Fig. 1 Fire ambient temperature curve for tunnels according to UNI 11076

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A finite element insight on reinforced concrete tunnels under fire conditions

Mr. Paolo Cucino, SWS Engineering S.p.a., Italy, p.cucino@sws.it Mr. Matteo Cont, SWS Engineering S.p.a., Italy, m.cont@sws.it Mr. Alberto Omizzolo, SWS Engineering S.p.a., Italy, a.omizzolo@sws.it Mr. Daniele Schiavazzi, Enginsoft S.p.a., Italy, d.schiavazzi@enginsoft.it

Keywords: fire analysis

1. Introduction Accidental scenarios such as structural performance under fire conditions are becoming of increasing importance for structural designers. Especially for tunnels of significant length, the latter conditions may result in reduced post-fire operating performance with consequent severe reduction of the overall service efficiency. International standards are becoming increasingly aware of the importance of fire events in structural design. A transition from the traditional prescriptive methodology to a new performance-based approach is taking place within many codes worldwide. The availability of complex simulation software both for CFD and non linear structural analysis has given a significant contribution to the practical implementation of new approaches. Simple models are often a good choice to achieve accurate results and to produce reasonable designs at the same time. However, phenomena such as fire response of structures are intrinsically non linear and simple assumptions may result in member/section oversize. The present article investigates a possible modeling technique which can be applied to fire analysis of reinforced concrete tunnels. The size of the model in terms of total degrees of freedom is kept reasonable but a complete description of temperature dependent material constants is to be specified to obtain a realistic model response.

The increase of ambient temperature during a fire event can be described by a temperature vs. time curve as specified within the UNI11076 standard (see Fig. 1).

Fig. 2 Comprehensive vision of the reinforced concrete structure, with a detail of two joints

2. Finite element models The main purpose of the finite element model is to simulate the evolution in time of the structural response to a fire event in the most realistic way. Due to the complex material models outlined above, an advanced calculation methodology was considered appropriate to perform the fire verification task. A finite element model is thus put in place, keeping the following important features in mind: 1. Computational light-weight: due to the number of variables affecting the material properties,

full solutions need to be obtained within minutes.

2. The model needs to account both for thermal and mechanical analysis. A one-way coupling between these fields has been assumed.

3. Reinforced concrete needs to be simulated with particular reference to the interaction and congruence of concrete matrix and steel bars.

4. The soil behaviour needs to be simulated in a manner consistent with the reality. This is to catch the conseguences of mutual interactions between the reinforced concrete structure and the surrounding soil.

5. The structural joints, interposed between the different segments that compose the tunnel's ring, must behave like monolateral contacts, i.e. they must be able to transmit compression forces only.

3. Conclusions An efficient, design oriented, approach is proposed within the present work to describe complex physical phenomena such as the evolution of structural response under fire exposure for reinforced concrete tunnels. Starting from the application of a normalized fire curve in the time domain, proper thermal and mechanical properties are assigned to steel and concrete, in order to capture a realistic response. The results obtained can be considered as a starting point towards strength optimization procedures for new tunnels and at the same time they offer a time effective tool for a fire certification of existing structures. Furthermore, for revamping of existing tunnels, the developed procedure can be useful to minimize the cost related to the installation of protective layers.

A finite element insight on reinforced concrete tunnels under fire conditions

Mr. Paolo Cucino, SWS Engineering S.p.a., Italy, p.cucino@sws.it Mr. Matteo Cont, SWS Engineering S.p.a., Italy, m.cont@sws.it Mr. Alberto Omizzolo, SWS Engineering S.p.a., Italy, a.omizzolo@sws.it Mr. Daniele Schiavazzi, Enginsoft S.p.a., Italy, d.schiavazzi@enginsoft.it

