# Early-Age Cracking in Concrete: Causes, Consequences, Remedial Measures, and Recommendations
## 6 Modeling of Early-Age Cracking  
It is complex to quantify the early-age fine cracks in construction practice. Many models are available to calculate the crack width based on the bond behavior of hardened concrete and \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt}} \hline \hline
**Properties** & **Factors** \\ \hline \multicolumn{2}{p{113.8 pt}}{**Thermal Properties:**} \\ \hline Heat of hydration & The type, total content, and chemical composition of cement; the ambient temperature and the admixtures used. \\ \hline Specific heat capacity & The mixture composition, moisture content, and ambient temperature. \\ \hline Thermal conductivity & The density, water content, temperature, and mineralogical characteristics of aggregates. \\ \hline Thermal diffusivity & The aggregate type used and water content. \\ \hline Coefficient of thermal expansion & The type and content of cement, the type of aggregate, and water-to-cement ratio; the age, temperature, and relative humidity of concrete. \\ \hline \multicolumn{2}{p{113.8 pt}}{**Mechanical Properties:**} \\ \hline Compressive strength & Calcium silicate hydrate (CSH) gel/space ratio, water-to-cement ratio, the type of cement, the presence of additives, and curing condition. \\ \hline Tensile strength & The type, density, and grading of aggregate; curing type and concrete age. \\ \hline Modulus of elasticity & Concrete temperature, water-to-cement ratio, cement type, aggregate properties, and curing conditions. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Factors which influence the thermal and mechanical properties of hardening concrete. reinforcing steel as well as the development of tensile stresses. The effect of reinforcement has not been considered in crack width calculations. This may be reasonable for normal-strength concrete but not for high-strength concrete. This is because reinforcement produces a \"strain enhancing effect\" in high-strength concrete that reduces the probability of major through-cracks in reinforced concrete elements [17]. Simulation and modeling are useful to find the uncertainties and weak spots in experimental studies and allow quantitative prediction. Thus, many researchers take the effort in developing and improving the models to provide a better understanding and predict the cracking in concrete at the early-age. [PERSON] et al. [82] provided a review on the modeling of service life of massive concrete structures. They divided the models into two groups: deterministic models and the models considering the stochastic nature of cracking. However, their review was limited to finite element modeling. Meanwhile, [PERSON] et al. [83] reviewed the literature on the modeling of cement hydration induced heat development in massive concrete structures; they presented several approaches, such as affinity-based models, microstructural models, data mining, and inverse analysis. The hydration process of concrete involves many disciplines, and therefore this paper has grouped the premature concrete cracking related models available in literature, according to the thermal, mechanical, chemical, and hygroscopic criteria (refer to Table 2). It was found that the mechanical criteria are involved in the most models, because stress and strain always play key roles in the development of cracking. Thermal stress and chemical reaction between cement and water are also associated with the cracking of concrete. Hydro-related criteria are involved too because of the moisture involvement and movement. Thermal stress is one of the main reasons of cracking in hardening concrete and therefore many researchers considered it in the modeling of early-age cracking. [PERSON] and [PERSON] [101] provided Double Power Law (DPL), which was used by [PERSON] and [PERSON] [81] to determine the stress evolution and crack propagation in concrete from finite element simulations.