Thermo-hydric analysis of concrete–rock bilayers under fire conditions

Engineering Structures 59 (2014) 765–775

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Thermo-hydric analysis of concrete–rock bilayers under fire conditions Anna Paula G. Ferreira a, Michèle C.R. Farage a,⇑, Flávio S. Barbosa a, Albert Noumowé b, Norbert Renault b a b

Computational Modeling Graduation Program, Federal University of Juiz de Fora, Campus Universitário s/n, Martelos, 36036-330 Juiz de Fora, MG, Brazil University of Cergy-Pontoise, Laboratoire de Mécanique & Matériaux du Génie Civil, EA 4114, F-95000 Cergy-Pontoise, France

a r t i c l e

i n f o

Article history: Received 15 January 2013 Revised 20 September 2013 Accepted 29 November 2013 Available online 29 December 2013 Keywords: High temperatures Concrete CAST3M

a b s t r a c t High temperatures due to fire are amongst the most critical situations to which concrete may be exposed. For safety purposes, it is important to understand and preview the consequences of fire on the structural integrity of concrete. Concerning high temperatures, the mechanical degradation suffered by a concrete structure is related both to energy and mass transport. Therefore, a realistic modeling of such a condition shall take into account not only a thermal analysis but also the complex physical–chemical reactions developed among the components of that heterogeneous material. This approach is adopted in the present study as an effort to better reproduce the consequences of fluid flow and chemical processes – cement hydration and dehydration – in the material. Numerical simulations of the hygro-thermal behavior of concrete–rock bilayers subjected to fire conditions are performed through a transient and nonlinear model. The adopted model was evaluated by comparisons with data from an experimental program concerning thermal tests on a set of concrete–rock bilayer specimens, aiming to reproduce real world situations observed in some structures, such as tunnels. Ó 2013 Elsevier Ltd. All rights reserved.

1. Introduction The use of concrete in civil structures that may be subjected to adverse conditions shall be based on studies about their behavior in such situations. Concerning fire exposure, there are several records of accidents involving concrete structures – such as tunnels – with catastrophic consequences, which justifies the experimental and numerical studies related to the subject [1,2], in order to minimize risks and ensure the safety of users. Cafaro and Bertola [3] and Vianello et al. [4] list a number of tunnel fires with casualties occurred in Europe during the last decades, for instance: Mont Blanc, France–Italy, in 1999 (39 casualties), Tauern, Austria, in 1999 (12 casualties) and Gothard, Switzerland, in 2001 (11 casualties). High temperatures may lead the porous microstructure of concrete to deterioration and loss of efficiency of the whole structure [5]. Many phenomena and interactions are involved in the evolution of properties that occurs inside the heated concrete, which makes this type of problem highly non-linear [6]. Thus, to properly describe the behavior of concrete subjected to thermal loads, it is important to consider the coupled heat conduction, the fluid flow and the mechanical behavior. Cracking and spalling ⇑ Corresponding author. Address: Departamento de Mecânica Aplicada e Computacional, Faculdade de Engenharia, Universidade Federal de Juiz de Fora, Campus Universitário s/n, Martelos, 36036-330 Juiz de Fora, MG, Brazil. Tel.: +55 32 2102 3470; fax: +55 32 2102 3401. E-mail address: [email protected] (M.C.R. Farage). 0141-0296/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.engstruct.2013.11.033

in heated concrete are important issues that depend both on hygro-thermal and thermo-mechanical factors [7–9]. Specifically in accidental fire exposures, the temperature increase is in general very fast, causing higher damage than the observed in structures designed to support long periods of high temperature exposure [10]. Concerning tunnels, it is also of interest to investigate the concrete–rock interface, in order to verify whether that region is even more susceptible to fire effects. To this end, the present work presents the results of a hygro-thermal model applied to a concrete–rock bilayer sample. Experimental results were employed for validation of the model, which was implemented in the CAST3M code, developed at the French Atomic Research Center (CEA, France) [11].

2. Concrete and rock under fire conditions 2.1. General aspects This section provides an overall description of the effects of fire on the materials employed in this study: concrete and rock.

