Chapter 6 Bayesian Updating of a Cracking Model for Reinforced Concrete Structures Subjected to Static and Cyclic Loadings Henriette M. Imounga, Emilio Bastidas-Arteaga, Moutou Pitti Rostand, and Serge Ekomy Ango Abstract Several reinforced concrete structures fail by fatigue loads. The effects of this type of loading are complex. Many mechanical models based on the damage theory could be used to represent the behavior of reinforced concrete under cyclic loading. Their use requires, among others, knowledge of the material characteristic parameters and its related uncertainties that could be determined from experimental tests. However, the models are time-consuming and the experimental data scarce. In this chapter, we propose a Bayesian network–based methodology to propagate uncertainties in the damage theory model. The proposed methodology is useful to identify the uncertainties of the damage model used when some parameters are measured. The methodology is illustrated with a reinforced concrete beam subjected to cyclic loading. The results obtained were compared with those of the experimental tests to validate the proposed methodology. The good agreement indicates that our approach is capable of propagating uncertainties and integrating data from experimental tests. The proposed approach could be also used to identify the uncertainties of the model used by introducing experimental measurements. Keywords Cracking · Cyclic loading · Bayesian network · Reinforced concrete · Damage theory 6.1 Introduction During their operation, reinforced concrete structures are subjected to stresses of several types responsible for their rapid deterioration. To reproduce or predict the degradation processes of these structures, numerical models validated by experimental tests have been developed for many authors. In the case of fatigue loads, several models based on the damage theory are useful to describe the mechanical behavior of concrete after each loading cycle (loading-unloading) [1–3]. The purpose of these models is to assess the effects of micro-cracking in concrete, using a bounded variable (scalar or tensor) called the damage variable. For the models of damage, the behavior law relating stress to deformation is written as follows: σ =(I −D)C: ε (6.1) where σ is the stress tensor, ε the strain tensor, I the unity tensor, C is the tensor of elastic behavior, and Dis the tensor of damage. These models take into account intrinsic parameters of the material, such as the elastic modulus, the stresses H. M. Imounga Université des Sciences et Technique de Masuku, Franceville, Gabon UBL, Université de Nantes, Nantes, France e-mail: henriette.imounga@etu.univ-nantes.fr E. Bastidas-Arteaga UBL, Université de Nantes, Nantes, France e-mail: henriette.imounga@etu.univ-nantes.fr; emilio.bastidas@univ-nantes.fr M. P. Rostand ( ) Université de Clermont Auvergne, CNRS, SIGMA Clermont, Institut Pascal, Clermont-Ferrand, France IRT, CENAREST, Libreville, Gabon e-mail: rostand.moutou_pitti@uca.fr S. Ekomy Ango IRT, CENAREST, Libreville, Gabon e-mail: ekomyango@yahoo.fr © The Society for Experimental Mechanics, Inc. 2021 S. Xia et al. (eds.), Fracture, Fatigue, Failure and Damage Evolution, Volume 3, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-60959-7_6 45
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