**4.3 Particle size curves of mixtures**

In this study, we adapted 12 concrete formulation tests for 12 projects carried out at the wilaya in the State of Adrar which are detailed in **Table 3**. Example of the particle sizes of the Granular Mixtures based on the particle sizes of different granular classes, **Figure 8** with cement and **Figure 8** without cement.

As for the concrete studies, we adopted the studies using dune sand that we have already studied, knowing that the concrete compositions included in this study are part of an executive study for projects scheduled to be implemented in arid regions.

Thus, the concrete compositions were studied in coordination between the building materials laboratory of the University of Adrar and the local technical laboratories, so that the study was carried out with the laboratory assigned to monitoring and control at the site. of the project. This within the framework of cooperation and the exchange of experiences between the university and the technical operator. These laboratories include the ARTS Soil Analysis Laboratory, Regional workshop of Saharan techniques, the LECT Technical Studies and Controls Laboratory and the LAMCO Building Materials analysis laboratory [26–28].

As for the aggregate materials used in these concrete structures, in addition to the sand dunes which were under study, the aggregates used locally come from quarries (Ouainna, Koussane, Cherouine, etc.), with two classes of CPJ cement. 42.5 and CRS 42.5.

In **Figure 8** we apply the hypothesis of fractal analysis and show through it an example of the granular mixture with its components, which is dedicated to the first concrete project, and through it we give a typical idea of granular mixtures applied in the field, giving us a clear picture of the conversion of the granular distribution into a fractal distribution from which we derive the fractal dimension of the concrete mixture, which is DF = 2.66 with a correlation coefficient of R2 = 0.99. This granular mixture used, contains four granular classes, which are 03 classes of gravel and one of dune sand in addition to the cement class, which we have considered as a granular class in the dry concrete mix.

The variable component in our approved concretes is the variety of dune sands used, and we present in **Table 3** below a summary of the identification they concrete used through their dry granular mixtures used. The fractal dimension of concretes used in executive projects on site and not limited to laboratory research only. We draw attention to a necessary parameter, namely that we have taken into account the effect of cement as a granular material which participates in the

#### **Figure 8.**

*Transformation of a grain size curve of the granular mixture of Oued zine to a fractal line (mixture 01) a) particle size curves, b) fractal line.*

granular mixture by filling the pores with particles, while maintaining its main role in concrete, which is the main binder.

We have presented the values the fractal dimension of the cement used. Since we only used three classes of cement in the concrete compositions listed in **Table 2**, their values the fractal dimension of these classes, respectively, are as follows:


This is in accordance with what is indicated in the three cement classes mentioned in **Table 3**.

But it seems very clear that the difference in the values the fractal dimension of the granular concrete mixtures is due to all the different granular classes used in the concrete, which have shown their effect on the granular distribution in the granular mixture. The smallest value of the fractal dimension of concrete is DFb = 2.61 and the highest value obtained from the fractal dimension of concrete is DFb = 2.87. This confirms the previous results of researcher Chouicha [2], which indicates that the optimal value of the fractal dimension does not exceed the value 3.
