Crack width of reinforced concrete structures under imposed deformations

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When concrete is subjected to imposed deformations, stresses may develop. If at any point in time this stress exceeds the tensile strength of the material, the concrete will crack. Early-age cracking of concrete structures may lead to problems with durability, serviceability and aesthetics. During hardening of concrete the material properties are still in development. Therefore, to be able to predict the crack width, understanding of the stress- and strength development is required. In addition, concrete is a visco-elastic material which means that stresses are affected by phenomena such as creep or relaxation. If the design codes predict the crack width in concrete structures under imposed deformations accurately remain subject of debate. The CROW report published in 2021 [9] provided the starting point for this research. The aim of this study was to gain more insight on the background of the design codes, and to explain the fundamentals of the crack width prediction in case of imposed deformations. For this purpose, the following research question was formulated:
”What is the applicability of the design codes regarding the crack width prediction of reinforced concrete structures under imposed deformations?” From the literature study it became clear that the main difference between the design codes was related to which boundary conditions and cracking theory were applied. The majority of the design codes applied the well known tension bar model theory where both ends are fully restrained. In addition, there were also codes using the continuous base restraining theory in which the tensile member is continuously restrained along one edge. This made a huge difference in the prediction of the crack width. From the finite element analysis which was performed, it turned out that there is a difference between the steel stress development of imposed loading and imposed deformations. In addition, in case of imposed loading less cracks were developed than under imposed deformations. However, from this specific numerical analysis it turned out that the maximum crack spacing and crack width is smaller in
the imposed loading model in comparison to the imposed deformation model. The only explanation for this is that in case of imposed loading the cracks are more evenly distributed. A case study was used to simulate the hardening process of concrete in combination with autogenous shrinkage as imposed deformation and compared with a finite element analysis. The goal was to determine a set of model properties that are useful for future engineers. The accuracy of the input parameters was verified with the experimental work carried out by M. Sule. Overall, when performing a non-linear finite element analysis a lot of knowledge was required. It turned out that specific choices such as the constitutive model type, the kinematic and equilibrium condition have a major impact on the outcome. Using the modified Bar model of Lokhorst in combination with this numerical approach resulted in good agreement with the experimental findings.

The parameter study showed that regarding the tension bar models, the bar diameter has the largest influence on the crack width prediction. While with respect to the continuous models there was no onesided answer to the question which parameter had the largest influence on the crack width prediction. In one of the design codes based on the continuous model theory named CIRIA [8] the degree of restraint clearly stands out as the most important parameter. Whereas in the another design code based on this theory, namely the ICE [4], all parameters that were investigated in this thesis have limited effect on the crack width prediction. The design codes considered in this master thesis do not yet fully represent the crack width due to the hardening of concrete or due to autogenous shrinkage. The design codes are applicable for the
crack width prediction of reinforced concrete structures under imposed deformations if conservative assumptions such as a weak bond between concrete and steel reinforcement are taken into account. It is clear that the problem treated in this report has more complexity than what one initially may think.
Opinions on how to determine the crack width of reinforced concrete tensile members under imposed deformations differ. The difference is related to the type of restraint and the cracking theory which are suggested in most used analytical design models. This report contributes to a better understanding of
the crack width development under imposed deformations through non-linear finite element analyses and verification with experiments. The results from this master thesis suggest that an approach to a more consistent crack width prediction under imposed deformations should investigate how bond in the interface between concrete and steel influences cracking. This has lacked attention in the current formulas in the design codes.