmental linings

in the GCC countries.

Major issues to be considered for the successful application of the concepts:

Application limits of the concepts must be derived.

These Application limits are related to:

• The geotechnical environment (e.g. ground stiffness & acting overburden geostatic load)

• The seismic / tectonic regime

• The topography

of every tunnel location

The Application limits are related to well determined safety and serviceability

requirements of the unreinforced & steel reinforced concrete tunnel final lining behaviors.

The Design and Construction must fulfill these requirements.

Major issues to be considered for the successful application of the concepts:

The Safety and Serviceability Requirements of the unreinforced and SFRC

tunnel final linings behaviors are described in existing Design Codes and

Design Recommendations.

Realistic cost-effective in situ concrete construction solutions, which

prevent from the formation of the initial cracking, caused during the

temperature cycle: “Dissipation of the hydration heat and subsequent

shrinkage”.

Main advantages and material properties of steel fiber reinforced concrete:

Ductility in tension and in compression

Impact resistance

High resistance against spalling

Increased Durability

Low crack widths under service conditions

Flexural strength in all three directions

Applications & Effectiveness of steel fiber reinforced concrete in segmental linings

Steel fiber reinforced concrete segmental linings can be used for loading

cases, which result to high compressive forces and relatively low bending

moments.

There are no costs from the provision and storage of reinforcement cages.

No reinforcement works is necessary, thus the working process is

accelerated.

In case of cracking, load transfer across the crack is assured. Load bearing

capacity of steel fiber reinforced concrete segmental lining is ensured.

The increased ductility of the steel fiber reinforced concrete in segmental

linings results to lower “absorbed” forces.

OUTLINE OF THE PRESENTATION

1. Recent tunnel cases with unreinforced and Steel Fiber Reinforced Concrete

tunnel linings

2. Existing Design Codes and Design Recommendations framework

3. Numerical analyses of the unreinforced concrete tunnel linings under static

and seismic loading conditions. T1 & T2 tunnels of Maliakos - Kleidi Motorway

and T26 tunnel of Athens - Patras Motorway in Greece.

4. Numerical analyses of SFRC tunnel linings under static loading conditions.

5. Some critical thoughts about the geostatic loads on to the tunnel final linings.

6. Some critical thoughts about the ground elastic modulus for the design of

tunnel linings

7. Conclusions

Relevant Codes, Standards, Guidelines & Recommendations

Eurocode 2 EN 1992 - 1 / Section 12: Plain and lightly reinforced concrete

structures

AFTES Recommendations in respect of the use of plain concrete in tunnels

(e.g. crack depth and loads eccentricity limits)

Rudolf Pottler publication: “The unreinforced inner lining of rock tunnels -

stability analysis and deformation of the crack area” (e.g. crack width

estimation)

DAUB Recommendations for executing and application of unreinforced tunnel

inner linings

FIB Model Code for Concrete Structures 2010

Eurocode 2 EN 1992 - 1 / Section 12: Plain (unreinforced) and lightly reinforced concrete structures

Eurocode 2 EN 1992 - 1 / Section 12: Plain (unreinforced) and lightly reinforced concrete structures

Concrete additional design assumptions (Clause 12.3.1):

1. Design compressive strength: fcd = acc,pl(fck/γc)

2. Design tensile strength: fcd = acc,pl(fctk,005/γc)

where: acc,pl & act,pl = 0.8, due to the less ductile properties of plain concrete

fck is the characteristic compressive strength of concrete

fctk,0.05 is the characteristic axial tensile strength of concrete and

γc =1.50 for persistent and transient actions, 1.20 for accidental actions

Eurocode 2 EN 1992 - 1 / Section 12: Plain (unreinforced) and lightly reinforced concrete structures

Concrete additional design assumptions (Clause 12.3.1):

3. Tensile stresses can be considered in the design, by extending linearly the stress- strain diagram of concrete into the tensile region, up to the design tensile strength fctd

Eurocode 2 EN 1992 - 1 / Section 12: Plain (unreinforced) and lightly reinforced concrete structures

