CONCRETE BUFFERS FOR THE CONTAINMENT OF HIGH LEVEL RADIOACTIVE WASTE: CASTING CONDITIONS AND THM BEHAVIOUR

Transcription

1 CONCRETE BUFFERS FOR THE CONTAINMENT OF HIGH LEVEL RADIOACTIVE WASTE: CASTING CONDITIONS AND THM BEHAVIOUR B. Craeye (1), G. De Schutter (1), H. Van Humbeeck (2), W. Wacquier (2) and A. Van Cotthem (3) (1) Magnel Laboratory for Concrete Research, Department of Structural Engineering, Ghent University, Belgium (2) ONDRAF/NIRAS, Belgian Agency for Radioactive Waste and Enriched Fissile Materials, Belgium (3) Technum-Tractebel Engineering, Belgium Abstract In the framework of the feasibility demonstration program of the Belgian Supercontainer concept, extensive laboratory tests and finite element calculations were performed to accurately simulate the Thermo Hydro Mechanical (THM) behaviour of the Supercontainer concrete Buffer during construction and to predict and prevent early-age crack formation. The Supercontainer is the current Belgian reference concept for the final disposal of heat emitting waste designed by ONDRAF/NIRAS, the Belgian Agency for Radioactive Waste and Enriched Fissile Materials. The concept is based on a multiple barrier system where every component has its own specific safety function or role requirements. In this reference concept, the vitrified High Level Waste (HLW) and Spent Fuel assemblies (SF) are encapsulated into a watertight carbon steel overpack surrounded by a cylindrical concrete Buffer which will then be disposed in a deep clay layer. The laboratory test program was finalised and has allowed to characterize the mechanical, thermal and maturity-related behaviour of the two types of concrete currently considered for the choice of the cementious Buffer: a Self-Compacting Concrete (SCC) and a Traditional Vibrated Concrete (TVC). The measured data were then used to simulate the behaviour of the concrete Buffer during construction by using a 2.5D (2D axisymmetrical) thermal and crack modelling program. This includes the fabrication of the concrete, the emplacement of the heat-emitting waste canisters, and the closure of the container. That way, it is possible to take into account different casting conditions. The simulations showed that through-going cracks in the concrete Buffer, which will considerably ease the transport mechanisms inside the Supercontainer and reduce the radiological shielding role of the buffer, are not expected. 153

2 1. INTRODUCTION 1.1. The Supercontainer concept The Supercontainer is intended for the disposal of vitrified High Level heat-emitting Waste and for direct disposal of Spent Fuel assemblies (UOX, MOX). The focus of the study lies on the Supercontainer meant for the disposal of vitrified HLW. In this concept (Figure 1, Figure 2), the vitrified waste canisters are enclosed in a carbon steel overpack of about 30 mm thick. This overpack has to prevent contact of the waste with the water coming from the host formation during the thermal phase i.e. several 100 s of years for vitrified waste. For corrosion protection purposes, the overpack is embedded in a high ph concrete buffer (high alkaline concrete) [3,4]. This buffer, with a thickness of about 70 cm, also performs as a welldefined radiological protection buffer for the workers, simplifying underground waste transportation operations. This buffer is surrounded by a stainless steel [4] cylindrical envelope (also called liner). This liner serves as a mould for the casting of the concrete buffer and provides sufficient mechanical strength and confinement during transportation. Figure 1: 3D view of the disposal gallery for vitrified waste The outside radius of the Supercontainer, enclosing 2 waste canisters, is about 1.9 m and its total outer length is 4.2 m totalizing a weight of 30 ton per Supercontainer. The fabrication steps of the Supercontainer are illustrated at Figure 2. This includes: (a) the fabrication of the concrete shell (cast in one), (b, c) the emplacement of the overpack (in hot cell), (d, e) the filling of the annular gap and (f, g, h) the closure of the container. Figure 2: The different construction steps of the Supercontainer 154