2.2. Concrete When exposed to heating, concrete passes through different phases, as described by Dal Pont [12]:

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1. As soon as the heating starts, temperature rises on the heated surface. The moisture inside the concrete, composed of liquid water and water vapor, moves toward the cold area of the concrete specimen by diffusion. 2. When temperature reaches 100  C, water begins to boil. The water vapor moves toward the cold zones and condenses. The latent heat required for the boiling of water slows the increase of temperature until the complete boiling of water in that portion of concrete. 3. At the same time, the vapor that condenses in the cold zone may bind to the non-hydrated cement and a new hydration takes place. At this phase, the formation of new calcium silicate hydrate (CSH) provides an improvement of mechanical properties of concrete. 4. The increase of temperature also causes dehydration. Around 105  C, the chemical bonds that form the CSH begin to be destroyed, transforming the hydrated products in anhydrous products and water. The water that is released into the concrete vaporizes, absorbing heat. The dehydration reaction progressively reaches several hydrated products that are part of the concrete: as soon as temperature rises, more free water is generated and more water vaporizes. The vaporization is an endothermic reaction and influences the heating of concrete, slowing down the heat propagation. 5. Free water tends to move toward cold zones of concrete. Since concrete and, in particular, the high performance concrete (HPC) has a low permeability [13], liquid water and water vapor do not penetrate so quickly in cold area. In addition, the formation of water after dehydration is faster than the release of water and vapor. The result of the combination of this two effects is that the pore pressure increases and may reach values of the order of several atmospheres. It is also observed that the peak pressure moves toward the cold regions of the concrete progressively increasing its value. As indicated in a number of experimental studies [14–16], the increase in gas pressure in the pores is also the basis of the phenomenon of spalling. The spalling is the detachment of fragments of the concrete surface exposed to the heating and may seriously damage the integrity of the entire structure by direct exposure of structural steel to fire, increasing the risk of buckling under compression, the loss of the isolation property and other consequences. This phenomenon is usually explained by two mechanisms [15,17]: Thermo-mechanical process: Characterized by high temperature gradients, especially in the first centimeters of the exposed surfaces. Those gradients are, in general, due to rapid heating (as accidental fires, for instance) and induce high compressive stresses near the exposed surface – which may locally exceed the concrete compressive strength and cause the ejection of pieces. Hygro-thermal process: The movement of fluids is due to pressure and molar concentration gradients (Darcy’s Law and Fick’s Law). The fluids tend to move to the inner and colder areas of concrete. Thus, water vapor begins to condense and an obstruction of humidity (‘‘moisture clog’’) is gradually created near the exposed surface. This obstruction is considered as a region of concrete with high content of water, acting as a barrier to the fluid flow, which increases pore pressure. These pressures may locally exceed the concretes tensile strength and result in the occurrence of spalling. It is well known that high performance concretes are more susceptible to explosive spalling due to its lower permeability and porosity. Those characteristics lead to the development of higher pressures inside the pores since the fluid flow is difficult.

2.3. Rock As observed in the concrete, high temperatures modify the microstructure of rock. This material also presents differential expansion, since it is composed of minerals with different properties which may also present anisotropy of thermal expansion [18,19]. This phenomenon causes a stress concentration in the contact of the grains, resulting in cracking. There are models developed to predict the thermo-mechanical behavior of rocks – some of them may be found in the works of Hettema [20] Fredrich and Wong [21] apud Lion [19,22] and Nguyen et al. [22]. Studies cited by Yavuz et al. [23] identified the following microstructural processes in a limestone due to temperature: (a) Exposure to 100  C causes dilatation of calcite and compaction of grains. However, the compaction effect does not block the migration of water in the pores due to clay content; (b) Up to 200  C the shrinkage of clay against dilatation of calcite is observed. Pores generate space for the expansion of components and thus no effective porosity increase is measured; (c) At 300  C, the expansion of calcite is most remarkable and effective than the shrinkage of the clays, but no crack is observed in the grains; (d) Cracking within the grains starts at 400  C and separation along the contact surfaces of the grains is observed. Thus, with the microcracking, effective porosity approaches the total porosity by connection of closed pores. (e) Cracking within grains and separation along the grain boundaries continues up to 500  C, and the effective porosity is slightly larger than the initial porosity.

