# Predicting the [PERSON]'s Modulus of Concrete Using a Particle-Based Movable Cellular Automata Method
## 1 Introduction
In [10], which reviewed the areas where machine learning has impacted concrete science, several main issues are highlighted: the requirement for high-quality data to learn patterns and relationships, lack of consistent reporting of experimental results in the literature, and small datasets that are often insufficient. The reviewed studies indicate that the set of parameters selected by researchers in machine learning methods varies, which makes it difficult to compare results or draw general conclusions. Some studies only consider compressive strength. In many cases, multiple input parameters are taken into account; however, for typical cement, sensitivity analyses show that the mix proportions (cement content and coarse aggregate content) and water/cement ratio are the key factors in predicting the elastic modulus. In this study, the static elastic modulus is determined on the basis of the mechanical properties of concrete components using a particle-based method originating from cellular automata. Classical cellular automata, in which the state of a single cell depends on its connections and interaction rules, were first discovered in the 1940s by [PERSON] and [PERSON] were later described in detail in [11]. They continue to be applied in the modelling of various physical and biological phenomena [12; 13]. Over time, this concept has evolved; in some cases, cellular automata are combined with other mathematical techniques to enhance their functionality, such as genetic algorithms [14] or fuzzy logic [15; 16]. The movable version of cellular automata, known as the Movable Cellular Automata (MCA) method, belongs to the class of computational particle based methods such as DEM. These methods differ in the philosophy of the approach, their representation of elements, and the way interactions between automata are described. The Discrete Element Method (DEM), which enables the modelling of interactions between individual rigid bodies (particles), was introduced in [17] in the context of modelling granular materials such as sand, gravel, and coal. In the 1980s, it was mainly used in the analysis of flows of granular material. In the 1990s, more advanced algorithms were developed that allowed for modelling interactions between elements in more complex systems, including concrete [18; 19; 20; 21; 22; 23; 24; 25; 26; 27]. The MCA (Movable Cellular Automaton) method, first introduced in [28], is based on classical cellular automata; in contrast to the classical approach, however, the interactions among the elements lead to changes in both their state and their spatial movement. The surroundings of the elements can also change. The evolution of the simulated system is defined by the internal state of the elements, their mechanical properties, and the interaction law among them. The MCA method is based on the mesomechanics of heterogeneous media described in [29; 30], which states that the behaviour of solids at the meso level can be described using volume elements of various sizes and that their motion occurs through a shear-rotation mechanism. In the MCA method, fracturing of a specimen results from local displacements induced by increasing internal forces within the automata network. This method allows for the modelling of complex mechanical systems on a mesoscopic scale, enabling the study of defect propagation [31], friction and wear in real systems [32; 33; 34; 35], and crack formation and development under different mechanical loading conditions [36; 37]. The first simulations indicating that the MCA method is suitable for simulating the mechanical behaviour of heterogeneous materials such as concrete were presented in [31]. In [38], this method was implemented to obtain the mechanical properties of zirconium alumina concrete, with the effect of the strain rate on material behaviour analysed in the case of uniaxial compression and tension. To the best of the authors' knowledge, the aforementioned studies are the only ones in which the MCA method has been used to estimate the mechanical properties of concrete.