**1. Introduction**

Civil engineering practitioners such as researchers, engineers, technicians and those interested in it have always favored the best concrete formulas based on classical or modern methods. The methods used were either experimental (laboratory tests), or empirical or semi-empirical method or analytical methods. The current results of concrete production always indicate that they are oriented towards modern methods which are mainly based on numerical modeling [1–10].

Scientific research in the field of civil engineering, as in many other applied sciences and technologies, is a major use of its implementation according to modern tools, in particular calculation tools [1, 3]. The main objective of this study is to discover the best methods that help in the economic aspect, in particular the building materials when testing, in addition to saving time and effort lost in their realization without taking them into account. Thus, it was more interesting to use technology (electronics and computer) with analytical methods and concrete models to achieve experimental methods.

On the other hand, our main goal is to take advantage of recent studies [5–10] that rely on granular distribution to quantify aggregate dosages. According to the parameters of the fractal dimension FD [1–4] and the granular extent D/d [2].

On the other hand, we emphasize the importance of extending the determination of the granular distribution by using the fractal distribution as a new model to determine the granular mix class of concrete. Our experimental results, which we adopted in this study, allow us to determine a numerical value as one of the physical properties of the aggregate, which is the fractal dimension (FD). It facilitates the formulation of concrete by precisely specifying the components of the aggregate. Our objective in this study is to create a large database which helps us to save time and materials in experimental studies within the framework of concrete formulation methods to determine dosages of granular materials, which is certainly useful in the field of civil engineering. Initially, we rely on the study of a component to facilitate the process and start from the simplest operations. We took, for example, the study of the effect of the sand component [4]. It should be noted that this work is mainly based on the data, which takes the aggregate as the basic component in the production of concrete so that as it is known, 80% of the concrete is composed of aggregate, in order to obtain a good granular distribution (continuous granulometry). We emphasize that the appropriate selection of aggregates according to the desired concrete requirements allows us to achieve one of the most important characteristics that distinguish concrete, which is the compressive strength of concrete [3, 4]. In addition, the new definition of granularities by fractal dimension helps in choosing the classes of aggregate to be used in concrete. We confirm that one of the main objectives of this study is to highlight the optimal importance of the fractal dimension parameter and its results, which brings us to the possibility of knowing how to determine the reference particle size curve of granular mixtures at using the fractal model for granular concrete mixtures.