3. Experimental program The experimental data employed herein were obtained at the Laboratoire de Mécanique et Matériaux du Génie Civil (L2MGC) of the University of Cergy-Pontoise, France [24,25]. Tested specimens consisted of concrete–rock bilayers made of conventional concrete and high performance concrete and limestone (Fig. 1), aiming to reproduce a typical sample of a tunnel structure. The goal was to submit the double layered blocks to temperatures up to 600  C and 750  C, measuring the temperature evolution at specific points along the height and observing the different effects of temperature on the two types of concrete, rock and interface region. 3.1. Concretes formulations Two different types of concrete were employed in the study: conventional concrete (CC) and high performance concrete (HPC). Each type of concrete was used in the fabrication of two bilayer samples, as shown in Fig. 2. The compositions of the tested

Fig. 1. Bilayer samples made of concrete and rock.

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3.5. Experimental results

Fig. 2. Geometry of samples and location of thermocouples.

Table 1 Formulation of concretes (kg/m3). Constituent

Conventional concrete

HP concrete

Cement CEM I 52.5 Silico-calcareous gravel Silico-calcareous sand Water Superplasticizer

362 956 692 217 –

500 987 715 150 4.71

concretes are given in quantity of the component per unit volume of produced concrete, as shown in Table 1. 3.2. Rock characteristics It was employed a type of limestone, which is a sedimentary rock. Its main component is calcite (calcium carbonate – CaCO3). In lower concentrations it is possible to verify the presence of silica, clay, iron oxide or carbonaceous material [26]. 3.3. Instrumentation Four bilayer samples were prepared, two of of them made of conventional concrete (CC), to be submitted to thermal loading up to 600  C (CC-600) and up to 750  C (CC-750), respectively, and two samples in high performance concrete (HPC), for exposure to temperatures up to 600  C (HPC-600) and 750  C (HPC-750). The samples have dimensions 33  33  30 cm3, of which 7 cm is the height of the rock and 23 cm correspond to the height of the concrete. Fig. 2 shows the scheme adopted to monitor the evolution of temperature during the thermal tests. For each sample five thermocouples were installed along the central axis of the prismatic sample, arranged in the following positions: the upper surface of the concrete, half of concrete layer, rock–concrete interface, half of rock layer and the bottom surface of the rock. Those points were chosen in order to provide data for comparison and parametric adjustment of the modeling, aiming to reproduce the temperature evolution in the samples, through concrete, rock and the interface regions. The blocks were isolated with fiberglass (except for the upper surface, which was directly exposed to heating) so as to assure one-directional heating – for simplification purposes concerning the numerical simulations. 3.4. Thermal loading

where T is temperature in  C and t is the time in minutes.

4. Hygro-thermal modeling The equations governing fluid flow in porous media are given by the law of mass conservation, Darcy’s law and an equation of state [12,29,30]. We adopt the hypothesis that the mass flows due to dispersion and diffusion are small compared to advective flow, and thus are neglected [31]. The mass conservation is given by the balance equation in each phase (liquid and vapor) (see Eq. (2)).

Table 2 Material properties experimentally measured.

Samples remained one month after its fabrication in the laboratory, packed in plastic covers, under the approximate temperature of 20  C, and then were subjected to heating. The evolution of the oven temperature was programmed according to the standard fire curve ISO 834, given by the following equation:

T ¼ 345logð8t þ 1Þ þ 20;