Verification Criteria at the Ultimate Limit States are described in Clause 12.6:

Clause 12.6.1 describes the design resistance to bending and axial force:

Computed axial force N < NRd = fcd × b × hw × (1-2e/hw)

fcd is the concrete design compressive strength

NRd is the ultimate axial force,

b is the overall width of the lining section

hw is the overall thickness of the lining section and

e is the load eccentricity

No limit to acceptable crack depth

Eurocode 2 EN 1992 - 1 / Section 12: Plain (unreinforced) and lightly reinforced concrete structures

Verification Criteria at the Ultimate Limit States are described in Clause 12.6:

Clause 12.6.3 describes the design resistance to shear:

For a tunnel lining section subjected to a shear force V and an axial force N, acting over a compressive area Acc, then:

the shear component of design stress τcp = 1.5(V/Acc) ≤ fcvd

where fcvd is the concrete design strength in shear and compression

AFTES Recommendations in respect to the use of plain concrete in tunnels

Verification Criteria at the Ultimate Limit State (based on Eurocode 2):

Design resistance to bending and axial force.

If the computed axial forces N < NRd0 = 0.027(fck × b × hw), NO particular check is needed.

fck is the characteristic compressive strength of concrete, b is the overall width of the lining section and hw is the overall thickness of the tunnel lining section

Verification Criteria at the Ultimate Limit States (based on Eurocode 2)

Design resistance to bending and axial force.

If the computed axial forces N>NRd (ultimate axial force), then Reinforcement MUST be provided or Redesign of the section is NECESSARY

NRd = 0.57 × fck × b × hw (1-2e/hw) (basic ULS)

NRd = 0.74 × fck × b × hw (1-2e/hw) (accidental ULS)

Load eccentricity e = (M / N), M is the computed bending moment

AFTES Recommendations in respect to the use of plain concrete in tunnels

Verification Criteria at the Ultimate Limit State (based on Eurocode 2)

Design resistance to bending and axial force.

If the computed axial forces NRd0 < N<NRd then:

Load eccentricity e=M/N > 0.3 × hw

Load eccentricity e=M/N < 0.3 × hw

AFTES recommends the limitation of the load eccentricity: e< 0.3xhw and imposes the crack depth limitation to the ½ of the unreinforced tunnel lining thickness (major serviceability criterion for the unreinforced concrete tunnel final linings)

Unreinforced: UNACCEPTABLE

Unreinforced: ACCEPTABLE

AFTES Recommendations in respect to the use of plain concrete in tunnels

Serviceability criterion of the unreinforced concrete tunnel final linings related to the maximum accepted crack width (Pottler’s publication)

DAUB - German Recommendations for executing and application of unreinforced Tunnel final (inner) linings

DAUB attempts to restrict the application fields of unreinforced tunnel final linings, due to high possibility of cracking, as an effect of their low tensile strength.

According to DAUB, unreinforced tunnel final linings are suitable for blocks of standard geometry in road tunnels, provided that these are located in solid rocks and not in excessive depths.

DAUB - German Recommendations for executing and application of unreinforced Tunnel final (inner) linings

DAUB proposes:

Unreinforced tunnel linings can be executed at maximum block lengths of 12m to 12.5m.

For road and railway tunnels, the minimum thickness of unreinforced tunnel linings is 30cm. Smaller thicknesses are possible for relative smaller tunnel sections.

DAUB - German Recommendations for executing and application of unreinforced Tunnel final (inner) linings

DAUB proposes:

Suitable concrete mixes, which restrict the maximum temperature during the setting process, but result to short stripping periods.

• Cement / fly ash combinations are advantageous.

• The addition of hard coal fly ash reduces the hydration heat effect, improves processability, diminishes the danger of demixing and caters for a denser concrete texture.

