Validation of Sequentially Linear Analysis for Quasi-Brittle Behaviour of Reinforced Concrete Structures under Proportional and Non-Proportional Loading

Abstract

The aim of this thesis was to objectively and quantitatively assess the accuracy and robustness of two-dimensional sequentially linear analysis (SLA) in comparison to nonlinear finite element analysis (NLFEA), for a range of experiments of reinforced concrete structures with proportional and non-proportional loading schemes. Non-proportional loading refers to when two or more load cases act on a structure that do not increase or decrease in a proportional way. Accuracy was defined as the degree to which the finite element model's results match the experimental results. Robustness was defined as the method's ease of completing the computation and objectivity with respect to user-specified input. In selecting the benchmarks, experiments with brittle or quasi-brittle failures were targeted. Two experiments with proportional loading (a shear beam and a corbel) and three with non-proportional loading (a shear wall, a flexural beam, and a frame) were selected as the benchmarks. The frame is a single-span, double-storey frame, and thus consists of more structural elements than the other benchmarks. Each experiment chosen had previously been analysed using NLFEA by either the experiment conductor or another in academia. The five benchmark cases were modelled with SLA using a consistent solution strategy. The material constitutive models were discretised using the (standard) ripple band width saw-tooth law, which defines an upper and lower band of the softening and plasticity relations via a factor (p) of the material strength. Four performance parameters were devised to assess the performance of the SLA and NLFEA for each benchmark in the pre-peak, peak and post-peak stages, by comparing the modelling of the structural stiffness, peak load, ductility and ability to model post-peak behaviour to experimental results (where applicable). Inhibitors to the method's accuracy include the inaccurate modelling of stress reversal, which creates unrealistic crack openings and closures; delayed and limited yielding of reinforcement due to the discretisation of the Von Mises plasticity, resulting in overestimation of structural capacity and underestimation of ductility; lack of consideration of geometrical non-linearity; and small inaccuracies in the modelled saw-tooth relations resulting in some overestimation of reduced strength values during material softening and spurious transverse crack strains. Additionally the accuracy was limited by the simplification of the concrete material model and use of the linear tensile softening relation. Inhibitors to the robustness of the SLA included lack of objectivity to some user-specified input and intermittent proportional loading limiting the amount of post-peak behaviour successfully modelled in the non-proportionally loaded benchmarks. Overall, SLA was found to have a comparable level of accuracy with NLFEA in modelling reinforced concrete structures in both proportional and non-proportional loading scenarios, with many benefits observed in terms of increased robustness. The inaccurate stress reversal algorithm can severely affect the robustness of non-proportionally loaded cases and resolving this inaccurate formulation of crack closure in SLA should be a priority in future developments.