3 1.2. Early age behaviour of massive concrete The early age behaviour of massive concrete has become increasingly important. Massive hardening concrete elements, characterized by a low tensile strength, are very prone to early age thermal cracking due to the heat of hydration. The service life of such concrete elements, can be severely reduced by the presence of even small thermal cracks [5]. The main technological problem related to the fabrication of the concrete buffer of the Supercontainer, is the effect of the heat of hydration during hardening of the fresh concrete. On the other hand, the early age shrinkage, such as autogenous shrinkage, must also be taken into account. Finally creep, defined as the time-dependent increase of deformation under sustained load, affects the stress distribution. All these effects should be taken into account in design, construction and operation of radioactive waste repositories. 2. CONCRETE BUFFER COMPOSITION Two types of concrete are considered for the buffer surrounding the overpack: a Self- Compacting Concrete (SCC) [6] and a Traditional Vibrated Concrete (TVC). In comparison with TVC, SCC has a higher amount of limestone filler, makes more use of superplasticizer (carboxylate-based admixture) and needs no additional vibration energy. Preference is given to the use of SCC because it will ease considerably the precast process and complies with all other requirements. These requirements are based on certain restrictions to the different components of the buffer. It is recommended that CEM I, Portland Cement (no fly ashes, no blast furnace slag), is used with additional restriction that the cement has a low SO 3 content (< 2%) and that the compound content of C 3 A should not exceed 5%. This is to reduce ettringite formation and to reduce the formation of dense hydrogarnet with resulting increase of permeability and porosity. The cement must have high sulphate resistance to better resist to sulphur species present in Boom clay fluids. Cement with limited hydration heat production is also preferable (to avoid or limit cracking). The use of limestone aggregates containing not more than 2% each of magnesium, silicon and aluminium (as oxides) is also recommended to prevent the risk Alkali-Aggregate Reaction resulting in possible expansion and cracking. Other organic additives should be avoided except, as low quantity as possible, superplasticizer. Other wanted properties are listed below: Good workability - preferably pompable; Sufficient tensile and compressive strength in order to resist to normal and accidental loads; a C30/37 or better concrete is a good starting point; Micro-cracks are allowed (and cannot be avoided) but radial, through-going cracks that might jeopardize the radiological shielding capacity and ease the transport mechanisms should be avoided; Good quality, homogeneous and dense concrete (no quantitative values imposed). Based on these requirements, a laboratory characterization program was performed and the following concrete compositions were selected (Table 1a, Table 1b). 155

4 Table 1a: Composition of the self compacting concrete SCC Component [kg/m³] Cement CEM I/42,5N HSR LA LH 350 Limestone filler 100 Limestone 0/4 840 Limestone 2/6 327 Limestone 6/ Superplasticizer glenium 27/ Water 175 Table 1b: Composition of the traditional concrete TVC Component [kg/m³] Cement CEM I/42,5N HSR LA LH 350 Limestone filler 50 Limestone 0/4 708 Limestone 2/6 414 Limestone 6/ Limestone 6/ Superplasticizer glenium 27/20 4 Water DETERMINATION OF THE CONCRETE PROPERTIES The determination of the concrete properties of the Self-Compacting Concrete (SCC) and the Traditional Vibrated Concrete (TVC), is part of an intensive laboratory characterization program [2]. Several thermo-physical, mechanical and maturity related tests are performed to predict the difference between these two compositions and will be implemented in the material database of the finite elements programme HEAT [7]. This material database can be subdivided into three categories: thermal properties, maturity related properties and mechanical properties. The next paragraphs indicate the most important concrete properties. The methods, protocols and principles used for these tests, are explained in [2] Thermal properties The specific heat of the SCC is measured at 2420 kj/m³k while the value for TVC is slightly higher, 2440 kj/m³k. Also the heat conduction coefficient is higher in case of TVC (2.02 W/mK) in comparison with SCC (1.89 W/mK), making SCC more of an insulator than TVC. Although in reality these properties depend on the hydration process, only constant values are considered in HEAT. The heat production is simulated using the results of the adiabatic hydration tests [8]. The results indicate a higher but slightly slower heat production for SCC. The cumulated hydration heat after 144 hours runs up to a value of 325 kj/kg for SCC. These values will be used as internal heat source during the simulations. The coefficient of thermal dilation (CTD) can be somewhat higher at very early age and therefore it is taken time dependent with al value of 8 µm/(m C) for hardened SCC and 7.5 µm/(m C) for hardened TVC Maturity related properties For the maturity concept, the reference temperature T ref is set at 293 K (20 C). The ratio E/R (activation energy on universal gas constant), used for the characterization of the hydration process, can be determined from the results of the isothermal hydration tests at different temperatures (10 C, 20 C and 35 C) [9]. E/R is equal to 4491 K for SCC and 4571 K for TVC. E is the apparent activation energy, R is the universal gas constant. 156