FIB Model Code for Concrete Structures 2010

Significant relevant clause for FRC: Clause 5.6

“……Structural design of FRC elements is based on the post-cracking residual strength provided by fibre reinforcement….Fibres can be used to improve the behavior at SLS since they can reduce crack spacing and crack width, thereby improving durability. Fibres can be used to improve the behavior at ULS where they can partially or totally substitute conventional reinforcement……”

Fiber reinforced concrete structures

Behavior in compression:

Generally the compressive relations valid for plain concrete also apply to FRC.

Fiber reinforced concrete structures

Behavior in tension

Nominal values of the material properties can be determined by performing a three-point bending test on a notched beam according to EN 14651.

Fiber reinforced concrete structures

Fj[N]: load corresponding to CMOD = CMODj

CMOD: crack mouth opening displacement

Behavior in tension

Nominal values of the material properties can be determined by performing a three-point bending test on a notched beam according to EN 14651.

Fiber reinforced concrete structures

Fj[N]: load corresponding to CMOD = CMODj

CMOD: crack mouth opening displacement fR1

fR3

Classification

• Characteristic flexural strength, serviceability conditions: fR1k

• Characteristic flexural strength, ultimate conditions: fR3k

• Example of FRC class: 4c

The first number “4” defines the minimum value fR1k: 4MPa

The letter “c” defines the ratio the range of the ratio fR3k/fR1k

Fiber reinforced concrete structures

a: 0.5 < fR3k/fR1k < 0.7

b: 0.7 ≤ fR3k/fR1k < 0.9

c: 0.9 ≤ fR3k/fR1k < 1.1

d: 1.1 ≤ fR3k/fR1k < 1.3

e: 1.3 ≤ fR3k/fR1k

Limit of Proportionality:

Classification

• Characteristic flexural strength, serviceability conditions: fR1k

• Characteristic flexural strength, ultimate conditions: fR3k

• Example of FRC class: 4c

The first number “4” defines the minimum value fR1k: 4MPa

The letter “c” defines the ratio the range of the ratio fR3k/fR1k

• Fibre reinforcement can substitute (also partially) conventional reinforcement at ultimate limit state, if the following relationships are fulfilled: fR1k/fLk>0.4, fR3k/fR1k>0.5.

Fiber reinforced concrete structures

Partial safety factors for FRC strength

• Design Compressive strength: As plain concrete, fcd = fck / γc

• Design Tensile strength (limit of linearity): As plain concrete, fctd = fctk / 1.5

• Design Tensile strength (residual strength): γF=1.50

Design Serviceability residual tensile strength fFtsd = fFtsk / γF = f(fR1k)

Design Ultimate residual tensile strength fFtud = fFtuk / γF = f(fR3k)

Fiber reinforced concrete structures

The design of FRC structures is a challenging procedure since some of the design parameters are not determined via the relevant codes, but using results of laboratory tests.

It is critical to choose the concrete mix and carry out the laboratory tests in the initial stages of the design to calculate / verify all the design strength values.

In tunnelling it is useful to carry out a sensitivity analysis for anticipated range of the geotechnical parameters to determine the limitations of this design approach.

Fiber reinforced concrete structures

OUTLINE OF THE PRESENTATION

1. Recent tunnel cases with unreinforced and Steel Fiber Reinforced Concrete

tunnel linings

2. Existing Design Codes and Design Recommendations framework

3. Numerical analyses of the unreinforced concrete tunnel linings under static

and seismic loading conditions. T1 & T2 tunnels of Maliakos - Kleidi Motorway

and T26 tunnel of Athens - Patras Motorway in Greece.

4. Numerical analyses of SFRC tunnel linings under static loading conditions.

5. Some critical thoughts about the geostatic loads on to the tunnel final linings.

6. Some critical thoughts about the ground elastic modulus for the design of

tunnel linings

7. Conclusions

Located in North Greece

Two bore NATM tunnel with cross section 120m2. Length = 6km

Geological conditions: Marbles and Amphibolites (mostly competent rock mass conditions)

Numerical parametric analyses – Static conditions

Eurocode Part1-1/Section 12 and AFTES recommendations for plain concrete were adopted

3-D non-linear Finite Element code was used

Willam & Warnke constitutive model to simulate concrete response (cracking and crushing) was adopted

Basic Ultimate Limit States (for different load cases and lining types) were calculated

The numerical parametric analyses examined the effect of the in-situ rockmass properties on to the linings response

Willam & Warnke Unreinforced concrete constitutive model (1975)

Major advantages of the model:

Simulate concrete non-linear stress-strain response, as well as concrete cracking/crushing in three-dimensions.

