# Early-Age Cracking in Concrete: Causes, Consequences, Remedial Measures, and Recommendations
## 6 Modeling of Early-Age Cracking
This model involves the changes of the adsorption-desorption, evaporation-condensation, chemical reactions (hydration), different fluid flows, and the nonlinearities with regard to temperature and moisture content, as well as the progress of concrete maturity (hydration degree). A direct coupling between the shrinkage phenomenon and material creep has also been modeled through the modified microspore stress-solidification theory [88]. A nonlinear viscoelastic constitutive model for hardening concrete in an immersed tunnel was developed by [PERSON] et al. [42], where casting temperature, formwork conductivity, formwork removal time, curing temperature, and ambient temperature are computed by a stochastic multiscale method to determine the uncertainty and identify the influencing factors. It was found out that the casting and curing temperatures are the most influencing factors in the model. Moreover, a new model on the internal relative humidity of concrete was developed by [PERSON] et al. [92] to determine the drying shrinkage stress and thermal dilation coefficient of concrete. The temperature, age, and internal relative humidity of concrete were considered in this model. It provides better results than the predrilled-hole method since the effect of environment was not taken into consideration. [PERSON] et al. [96] used an inverse numerical analysis to develop a model for the moisture diffusion coefficient by considering the relative humidity, temperature, and age of concrete. This model is able to describe the diffusion process occurring in early-age concrete. In the same year, [PERSON] [99] deduced three-dimensional finite element thermal analysis to predict the temperature and moisture distribution in hardening concrete. The fundamental parameter considered in his analysis was the degree of cement hydration. The effects of temperature, aging, and the variation of relative humidity due to moisture diffusion and self-desiccation were also considered in this model. Many researchers have also developed models for massive concrete structures. [PERSON] and [PERSON] [93] extended the basic creep model by including the effects of hydration to predict the behavior of a massive wall; they also used the concept of chemical affinity to predict the evolution of temperature and hydration. Besides, [PERSON] et al. [95] developed a simulation model on the construction of a real massive structure to unveil the creep effect and creep-damage coupling. In this modeling exercise, the effects of environment, such as wind and ambient temperature, on the concrete properties were studied. In the simulation model on a massive wall [95], it was found that the ignorance in thermal properties and constant thermal capacity are the main reasons of error in the estimation of the stress that causes the early-age cracking in concrete. [PERSON] et al. [51] investigated the distribution of temperatures within a hardening massive concrete element using the finite element method. This model could quantify the maximum allowable temperature difference within the concrete core and surface to prevent cracking. The temperature distribution observed during the experiment was well quantified by the developed model. Moreover, [PERSON] and [PERSON] [98] developed a numerical model for analysis of the early-age thermal-shrinkage stresses in an externally restrained concrete wall and found that the restrain coefficient defines the inclination of the total stress curve in wall cross section. Temperature, moisture, and the chemical reactions of cement were mainly considered in this model. [PERSON] and [PERSON] [38] provided a better understanding of massive concrete by introducing the concept of equivalent thickness, which is defined for a separable heat flow area of concrete element, irrespective of the shape or size of concrete structure. The equivalent thickness concept could facilitate to provide a faster estimation of the early-age cracking tendency of massive concrete elements due to temperature rise.