5 3.3. Mechanical properties The behaviour of SCC and TVC concerning autogenous shrinkage [10] is quite similar: first a swelling occurs with a peak at approximately 16h (TVC) and 18h (SCC) after casting, followed by autogenous shrinkage development. An average autogenous shrinkage value of - 76 µm/m (TVC) and -96 µm/m (SCC) is noticed after 144 hours, measured from the top of the swelling peak until the end of the test period (144 h). Shrinkage is taken negative. To predict the long term shrinkage behaviour of the SCC and the TVC, additional tests were carried out according to the Belgian Code NBN B on two covered prismatic test pieces (height 500 mm, side 150 mm). The shrinkage development for TVC (-80 µm/m after 1 year) is slightly lower than for SCC (-100 µm/m after 1 year). The creep of the concrete can be determined according to the Belgian Code NBN B At the age of 2 days, 7 days, 14 days and 28 days, the tests specimens are placed in the creep apparatus and loaded immediately. The loading is 30% of the momentaneous strength of the test pieces (0.3 f c ). First the total deformation is determined on covered test pieces placed inside a creep apparatus that can maintain a constant load for a long period of time. Subtracting the instantaneous deformation (when the loading is placed on the test specimens) and the value of the autogenous shrinkage from the mean value of the total deformation, the basic creep value is obtained. From the comparison (Fig. 10), it is shown that SCC and TVC have the tendency to have larger basic creep compliance at younger ages. (Figure 3). This ratio also indicates higher values for SCC at all times of placement of loading. Basic creep compliance [µm/m/mpa] SCC TVC 0 2d 7d 14d 28d Time of placement of loading Figure 3: Basic creep compliance of SCC and TVC. The experimental results of creep have been obtained under compression, assuming the creep is identical in compression and tension. Both the autogenous shrinkage and creep tests are carried out in conditioned environment with an overall temperature of 20 C and a relative humidity of 60%. The Poisson s ratio is taken time dependent. Its value is equal to 0.5 if the age of the concrete is below 7 hours and is equal to 0.2 from 12 hours. It varies linear between those two values. The compressive strength development of the concrete is modelled according to equation (1a): f c ( t) = f ( 28) cm 28 exp s 1 t (1a)

