**5. Transformation of grain size curves using software**

**Table 1** shows details of how to transform a grain size curve into a fractal line for a single type of cement, and analytically we draw the fractal line of the cumulative grain sizes according to the grain dimensions with a scale logarithmic. But the granular mixture is made up of several different constituents, which makes it somewhat difficult to calculate the different arithmetic operations involved in fractal analysis.

The different required steps on which the proposed software is based can be addressed through two main sections.

First: enter the necessary data relating to each component of the mixture, namely the granular extent, the density and the standardized dimensions of the sieves, as well as the experimental data for the particle size analysis of each granular class.

Second: this software would draw the particle size curve of the granular mixture composed of several granular constituents, then display the transformed fractal line, and plot the linear fit and give its linear relationship followed by the correlation coefficient R2.

We proposed to name the program GranuFract in relation to the transformation of the particle size curve into a fractal line.

**Figure 9** shows the image designed in the GranuFract software to capture basic information (density, cumulative sieve, and dimensions of sieve openings) to obtain the fractal distribution.

Concerning the transformation of the particle size curves to a fractal line, we adopted the method of fractal analysis carried out in the previous works [1, 29–31], as shown in **Figure 8**.

The GranuFract program allows us to easily determine the granular distribution of granular mixtures. This also helps us in the possibility of processing discontinu ous grain size curves, that is to say by knowing the coordinates of each grain. It also helps to infer the variance of the coordinates to correct for items that have missing items (**Figure 10**).

*Application of a Granular Model to Identify the Particle Size of the Granular Mixtures… DOI: http://dx.doi.org/10.5772/intechopen.99969*

#### **Figure 9.**

*Main window for entering basic information in the GranuFract software.*

#### **Figure 10.**

*Application of the transformation of a particle size distribution to a fractal distribution [1]. (a) Fractal line of the mixture. (b) Presentation of their coordinates.*