Summary Fire performance evaluation is becoming an important part of the overall structural performance assessment and is assuming an increasing role within international standards. Simple approaches, based on single section performance, fail often to give a realistic description of the phenomenon especially for statically indeterminate structures, where thermo-mechanical coupling and non linear dependency of stress, moduli and expansion need to be accounted for. In this article we propose a well manageable and rational computational approach. It’s dedicated to the structural-fire-analysis of precast concrete segmental tunnel linings. In particular, the concrete and the steel reinforcement bars are differentially modelled. In this way, Concrete is described with plate elements and the steel bars with elastic-plastic trusses to duly describe the actual configuration of the bars. Special contact blocks are used to simulate the only-compression-behaviour on the structural joints, between different segments that compose the tunnel's ring. A single model can be thus employed to perform a full quasi static one-way-coupled thermo-mechanical analysis, where first temperatures and then internal plastic stresses are computed. Due to the number of temperature dependent constitutive relationships adopted within a single model, many simplified tuning exercises where investigated to match known results for situations where some of the simulation variables were kept constant. Finally, a case study is presented where the structural performance is evaluated after 120 minutes of fire exposure for the railway tunnel located in Cefalù and denominated “Raddoppio Fiumetorto-Cefalu’-Castelbuono tratta Ogliastrillo-Castelbuono” part of the Italian Sicily Railway.

Keywords: fire analysis

1. Introduction Accidental scenarios such as structural performance under fire conditions are becoming of increasing importance for structural designers. Especially for tunnels of significant length, the latter conditions may result in reduced post-fire operating performance with consequent severe reduction of the overall service efficiency. International standards are becoming increasingly aware of the importance of fire events in structural design. A transition from the traditional prescriptive methodology to a new performance-based approach is taking place within many codes worldwide. The availability of complex simulation software both for CFD and non linear structural analysis has given a significant contribution to the practical implementation of new approaches. Simple models are often a good choice to achieve accurate results and to produce reasonable designs at the same time. However, phenomena such as fire response of structures are intrinsically non linear and simple assumptions may result in member/section oversize. The present article investigates a possible modeling technique which can be applied to fire

Fig. 1 Fire ambient temperature curve for tunnels according to UNI 11076

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2. Fire analysis of tunnels: The Eurocode approach Although fire design procedures can be found within many international standards, the present article focuses on the Eurocode guidelines. Procedures for structural analysis and verification of concrete structures under fire conditions can be found in UNI-EN 1992-1-2. Three approaches are possible within the latter standard: 1. Detailing according to recognized design solutions.

2. Simplified calculation methods for specific types of members.

3. Advanced calculation methods for simulating the behaviour of structural members. The most effective approach to follow can be typically chosen with reference to the peculiar geometry under investigation, external restraint distribution and internal degree of continuity. Concrete tunnels are typically statically indeterminate structures interacting significantly with a surrounding non linear material such as soil. An advanced calculation method is therefore the only possible way to obtain a realistic time dependent response that accounts for temperature variations.

3. Thermo-mechanical material models 3.1 External actions: fire ramp

The increase of ambient temperature during a fire event can be described by a temperature vs. time curve as specified within the UNI11076 standard (see Fig. 1).

3.2 Thermal properties Thermal properties as functions of temperature are specified for concrete. Steel bars are assumed to give a negligible contribution to the heat transfer due to fire exposure.

Fig. 2 Thermal Conductivity, Specific Heat and Density of concrete according to UNI EN 1992-1-2:2005

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3.2.1 Concrete The following temperature dependent material properties are needed to perform a transient thermal analysis which results in a through-thickness temperature distribution for the tunnel walls at different instants in time: 1. Thermal conductivity vs. temperature. 2. Specific heat vs. temperature. 3. Density vs. temperature. The adopted curves are highlighted in Figure 2

3.3 Mechanical properties Mechanical properties of steel and concrete are specified through stress vs. strain curves. The following temperature dependences are considered: 1. Yield stress vs. temperature.

2. Elastic modulus vs. temperature.

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Fig. 4 Stress vs. strain relationship for concrete and steel at increasing temperature

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3. Linear thermal expansion coefficient vs. temperature. The thermal expansion coefficients used within the numerical simulations are illustrated in Figure 3.

Temperature dependent stress vs. strain curves for concrete and steel are illustrated in Figure 4. Only compression stiffness is considered for concrete throughout the present article.

3.4 Boundary conditions: Thermal convection and radiation Section heat transfer analysis is performed in 2D using both convection and radiation boundary conditions. A convection coefficient equal to 25 [W/mq °C] is assumed for surfaces with direct exposure to fire. A value equal to 9 [W/mq °C] is adopted for all other surfaces.