6 with f c (t) the compressive strength at time t, f cm (28) the mean value of the compressive strength at 28 days in ideal conditions, and s a parameter depending on the cement type. Table 2 gives a summary of the obtained values for compressive and tensile strength. Table 2: Compressive strength f c and tensile strength f ct of SCC and TVC (S = standard deviation) Age SCC f c (MPa) S f ct (MPa) TVC f c (MPa) S f ct (MPa) The modulus of elasticity is determined on 9 cores taken out of an in situ cast column. At the time of testing, the concrete has an age of 28 days. At an age of 28 days E c equals 36.1 GPa for SCC and 32.4 GPa for TVC. The visco-elastic behaviour is modelled by mean of a Maxwell Chain Fitting approach. The chain parameters are determined by means of the above mentioned creep test results [2]. The drying shrinkage and the moisture transport are kept out of consideration in these simulations. It s mainly the heat transportation that is of our main interest. Softening behaviour is not taken into account. 4. SIMULATION RESULTS AND STRENGTH VERIFICATION 4.1. The numerical simulation tool For the numerical simulation of the first stage of manufacturing of the Supercontainer, the finite elements programme HEAT has been used. HEAT calculates the stresses (due to temperature rise caused by hydration heat) and the strength in the concrete structure using a state parameter approach linked by the material database [7]. The information belonging to each material in this database is obtained with experiments (see paragraph 3.). First, the actual state parameters are calculated (like degree of hydration, maturity and temperature), and afterwards, stress calculations are realized. The programme simulates the hydration process in the structure and calculates the stresses and strength in the concrete structures. Although the simulation tool is mainly two-dimensional, an accurate simulation is possible in case of an axisymmetrical structure. In order to obtain a more realistic simulation, the use of a threedimensional finite element method is inevitable but will be more cumbersome and timeconsuming. The simulations of HEAT are based on a number of material models to calculate the effect of the environment on the material in a structure. The models that are of importance 158

7 for the determination of cracks in young concrete are outlined. For further information, reference is made to the literature [2, 7] Geometry and boundary conditions The geometry of the construction is implemented into HEAT by defining several macroelements. An axisymmetrical cross-section of the Supercontainer has been made and will be applied as the two-dimensional model (Figure 4). In a first construction stage, the concrete buffer is cast. The initial temperature of the macro-elements is set at 20 C and the environmental temperature will be kept at a constant value of 20 C. The inside steel formwork, with a thickness of 10 mm, is removed after 48 h. The outside steel liner (thickness = 6 mm), considering it will be used, on the other hand will not be removed at all. The wind speed has a velocity of 1 m/s, but will be held out of consideration at the inside of the container. Before releasing of the internal formwork, the convection coefficient is 5.59 W/m²K and after releasing the formwork its value is 5.6 W/m²K (this is an insignificant difference). The steel formwork provides almost no insulation. The convection coefficient is 9.6 W/m²K on top of the container (free surface) and 2.0 W/m²K at the bottom (massive concrete floor). The container is simply supported by the concrete border (kinematic boundary condition). For the simulation of the next three construction stages of the Supercontainer (Figure 2, steps b to h), with the insertion of the heat-emitting canister after 240 hours, the same boundary conditions are used until the time of emplacement. Afterwards the convection coefficients at the outer surface are undisturbed. On the other hand, a heat source is placed inside the concrete buffer, at the inner surface. A limestone filler is being placed, directly after the canister is inserted into the buffer, to fill the annular gap according to stage 3 of manufacturing of the Supercontainer (Figure 4). The temperature is 20 C at the inner surface up to 240 hours, and then rises uniformly to 83 C after 1344 hours due to the heat-emitting vitrified waste [12]. The macro-layers are divided into elements, yielding the mesh given in Figure 4. Towards the edges of the supercontainer, the size of the elements is reduced. Point 12 Point 4 Point 9 Figure 4: The axisymmetrical cross-section of the supercontainer (left) and the finite element mesh (right). 3 important points are identified: point 4 (in the core), point 9 (near the outer surface) and point 12 (near the inner surface) 159