Adopts different strength values in compression and in tension.

Accounts directly lining stiffness degradation due to cracking.

However it requires very fine 3D finite element mesh (element size ≈0.05m).

octahedral plane

σx=σy=σz

r1

r2

r2

r2

r1

r1 n

σz

fcd

σx

fcd

σy

fcd

Properties of the Unreinforced Concrete used in Willam & Warnke constitutive model

Summary of C30/37 properties according to Eurocode 2

Numerical simulation of concrete tunnel lining - geomaterials interaction

“Stick-slip” elastic springs

Force

Displacement

Ki

compression

tension

Ki values = f(rockmass,

lining geometry)

Final Lining Type Load Case Description Rockmass modulus

of deformation Maximum rockmass load

LC11 temperature

1000MPa

0

LC13 rockmass+temperature 180KPa

LC100 de-moulding stage 0

LC31 explosion 0

LC11 temperature

300MPa

0

LC13 rockmass+temperature 220KPa

LC100 de-moulding stage 0

LC31 explosion 0

Examined ULS cases

1

ANSYS 9.0ELEMENTS

ANSYS 9.0ELEMENTS

Examined ULS cases

Additional parametric analyses for closed tunnel section:

Uniform face conditions: Erockmass = 150MPa, 800MPa

Mixed face conditions: Erockmass (vault / invert) = 150MPa / 800MPa, 800MPa / 150MPa

Maximum rockmass load 220KPa

Estimation of cracking development in competent rockmass conditions E=1GPa - Rockmass load case

Estimation of cracking development in competent rockmass conditions E=1GPa - Rockmass load case

-12 -10 -8 -6 -4 -2 0axial stress (MPa)

Estimation of cracking development in competent rockmass conditions E=0.3GPa - Rockmass load case

https://www.db-international.de

Estimation of cracking development in competent rockmass conditions E=0.3GPa - Rockmass load case

δmax=2.39cm δmax=4.56cm

Open tunnel section

Erockmass=1 GPa

Tunnel section with

closed invert

Erockmass=0.3GPa

Tunnel linings - Calculated deformed shape under rockmass loadings

OUTLINE OF THE PRESENTATION

1. Recent tunnel cases with unreinforced and Steel Fiber Reinforced Concrete

tunnel linings

2. Existing Design Codes and Design Recommendations framework

3. Numerical analyses of the unreinforced concrete tunnel linings under static

and seismic loading conditions. T1 & T2 tunnels of Maliakos - Kleidi Motorway

and T26 tunnel of Athens - Patras Motorway in Greece.

4. Numerical analyses of SFRC tunnel linings under static loading conditions.

5. Some critical thoughts about the geostatic loads on to the tunnel final linings.

6. Some critical thoughts about the ground elastic modulus for the design of

tunnel linings

7. Conclusions

Eurocode Part1-1/Section 12 and AFTES

recommendations for plain concrete were

adopted. Seismic actions resulting in low axial forces did not require an eccentricity

check (no restrictions in crack depth).

Eurocode 8 EN-1998 was used to determine seismic actions, concrete

properties, factors of safety for the

accidental load case etc.

Competent limestone conditions E = 1GPa

and irregular topography were examined.