Fig. 5 Comprehensive vision of the reinforced concrete structure, with a detail of two joints

An emissivity equal to 0.56 is adopted for boundary radiation. The ambient temperature for both convection and radiation heat exchange is applied using the UNI11076 fire ramp. The latter temperature rise is uniformly applied to the tunnel surfaces that are directly exposed to air, while the remaining parts are protected by the lateral walkways and rail installation layout. A constant room temperature equal to 20 °C is specified for the latter locations.

4. Finite element models The main purpose of the finite element model is to simulate the evolution in time of the structural response to a fire event in the most realistic way. Due to the complex material models outlined above, an advanced calculation methodology was considered appropriate to perform the fire verification task. A finite element model is thus put in place, keeping the following important features in mind: 1. Computational light-weight: due to the number of variables affecting the material properties,

full solutions need to be obtained within minutes.

2. The model needs to account both for thermal and mechanical analysis. A one-way coupling between these fields has been assumed.

3. Reinforced concrete needs to be simulated with particular reference to the interaction and congruence of concrete matrix and steel bars.

4. The soil behaviour needs to be simulated in a manner consistent with the reality. This is to catch the conseguences of mutual interactions between the reinforced concrete structure and the surrounding soil.

5. The structural joints, interposed between the different segments that compose the tunnel's ring, must behave like monolateral contacts, i.e. they must be able to transmit compression forces only.

4.1 Model description The described finite elements model has been developed using great attention both in the structure and in the geotechnical issues. In figure 5 we see a comprehensive vision of the reinforced concrete structure, with the surrounding soil. In the figure we see also the crown of the tunnel with the detail of two structural joints, they are modelled with contact elements, with only monolateral behaviour.

Fig. 6 Temperature through the structural section at different temporal instants

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More specifically, particular devices are applied as follows: 1. The soil’s behaviour, wich is elastic-plastic, is described by using “plate” elements. The

mathematical formulation belongs to the type of “plain strain”. The breaking domain is the Mohr-Coulomb type. The in-situ applied stresses are isotropic. There is no groundwater in the soil.

2. The concrete's behaviour is described by using an elastic-plastic constitutive law. The plasticization level depends by the temperature, as every other mechanical parameters. The concrete is described by using eight nodes “plate” elements. The mathematical formulation belongs to the type of “plain strain”.

3. The steel bars for their part, are described using “truss” finite elements, with an elastic-plastic constitutive law. Their position follows the one of the executive project for the tunnel's segments. As seen for the concrete, the mechanical parameters of the steel are temperature dependent

4. The finite elements of the “contact” type are used to simulate the structural joints in their behaviour. Viewing in a direction that is perpendicular to the structural joint section and parallel to the ring perimeter, they react only in compression. In a direction that is perpendicular to the ring perimeter they have a frictional behaviour that belongs to the concrete’s type. This is the correct way to simulate the physical behaviour of the monolateral constraint without reaction in the case of traction.

All finite element analysis were performed with the Strand7 finite element analysis system. 4.2 Model benchmarks Various benchmarks are performed with scenarios of increasing complexity from the simple heat transfer to the fire analysis under external loads. By solving the two dimensional heat transfer model, nodal temperatures are essential to assemble the correct model stiffness at given simulation times. As a consequence, thermal heat transfer was considered as a proper starting point for the benchmark procedure. The figure 6 shows the diagram of temperature in the crown of the tunnel at two different temporal instants: T1 = 30 min; T2 = 120 min.

To prove the goodness of the obtained results from the heat transfer model, an independent simulation has been made, using a different commercial solutor, that is named Solveheat. In the figure is shown the good overlap of the two temperature diagrams, in both the considered temporal instants.

Fig. 7 Steel reinforcement layout drawing for the typical concrete segment

5. Case study The principles outlined above, are applied to perform the fire verification of tunnel sections part of the railway “Fiumetorto-Cefalu’-Castelbuono” in Italy. 5.1 Location of tunnel section A steel reinforcement layout drawing for the typical concrete segment is illustrated in Figure 7.

