This paper presents a solution strategy, based on a parallel Genetic Algorithm (GA), to optimize the construction of massive concrete structures. The optimization process aims at minimizing the construction cost, considering the following design variables: the concrete mixes, the placing temperature, the height of the lifts, and the time intervals between placing the lifts. The cracking tendency is taken into account by a penalty scheme imposed to the fitness function of the GA. A thermo-chemo-mechanical model is used to calculate the transient fields of hydration, temperature, stress, strain, and cracking tendency. This model is implemented in a finite element code that is, in turn, parallelized. To demonstrate the efficiency of the proposed methodology, the simulation of the construction of a structure similar to the real thick foundation of an industrial building is presented. It shows that the optimization procedure here presented is feasible and is ready to be used in real engineering applications.

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.

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.

In this paper, concrete cracking is investigated in dynamics through finite element modeling. A probabilistic semi-explicit model, previously developed and validated for static loading, is extended for dynamic loading. The model in statics is based on two material mechanical parameters: the tensile strength and the critical strain-energy release rate in mode I, $G_{IC}$, of the Linear Elastic Fracture Mechanics (LEFM) theory. Concerning the dynamic aspects of the model, the tensile strength rate effect is modeled by an empirical dynamic-to-static strength ratio (Dynamic Increase Factor—DIF) and a similar formulation is proposed for $G_{IC}$. The structural rate effect is naturally captured when mass and damping are included in the equation of motion. For static and dynamic loading, only macroscopic crack propagation is considered. Some numerical simulations in statics and dynamics are presented in the present paper. The main results related to this work can be summarized as follows: the dispersion of the numerical results related to the load–displacement curves decreases with the loading rate. The crack pattern considerably changes with loading rate (numerically and experimentally); the agreement between the experimental and numerical results (load–displacement curves and crack pattern) indicates the model is promising for engineering applications.

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.