Table 2 shows a summary of the properties of concrete and rock: compressive strength (fc ), tensile strength (ft ), modulus of elasticity (E), Poisson’s ratio (m), porosity (/), bulk density (qb ), real density (qr ) and thermal conductivity. Figs. 3 and 4 show the degradation suffered by the CC-600 and the CC-750 samples, respectively. The lateral cracking is pronounced, there is a ‘‘mapped’’ cracking in the exposed surface and we can see the beginning of disintegration of the aggregate near the surface. The high performance concrete HPC-600 presents a lower lateral cracking, but otherwise suffered superficial spalling, as shown in Fig. 5. The HPC-750 was completely disintegrated after successive spallings, as one can see in Fig. 6. In spite of the fact that the experimental program aimed to provide temperature evolution data for modeling validation purposes, the aspects of the tested samples allow a number of further considerations, based on information available in the literature. The high performance concrete proves its greater tendency to spalling phenomenon [14], which may be due to a combination of the hygro-mechanical and thermo-mechanical processes mentioned in Section 2.2. While conventional concrete presented ‘‘mapped’’ cracking in both of the maximum temperatures, the HP concrete lost fragments, which may denote the occurrence of local strain incompatibilities between the mortar and the aggregates [14]. This effect may be identified in Fig. 5. Even suffering little cracking, the HPC-600 suffered some spalling on the upper surface – possibly as a consequence of thermo-hygral processes described by Mindeguia et al. [15]: being denser, less permeable and less porous than the conventional concrete, high performance concrete imposes major obstacles to the flow of fluid masses. This difficulty to migrate quickly toward the coldest zones generates high pressures in the concrete, leading to spalling. We observe that only the CC-750 presents cracks that approaches and crosses the interface with the rock – possibly due to differences among the thermal behavior of concrete and rock, leading to differential thermal strains. It is important to notice that, according to Akca and Zihniog˘lu [27], size and shape of samples may directly affect the heating rate of concrete – thinner specimens being more susceptible to thermal degradation than larger ones. Nevertheless, this aspect was not dealt with herein, since all tested blocks had the same geometry. The experimental temperature data will be used to verify the results of the numerical model, which is dealt with in the following sections. More detailed information about experimental temperature evolutions and instrumentation is available in Ref. [28].

ð1Þ

Property

Unit

Conventional concrete

HP concrete

Rock

fc ft E

MPa MPa GPa

35.9 3.7 35.6 – 2150 – 1.86

81.2 5.2 45.2 – 2330 – 2.06

39.8 4.2 17.7 0.3 2296 2671 –

m qb qr k

kg/m3 kg/m3 W/mK

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It is assumed that the vapor and liquid phases are separated by a curved interface. Being the two phases in thermodynamic equilibrium, the pressures of liquid water (pl ) and vapor (pv ) may be related by the Clapeyron equation (see Eq. (4)).

RT pv pl ¼ pv s ðTÞ þ ql ðTÞ ln ; Mv pv s ðTÞ

(a) Heated surface

ð4Þ

where R represents the ideal gas constant and Mv the molar mass of water vapor. As the total saturation is equal to 1, we can write the saturation of water vapor as a function of liquid water saturation and the model will then take two unknowns: the saturation of liquid water and temperature. Combining the mass conservation equations, the expression of the flow given by Darcy’s law and the Clapeyron equation, we have Eq. (5), which represents the water mechanisms:

(b) Lateral surface

Fig. 3. CC-600 after heating

½ql ðTÞ  qv ðTÞ/ðdÞ

@Sl _ ¼ r½DðSl ; d; TÞrSl  þ d; @t

ð5Þ

where D is the hydraulic conductivity, given by Eq. (6):



(a) Heated surface

DðSl ; d; TÞ ¼

(b) Lateral surface

Fig. 4. CC-750 after heating.



qv ðTÞ q ðTÞ q 1 @pv k ðS ÞK ðdÞ þ l k ðS ÞK ðdÞ l ; lv ðTÞ v l v ll ðTÞ l l l qv Sl @Sl

being lv and ll the dynamic viscosities of the two phases, kv and kl the relative permeabilities and K v and K l the intrinsic permeabilities and d represents water mass generated by dehydration. For the thermal part, by combining the equation of conservation of entropy and the expression of the heat flux given by Fourier’s law, we obtain the equation of heat conservation (see Eq. (7)):

_ cðSl ; dÞ ¼ rðkðSl ; dÞrTÞ  Ll!v ðTÞml!v  Ls!l d;

(a) Heated surface

ð6Þ

ð7Þ

where L is the latent heat of phase change, ml!v is the mass of vaporized water, d_ is the kinetics of dehydration and cðSl ; dÞ is volumetric heat capacity of concrete, that is given by Eq. (8):

(b) Lateral surface

cðSl ; dÞ

Fig. 5. HPC-600 after heating.

@T ¼ qs C s þ /ql ðTÞSl C l þ ðd0  dÞC ll ; @t

ð8Þ

where qs and ql are densities of the solid part of concrete and of the liquid water; C s ; C l and C ll are the specfic heat capacity of solid part, free water and chemically bound water, respectively, and d0 and d are the initial mass of water chemically bound and the mass of water generated by dehydration, respectively. Dehydration is

(a) Heated surface

(b) Lateral surface

Fig. 6. HPC-750 after heating.

