# Predicting the [PERSON]'s Modulus of Concrete Using a Particle-Based Movable Cellular Automata Method
## 1 Introduction  
The elastic constants, Young's modulus, and Poisson's ratio are considered to be fundamental mechanical properties of concrete that are required for analysis and design of buildings, roads, bridges, and other infrastructure elements primarily made of concrete. Young's modulus defines the ability of concrete to deform under stress. The higher the Young's modulus, the stiffer the concrete and the less prone it is to deformation under loading. Knowing the Young's modulus of concrete enables engineers to ensure that it can withstand the expected loads without excessive deformation, which could lead to damage or even fracture. Many researchers have attempted to predict the elastic modulus of concrete. In recent years, many studies have involved various machine learning techniques [1, 2, 3, 4]. Prediction ofelastic modulus with artificial neural networks was described in [1], where it was estimated based on compressive strength with coefficients of determination \(R^{2}\) up to 0.75. In [2], ten different machine learning models were applied to predict the elastic modulus of ultra-high-performance concrete, including linear regression, ANN, SVR, decision tree, random forest, and XGBoost, again on the basis of the given compression strength. XGBoost, which is a fast gradient-boosted decision tree algorithm, provided the best prediction performance with \(R^{2}=0.89\), while linear regression showed the worst performance. In [3], Random Forest (RF) and Artificial Neural Network (ANN) techniques were implemented to predict the properties of concrete infrastructure based on non-destructive acoustic, electrical, and electromagnetic measurements. Among these, only the Ultrasonic Pulse Velocity (UPV) method was found to be significant for predicting the elastic modulus. In [4], the cement and metakaolin dosages were found to have the greatest influence on the prediction of concrete fracture toughness among the ten input variables, which included concrete composition, specimen dimensions, and notch height. There are a number of different prediction models that use machine learning techniques concerning recycled aggregate concrete, in which the natural coarse aggregate is partially or fully replaced by coarse recycled concrete aggregate [5; 6; 7; 8; 9]. In [5], machine learning methods were implemented to predict the mechanical properties of concrete after exposure to high temperatures. Several methods were applied; according to the sensitivity analysis, none of these showed temperature to be a significant influence on any of the investigated mechanical properties of concrete, whereas exposure time was always a critical factor. When predicting the elastic modulus, the cement content and proportion of recycled aggregate were also important. In [6], sensitivity analysis of the parameters influencing the elastic modulus was performed using a numerical model based on Grey System Theory (GST). Simulations showed that the water/cement (w/c) ratio, aggregate/cement ratio (a/c), and ratio of the maximum size of recycled aggregate concrete to the maximum aggregate size had a comparable effects on the elastic modulus. Sensitivity analysis is not performed in every study. For example, the database in [7] included thirteen input parameters used to predict the modulus of elasticity, but their individual influences on the outcome are unknown. In [8], the compressive strength of confined concrete was correlated with approximately seven factors (the compressive strength of unconfined concrete, the magnitude and diameter of hemp ropes, specimen size, cross-sectional shape, rope thickness, and rope tensile strength); however, neither sensitivity analysis nor the database itself were presented. In [9], reducing the number of input factors from fourteen to six (retaining only mix proportions and curing ages) altered the coefficient of determination (R\({}^{2}\)) results for validation of the elastic modulus in the third decimal place.