This paper focuses on the use of numerical tools, as a finite elements method, to conceive fiber reinforced concrete (FRC) eco-constructions. It highlights the fact that these are the most suitable tools (much more than the Eurocodes, for example) to predict the cracking process of FRC constructions at their service limit state and, therefore, to predict their durability. Following a critical analysis of the existing finite element models for FRC cracking, it describes in more detail a probabilistic one. This model appears very suitable for providing precise information about crack openings that are inferior or equal to 300 microns. Finally, it presents an example of the use of this numerical model to optimize an FRC track slab in order to reduce its carbon footprint. This study, although partial and incomplete, shows that the best way to reduce the carbon footprint of this type of construction is to reduce its thickness.

This paper introduces a three-dimensional (3D) semi-explicit probabilistic numerical model for simulating crack propagation within the framework of the finite element method. The model specifically addresses macrocrack propagation using linear volume elements. The criteria governing the macrocrack propagation is based on the softening behavior observed in concrete under uniaxial tension. This softening behavior corresponds to a dissipated cracking energy that is equal to the mode I critical fracture energy $\left(G_{IC}\right)$ used in the Linear Elastic Fracture Mechanics theory (LEFM). The probabilistic nature of this model revolves around the random distribution of two mechanical properties: tensile strength $\left(f_t\right)$ and fracture energy, which varies based on the volume of finite elements. The scattering of the fracture energy increases as the volume of finite elements decreases in order to consider the strong heterogeneity of the material. This work primarily aims to estimate the relationship between the standard deviation of $G_{IC}$ and the volume of finite elements through the development of the numerical model. For this purpose, an inverse analysis is conducted based on a fracture mechanical test simulation. This test involves macrocrack propagation in a large Double Cantilever Beam (DCB) specimen with a crack length exceeding two meters. The proposed inverse analysis procedure yields highly significant results, indicating that the numerical model effectively evaluates both crack length and crack opening during propagation.

This paper presents an extension of the validation domain of a previously validated three-dimensional probabilistic semi-explicit cracking numerical model, which was initially validated for a specific concrete mix design. This model is implemented in a finite element code. The primary objective of this study is to propose a function that enables the estimation of the critical fracture energy parameter utilized in the model and validate its effectiveness for various concrete mix designs. The model focuses on macrocrack propagation and introduces significant aspects such as employing volume elements for simulating macrocrack propagation and incorporating two key factors in governing its behavior. Firstly, macrocrack initiation is linked to the uniaxial tensile strength $(f_t)$. Secondly, macrocrack propagation is influenced by a post-cracking dissipation energy in tension. This energy is taken equal to the mode I critical fracture energy $(G_{IC})$ based on the linear elastic fracture mechanics theory. Importantly, both $f_t$ and $G_{IC}$ are probabilistic properties influenced by the volume of concrete under consideration. Consequently, in the numerical model, they are dependent on the volume of the finite elements employed. To achieve this objective, numerical simulations of fracture mechanical tests are conducted on a large double cantilever beam specimen. Through these simulations, we validate the proposed function, which is a crucial step towards expanding the model’s applicability to all concrete mix designs.

In this paper, the development of a 3D adaptive probabilistic explicit cracking model for concrete is reported. The contribution offered herein consists in a new adaptive mesh strategy designed to optimize the use of interface elements in probabilistic explicit cracking models. The proposed adaptive mesh procedure is markedly different from other strategies found in the literature, since it takes into account possible influences on the redistribution of stresses after cracking and can also be applied to purely deterministic cracking models. The process of obtaining the most appropriate adaptive mesh procedure involved the development and evaluation of three different adaptivity strategies. Two of these adaptivity strategies were shown to be inappropriate due to issues related to stress redistribution after cracking. The validation results demonstrate that the developed adaptive probabilistic model is capable of predicting the scale effect at a level similar to that experimentally observed, considering the tensile failure of plain concrete specimens. The results also show that different softening levels can be obtained. The proposed adaptive mesh strategy proved to be advantageous, being able to promote significant reductions in the simulation time in comparison with the classical strategy commonly used in probabilistic explicit cracking models.

This work presents the application of a finite element model utilizing a three-dimensional (3D) probabilistic semi-explicit cracking model to analyze the rupture process of a large concrete wall beam. The numerical analysis predicts both the global behavior of the structure and its primary rupture mechanisms, utilizing three different finite element mesh refinements to ensure robustness. A Monte Carlo (MC) procedure is integrated into the modeling approach to account for probabilistic variations of the material properties. The statistical analysis derived from this probabilistic model may sometimes result in overly conservative safety coefficients, particularly when using a coarse mesh. Additionally, the detailed understanding of the structure’s cracking process, regardless of its rupture mechanism, may experience some reduction in precision. Due to the necessity of numerous simulations to achieve statistically significant results, the MC procedure can become computationally expensive. To address this, a straightforward parallelization of the Monte Carlo procedure was implemented, allowing multiple finite element analyses to be conducted concurrently. This strategy significantly reduced computational time, thereby enhancing the efficiency of the numerical model in performing numerical simulations of structural engineering.