**6. Validation of software results**

It is necessary to verify the data obtained from the program GranuFract, we have adopted ... the necessary procedures to compare the results that they obtained from the proposed software GranuFract and those that they obtained in the usual way, that is ie a graphical analysis using one of the mathematical programs "Origlab" and after a series of calculations The repeated values for each component of the granular mixture shown in **Figure 11 (a)** and **(b)** [1] we give the adopted values of the fractal dimension resulting from the two methods, they obtained values with an ideal correlation coefficient, and the standard deviation is 0.05. The values obtained by verification are:

According to 'GranuFract': DF = 2.82; R<sup>2</sup> = 0.99.

According to 'Originlab': DF = 2.83; R2 = 0.99.

We draw the attention of those interested in such a study represented in the use of mathematical models to find solutions to the framework of the search for

**Figure 11.**

*Example of the validation of the transformation of a particle size curve to a fractal line [1]. a) Fractal line by GranuFract software, b) fractal line by originlab software.*

concrete materials, that our main objective of this work is to highlight what we have achieved through to laboratory research and modeling in the application of the fractal analysis represented in the fractal dimension parameter and its positive results which have helped us to determine the granular distribution of the granular components of concrete through the granular mixture - the fractal line.

As for the proposed program, we look forward to improving and generalizing it by expanding a database that depends on a lot of experimental data for different components, including mineral additives and adjuvants, through which we hope to achieve a program to complete which will allow us to generalize it to all types of concrete, including innovative concrete.
