Ilias Michalis PMV Workshop Dubai 2014
-
Upload
ilias-michalis -
Category
Documents
-
view
1.086 -
download
2
Transcript of Ilias Michalis PMV Workshop Dubai 2014
![Page 1: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/1.jpg)
Evaluating the application limits of Unreinforced & Steel Fiber Reinforced Concrete (SFRC) for tunnel final linings
Ilias Michalis, MSc, DICTechnical Manager Underground Works, Qatar Rail
Dr. Petros FortsakisTunnel Expert, Qatar Rail
Konstantinos Seferoglou, MScGeotechnical Expert, Qatar Rail
Dr. Zheng HuangTunnel Expert, Qatar Rail
https://www.db-international.de
![Page 2: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/2.jpg)
https://www.db-international.de
OUTLINE OF THE PRESENTATION 1. Recent tunnel cases with unreinforced and Steel Fiber Reinforced
Concrete tunnel linings2. Existing Design Codes and Design Recommendations framework3. 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
![Page 3: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/3.jpg)
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?
https://www.db-international.de
![Page 4: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/4.jpg)
https://www.db-international.de
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
![Page 5: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/5.jpg)
https://www.db-international.de
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
![Page 6: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/6.jpg)
https://www.db-international.de
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 Conglomerate
sSTEP
(Strategic Tunnel enhancement Programme)
U.A.E (Abu Dhabi)
Hydraulic 2012 15.6 31.2 28 Claystones & Mudstones SiltstonesGypsum
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
![Page 7: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/7.jpg)
https://www.db-international.de
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
rocksGold Coast
Desalination TunnelsAustralia Hydraulic 2008 (planned) 4.2 9.1 30 Sandstones &
Mudstones
RECENT TUNNELS WITH STEEL REINFORCED CONCRETE TUNNEL FINAL LININGS
![Page 8: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/8.jpg)
https://www.db-international.de
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.
![Page 9: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/9.jpg)
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.
![Page 10: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/10.jpg)
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.https://www.db-international.de
![Page 11: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/11.jpg)
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”.
https://www.db-international.de
![Page 12: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/12.jpg)
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
https://www.db-international.de
![Page 13: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/13.jpg)
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.
https://www.db-international.de
![Page 14: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/14.jpg)
https://www.db-international.de
OUTLINE OF THE PRESENTATION 1. Recent tunnel cases with unreinforced and Steel Fiber Reinforced
Concrete tunnel linings2. Existing Design Codes and Design Recommendations framework3. 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
![Page 15: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/15.jpg)
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
https://www.db-international.de
![Page 16: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/16.jpg)
https://www.db-international.de
Eurocode 2 EN 1992 - 1 / Section 12: Plain (unreinforced) and lightly reinforced concrete structures
![Page 17: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/17.jpg)
https://www.db-international.de
Eurocode 2 EN 1992 - 1 / Section 12: Plain (unreinforced) and lightly reinforced concrete structuresConcrete 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 concretefck is the characteristic compressive strength of concretefctk,0.05 is the characteristic axial tensile strength of concrete andγc =1.50 for persistent and transient actions, 1.20 for accidental actions
![Page 18: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/18.jpg)
https://www.db-international.de
Eurocode 2 EN 1992 - 1 / Section 12: Plain (unreinforced) and lightly reinforced concrete structuresConcrete 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
![Page 19: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/19.jpg)
https://www.db-international.de
Eurocode 2 EN 1992 - 1 / Section 12: Plain (unreinforced) and lightly reinforced concrete structuresVerification 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 strengthNRd is the ultimate axial force,b is the overall width of the lining sectionhw is the overall thickness of the lining section and e is the load eccentricity
No limit to acceptable crack
depth
![Page 20: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/20.jpg)
https://www.db-international.de
Eurocode 2 EN 1992 - 1 / Section 12: Plain (unreinforced) and lightly reinforced concrete structuresVerification 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
![Page 21: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/21.jpg)
https://www.db-international.de
AFTES Recommendations in respect to the use of plain concrete in tunnelsVerification 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
![Page 22: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/22.jpg)
https://www.db-international.de
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 NECESSARYNRd = 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
![Page 23: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/23.jpg)
https://www.db-international.de
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: UNACCEPTABLEUnreinforced: ACCEPTABLE
AFTES Recommendations in respect to the use of plain concrete in tunnels
![Page 24: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/24.jpg)
https://www.db-international.de
Serviceability criterion of the unreinforced concrete tunnel final linings related to the maximum accepted crack width (Pottler’s publication)
![Page 25: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/25.jpg)
https://www.db-international.de
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.
![Page 26: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/26.jpg)
https://www.db-international.de
DAUB - German Recommendations for executing and application of unreinforced Tunnel final (inner) liningsDAUB 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.
![Page 27: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/27.jpg)
https://www.db-international.de
DAUB - German Recommendations for executing and application of unreinforced Tunnel final (inner) liningsDAUB 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.
