Probabilistic Reliability Assessment for Non-Linear Finite Element Analysis of Reinforced Concrete Beams

Abstract

Non-linear finite element analysis (NLFEA) is a powerful numerical solution method that can enhance accurate determination of the structural resistance for a more efficient design. However, the implementation of NLFEA for the design of reinforced concrete structures is lagging behind as related uncertain- ties have not been quantified adequately yet. Multiple studies have been conducted to evaluate the effect of modelling choices, which has led to the RTD1016 Dutch Guideline. This guideline enables a better quantification of the uncertainties related to NLFEA for the proposed solution strategy. In this research, a full probabilistic approach is applied to improve the quantification of uncertainties related to NLFEA, and thereby enhance its application for the design of reinforced concrete structures. In particular, to the ultimate limit state (ULS) of simply supported beams subjected to both ductile and brittle failure modes. To achieve this goal, 48 benchmark beams were selected from literature for calibration purposes. Material induced uncertainties of concrete and reinforcement were incorporated through an optimized Latin hypercube sampling strategy. The beams were modelled in a 2D plane in software program Diana based on a total strain crack model and Von Mises plasticity. A displacement-controlled analysis was performed to determine the numerical ultimate resistance. In total, 1104 analysis were performed of which the model uncertainty was quantified and the failure mode was determined by the ductility index. Based on this, a global reliability method was defined as a function of the failure mode. A comparison with existing reliability methods was made in terms of accuracy and robustness. Furthermore, a standalone multivariate non-parametric Bayesian network (NPBN) was developed that allows for extensive reliability assessment possibilities. The research has shown how a full probabilistic approach with benchmarking can be applied. A reliability method as a function of the failure mode was proposed that showed improved efficiency compared to existing reliability methods (GRF,PRF,ECOV). For a 50 year design lifetime, a mean unity check of 77% was attained for the ductile failure mode and 66% for the brittle failure mode. For specific types of concrete and reinforcement, even higher efficiency can be obtained by reduced coefficients of variation of the material parameters. Furthermore, a NPBN was constructed which describes the NLFEA behaviour of reinforced concrete beams. Additional research is necessary to improve the model application, but it has been demonstrated how such a model can be established and used for reliability assessment of reinforced concrete beams. The findings of this study suggest that the design of reinforced concrete beams by NLFEA can be applied for efficient design, while respecting safety standards. The full probabilistic approach enabled an improved quantification of the design resistance. Thereby, this research contributes to the implementation of NLFEA for the design of reinforced concrete structures.