Thermal crack estimation in early age concrete : models and methods for practical application

Abstract: Control of thermal cracking in young concrete is of great importance to ensure a desired service life time and function of a structure. Making reliable thermal stress estimations, and thereby conclusions about cracking risks, involves advanced modelling of material properties and structural restraint. The main objective of this thesis is to further develop and, for safer application in engineering practice, simplify: (I) Modelling of material properties (II) Modelling of structural restraint (III) Methods for crack estimation (I) - A new basic creep model, primarily aimed for early age concrete in thermal stress analysis, is formulated based on piece-wise linear curves in logarithm of time. The new model is, in relation to other commonly used creep models, a flexible and robust formulation that enables it to make reliable creep modelling with very few test data. Another advantage with the formulation is that the appearance of negative relaxation in linear viscoelastic modelling is very small and negligible with respect to thermal stresses. The model shows very good agreement directly with experimental creep data and indirectly with measured thermal stresses, whereby the formulation has been used to model the viscoelastic behaviour of the concrete. The formulation also has the best correlation with experimental data compared to other creep models that have been analysed in this thesis. Based on the new formulation, creep prediction formulas are established and evaluated. It is shown that general model parameters can be established whereby the long-term creep behaviour is clearly dependent on the modulus of elasticity with larger creep deformations for lower E-modulus. An average error related to creep of 15 percent is what can be expected from most thermal stress analyses that are performed with standard sets of creep data today. By use of the established prediction formulas it is possible to reduce the error by almost two thirds ( ) only by adding the results from a test of the modulus of elasticity at the age of 28 days. For more advanced applications, where even better accuracy is required, it is recommended that at least a creep compliance test is performed at two loading ages, of which one at the age of 28 days. (II) - Modelling of the restraint to which a structural element is subjected is one of the most important issues that have to be considered in a thermal stress analysis. Here it is shown that the complex structural restraint behaviour can be described by means of simple restraint coefficients giving an agreeing thermal stress development compared to both more exact Finite Element (FE) calculations and measured stresses. It is also shown that it is possible to evaluate the structural restraint coefficients by means of simple elastic approaches with acceptable accuracy compared to more realistic viscoelastic approaches and the “true” restraint behaviour of a real full-scale structure. (III) - Simplified direct methods for estimation of thermal through cracking are established as a direct calculation during contraction from the time when a restrained hardening concrete element is stress free to the time when the maximum risk of cracking appears. In the methods, that are based on stress, strain and temperature formulations, the ageing of the concrete is considered by means of coefficients dependent on the age at loading, which here is defined as the age when the element is stress free. Comparisons with a more advanced differential type of method shows very good accuracy, which means that the simplified direct methods can be used to estimate thermal cracking risks. A strain based method is then reformulated for practical application by describing a newly cast structural concrete element and an adjoining structure as one system where only the differential elastic deformations between the two parts contribute to the stress development. Based on a given water to binder ratio of the concrete, a known temperature development and a defined restraint coefficient for a decisive part of the structure, the risk of thermal cracking can be estimated. An application of the simplified method, performed with results from field tests and observations, shows that it is possible to estimate thermal cracking risks with good accuracy.