@ð/qa Sa Þ ¼ r  ðqa ua Þ þ qa ; @t

ð2Þ

where a represents the liquid or the vapor phase, /; Sa and qa are the porosity of the media, the saturation of the phase and the increase (or decrease) in mass due to a source. Darcy’s law is written for each phase, according to Eq. (3):

ua ¼ qa

K a kra Sa

la

rpa ;

ð3Þ

where ka ; pa ; la and qa are the effective permeability, the pressure, the viscosity and the density of phase a.

Fig. 7. Structure of the hygro-thermal algorithm.

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Fig. 8. Modeled structure and boundary conditions.

Table 3 Data for the model – concrete. Data

Unit

CC

HPC

Cement, water, aggreg. contents Bound water Bulk density Thermal conductivity Porosity Gas permeability

kg m3 kg m3 kg m3 W m1 K1 % m2

See Table 1 0.9  qty. cement  0.21 2150 1.86 14 1  1017

See Table 1 0.9  qty. cement  0.21 2330 2.06 9.5 1  1019

considered to take place for temperatures higher than 60 ° C, based on experimental data reported by Gallé et al. [32], following Eq. (9): Table 4 Data for the model – rock.

d¼

Data

Unit

Rock

Bulk density Thermal conductivity Porosity Gas permeability

kg m3 W m1 K1 % m2

2296 1.5 14 1  1019

T > 60  C

ð9Þ

The coupled transport of water and heat in concrete is governed by the system formed by Eqs. (5) and (7). 5. Numerical analysis 5.1. The CAST3M code

Table 5 Specific heat.

CAST3M is an open source code developed in the French Atomic Energy Agency (CEA) in France. It is a code to solve partial differential equations through the finite element method, allowing the incorporation and adaptation of models by the user [33]. It employs a

Specific heat (J kg1 C1) Cement Aggregate Bound water Free water Rock

750 800 3760 4184 674

Table 8 Evolution of rock properties.

Table 6 Initial temperature and saturation.

Temperature Saturation

d0 ðT  60Þ; 540

Parameter

Rock

Qty. of dehydrated water (kg/m3) Porosity (%) Intrinsic permeab. to gas (m2)

No dehydration /r ¼ 14% (constant)

Intrinsic permeab. to water (m2)

K rl ¼ 1  1021 (constant) pffiffiffiffiffiffiffiffiffiffiffiffiffi r 1=m 2m krv ðSl Þ ¼ 1  Sl ð1  Sl Þ  2 ffiffiffiffi p 1=m m r krl ðSl Þ ¼ Sl 1  ð1  Sl Þ

K rv ¼ 1  1017 (constant)

Relative permeab. to gas (m2)

Concrete

Rock

Relative permeab. to water (m2)

24  C 39% on the surface and 95% on the rest

24  C 70%

Thermal conductivity (W/mK)

kr ¼ k

f

ks kf T þks /m297

Table 7 Evolution of concrete properties. Parameter Qty. of dehydrated water (kg/m3) Porosity (%)

CC d¼ /

HPC d0 540 ðT

 60Þ dðTÞ

cc

¼ /ð60Þ þ q

cc

ad K cc v0 e ad K cc e l0

hyd

Intrinsic permeab. to gas (m2)

K v ðdÞ ¼

Intrinsic permeab. to water (m2 )

K cc l ðdÞ ¼

Relative permeab. to gas (m2 )

pffiffiffiffiffiffiffiffiffiffiffiffiffi 1=m 2m ¼ 1  Sl ð1  Sl Þ  2 pffiffiffiffi cc 1=m m krl ðSl Þ ¼ Sl 1  ð1  Sl Þ  T   T 2 þ 0:0107 100 kcc ¼ 2  0:2451 100

