Theme 1 – EDF Benchmark VeRCoRs Workshop Prediction of the early-age behaviour of the gusset of the nuclear containment vessel F. Kanavaris1*, D. Robinson2, M. Soutsos3 and J. F. Chen4
School
of
Planning,
Architecture
and
Civil
Engineering,
Queen’s
University
Belfast,
Belfast BT9 5AG, UK
1
[email protected] (* presenting author)
2
[email protected]
3
[email protected]
4
[email protected]
1. Main features In order to investigate the early-age behaviour of the gusset numerical modelling applying coupled thermal stress finite element analysis (FEA) was performed using the commercially available FEA package LUSAS, for the prediction of temperature profiles and induced stresses and strains and hence to determine the cracking susceptibility of the gusset for up to 32 days (i.e. 3 pouring stages). To assess the accuracy of the model, results were compared with data provided from Électricité de France (EDF) for the VeRCoRs Benchmark. An overview of the modelling approach applied will be discussed below, as an attempt to maintain conciseness throughout the paper.
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1.1. Finite element model details and input parameters The containment structure was modelled in 3D geometry using the commercially available FEA software LUSAS. The first three pouring stages were considered, i.e. from 0 to 32 days. Figure 1 shows the modelled geometry of the structure for the concreting stages considered. Meshed model with structural supports is shown in Figure 1(c). Hexahedral elements with quadratic interpolation were chosen for coupled thermal stress analysis.
Figure 1: Geometry and finite element mesh for the considered concreting stages Mechanical and thermal properties considered for the elastic and thermal material models respectively were obtained from shared results as part of the Benchmark VeRCoRs and these were: Elastic modulus Ecm = 33.5 GPa, coefficient of thermal expansion α = 10.5x10-6, Poisson’s ratio ν = 0.2, mass density ρ = 2370 kg/m3, thermal conductivity k = 1.82 W/m°K, specific heat capacity Cp = 880 J/kg°K and convection heat-transfer coefficient hconv = 8 W/m2°K. For the radiation heat-transfer coefficient, concrete emissivity, ε, was chosen to be equal to 0.88 (1 for a perfect black body) as recommended in literature [1,2]. The ambient temperature profile was included on hourly basis and the analysis step size was set to have the same increment. The development of mechanical properties with time and concrete heat of hydration were calculated in LUSAS in accordance with CEB-FIP MC90 [3,4] and the hydration model developed by Schindler et. al. [5,6] respectively, where the latter is based on concrete composition.
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2. Results Several temperature and strain sensors were placed into the gusset to monitor concrete behaviour. The points where the sensors were located were specified by EDF and are presented in Table 1 below. Sensor Type Name Angle (Gradians) Level (m) Radius (mm) Temperature & Strain G1 172.8 -0.21 7400 Temperature & Strain G2 172.8 -0.21 7610 Temperature G102 172.0 -0.25 7500 Temperature & Strain F1 171.4 -0.88 7205 Temperature & Strain F2 172.7 -0.88 7605 Temperature F102 172.0 -0.95 7400 Table 1: Details of points of interest and sensor locations in the gusset Temperature contours plots for different stages and comparison between actual and predicted from FEM temperature profiles in the gusset are shown in Figures 2 and 3 respectively.
Figure 2: Temperature contour plots for different concreting stages It can be seen that the predicted from the model results are in good agreement with the in-situ recordings with the exception of points F1 and F2 where the peak temperatures were overestimated by approximately 4 and 5 °C respectively [Figures 3(d) and 3(f)] and of point
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G102 where the second, smaller, temperature peak (upon pouring of the second stage) was underestimated by approximately 6 °C. Peak concrete temperature was as high as 50 °C and abrupt cooling to ambient was observed, which significantly increase the thermal gradients in the structure and therefore, risk of cracking. 60
a) G1 FEM
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40
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d) F1
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Figure 3: Comparison between actual and predicted temperature profiles at different locations in the gusset Figure 4 demonstrates a comparison between the recorded and the predicted horizontal strains in different locations in the gusset, while Figure 5 shows the estimated induced stresses at the aforementioned locations. As expected, the strain development follows similar pattern with the temperature profile in the structure. Compressive (negative) strains and stresses develop during the heating period and as soon as peak temperature is reached and the cooling period 4
is initiated, compressive strains and stresses are relieved and tensile (positive) strains and stresses occur. 300
a) Points G1 & F1
300
b) Points G2 & F2
250
250
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200
Strain (μm/m)
150
F1-FEM
F1-Actual
100
150
G2-FEM F2-FEM
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Figure 4: Comparison between actual and predicted horizontal strains at different locations in the gusset Analogous behaviour of similar concrete structures has been demonstrated by other researchers [7]. Again, the model predicted the strain development relatively accurately. As it can been seen from Figure 4, the magnitude of strain at points G1 and G2 appears overestimated as concrete temperature approaches the ambient, i.e. after approximately 2.5 days, however, this may be attributed to the fact that elastic analysis was considered and cracking in the actual structure has been initiated, hence, the actual strain is relieved [8]. This can be also observed from Figures 5(a) and 5(b), where the induced tensile stresses which occur during the cooling to ambient period are as high as 1.5 MPa in a few days.
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4
a) Points G1 & F1
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b) Points G2 & F2
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3 G2-FEM G1-FEM
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F1-FEM
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Age (days)
Figure 5: Predicted stress development at different locations in the gusset
3. Conclusions Control of early-age thermal cracking in safety-critical concrete structures, such as nuclear containments, is of great importance to ensure and maintain their service life and safe functionality. A 3-dimensional finite element model of the gusset was developed in order to investigate the early-age behaviour of the structure during the first three pouring stages. The model produced relatively accurate results of temperature, strain and stress development at various locations of the structure, highlighting the risk of cracking occurrence.
References 1. Incorpera, F. P. and DeWitt, D., “Fundamentals of heat and mass transfer”, 3rd edition, John Wiley & Sons, New York, 1990, pp. 919. 2. Ruiz, J. M., Schindler, A. K., Rasmussen, R. O., Kim, P, J. and Chang, G. K., “Concrete temperature modelling and strength prediction using maturity concepts in
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the FHWA HIPERPAV software”, Proceedings of the 7th International Conference on Concrete Pavements, Orlando, Florida, USA, 2001. 3. Comite Euro-International du Beton, “CEB-FIP Model Code 1990”, Thomas Telford, London, UK, 1991, pp. 437. 4. LUSAS v. 14.7, “Theory manual volume 1”, Issue 1, Surrey, 2011, pp. 239. 5. Schindler, A. K. and Folliard, K. J., “Heat of hydration models for cementitious materials”, ACI Materials Journal, Vol. 102, No. 1, 2005, pp. 24-33. 6. LUSAS v. 14.7, “Theory manual volume 1”, Issue 1, Surrey, 2011, pp. 304. 7. Klemczak, B. and Knoppik-Wrobel, A., “Analysis of early-age thermal and shrinkage stresses in reinforced concrete walls”, ACI Structural Journal, Vol. 111, No. 2, 2014, pp. 313-322. 8. Bamforth, P. M., “Early-age thermal crack control in concrete”, CIRIA C660, London, 2007, pp. 32.
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