8 4.3. Simulation results Construction of the outer concrete buffer First, we take a look at the behaviour of the concrete buffer during casting (construction stage 1, the first 240 h): the standard casting temperature of the fresh concrete and the outside environmental temperature is 20 C. Due to the exothermic hydration of the cement (heating phase), the massive concrete structure heats up. The highest temperature occurs inside the core of the bottom of the concrete buffer (point 4), the lowest temperatures appear near the outer edge (point 9). For SCC the maximum temperature is C at 41 h (Figure 5). The temperature peak of TVC is slightly lower (52.76 C) and occurs 4 hours earlier (at 37 h). Due to these non-uniform temperature distributions, stresses are induced inside the concrete buffer. As the buffer warms up, compressive stresses appear in the middle of the buffer caused by the expansive behaviour due to the hydration heat. The concrete at the outer edge of the buffer undergoes this expansive nature, creating tensile stresses as shown in Figure 5. a) b) Figure 5: a) Contourplot of the temperature inside SCC after 41 h; b) contourplot of the induced stresses in SCC after 36 h According to Reinhardt and Cornelissen [11] f ct, equals 0.7 times f ct,0 due to the long term effect of tensile strength, therefore the factor 0.7 is used as a safety limit. The region with the highest tensile stress build up during the heating period of the first construction stage is located near the outer surface of the buffer (point 9, Figure 4 and Figure 7) and is the largest in the tangential direction. The stress-strength ratio S zz /0.7 f ct is also higher for SCC in comparison to TVC. Near the outer surface, this ratio has a value of approximately 0.9 for SCC and 0.7 for TVC. During the cooling period, thus before the heat source is inserted, there are regions inside the buffer that may experience tensile stresses (point 4). These stresses, in the middle of the buffer are much lower than the tensile stresses near the outer surface during heating. It must be noticed that the tensile stresses in the middle of the buffer during the cooling period are higher for TVC. 160

9 Before insertion of the canisters, the tensile stresses remain smaller than 0.7 f ct. There is a 1 % higher temperature rise and 20 % higher autogenous shrinkage in SCC, leading to 30 % higher tensile stresses in SCC in comparison with TVC at the end of the heating phase in point 4. On the other hand, the tensile stresses occur 4 h earlier. TVC experiences a lower cracking risk according to Figure Insertion of canister and closure of the Supercontainer in hot cell 240 hours after the casting, the two heat-emitting canisters are inserted (in hot cell). Directly filling the remaining annular gap with a cementitious filler (SCC) and closing the Supercontainer by fitting the concrete lid, are the two remaining construction steps. We are considering 3 construction cases (CC) according to Table 3. Table 3: 3 considered construction cases for the Supercontainer fabrication CC1 CC2 CC3 Buffer fresh SCC fresh TVC fresh SCC Filler fresh SCC fresh SCC fresh SCC Lid fresh SCC fresh SCC precast SCC When the heat-emitting canister is inserted and the remaining annular gap is filled with fresh SCC filler, the temperature inside the buffer will rise due to the heat emitting canisters and due to the hydration heat of the hardening SCC filler and concrete lid. The highest temperature in the buffer occurs at the concrete next to the heat source (point 12). The temperature after 1344 hours is still higher for SCC (51.3 C compared to 50.6 C for TVC). A typical contourplot of the temperature is given in Figure 6. Figure 6: Contourplot of the temperature after 1344 h for construction case 1 (CC1) The most significant question however is whether the tensile stresses, due to the developed thermal gradients, the autogenous shrinkage of the concrete, and taking into account the creep effect, will exceed the tensile strength of the concrete buffer, giving cause to the undesired early age cracking. Looking at the most important parameter concerning crack formation, e.g. the axial, tangential and radial stresses inside the concrete buffer, we notice that those stresses remain smaller than 0.7 f ct (Figure 7). Due to the heat emitted by the waste canisters, the 161