Ch. 106+040

LEFT BORE

GU - III (L)

2-D Dynamic numerical analyses

0 1 2 3 4 5 6 7 8 9 10 11 12

-0.5-0.4-0.3-0.2-0.1

00.10.20.30.40.5

a max (g

)0 1 2 3 4 5 6 7 8 9 10 11 12

-0.5-0.4-0.3-0.2-0.1

00.10.20.30.40.5

a max (g

)

0 1 2 3 4 5 6 7 8 9 10 11 12Time (sec)

-0.5-0.4-0.3-0.2-0.1

00.10.20.30.40.5

a max (g

)

amax=0.14g

amax=0.35g

amax=0.16g

Argostoli ARG83-1

Dinar

Kozani

0 1 2 3 4 5 6 7 8 9 10 11 12Time (sec)

-0.5-0.4-0.3-0.2-0.1

00.10.20.30.40.5

a max (g

)

amax=0.50g

Aigio

2-D Dynamic numerical analyses

Eccenticity check according to AFTES (Erockmass = 1GPa)

0 1 2 3 4 5 6

0

400

800

1200

1600

2000

axi

al f

orc

e (

kN)

NRdo

0 1 2 3 4 5 6

-20

-10

0

10

20

be

nd

ing

mo

men

t (k

Nm

)

0 1 2 3 4 5 6time (sec)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

ecce

ntr

icity

(m

)

e=0.3hw

N>NRdo zoneexcitation: Aigio

orientation: (-)location: A1-IVbResults in critical points along

the tunnel cross-section

Zone of high axial force requirement for low

eccentricity (crack control)

Conclusion: In competent rock

mass conditions (E=1GPa), an

unreinforced lining may be

sufficient, even in areas of high

seismicity

OUTLINE OF THE PRESENTATION

1. Recent tunnel cases with unreinforced and Steel Fiber Reinforced Concrete

tunnel linings

2. Existing Design Codes and Design Recommendations framework

3. Numerical analyses of the unreinforced concrete tunnel linings under static

and seismic loading conditions. T1 & T2 tunnels of Maliakos - Kleidi Motorway

and T26 tunnel of Athens - Patras Motorway in Greece.

4. Numerical analyses of SFRC tunnel linings under static loading conditions.

5. Some critical thoughts about the geostatic loads on to the tunnel final linings.

6. Some critical thoughts about the ground elastic modulus for the design of

tunnel linings

7. Conclusions

Assumptions

Structural models used to simulate the ring and the ground

A 3d shell elements supported by non linear springs to simulate the ground

A simple linear beams on non linear springs to simulate the ground

Assumptions

Consideration of “full” overburden load (no “arching”)

Concrete parameters

• Concrete category: C50/60

• Design compressive strength fcd=0.85×fck/γc, γc=1.50

• Design tensile strength fctd=fctk,0.05/γc, γc=1.50

Numerical model

• Beam elements on springs & shell elements on springs

• Non linear bedding (springs) with zero tensile strength

• Normal bedding value: C=Erockmass/R, Tangential bedding value: Ct=0.1C

where R: Tunnel radius

-10000

-8000

-6000

-4000

-2000

0

2000

-400 -200 0 200 400

M (kNm/m)

N (

kN

/m

)

Investigation of the tunnel’s ring response – Full overburden approach

Load assumption 1 Load assumption 2

Investigation of the tunnel’s ring response – Full overburden approach

Bending moment (M)

Load assumption 1

Load assumption 2

Normal forces (N) Bedding springs

Parametric analyses with full overburden approach - Unfavorable load combination in ULS

Load assumption 1

C50/60, d=0.30m

Maximum overburden height H vs Eground and Ko

Comparison of the two loading assumptions

Upward pressure applied on the tunnel invert

NO upward pressure applied on the tunnel invert

Load assumption 1 “+” Application of grouting pressure

Maximum overburden height for SFRC concept vs Eground and Ko

For Erockmass < 1GPa, the grouting

pressure is beneficial, since the

overburden height (for which SRFC

concept is applicable) increases

For Erockmass ≥1GPa, the grouting

pressure has no benefit

OUTLINE OF THE PRESENTATION

1. Recent tunnel cases with unreinforced and Steel Fiber Reinforced Concrete

tunnel linings

2. Existing Design Codes and Design Recommendations framework

3. Numerical analyses of the unreinforced concrete tunnel linings under static

and seismic loading conditions. T1 & T2 tunnels of Maliakos - Kleidi Motorway

and T26 tunnel of Athens - Patras Motorway in Greece.

