Proceedings of the International rilem conference Materials, Systems and Structures in Civil Engineering 2016
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- Bu səhifədəki naviqasiya:
- 2.2 Reference case and limitations of the model
- THERMAL PROPERTIES parameter unit value
- MECHANICAL PROPERTIES parameter unit value
- Finite Element mesh
- Group control of elements.
- Softening behaviour.
53 International RILEM Conference on Materials, Systems and Structures in Civil Engineering Conference segment on Service Life of Cement-Based Materials and Structures 22-24 August 2016, Technical University of Denmark, Lyngby, Denmark
For the reference case, a wall on foundation was chosen with the dimensions as specified in Fig. 4. Material, environmental and technological data used are given in Tab. 1. The wall was concreted 3 weeks after the foundation. The structure was kept in formwork during the whole analysis. The initial temperature of concrete was T
= 25°C and the ambient temperature was T a = 20°C. The initial temperature of soil was equal to the ambient temperature. Final geometry of the wall and input data were chosen after extensive parametric study.
a) longitudinal view yz plane, x = 0 b) transverse view xy plane, z = 0 Figure 4. Analysed wall on foundation: geometry and FE mesh for ¼ of wall. Reference case
Table 1: Parameters used in the study. THERMAL PROPERTIES parameter unit value Thermal conductivity, W/(m·K) 2.6 Specific heat, c b kJ/(kg·K) 1.0 Density, kg/m 3 2500
Amount of cement, C c kg/m
3 340
Total heat of hydration, Q tot
J/g 400
Coefficients a 1 and a 2 -
470, -0.1
Coefficient of heat exchange, p W/(m
2 ·K) 4.0
Thermal expansion coefficient, T 1/K
10 -6
MECHANICAL PROPERTIES parameter unit value Final value of compressive strength, f c , 28 MPa 38
Final value of tensile strength, f t , 28 MPa 2.9
Final value of modulus of elasticity, E c,28 MPa
33 Coefficient s for cement - 0.25
Coefficient n for tensile strength - 0.6 Coefficient n for modulus of elasticity - 0.4 54 International RILEM Conference on Materials, Systems and Structures in Civil Engineering Conference segment on Service Life of Cement-Based Materials and Structures 22-24 August 2016, Technical University of Denmark, Lyngby, Denmark
During the parameter study some limitations of the model were encountered which needed to be addressed. The following issues should be mentioned: Finite Element mesh. To capture the most important phenomena, the mesh was densified in the areas of expected damage intensification, i.e. at the joints between the subsequent elements (soil – foundation – wall) and over the width of the wall. Especially a small element size in the core of the wall was needed to realistically simulate the decrease of Eigenstresses during the cracking process. In this regard the model is mesh-dependent, so the same size of finite elements was used in all the analysed models to allow for comparison among them. Group control of elements. In the model, mechanical properties of hardening concrete (strength, elastic modulus) vary in time according to the assumed ageing functions but, because of computational limitations, the aging of each element could not be simulated independently. To still achieve representative results, groups of elements with comparable aging were defined and mechanical properties assigned according to the mean values of the equivalent age. With respect to the very smooth cooling phase (the wall was continuously kept in the formwork for the whole time), it was adequate to divide the wall only into 4 groups: groups for surface elements (to the depth of 5 cm) and core elements. The elements at the axis of symmetry at the length were also assigned to 2 separate groups to avoid numerical problems at the beginning of cracking. Besides, two additional groups of contact elements were introduced: between the soil and the foundation and between the foundation and the wall. The groups of elements are marked with different colours in Fig. 4. Cracking. The model assumes smeared cracking, whereby a set of finite elements in which DIF reached 1 in tension was considered as cracks. The first crack was always induced in the plane of symmetry by a reduced tensile strength of 0.95 f t,28 , which ensured the worst-case scenario to happen.
reaches the value of 1 and concrete exhibits softening behaviour in this element according to the assumed softening law. Although this softening behaviour can be observed in the results of this study, the extent of this effect seems, from the authors’ point of view, to be underestimated. Thus, verification and recalibration of the softening function is required before further investigations. 2.3 Results Figures 5 and 6 show development of cracks indicated by damage intensity factor (DIF) in the reference wall (of 10.5 m length). Areas of expected cracks are marked in red. Figure 5 shows a map of DIF right before the primary crack starts to develop in the axis of symmetry of the wall. It can be observed that some locally restricted damage has already developed in the interior of the wall which complies with the before explained influence of Eigenstresses. Directly after the state of Fig. 5 a primary crack forms in the axis of symmetry between 16 and 18 days. The final state is shown in Fig. 6 and it can be seen that this crack goes through the whole thickness of the wall. The softening behaviour which can be observed in the vicinity of this crack starts directly at the beginning of formation of this crack at 16 days. Moreover, the crack develops from the interior towards the surface of the wall as the wall is kept in the formwork, so any pre-damage on the surface due to temperature shock after early stripping was avoided. The crack reaches on average ~50 % of the height of the wall. As it should be expected from the length-to-height ratio of the wall (L/H = 3.5), the crack does not Yüklə 8,6 Mb. Dostları ilə paylaş:
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