![Page 28: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/28.jpg)
https://www.db-international.de
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
![Page 29: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/29.jpg)
https://www.db-international.de
Behavior in compression: Generally the compressive relations valid for plain concrete also apply to FRC.
Fiber reinforced concrete structures
![Page 30: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/30.jpg)
https://www.db-international.de
Behavior in tensionNominal 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 = CMODjCMOD: crack mouth opening displacement
![Page 31: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/31.jpg)
https://www.db-international.de
Behavior in tensionNominal 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 = CMODjCMOD: crack mouth opening displacement
fR1
fR3
![Page 32: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/32.jpg)
https://www.db-international.de
Classification• Characteristic flexural strength, serviceability conditions: fR1k
• Characteristic flexural strength, ultimate conditions: fR3k
• Example of FRC class: 4cThe first number “4” defines the minimum value fR1k: 4MPaThe letter “c” defines the ratio the range of the ratio fR3k/fR1k
Fiber reinforced concrete structures
a: 0.5 < fR3k/fR1k < 0.7b: 0.7 ≤ fR3k/fR1k < 0.9c: 0.9 ≤ fR3k/fR1k < 1.1
d: 1.1 ≤ fR3k/fR1k < 1.3e: 1.3 ≤ fR3k/fR1k
Limit of Proportionality:
![Page 33: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/33.jpg)
https://www.db-international.de
Classification• Characteristic flexural strength, serviceability
conditions: fR1k
• Characteristic flexural strength, ultimate conditions: fR3k
• Example of FRC class: 4cThe first number “4” defines the minimum value fR1k: 4MPaThe 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
![Page 34: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/34.jpg)
https://www.db-international.de
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=1.50Design Serviceability residual tensile strength fFtsd = fFtsk / γF = f(fR1k)Design Ultimate residual tensile strength fFtud = fFtuk / γF = f(fR3k)
Fiber reinforced concrete structures
![Page 35: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/35.jpg)
https://www.db-international.de
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
![Page 36: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/36.jpg)
https://www.db-international.de
OUTLINE OF THE PRESENTATION 1. Recent tunnel cases with unreinforced and Steel Fiber Reinforced
Concrete tunnel linings2. Existing Design Codes and Design Recommendations framework3. 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
![Page 37: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/37.jpg)
https://www.db-international.de
Located in North Greece Two bore NATM tunnel with cross
section 120m2. Length = 6km Geological conditions: Marbles and
Amphibolites (mostly competent rock mass conditions)
![Page 38: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/38.jpg)
https://www.db-international.de
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
![Page 39: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/39.jpg)
https://www.db-international.de
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
σ x=σ y=σ zr1
r2
r2
r2
r1
r1 n
σ z
fcd
σ x
fcd
σ y
fcd
![Page 40: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/40.jpg)
https://www.db-international.de
Properties of the Unreinforced Concrete used in Willam & Warnke constitutive modelSummary of C30/37 properties according to Eurocode 2
![Page 41: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/41.jpg)
https://www.db-international.de
Numerical simulation of concrete tunnel lining - geomaterials interaction“Stick-slip” elastic springs
Force
D isp lacem ent
K i
compression
tension
Ki values = f(rockmass, lining
geometry)
![Page 42: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/42.jpg)
https://www.db-international.de
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 0LC31 explosion 0LC11 temperature
300MPa
0
LC13 rockmass+temperature 220KPa
LC100 de-moulding stage 0LC31 explosion 0
Examined ULS cases
1
ANSYS 9.0ELEMENTS
ANSYS 9.0ELEMENTS
![Page 43: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/43.jpg)
https://www.db-international.de
Examined ULS casesAdditional 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
![Page 44: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/44.jpg)
https://www.db-international.de
Estimation of cracking development in competent rockmass conditions E=1GPa - Rockmass load case
![Page 45: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/45.jpg)
https://www.db-international.de
Estimation of cracking development in competent rockmass conditions E=1GPa - Rockmass load case
-12 -10 -8 -6 -4 -2 0axia l stress (M Pa)
![Page 46: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/46.jpg)
https://www.db-international.de
Estimation of cracking development in competent rockmass conditionsE=0.3GPa - Rockmass load case
![Page 47: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/47.jpg)
https://www.db-international.de
Estimation of cracking development in competent rockmass conditionsE=0.3GPa - Rockmass load case
![Page 48: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/48.jpg)
https://www.db-international.de
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
![Page 49: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/49.jpg)
https://www.db-international.de
OUTLINE OF THE PRESENTATION 1. Recent tunnel cases with unreinforced and Steel Fiber Reinforced
Concrete tunnel linings2. Existing Design Codes and Design Recommendations framework3. 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
![Page 50: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/50.jpg)
https://www.db-international.de
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.