10 tensile stress build-up in the middle of the buffer gets counteracted. Near the outer edge (point 9) the compressive stresses created during the cooling phase can be seen as a counter value for the tensile stresses induced by the heat of the canisters. The hydration heat of the hardening SCC filler contributes to the slightly small deviations of the uniform stress curves shortly after the canisters are inserted. The stress-strength ratio S zz /0.7 f ct indicates that the tensile stress development inside the buffer (point 4) during the cooling is being reduced due to the insertion of a heat source. Near the outer surface (point 9), there is a build up of tensile stresses due to the heating of the canister, but these tensile stresses are counteracted by the compressive stress build up due to the cooling phase at stage 1. Finally, at the inner surface (point 12) there is a major compressive stress build up: the concrete at the inner surface wants to expand more than the concrete inside the buffer. TVC in comparison with SCC has higher tensile and compressive stresses during stages 2-4 (insertion of the canisters and closure of the Supercontainer, Figure 2), but stress-strength ratio S zz /0.7 f ct for both cases remains smaller than 1 at all times. Tensile stress 1,00 0,80 0,60 0,40 Canister insertion SCC 4 SCC 9 SCC 12 TVC 4 TVC 9 TVC 12 SZZ/0,7 fct (-) 0,20 0, ,20-0,40-0,60-0,80-1,00 Compressive stress Time (h) Figure 7: Time plot of tangential S zz /0,7f ct ratio at points of the concrete buffer for CC1 and CC2. Finally we want to take a closer look at the early age behaviour of the freshly cast concrete filler and lid. For the choice of those types of structural elements we decide in favour of SCC because it will ease considerably the precast process in hot cell and under thermal load. As a reference we consider the first construction case (CC1) where fresh SCC is being used for the filler and the lid. Subsequently we examine the behaviour of the Supercontainer when TVC is being used for the concrete buffer (CC2), and when a precast SCC lid is placed on top of the waste canister for the closure of the Supercontainer (CC3). 162

11 Tensile stress 1,00 0,80 0,60 0,40 0,20 Cooling-phase (hydration) Heating-phase (canister) SCC 5 SCC 8 SCC 13 Point 13 0,00-0, Point 8-0,40-0,60-0,80 Point 5-1,00 Heating-phase (hydration) Compressive stress Time (h) Figure 8: Time plot of tangential S zz /0,7f ct ratio at points of the concrete filler for CC1. 3 important points are identified: point 5 (bottom), point 8 (middle height) and point 13 (top) Inside the filler we can distinguish 3 different stress build-up stages (Figure 8). First the concrete fillers expansion is being prevented by the hardened buffer and the waste canister and comes under compression (heating-phase due to hydration). Afterwards, when the peak of hydration heat is surpassed, the shrinkage during cooling of the filler experiences resistance which results in an appearance of tensile stresses (cooling-phase after hydration). Finally the heat originating from the heat-emitting canisters sets up, leading to a final compression in the SCC filler (heating phase due to external heat source). Due to the smaller amount of concrete needed for filling the annular gap between the buffer and the canisters, no cracking is determined in these concrete filler layers. At all times the stresses remain smaller than 0.7 f ct. Looking at the temperature development inside the cast lid, the highest temperature due to heat of hydration occurs near point 17 in the middle of the lid (Figure 9). Afterwards, when the hydration peak is passed and due to the heat emitted by the canisters, the temperature rises. This increase is higher near the heat source: the temperature rise in point 2 is higher than in point 14 (Figure 9). The same 3 stress-stages behaviour can be found inside the core of the freshly cast lid: pressure due to heat of hydration, followed by tension caused by the cooling after hydration and finally the heat of the canister creates a compressive behaviour (Figure 10). A hardened lid experiences lower stresses in comparison to a freshly cast lid (Figure 10). Due to the smaller amount of concrete needed for stage 3 (filler) and stage 4 (lid), no cracking is determined in these concrete layers. On the other hand, due to the heat of the canister, the filler is being pressed between the canister and the hardened concrete buffer. 163

