Mesoscale modeling of concrete time-dependent behavior

Creep and shrinkage of concrete are time-dependent deformations that influence primarily the serviceability, and in some cases also the safety, of reinforced concrete structures with and without prestressing. Shrinkage is mainly driven by both self-desiccation and moisture drying if exposed to lower relative humidity environments. In addition, and in combination to that, the large and widely unrecoverable creep deformations of concrete can cause significant modifications of action effects in structures in terms of internal stress distributions, excessive deflections and loss of prestressing forces, and produce large cracks. All these effects affect the serviceability and the durability of structures and may impact on their structural safety as well.Many models were formulated to explain and simulate the time-dependent behavior of concrete, among others. Also, several methods have been presented in the literature to simplify the calculation of creep strain for structural calculations, such as the effective modulus method, rate of creep method, the ageing coefficient method (AAEM method), and the approach based on the aging linear viscoelastic theory. More refined and advanced approaches for detailed numerical analyses of the structural effects of creep and shrinkage of concrete in complex, heterogeneous and sequentially built structures have also been developed in recent times. However, time-dependent behavior of concrete must be contextualized in a wider comprehensive framework since it is a result of interplay between multiple chemical, physical, and mechanical processes that are functions of the material composition and its curing as well as the surrounding environmental and loading conditions.

The nature and scales at which all these aforementioned processes take place represent a challenge for the numerical modeling. Concrete is a heterogeneous material made of two components having very large differences: a cementitious matrix and aggregates. The aggregates are typically much stiff, less porous and their time-dependent deformations are orders of magnitude lower than those of the cementitious matrix. Staying at the mesoscale, these two phases represent the main heterogeneity of concrete since at this scale the contribution of the matrix/aggregate interface, called the Interfacial Transitional Zone (ITZ), can be lumped together with the matrix and distinguish them from the aggregate to represent the main heterogeneity of concrete. By differentiating aggregate from the matrix, mesoscale interaction at that level can be directly captured; for example, when concrete is loaded in compression, the meso-structure experiences a well-known splitting mechanism of the aggregates. Mesoscale models are capable of resolving the stresses and strains at such level and can differentiate between tensile and compressive deformations, while macroscopic models have to average it. This distinction becomes very important during damage and creep/shrinkage interaction or when internal self-equilibrated stresses are the only source of loading like in non-uniform drying or free expansion under ASR progression in which cases the macroscopic stresses are equal to zero. Hence, macroscopic continuous models have to explicitly account for these lower-scale phenomena in their constitutive laws.

In the literature there are many meso-scale approaches based on continuum finite element (FE) models and discrete models, such as the classical particle discrete element methods (DEM), the lattice methods, a comprehensive approach that combines both of them called Lattice Discrete Particle Model, the Rigid-Body-Spring Networks (RBSN), and interface element models with constitutive laws based on non-linear fracture mechanics. Only through physically based constitutive approaches the problem of establishing reliable prediction models can be overcome, but this still requires a calibration on an extensive database.

In this paper, a recent mesoscale approach capable of representing remarkably well the concrete time-dependent behavior will be first reviewed. This mesoscale approach consists of the combination between the mesoscale discrete model termed Lattice Discrete Particle Model (LDPM) that is a comprehensive concrete model. It represents the internal structure (heterogeneity) of the material using an assemblage of coarse aggregates that interact at discrete interfaces. The model has been successfully used in modeling concrete samples and reinforced concrete structures under various static and dynamic loading conditions. The LDPM was recently coupled with a hygro-thermo-chemical (HTC) model resulting in a multi- physics framework that later was extended to account for coupled creep, shrinkage and ASR deformations. In this framework, creep and shrinkage deformations are modeled based on a discrete version of the Microprestress-Solidification theory. Finally, different experimental data sets available in the literature are here used to show the capabilities and the unique features of the proposed computational framework. Since the computational framework consists of several components, it requires an objective solid calibration strategy of the numerous parameters. In the numerical applications the calibration of each model component based on suitable test data is first presented. Then, the validation is performed using the experimental data that were not employed for the calibration. The examples considered in the manuscript deal with the creep and shrinkage under varying hygro-thermal conditions, the aging effects on strength, the tertiary creep and its application to time to failure analysis, the deterioration effect of the Alkali-Silica-Reaction (ASR) coupled with creep and shrinkage.

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