A typical tunnel section is made up using the following components: a 40 cm thick precast concrete segment that is installed in the ring’s perimeter of the tunnel.

5.2 Loads and type of analysis A complete set of external load conditions are considered acting on the tunnel at the beginning of the fire event. 1. Self weight of concrete.

2. In situ stress soil.

3. Live loads.

4. Concrete shrinkage.

5. Load from the lateral walkways.

6. LM71- 2: vertical train load with dynamic amplification factor.

7. Train skewing.

8. Centrifugal force.

Partial amplification factors comply with Eurocode specifications for accidental load combinations. A quasi-static analysis is performed were no inertia terms are accounted for. Static loads are applied at the first time increment and nodal temperatures are read from the transient heat analysis file at increasing simulation times.

Fig. 8 Temperature distribution at two different temporal instants: T1=30min; T2=120min

Fig. 9 Tensions distribution: T = 0 min

Fig. 10 Tensions distribution: T = 30 min

5.3 Results The two dimensional heat transfer model gives the results in terms of achieved temperature value, as shown in the figure 8.

The structural model gives the results in terms of achieved tensions and deformations values, as shown in the following figure 9, 10, 11, 12, 13.

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Fig. 12 Radial displacements: T = 120 min

Fig. 13 Tensions in the soil: T = 120 min

6. Conclusions An efficient, design oriented, approach is proposed within the present work to describe complex physical phenomena such as the evolution of structural response under fire exposure for reinforced concrete tunnels. Starting from the application of a normalized fire curve in the time domain, proper thermal and mechanical properties are assigned to steel and concrete, in order to capture a realistic response. Numerical simulation can be considered as the most effective way to handle fire design tasks for

general geometries. Scale models are difficult to set up for these problems and analytical correlations, useful for design, are therefore limited. International standards are becoming, on the other hand, very demanding on analysis of increasing complexity and rigorous models must be created to be fully compliant to code requirements. The results obtained can be considered as a starting point towards strength optimization procedures for new tunnels and at the same time they offer a time effective tool for a fire certification of existing structures. Furthermore, for revamping of existing tunnels, the developed procedure can be useful to minimize the cost related to the installation of protective layers.

7. Acknowledgment The present work was carried out with the support of SWS Enginering S.p.a. and Enginsoft S.p.a.

8. References

[1] Strand7 Software, “Strand7/Straus7 Theoretical manual”, Edition 1, January 2005. [2] EN 1991-1-2: “Eurocode 1: Actions on structures – Part 1-2 : General actions – Actions on

structures exposed to fire”. [3] EN 1992-1-2: “Eurocode 2: Design of concrete structures - Part 1-2: General rules -

Structural fire design”. [4] D.M. Infr. e Trasp., “Sicurezza nelle gallerie ferroviarie. Analisi dei rischi – Misure di

prevenzione e protezione – Approvazione dei progetti”, 28 ottobre 2005 (G.U. n.83 del 8.4.2006).

[5] UNI 11076, “Modalità di prova per la valutazione del comportamento di protettivi applicati a soffitti di opere sotterranee, in condizioni di incendio”, 1 luglio 2003.

[6] UNI 9502, “Procedimento analitico per valutare la resistenza al fuoco degli elementi costruttivi di conglomerato cementizio armato, normale e precompresso”, 8 maggio 2001.

[7] D.M. LLPP. 16 gennaio 1996 (G.U. n.29 del 5.2.1996), “Norme tecniche per l'esecuzione delle opere in cemento armato normale e precompresso e per le strutture metalliche”

[8] BUCHANAN, A. H.: “Progetto delle strutture resistenti al fuoco. Edizione italiana aggiornata agli Eurocodici”, Editore Ulrico Hoepli, Milano, 2009.

[9] CEFARELLI G., NIGRO E., PRINCI P., PUSTORINO S.: “Progettazione di strutture in acciaio e composte acciaio-calcestruzzo in caso di incendio”, Editore Ulrico Hoepli, Milano, 2010.

[10] CAPPELLETTI S.: “Prevenzione Incendi - Tecnica e pratica”, Edizioni di Legislazione Tecnica, Roma, 2009.