Relative permeab. to water (m2 ) Thermal conductivity (W/mK)

cc krv ðSl Þ

d0 d ¼ 540 ðT  60Þ

/hpc ¼ /ð60Þ þ qdðTÞ hyd

hpc ad K hpc v ðdÞ ¼ K v 0 e

K hpc ðdÞ ¼ K hpc ead l l0 pffiffiffiffiffiffiffiffiffiffiffiffiffi hpc 1=m 2m krv ðSl Þ ¼ 1  Sl ð1  Sl Þ  2 pffiffiffiffi hpc 1=m m krl ðSl Þ ¼ Sl 1  ð1  Sl Þ khpc ¼ kcc þ 0:3

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language that is based on object-oriented programming, named GIBIANE, and the objects are created using pre-defined operators, written in the language ESOPE [34]. In this work the implementation is made in GIBIANE. The employed algorithm is summarized in Fig. 7. The procedure THCR is an adaptation of the code presented by Ranc et al. [35] to the problem of bilayer samples. The procedure that solves the equations is internal to thermal and hydraulic loops and Table 9 Evolution of the model parameters. Parameter Saturated vapor pressure

pv s ¼ patm exp

Porosity Volumetric mass of liquid water (%) Volumetric mass of liquid water Dynamic viscosity of vapor Dynamic viscosity of water Latent heat of vaporization Latent heat of dehydration

MDHv T373:15 R

373:15T

r

/ ¼ 14% (constant) h

ql ðTÞ ¼ 314:4 þ 685:6 1 



1=0:55 i0:55 T 374:4

lv ðTÞ ¼ 3:85  108 T þ 105   ll ðTÞ ¼ 2:414  105 exp 570:58058 Tþ133:15 2450:25026:433949T Ll!v ¼ 10:0019057413T7:0023846T 2

Ll!v ¼ 2.5  106 J kg1

it is possible to adopt an explicit or implicit resolution by the theta method. 5.2. Mesh, initial data and evolution of properties As the experimental thermal measurements are taken along an axis of the sample, the numerical analysis is accomplished in 2D for the structure shown in Fig. 8. This figure also shows the band of the sample used in computer simulation, with its respective boundary conditions. The figure also presents the typical aspect of finite element mesh composed of 400 triangular and linear elements employed in the analysis. It is observed that the number of mesh elements was established after a convergence analysis with successive refinements, leading to the configuration shown in Fig. 8 Both materials are considered isotropic, but differ from each other in the value of their properties. The initial data and properties are defined at the beginning of the calculation for each type of concrete and rock and they are listed in Tables 3 and 4. The specific heat is given for each material to calculate the total volumetric specific heat. The values are shown in Table 5. Table 6

Fig. 9. Numerical and experimental temperatures for conventional concrete (CC) at each point of analysis.

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shows the initial conditions of temperature and saturation in the two materials. Properties of concretes and rock vary with temperature, saturation and dehydration (for concrete). Tables 7 and 8 show these evolutions, while Table 9 shows other values that vary during the calculation. More information about the adopted parameters and empirical functions present in Tables 7–9 is available in Ref. [28]. 5.3. Numerical results The numerical results for absolute temperature are compared with experimental data in Figs. 9 and 10. Figs. 11 and 12 show the rate of change of the temperature with respect to time. Every graphic shows four curves, describing the experimental and numerical results obtained for heating up to 600 °C and up to 750 °C. Temperature at point T1 is not shown because those values were taken as input data for the numerical model. Such a comparison allowed the evaluation of the adopted model and the identification of necessary improvements for a better representation of the material’s behavior. In spite of the fact that the reference experimental program (described in Section 3) did not provide

771

measurements for saturation and vapor pressure, numerical results obtained for those quantities are shown herein, in Figs. 13–16 and, based on information from the litterature, allowed some further analysis of the employed thermo-hydric model. 5.3.1. Temperature evolution Figs. 9 and 10 compare the numerical temperature with the experimental measurements in the CC samples and HPC samples, respectively. Fig. 9 indicates that, for the conventional concrete, the curves only agree with their experimental counterpart up to around 60 °C – when dehydration is considered to begin. For temperatures above that limit the model clearly overestimates the values. By comparing the evolutions obtained for points T2, T3, T4 and T5, though, it is possible to notice that the farther is the analysed point from the heated surface, the lower is the gap among experimental and numerical curves. Similar pattern is observed for the HPC samples, as shown in Fig. 10 – except for the point T2 in HPC-600, where the curves are practically coincident up to around 120 °C. In order to verify whether those differences were caused by misadjusted model quantities, a tentative parametric analysis was performed, denoting that the adopted dehydration threshold

Fig. 10. Numerical and experimental temperatures for high performance concrete (HPC) at every point of analysis.

