# A Detailed Review on Foam Concrete Composites: Ingredients, Properties, and Microstructure
## 5 Mechanical Properties of Foam Concrete
### Models Predicting Strength  
According to the [PERSON] rule, when concrete is fully compacted, strength and \(\mathrm{w/c}\) ratio are taken in inverse proportion. In 1896, [PERSON] constructed the following equation with regards to the volumes of water, cement, and air in the mixture [95]. \[\mathrm{f_{c}=Kcc+a^{2}+w}\]  
where \(\mathrm{f_{c}=compressive strength}\) (MPa); \(c\), \(w\), \(a=absolute\) volumetric ratios of cement, water and air; and \(\mathrm{Kcc}\) is used as the Feret constant. [PERSON] reported that the strength for any \(\mathrm{w/c}\) ratio is chemical control, entrained and entrained air content, paste age, cement fineness, curing temperature and moisture. He reported the porosity strength model for Portland cement, preformed foam and produce foam concrete with water [96]. [PERSON] and [PERSON] reported that the defect size associated with pore size (at a given bulk density) is an important parameter in controlling the strength of foamed Portland cement [95,97]. It was demonstrated by [PERSON] and [PERSON] [95] that the compressive strength of foam concrete is a function of porosity and age. The presented multiplicative model (such as the equation derived by [PERSON]) was reported to be consistent with the results at all ages of up to 1 year. [PERSON] and [PERSON] [98] proposed similar relationships based on [PERSON]'s model and [PERSON]'s concept of the gel-space ratio. The model, based on [PERSON], uses the composition of the components and easily measurable parameters. The proposed model stands out with its good correlation with the measured values and its ease of application. [PERSON] et al. [99] studied the relationship between porosity and strength for porous concrete. A model was proposed for the relationship between porosity and strength. This new model was derived from [PERSON]'s theory, and it was reported that it could provide a better estimate for porous concrete compressive strength depending on material porosity. [PERSON] et al. (2018) explored the use of artificial neural networks for preformed foam concrete different from traditional prediction methods. For the model developed with artificial neural network (ANN), the cement content, w/c ratio, foam-cement ratio, and sand-cement ratio were used as variables. As a result, it was reported that the compressive strength, foam density, non-foaming density, and production efficiency of foam concrete mixtures were more accurate than the current parametric methods using ANN. [PERSON] et al. developed a deep neural network model to estimate the compressive strength of foamed concrete. A high-order neuron was developed to improve the performance of the created model. Compressive strength estimates were made using the data set, and the results obtained were compared with traditional artificial neural networks and second-order artificial neural network methods. The results showed that the model created can predict the strength of foamed concrete with high accuracy. In addition, according to the results, it was reported that the strength of foamed concrete was greatly affected by the density, followed by the water-cement and sand-cement ratios ([PERSON] et al., 2018). [PERSON] et al. (2018) evaluated the mechanical behavior of foam concrete, a cellular lightweight binder with entrained air spaces, using the phase-domain fracture model in the framework of finite elements. The aim of this study was to investigate the mechanical properties via microstructure analysis derived from X-ray micro-CT to speed up property evaluations in terms of experiments and simulations. In the study, a methodology for determining micro-scale material properties/parameters of foamed concrete is presented to predict the macroscopic mechanical behavior. The study confirmed that multiphase solid models can simulate real values depending on more accurate crack patterns that could result in failure.