Model Uncertainty of Non-Linear Finite Element Analysis of Reinforced Concrete Beams without Shear Reinforcement

Abstract

The aim of this thesis project is to investigate the model uncertainty of non-linear finite element analysis of reinforced concrete structures at ultimate limit state by focusing on concrete cracking model, concrete-reinforcement interaction model and mesh size. Following this, eight finite element modelling strategies are developed and 67 benchmark experiments on reinforced concrete beams without shear reinforcement are analysed.The measure of model uncertainty is using the ratio of experimental to numerical failure load and comparing predicted and experimental failure behaviour. A ratio that deviates form 1 indicates high model uncertainty with values <1 representing non-conservative predictions and values >1 representing conservative predictions.The eight modelling strategies are categorized into three groups. The first group is used to select shear retention model for the fixed crack concept and to study the behaviour of fixed and rotating crack concepts in combination with embedded reinforcement. The damage based and aggregate-size based shear retention models are investigated resulting in a mean model uncertainty ratio of 0.86 and 0.82 respectively. This indicates that on average both predict higher ultimate capacity when compared to experimental results with the aggregate size based shear retention model exhibiting higher model uncertainty. The aggregate size based model is not capable of predicting shear and mixed failure types while the damage based predicted accurate failure modes. On the other hand, the rotating crack model with embedded reinforcement shows failure due to delamination of the concrete cover. Replacement of the perfectly bonded embedded reinforcement by reinforcement with bond-slip demonstrated to predict accurate failure modes.The second group has the fixed crack model with damage based shear retention model and embedded reinforcement, which is referred to as F-EB-2-D and rotating crack model with bond-slip reinforcement named R-BS-2. Both modelling strategies have 50mm mesh size and result in mean model uncertainty ratio of 1.11 and 1.06 respectively which implies that on average both give conservative predictions of the ultimate capacity with R-BS-2 showing a better prediction. Both modelling strategies give higher model uncertainty for experiments with shear failure with F-EB-2-D and R-BS-2 predicting accurate failure modes for 48% and 51% of the experiments respectively. The beams with reinforcement ratio of ≤ 0.6% showed on average less model uncertainty in F-EB-2-D and R-BS-2. The third group is made by refining the mesh size of F-EB-2-D and R-BS-2 from 50mm to 25mm in critical section of the beams to formulate the modelling strategies F-EB-3-D and R-BS-3 . 16 experiments are re-analysed using this group and a lowered mean model uncertainty ratio of 0.93 and 0.95 is obtained for F-EB-3-D and R-BS-3 respectively although this is slightly non-conservative with accurate predictions for 81% of the 16 experiments. The correlation between model uncertainty and numerical failure mechanism is made using a ductility index which is defined as the ratio of the plastic dissipated energy in the reinforcement and the system. However the ductility index should be used together with model uncertainty if it is verified that the correct equations are solved accurately in the finite element analysis.