Aspects of modelling plain and reinforced concrete at elevated temperatures
Knox, Joanne Jennefer
Extreme events such as the Mont Blanc Tunnel fire in 1999 (Bettelini et al. 2001) or the Windsor Tower fire in 2005 (Calavera et al. 2005) have shown how concrete failure at elevated temperatures can be hazardous to the safety of members of the public. Generally, there is an absence of understanding of the mechanical behaviour of both plain and reinforced concrete at elevated temperatures, which is essential for computational modelling. Since fire is an extreme event, a certain amount of damage within the structure would be seen to be permissible within its performance objectives. This necessitates analysis in the post-peak regime. As a material, concrete has a very low value of thermal conductivity. This means that large thermal gradients often occur within concrete, causing differential expansion of the material. This, coupled with the change in mechanical properties at elevated temperatures, further complicates analytical analysis procedures. This study investigates issues associated with computational modelling of plain and reinforced concrete at elevated temperatures and its residual behaviour (behaviour when tested after the material has been heated, for example in a fire, and then cooled). In order to achieve this, first the constitutive material properties of both plain and reinforced concrete at ambient and elevated temperatures were investigated. The study showed that mesh sensitivity and localisation of strain softening occurs in plain concrete under both tensile and compressive loading. Path dependency of the stress-strain behaviour of plain concrete was also demonstrated, when it was subjected to loading and heating. Tension stiffening was included in the reinforced concrete material model, to represent the interaction between concrete and reinforcing steel. Complex behaviours were seen for simple reinforced concrete benchmark tests, due to changing material properties at elevated temperatures and differential thermal expansion of steel and concrete. Non-linear load-displacement relationships were seen as a result of complex load-sharing between concrete and reinforcement. A hypothesis was proposed – that variation of temperatures during heating and cooling of a specimen will cause damage, and hence material degradation, in plain and reinforced concrete. On investigation, it was seen that damage due to differential thermal expansion plays a small part in the reduction of elastic load-displacement slope and peak strength seen in experimental data on residual tests, indicating that other factors identified in previous research also affect the residual behaviour of plain and reinforced concrete. Indeed, in reinforced concrete, when tension stiffening was included, it was found that damage due to differential thermal expansion and contraction had a negligible effect on the residual response in the pre-peak regime. The study also found that for a simply supported beam pure thermal expansion caused a localised response, while pure thermal gradient gave distributed yield. When both were present, in this study, distributed yield with no mesh sensitivity was seen. Realistic heating of a restrained reinforced concrete plane strain model caused compressive stresses accompanied by tensile longitudinal total strains and tensile longitudinal plastic strains throughout the depth of the slab, with the largest values occurring near to the model supports. Damage and recovery variables were found to have no effect on the response of the model. When a portal frame was exposed to heating, plastic strains were distributed throughout the beam, with column rotation limiting downward thermal bowing due to a uniformly distributed load or thermal gradient present. Application of displacement loading causing plastic damage changed the behaviour of the structure under heating – instead of symmetrical compressive plastic strains being induced, areas of varying tensile and compressive strain were caused within the beam. Throughout, simple, easily reproducible simulations were used so that single parameters could be altered and considered. This was important, so that the important parameters to computational modelling could be identified. These can be used to guide experimental series to ensure that they are investigated, in order to improve computational material models. Not all variations of parameters were investigated in this study, but it is clear where further repetition would be beneficial (e.g. in varying thermal expansion and thermal gradient ratios in heating regimes). This study looks to address experimentalists and people working in structural analysis, who would be interested in the parameters investigated, as well as practitioners who may want to use these results.