**3.1 Dimensioning of fractal fracture on a concrete slab**

In the study of fractures, from a fractal point of view, the previously specified slab was used, **Figure 1**, on which loads were applied. Propagation of the crack depends on important factors, such as stress and intensity. It also depends on the curing of concrete and the resistance of such structural elements. To carry out such dimensioning of the slab on which loads were applied, a crack was chosen among all cracks

*Dimensioning of Fractal Fracture on a Concrete Slab DOI: http://dx.doi.org/10.5772/intechopen.105673*

#### **Figure 3.**

*(a) Vectorization of the (b) image with fractal axis and 4 fractal radius increases statuses of the fracture; (c), (d), (e), and (f) (Statuses 0, 1, 2, and 3).*

created and vectorization of the outline of the chosen fracture was carried out, **Figure 3a**, with CorelDraw 4X to obtain the axis of the fracture.

From here, a set of parts of that axis was sectioned and chosen to create the generator, which will be known as the starting point of the fractal. In this case, three strokes were chosen, which are constantly repeated throughout the fracture, **Figure 3a** and **b**. These strokes are repeated at a lower scale than the original one, within each separate section, called status. The main axis of the fracture is *status 0*, following scale or lower repetition, *status 1*, and so on, repeatedly, up to *status n*. In this study, we only used up to *status 3* of the fracture, since the scale with higher status becomes imperceptible. These repetitions at a lower scale were made with AutoCAD software.

Upon obtaining *status 0*, certain symmetry and proportionality were observed in the fracture. It showed a 70° tilt degree and a proportional radius increment in circles as the length of the fracture increased, **Figure 4**. Upon meshing with the vertical and horizontal axes, regarding the tilt of the radius increasing angle, it was observed that *Status 0* matched with the beginning and the end of the vertical axis and that the increments in radius upon writing *X* against *Y* showed almost the same proportion, **Figure 4**. After this process, the fractal dimension for each status was calculated using five of the well-known theoretical methods: (i) box dimension, (ii) perimeter-area dimension, (iii) information dimension, (iv) mass dimension, and (v) ruler dimension. The fundamental explanation for why all these methods were used for the calculation of the fractal dimension of the fractured slab is that each method provides different results for the fractal dimension of the fracture, and it has been wanted to manifest that the values obtained are very similar but slightly different. To estimate the fractal dimension, a fractal dimension calculator should be used, and this is carried out through the algorithm *box-counting* or *box-counting dimension*.

*Failure Analysis – Structural Health Monitoring of Structure and Infrastructure Components*