12 Point 10 Point 14 Point Point 2 T ( C) Time (h) Figure 9: Time plot of temperature inside the concrete lid at points for CC1. 4 important points are identified: point 2 (bottom lid), point 10 (middle top lid), point 14 right top lid) and point 17 (in the core of the lid) and point 14 1,00 0,80 0,60 Cooling-phase (hydration) fresh SCC 2 fresh SCC 10 fresh SCC 17 hard SCC 10 0,40 S ZZ /0,7 f ct (-) 0,20 Heating-phase (canister) 0, ,20-0,40-0,60-0,80-1,00 Heating-phase (hydration) Time (h) Figure 10: Time plot of tangential S zz /0,7f ct ratio at points of the concrete lid for CC1. 164

13 5. CONCLUSIONS The Supercontainer is the Belgian reference design on the matter of enclosing the vitrified HLW and the Spent Fuel assemblies. In the framework of the feasibility demonstration of the Supercontainer concept, this current study focuses on the extensive laboratory tests and finite elements calculations in order to characterize the THM behaviour of the Supercontainer concrete buffer and to verify the formation of early age cracking during construction. The effect of concrete properties (hydration heat, creep, shrinkage) and boundary conditions (temperature, type of formwork, wind velocity) are non-negligible towards simulation results: An extensive lab program was performed on the considered types of concrete: SCC and TVC. Two different concrete compositions are suggested, tested and compared. SCC experiences higher shrinkage and creep, has a higher heat of hydration production and has higher tensile and compressive strength. The simulations show that no early age cracking is expected in the Supercontainer during construction: The highest tensile stresses occur near the outer border of the buffer at the end of the heating phase. The highest compressive stresses occur in the middle of the bottom of the buffer during the cooling period and in the filler. No cracking is determined in the third and fourth stage concrete layers (filler and lid).the stresses in the lid are higher in case of freshly cast SCC. Tensile stresses remain smaller than the tensile strength at all times during construction. The effect of temperature and irradiation on the concrete properties needs to be investigated. A full-scale casting test is being planned to evaluate the simulation results. REFERENCES [1] Bel J., Van Cotthem A., De Bock C., 'Construction, operation and closure of the Belgian repository for long-lived radioactive waste, Proceedings of the 10 th International Conference on Environmental Remediation and Radioactive Waste Management, Glasgow, Scotland, September [2] Craeye B., De Schutter G., Van Humbeeck H., Van Cotthem A., Early age behaviour of concrete supercontainers for radioactive waste disposal, Nuclear Engineering and Design 239, 23-35, [3] CUR report 172, Duurzaamheid en onderhoud van betonconstructies (in Dutch), p [4] ONDRAF/NIRAS, A review of corrosion and material selection issues pertinent to underground disposal of highly active nuclear waste in Belgium, report [5] De Schutter G., Finite elements simulation of thermal cracking in massive hardening concrete elements using degree of hydration based material laws, Computer & Structures 80, , [6] De Schutter G., Bartos P., Domone P., Gibbs J., Self Compacting Concrete, Whittles Publishing, Caithness, UK, [7] Van Beek A., Schlangen E., Baetens B., Numerical model for prediction of cracks in concrete structures, Proceedings of the Intern RILEM Conf on Early Age Cracking in Cementitious Systems, EAC 01, Haifa, Israel, [8] De Schutter G., Fundamental and practical study of thermal stress in hardening massive concrete elements, Doctoral Thesis, Ghent, Belgium, [9] Poppe A.M., De Schutter G., Influence of fillers on the hydration and other properties of self compacting concrete, Doctoral Thesis, Ghent, Belgium, [10] Craeye B., De Schutter G., Experimental evaluation of mitigation of autogenous shrinkage by means of a vertical dilatometer for concrete, Proceedings of the International RILEM Conference on Early Age Shrinkage Induced Stresses, Copenhagen, Denmark,

14 [11] Reinhardt H.W., Cornelissen H.A.W., Zeitstandzugversuche an Beton, Baustoffe 85, Bauverslag, Wiesbaden, pp , [12] Weetjens E., Sillen X., Thermal analysis of the Supercontainer concept 2D axisymmetric heat transport calculations, SCK.CEN report, Belgium,