4. Numerical analyses of SFRC tunnel linings under static loading conditions.

5. Some critical thoughts about the geostatic loads on to the tunnel final linings.

6. Some critical thoughts about the ground elastic modulus for the design of

tunnel linings

7. Conclusions

The ground load applied on the tunnel lining is not a “property” of the ground - as it is assumed by the empirical methods - but depends very significantly on the construction procedure and the applied support measures.

The parameters that must be taken into account for the calculation of the tunnel load are:

• Rock mass strength and stiffness parameters

• Tunnel depth

• Dimensions and shape of the tunnel section

• Construction procedure (full face, sequential excavation etc.)

• Support stiffness and distance of the support from the tunnel face

• Face pressure or face treatment measures (forepolling, fiberglass nails etc.)

• Rock mass creep

The role of the geotechnical conditions (Fortsakis 2012)

0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00

TLF = (σc/po)0.3 (ED/Eshdsh)0.7

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.55

0.60

Μέση

πίεση

/ Μέση

γεωστατική

τάση

pm

/ p

o,m

Άνω όριο

Κάτω όριο

m

1.80 1.800.30 0.70o,m

c

o sh sh

p 1.40 p 1.40

p 0.50(1 K)γΗ(0.5TLF 1.85)σ ED

0.5 1.85p E d

Conventional method

Hoek-Brown materials

Fortsakis (2012)

Av

era

ge t

un

nel lo

ad

/ m

ean

geo

sta

tic s

tress

TLF = ( σc / po )0.3 ( ED / Eshdsh )

0.7

0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

σc / po,m

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

1.10

1.20

pF

L,m

/ p

sh

,m

dsh = 20cm, dFL = 60cm

dsh = 40cm, dFL = 40cm

Load transfer from temporary support to final lining (NATM method)

po,m=0.5(1+K)γΗ

σc=2∙c∙tan(45+φ/2)

pFL,m: Final lining average load

psh,m: Shotcrete average load

Fortsakis et al. (2014)

OUTLINE OF THE PRESENTATION

1. Recent tunnel cases with unreinforced and Steel Fiber Reinforced Concrete

tunnel linings

2. Existing Design Codes and Design Recommendations framework

3. Numerical analyses of the unreinforced concrete tunnel linings under static

and seismic loading conditions. T1 & T2 tunnels of Maliakos - Kleidi Motorway

and T26 tunnel of Athens - Patras Motorway in Greece.

4. Numerical analyses of SFRC tunnel linings under static loading conditions.

5. Some critical thoughts about the geostatic loads on to the tunnel final linings.

6. Some critical thoughts about the ground elastic modulus for the design of

tunnel linings

7. Conclusions

The use of F.E. analysis has become widespread and popular in tunnelling, as means of controlling and optimizing design tasks

F.E method is extremely powerful in stress - strain predictions

The quality of any stress - strain prediction (with F.E methods) depends on the adequate model being adopted (rockmass constitutive model)

More realistic prediction of rockmass movements requires the adoption of a non-linear stress - strain relation, before reaching the ultimate state

Non-linear elasticity, characterized by strong variations of rockmass stiffness, which depend on the magnitude of strain levels occurring during construction stages

In tunnelling design, pre-failure rockmass stiffness plays a crucial role in predicting the complete behavior of tunnels and their surrounding rockmass in Serviceability Conditions

Characteristic Rockmass stiffness (G) vs shear strain curves must be derived

These curves can be determined on the basis of reliable and accurate in-situ testing and conventional laboratory testing

In situ testing methods: Seismic & Geophysical methods, Dilatometer tests(DMT), Pressuremeter tests (PMT)

Conventional laboratory testing: UCS with stiffness measurement

Typical representation of rockmass stiffness variation as a function of the shear strain amplitudes

Proposed Rock mass stiffness value

measured in dilatometer tests and in

the initial loading cycles of

pressuremeter tests.

