Time-Dependent Finite Element Analysis in Restrained Concrete

Abstract

Concrete is widely used in civil engineering and despite its long history, accurate prediction of the hardening process, particularly in partially restrained conditions, remains a challenge. During the hardening of partially restrained concrete, residual stresses occur due to restrained deformations caused by factors such as heating/cooling and shrinkage of the concrete. Accurately predicting the development of these residual stresses during restrained hardening is critical for proper design calculations, as cracking must be controlled by reinforcement. However, predicting the development of these design stresses is complex and depends on a number of processes and parameters, including temperature development, development of mechanical properties and the degree of restraint. These stresses also decrease with time due to creep and relaxation, which further complicates predictions, especially when dealing with restrained concrete combined with shrinkage.

In addition, hardening concrete will eventually be subjected to external loads, resulting in additional stresses that may require additional reinforcement. However, when it is difficult to accurately predict the development of design stresses, approximations must be made. These approximations may either take full account of the stresses from both hardening and external loading, or reduce the residual stresses by some factor. Such factors may be based on design codes or rough estimates. Consequently, these approximations can lead to either over- or underestimation of the reinforcement required in the design, mainly due to a lack of understanding of the actual design stresses. Therefore, the research question investigated in this thesis is as follows:

What is the effect of applying time-dependent finite element analysis, including the combination of hardening processes and external loads, on improving the prediction of the development of design stresses for partially restrained concrete?

The research starts with a comprehensive literature review covering the stress development during hardening of restrained concrete, the current calculation methods and models and a validation experiment. The validation experiment, a Temperature-Stress Testing Machine (TSTM) found in literature, is modelled and the analysis results are compared with the experimental results to validate the accuracy of modelling the hardening of partially restrained concrete. A method is developed to accurately predict the hardening of restrained concrete using a combination of transient heat transfer analysis and structural non-linear analysis. This non-linear analysis uses a combination of time and load steps to apply the required degree of restraint. The finite element analysis, using measured thermal and material properties from the literature, shows good agreement with the TSTM experimental results.

In order to verify the accuracy of commonly used material models, the Eurocode and fib Model Code material models within DIANA FEA are compared with the results of the TSTM experiment. However, it was found that these material models have inaccuracies due to the use of large step sizes for the Kelvin chains that define the creep and Young’s modulus developments. Therefore, a viscoelastic material model based on the fib Model Code was developed and found to be more accurate. This material model was validated against the TSTM experiment and hand calculations. Although differences were found in the development of design stresses between the experimental results and the prescribed standards, these were mainly due to the difference in autogenous shrinkage and coefficient of thermal expansion.

Using the knowledge gained from the modelling of the TSTM experiment and the validated viscoelastic material model, a case study of the railway underpass in Leiden is performed. The chosen modelling approach is a time-dependent non-linear finite element analysis that includes all construction phases, hardening processes, and external loads within a 3D model of solid 3D elements. The model excludes concrete cracking, reinforcement and prestressing of the deck to limit complexity. This calculation method is expected to provide a more detailed insight into the development of design stresses and ensures high calculation accuracy and completeness compared to other methods. The use of a full 3D model was necessary to accurately model the temperature development in the hardening concrete, which has a significant effect on the design stresses…