# Predicting the [PERSON]'s Modulus of Concrete Using a Particle-Based Movable Cellular Automata Method
## 5 Discussion  
Predicting the elastic modulus of concrete is challenging due to its randomness and complexity. Some researchers have claimed that experimental results can be unreasonable. Traditional approaches to the design of concrete mixtures depend on a repetitive cycle of testing while adjusting the material proportions until satisfactory results are achieved. However, such approaches require significant investment of time and resources. Alternatively, machine learning approaches require large databases with high-quality data, which are not always easy to find in the literature due to a lack of standardized experimental descriptions and inconsistent reporting of results. This study presents an innovative approach to predicting the elasticity modulus of concrete using the Movable Cellular Automata (MCA) method, which considers interactions between automata representing cement paste, fine aggregate, and coarse aggregate based on the mechanical properties of each material. Unlike conventional approaches, which are confined to the macro scale, the MCA method allows for simultaneous analysis of meso-scale structures and their impact on macro-scale performance. The MCA method permits numerical estimation of mechanical properties based on a limited number of samples. This allows for the optimization of concrete mixtures by adjusting parameters such as the water/cement ratio, aggregate/cement ratio, and coarse aggregate/total aggregate ratio without the need for time-consuming and costly experiments. Currently, the MCA method does not account for the influence of processing steps (e.g., mixing, transportation, placement, and curing) on the mechanical properties of concrete. It also does not consider environmental conditions such as temperature and humidity. Another limitation is the lack of consideration of various chemical admixtures, such as water-reducing agents, which possess chemical compositions that may vary between manufacturers. Their effects on concrete performance are not currently included in the presented model. The sensitivity analysis conducted for hypothetical concrete showed that the coarse aggregate elastic modulus, water-to-cement (w/c) ratio, and coarse aggregate-to-total aggregate ratio have the greatest impact on the Young's modulus of concrete modeled using the MCA method. Figure 7: Results of numerical simulations of concrete containing Lightweight Expanded Clay Aggregate (LECA) based on [83] compared with experimental data and the European standard defining [PERSON]’s modulus based on compressive strength [82]. Numerical simulations were conducted employing selected studies available in the literature for different water/cement ratios, types of aggregates, and aggregate volumes. The results were then compared with experimental data. High accuracy was achieved, as evidenced by a high coefficient of determination (R\({}^{2}\)) of 0.84 and MSE of 2.43 GPa\({}^{2}\) for concretes with basaltic aggregates and an R\({}^{2}\) of 0.86 and MSE of 0.81 GPa\({}^{2}\) for concretes with lightweight expanded clay aggregate. Our simulations results confirm that the type and volume of coarse aggregate have the highest influence on the Young's modulus, while the water/cement ratio has the lowest. The MCA method accurately reproduces the actual elastic modulus; thus, its use can contribute to optimization of the elastic modulus by adjusting the water/cement ratio, total aggregate/cement ratio, and coarse aggregate/total aggregate ratio. In the near future, we intend to apply the MCA method to model concrete cracking and to study the influence of pore shape, location, and number on the mechanical properties of concrete. Another area of interest is application of the MCA method to analyze the effect of the shape and size of coarse aggregates on the overall performance of concrete. Conceptualization, D.A. and M.R. ; investigation, D.A. ; writing--original draft preparation, D.A. ; writing--review and editing, D.A. All authors have read and agreed to the published version of the manuscript.