Evaluating the application limits of Unreinforced & Steel Fiber Reinforced Concrete (SFRC) for tunnel final linings

Evaluating the application limits of Unreinforced &
Steel Fiber Reinforced Concrete (SFRC) for tunnel final linings
Ilias Michalis, MSc, DIC
Technical Manager Underground Works, Qatar Rail
Dr. Petros Fortsakis
Tunnel Expert, Qatar Rail
Konstantinos Seferoglou, MSc
Geotechnical Expert, Qatar Rail
Dr. Zheng Huang
Tunnel Expert, Qatar Rail
https://www.db‐international.de

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
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
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
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

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.

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.

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

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

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

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

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)
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

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

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 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 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.

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.
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.
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
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.

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)

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.

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).

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
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
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=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

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.

2-D Dynamic numerical analyses

2-D Dynamic numerical analyses
Eccenticity check according to AFTES (Erockmass = 1GPa)
Results 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

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

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

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)
Conventional method
Hoek-Brown materials
Fortsakis (2012)
Averagetunnelload/meangeostaticstress
TLF = ( σc / po )0.3 ( ED / Eshdsh )0.7

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)

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

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

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
Qatar Rail and specifically Mr. Daniel Leckel, Chief of Program Delivery
Dr. George Kouretzis, University of Newcastle in Australia
Deutsche Bahn International and specifically Mr. Michael Ahlgrimm, Executive
Director of Doha branch
Mr. Carsten Schulte of Hochtief Offshore Development Solutions GmBH
Dr. Isavella Vassilopoulou, Civil Engineer N.T.U.A.

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Evaluating the application limits of Unreinforced & Steel Fiber Reinforced Concrete (SFRC) for tunnel final linings

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Evaluating the application limits of Unreinforced & Steel Fiber Reinforced Concrete (SFRC) for tunnel final linings