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Fig. 11. Rate of change of the temperature with respect to time for the CC samples.

(60 °C) is adequate, in accordance with Gallé et al. [32]. A possible explanation for the observed discrepancies could be the extent of material damage suffered by the heated samples and the influence of cracking on the thermal conductivities present in Eqs. (5) and (7), respectively. The adopted thermo-hydrical modeling assumes thermal conductivity as a function of temperature (see Table 7), with no account of mechanical damage. The importance of adopting the latter dependence is rather controversial [36,37] and implies additional complexity to the modeling. Nevertheless the overestimated numerical temperatures justify deeper adjustments of the adopted input parameters and further evaluation on the relevance of considering mechanical effects on the present modeling. The slightly better results depicted for T2 in Fig. 10(a) could be justified by the little cracking suffered by the HPC-600 (as shown in Fig. 5(b)) – while for the HPC-750 the greatest differences were observed. This could also explain the evidence of better agreement amongst the numerical/experimental results for the points situated farther from the heated surface, since thermal damages are also related to the points positions. It is important to notice that only one oven was employed in the experimental program – the experiments were conducted sequentially, which may cause slight variations in the initial

condition of the samples, that were packed in covered plastic before testing. In spite of the divergence related to temperature evolution in absolute values, there is a clear correspondence among all the numerical curves and their experimental counterparts. Such a statement is based on Figs. 11 and 12, that exhibit the numerical and experimental curves of rate of change of the temperature with respect to time for the CC and the HPC samples, respectively. As one can notice, in this case the numerical and experimental curves show a quite good agreement – exception made for point T2 in the HPC-750 – which may be also attributed to measurement incertainties during the heating, given the high level of damage suffered by the concrete region in that sample (shown in Fig. 6). 5.3.2. Saturation and vapor pressure The experimental program did not comprise measurements related to saturation or vapor pressure in the heated samples. Nevertheless, numerical evaluations of those two quantities are presented herein, for the sake of qualitative analysis. The saturation evolution through the samples is shown in Figs. 13 and 14. Each curve is related to a given surface temperature. The x-axis represents the different heights on the central axis

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Fig. 12. Rate of change of the temperature with respect to time for the HPC samples.

Fig. 13. Evolution of saturation along the height of the CC sample.

Fig. 14. Evolution of saturation along the height of the HPC sample.

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peaks, ie, identifying regions with high water content, which may be related to the ‘‘moisture clog’’ previously cited. Also, HPC presents pressures about ten times higher than CC. Indeed, the HPC sample strongly deteriorated when heated up to 750  C (see Fig. 6). The numerical results concerning the evolution of saturation and vapor pressure are in good agreement with theoretical and experimental data available in the literature and enhance the assumption that thermal damage – and spalling – in concrete is a rather complex association of hygro-thermal and thermomechanical mechanisms. 6. Conclusions

Fig. 15. Evolution of vapor pressure along the height of CC sample.

The present work consisted of numerical analysis with experimental validation of the thermal behavior of concrete–rock bilayers subjected to high temperatures. The numerical program employed a thermo-hydric approach in order to evaluate the temperature distribution along the specimens, through a non-linear transient approach, implemented in a finite element code developed by the French Research Center for Nuclear Energy [11]. The numerical temperatures were compared to the experimental data, with significant discrepancies, specially concerning regions with important mechanical damage. In spite of the differences related to temperatures in absolute values, a clear numerical/experimental correspondence was identified in the rate of change of the temperature with respect to time. This fact indicates the need for further adjustments of the numerical input quantities – by considering the thermal conductivity of the concrete dependent of the mechanical damage. The numerical results obtained for saturation and vapor pressure are in good agreement with information available in the literature for conventional and high performance concretes. Acknowledgements This work was supported by the following agencies: Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), Fundação de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG), Universidade Federal de Juiz de Fora (in Brazil) and Université de Cergy-Pontoise (France).

Fig. 16. Evolution of vapor pressure along the height of HPC sample for high performance concrete (HPC).

References

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