Proposed Rock mass stiffness value

at the range of shear strain: 0.5x10-3

to 10-3.

ROCK MASS

STIFFNESS FOR

TUNNEL DESIGN

IN SERVICEABILITY

CONDITIONS

OUTLINE OF THE PRESENTATION

1. Recent tunnel cases with unreinforced and Steel Fiber Reinforced Concrete

tunnel linings

2. Existing Design Codes and Design Recommendations framework

3. Numerical analyses of the unreinforced concrete tunnel linings under static

and seismic loading conditions. T1 & T2 tunnels of Maliakos - Kleidi Motorway

and T26 tunnel of Athens - Patras Motorway in Greece.

4. Numerical analyses of SFRC tunnel linings under static loading conditions.

5. Some critical thoughts about the geostatic loads on to the tunnel final linings.

6. Some critical thoughts about the ground elastic modulus for the design of

tunnel linings

7. Conclusions

CONCLUSIONS

The concepts of the unreinforced and steel fiber reinforced concrete tunnel final linings are not prohibitive

During the recent years, a significant number of motorway and railway tunnels with unreinforced and steel fiber reinforced concrete tunnel final linings have been constructed successfully

Eurocode 2, EN 1992-1 / Section 12 and AFTES Recommendations, provide the necessary design code framework for the design of unreinforced concrete tunnel final linings

Fib Model 2010 (Design Code since November 2013) can be used for the design of steel reinforced concrete tunnel final linings

CONCLUSIONS

The structural integrity of the unreinforced concrete tunnel linings has been verified for the case of competent rock masses with Em > 800MPa - 1000MPa, even in areas of high seismicity and irregular topography

Unreinforced concrete tunnel linings in rock masses with 300MPa < Em ≤ 800MPa may exhibit significant cracking, in combination with spalling.

Unreinforced concrete tunnel linings of typical thickness 30cm to 40cm in rock masses with Em ≤ 300 MPa are characterized by high risk of concrete crushing. Must be avoided

At tunnel portals, as well as in areas of nearby or crossing active faults, the unreinforced concrete tunnel linings must be avoided

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CONCLUSIONS

The design of FRC structures is a challenging procedure since some of the design parameters are not determined via the relevant codes, but using results of laboratory tests.

It is critical to choose the concrete mix and carry out the laboratory tests in the initial stages of the design to calculate / verify all the design strength values.

In tunnelling it is useful to carry out a sensitivity analysis for anticipated range of the geotechnical parameters to determine the limitations of this design approach.

CONCLUSIONS

Steel fiber reinforced concrete tunnel final linings of typical thickness between 30cm to 35cm in rock masses with Em ≥ 800 MPa can be safely applied, even with the consideration of full geostatic load for overburden heights ≤ 30m.

Steel fiber reinforced concrete tunnel final linings in rock masses with 500MPa< Em< 800 MPa can be safely applied, even with the consideration of full geostatic load for overburden heights ≤ 20m.

In rock masses, which are characterized by high shear strength and stiffness, tunnel final lining loading conditions are significant lower than the ones of the initial geostatic stress field.

CONCLUSIONS

The use of face treatment measures or the application of face pressure may lead to increase of the final lining loads due to the decrease of the deconfinement.

In conventional tunnelling the load transfer from the temporary support to final lining depends on the stiffness of the support systems and the geotechnical conditions.

The interaction between twin tunnels may lead to increase of the applied loads and to an unsymmetrical load distribution.

Rock mass stiffness value at the range of shear strain: 0.5x10-3 to 10-3 (from in-situ dilatometer and pressuremeter testing results).

ACKNOWLEDGEMENTS

Dr. George Kouretzis, University of Newcastle in Australia

Mr. Carsten Schulte of Hochtief Offshore Development Solutions GmBH

Dr. Isavella Vassilopoulou, Civil Engineer N.T.U.A.

Dr. Petros Fortsakis, Tunnel Expert of Deutsche Bahn

THANK YOU FOR

ATTENDING