![Page 51: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/51.jpg)
https://www.db-international.de
2-D Dynamic numerical analyses
![Page 52: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/52.jpg)
https://www.db-international.de
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
![Page 53: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/53.jpg)
https://www.db-international.de
OUTLINE OF THE PRESENTATION 1. Recent tunnel cases with unreinforced and Steel Fiber Reinforced
Concrete tunnel linings2. Existing Design Codes and Design Recommendations framework3. 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
![Page 54: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/54.jpg)
https://www.db-international.de
AssumptionsStructural 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
![Page 55: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/55.jpg)
https://www.db-international.de
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=0.1Cwhere R: Tunnel radius
-10000
-8000
-6000
-4000
-2000
0
2000
-400 -200 0 200 400
M (kNm/ m)
N (k
N/m
)
![Page 56: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/56.jpg)
https://www.db-international.de
Investigation of the tunnel’s ring response – Full overburden approachLoad assumption 1 Load assumption 2
![Page 57: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/57.jpg)
https://www.db-international.de
Investigation of the tunnel’s ring response – Full overburden approach Bending moment (M)
Load assumption 1
Load assumption 2
Normal forces (N) Bedding springs
![Page 58: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/58.jpg)
https://www.db-international.de
Parametric analyses with full overburden approach - Unfavorable load combination in ULSLoad assumption 1C50/60, d=0.30m
Maximum overburden height H vs Eground and Ko
![Page 59: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/59.jpg)
https://www.db-international.de
Comparison of the two loading assumptions
Upward pressure applied on the tunnel invert
NO upward pressure applied on
the tunnel invert
![Page 60: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/60.jpg)
https://www.db-international.de
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
![Page 61: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/61.jpg)
https://www.db-international.de
OUTLINE OF THE PRESENTATION 1. Recent tunnel cases with unreinforced and Steel Fiber Reinforced
Concrete tunnel linings2. Existing Design Codes and Design Recommendations framework3. 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
![Page 62: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/62.jpg)
https://www.db-international.de
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
![Page 63: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/63.jpg)
https://www.db-international.de
The role of the geotechnical conditions (Fortsakis 2012)
0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00TLF = (σ c/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
Μέσ
η π
ίεση
/ Μ
έση
γεω
στατ
ική
τάση
p m /
p o,m
Άνω όριο
Κάτω όριο
m1.80 1.800.30 0.70o,m
co sh sh
p 1.40 p 1.40p 0.50(1 K)γΗ(0.5TLF 1.85) σ ED0.5 1.85p E d
Conventional methodHoek-Brown materialsFortsakis (2012)
Aver
age
tunn
el lo
ad /
mea
n ge
osta
tic
stre
ss
TLF = ( σc / po )0.3 ( ED / Eshdsh )0.7
![Page 64: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/64.jpg)
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
p FL,
m /
p sh,
m
dsh = 20cm , dFL = 60cm
dsh = 40cm , dFL = 40cm
https://www.db-international.de
Load transfer from temporary support to final lining (NATM method)
po,m=0.5(1+K)γΗσc=2∙c∙tan(45+φ/2)
pFL,m: Final lining average loadpsh,m: Shotcrete average load
Fortsakis et al. (2014)
![Page 65: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/65.jpg)
https://www.db-international.de
OUTLINE OF THE PRESENTATION 1. Recent tunnel cases with unreinforced and Steel Fiber Reinforced
Concrete tunnel linings2. Existing Design Codes and Design Recommendations framework3. 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
![Page 66: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/66.jpg)
https://www.db-international.de
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
![Page 67: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/67.jpg)
https://www.db-international.de
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
![Page 68: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/68.jpg)
https://www.db-international.de
Typical representation of rockmass stiffness variation as a function of the shear strain amplitudes
![Page 69: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/69.jpg)
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
https://www.db-international.de
![Page 70: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/70.jpg)
https://www.db-international.de
OUTLINE OF THE PRESENTATION 1. Recent tunnel cases with unreinforced and Steel Fiber Reinforced
Concrete tunnel linings2. Existing Design Codes and Design Recommendations framework3. 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
![Page 71: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/71.jpg)
https://www.db-international.de
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
![Page 72: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/72.jpg)
https://www.db-international.de
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
![Page 73: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/73.jpg)
https://www.db-international.de
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.
![Page 74: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/74.jpg)
https://www.db-international.de
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.
![Page 75: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/75.jpg)
https://www.db-international.de
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).
![Page 76: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/76.jpg)
https://www.db-international.de
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.
![Page 77: Ilias Michalis PMV Workshop Dubai 2014](https://reader033.fdocuments.net/reader033/viewer/2022061307/588920b21a28ab77528b53dd/html5/thumbnails/77.jpg)
THANK YOU FOR ATTENDING
www.sitename.com
A wealth of presentations and reports are available atwww.pmvlive.com/presentations
PLEASE DON’T FORGET TO COLLECT YOUR ATTENDANCE CERTIFICATE