Calibration of Model Uncertainty Safety Factors for NLFEAs of reinforced concrete beams with shear and flexural failure modes

Pushing the boundaries of the design phase beyond the physical constraints to satisfy the needs imposed by the modern complex structures has led to ongoing advancements in data-processing performance and the development of high-tech software. These tools allow engineers to perform non-linear numerical analysis (NLNA) for reinforced concrete (RC) elements through an exhaustive investigation of the overall structural response under potential load cases. By accounting for non-linearities in material, geometric properties, and boundary conditions, NLNA offers the highest level of approximation for defining the structural model, constitutive laws, and resistance mechanisms. The Codes have proposed several safety formats for the NLNAs of RC structures to address the corresponding source of uncertainty, providing a general framework for integrating them within the Global Resistance Format (GRF) and thus ensuring a balanced tradeoff among safety, efficiency, and cost. The thesis aims to investigate the discrepancy between numerical models and actual structures’ performance by analyzing RC beams that fail in a flexural and shear mode. Comparing experimental results in terms of maximum load with those from NLFE models, this work quantifies the uncertainties that arise during the modeling phase, known as epistemic uncertainties. By assuming 3 model hypotheses that include all possible tensile concrete behaviors and cover any analyst assumptions for its constitutive law in 2 different software, Atena and Diana, the results from 210 Non-Linear Finite Element Analyses (NLFEAs) were gathered. The approach allows us to obtain 6 solution strategies that guarantee a comprehensive characterization of the global resistance model uncertainty random variable. Consequently, a probabilistic analysis was conducted employing the Bayesian method, avoiding the possibility of making a work that is just a representation of a narrow set of RC structures. The purpose is to pursue general outcomes that could contribute to the development of the next generation of Eurocodes. The overarching idea of this strategy is to first apply a statistical inference procedure to detect the appropriate probabilistic model and fit it to the data sample through the estimation of its parameters. After that, the process involves the calibration of the model uncertainty safety factor by generating new information using the Bayesian updating process. The result is the definition of posterior probability functions, which reflect both the prior information and the new data. The strength of this approach lies in its ability to incorporate into the analysis existing knowledge from the literature. This procedure performs the updating operation twice, leading to more robust results and a reduction of model uncertainty, enhancing the reliability of the findings. Finally, after estimating the average posterior probability distribution, which is adopted to represent the resistance modeling uncertainty random variable θ and deleting the influence of experimental uncertainty from its key statistical parameters, the resistance model uncertainty partial safety factor γRd can be estimated. The assessment assumes 3 different reliability indexes, 2 FORM factor scenarios, and various service life cases, in line with the GRF of the fib Model Code for concrete structures 2010. These options ensure safety, reliability, and feasibility in the design process by choosing a conservative value that adequately tackles model uncertainties.