# Early-Age Cracking in Concrete: Causes, Consequences, Remedial Measures, and Recommendations
## 6 Modeling of Early-Age Cracking
The cracking assessment was performed based on the conception of linear elastic stress without considering the shape of the concrete structure, that is, the estimation process is applicable to any shape of structure. It can be considered as an improvement in the modeling process, as the previous simulations of the early-age cracking in concrete were reliant on the shape of concrete structures. [PERSON] and [PERSON] [102] proposed a simple model to predict the degree of plastic shrinkage cracking (PShC) in normal-strength concrete. The model is based on the amount of evaporated water from the freshly placed concrete before initial setting takes place, and can be expressed as follows. \[\text{PShC Severity}=\text{ER}\times\text{t}_{\text{set}}-\text{W}_{\text{bl}} \tag{1}\]  
where ER is the evaporation rate (kg/m\({}^{2}\)/h), t\({}_{\text{set}}\) is the time between the concrete placement and the initial setting time (h), and W\({}_{\text{bl}}\) is the total bleed water (kg/m\({}^{2}\)). Together with these parameters, drying time, air entry time, capillary water pressure, etc. are also carefully considered in the above model. The model demonstrates that the PshC will only occur once the bleed water is evaporated completely. The proposed PshC severity model efficiently correlated with the crack width induced by PshC in the case of a large number of concrete mixtures with or without reinforcing fibers. However, the authors did not consider the interaction between plastic settlement cracking (PSeC) and PshC. Due to this they observed some cracking in concrete even at a zero value of PshC severity. Shrinkage induces cracks in concrete overlays depending on the shrinkage stress, thus an estimation of this parameter is very important in understanding the formation of such cracks. Many models have been proposed to determine the shrinkage stress; however, sometimes those models are very complicated for practical use. [PERSON] [103] proposed a simple model to predict the shrinkage stress in overlay concrete, which is as follows. \[\sigma=0.009\epsilon_{\text{sh}} \tag{2}\]  
where \(\sigma\) is the shrinkage stress and \(\epsilon_{\text{sh}}\) is the free shrinkage strain in overlay concrete. The model was proposed based on an important assumption that both the substrate and overlay concretes are free to shrink. As the model is very much simplified, it can be used only for the quantitative assessment of shrinkage cracking tendency in overlay concrete. Most of the above-mentioned models were developed based on finite element and mathematical analyses, but some researchers have used Artificial Neural Network (ANN) to predict the early-age properties of hardening concrete. For example, [PERSON] and [PERSON] [97] used ANN to predict the early-age autogenous shrinkage of concrete. Initially, the model was developed considering the concrete mixtures under different curing temperatures. Later, the developed model was tested considering the other criteria such as cement content, water-to-cement ratio, the type and percentage of supplementary cementitious material, total aggregate volume, and hydration age. The developedANN model is able to predict the autogenous shrinkage behavior of traditional as well as high- or ultra-high-performance concrete mixture. There are various models available to predict the early-age cracking in concrete structures; these models could help construction stakeholders understand the limitations of their design, especially at the early stage. These modeling approaches can be categorized into two groups: mechanism-based modeling and factor-based modeling. The examples of mechanism-based modeling are listed in Table 2, while one of the factor-based modeling examples is ANN [97]. However, it was observed from the review of literature that there were lacks of standardized modeling techniques for the early-age cracking in concrete. The input data and predicted outcome from each modeling exercise was different from researcher to researcher.