*2.1. Materials*

A total of six cylinders that were 45.2 mm in diameter 50 mm in height were manufactured. Three of them were of plain high-performance concrete (PC), and the rest were steel fiber-reinforced high-performance concrete (SFRC). The mixing proportions by weight, in both cases, were: 1:2.00:0.015:0.31:0.035 (cement:fine aggregate:nanosilica:water:superplasticizer). The fiber-reinforced concrete was reinforced with 7.8 kg/m<sup>3</sup> of steel fibers Dramix OL 8/.16 (BEKAERT, Kortrijk, Belgium), which means that concrete had a fiber volume fraction of 0.1%. Fibers were 8 mm in length and 0.16 mm in diameter (aspect ratio 50). According to the technical information provided by the supplier, their tensile strength was 3000 MPa, and their modulus of elasticity was 200 GPa. The nanosilica used was MasterRoc MS 685 (BASF, Ludwigshafen am Rhein, Germany). The superplasticizer used was Glenium 52 (BASF, Ludwigshafen am Rhein, Germany). Siliceous aggregate was used, with a nominal maximum aggregate size of 4 mm. Portland cement with a high initial strength of CEM I 52.5 R was used.

Additionally, two prisms that were 40 × 40 × 160 mm were manufactured; one per mixture. A total of three cubes with 40-mm edges were obtained from each prism, and they were tested under compression in order to characterize the compression strength (according to EN 196-1:2016). The concrete compressive strength fc' was 68.9 MPa with a standard deviation of 1.9 MPa.

#### *2.2. Specimen Manufacturing Process*

The six cylinders above mentioned were cast in the same number of Polyvinyl chloride (PVC) molds with a 45.2-mm inner diameter, 50-mm outer diameter, and 50-mm height. At the bottom of each pipe, a PVC disc with a 60-mm diameter and 3-mm thickness was welded, in order to ensure a watertight joint (Figure 1). The concrete was built using a cement mortar mixer, and the manufacturing process followed the standard EN 196-1:2016 [44]. The molds were filled in two parts using a small aluminum scoop to form the specimens without applying vibration. However, some small punches were applied on the side of the molds, once it was filled with mortar, to help the mortar expel the entrapped air. The upper surface was smoothed with a trowel. Once all of the specimens were cast, they were kept in a moisture curing room, where they remained at 20 ◦C and 100% humidity.

**Figure 1.** Mold and specimen.

## *2.3. Scanning Process*

During the first week, a total of five scans were performed of each specimen, belonging to the following ages: one day, two days, three days, four days, and seven days. The CT scan used was a GE Phoenix v|tome|x device (General Electric, Boston, MA, USA), belonging to the 'Centro Nacional de Investigación sobre la Evolución Humana (CENIEH)', in Burgos, Spain. It was equipped with a tube of 300 kV/500 W. This facility emits a cone ray, which is received by an array of detectors. Thereby, the scanning process is fast, and highly accurate scans are produced of equal resolution in the X, Y, and Z axes. The rotation step around the Z-axis was 0.5◦, so 720 shots were carried out on each specimen. The CT scan has a post-processing software that provides flat pictures of 2048 × 2048 pixels. Thus, for a section of 45.2-mm diameter, the equipment provides a horizontal resolution of 25 × 25 μm2. The vertical distance between the cutting planes was fixed at 25 μm, so the CT scan produced 2000 pictures per specimen, such as the ones shown in Figures 2 and 3. The software assigns a grey level to each voxel (volumetric pixel), varying from zero to 255, where zero means black, and 255 means white, depending on the current density of the matter. Light grey voxels correspond to more dense points and dark grey voxels correspond to less dense points, i.e., pores. The final result of the CT scan is a matrix including X, Y, and Z coordinates of the voxel center of gravity and a number, from zero to 255, regarding the density. The total number of voxels in a specimen is approximately 4.3 × 109. The average time of scanning is around 1 h for each specimen, including the post-processing process. A more detailed explanation of the CT scan technology and the scanning process can be found in [40–45].

**Figure 2.** Slices belonging to plain concrete at different ages.

**Figure 3.** Slices belonging to steel fiber-reinforced concrete at different ages.

Next, the digital image processing (DIP) software AVIZO (FEI Visualization Sciences Group, Hillsboro, OR, USA) was used to identify and isolate each individual void inside the specimen. First, the software identified the voxels belonging to voids, which are the ones showing a grey color below a threshold. In this case, once the histogram of grey distribution was studied, a threshold of 65 was considered (Figure 4).

**Figure 4.** Histograms of grey scale.

Histograms revealed that the images have a grea<sup>t</sup> amount of dark-grey voxels. Most of them belonged to the empty space placed outside the mold. So, the next step was to delete all the voxels placed outside the inner face of the mold, because they did not belong to the concrete specimen. Moreover, the histograms of Figure 4 are not valid to obtain the percentage of voids in the specimen.

Then, all the voxels in contact were merged, since they belong to the same void. The software identified and isolated the different voids. The final result of the scanning was a dot matrix containing the Cartesian coordinates X, Y, and Z of the center of gravity of each individual void. Figures 5 and 6 shows the view of one specimen of each mixture along the timeline.

**Figure 5.** Three-dimensional (3D) views of the voids belonging to plain concrete at different ages. Age increases from **left** to **right**.

**Figure 6.** 3D views of the voids belonging to steel fiber-reinforced concrete at different ages. Age increases from **left** to **right**.

Moreover, in the case of SFRC, the fiber distribution and orientation were obtained (Figure 7). In this case, the fibers did not move over time.

**Figure 7.** 3D view of the fibers belonging to steel fiber-reinforced concrete.

It can be noticed that a relevant part of the big pores was placed in the region that came in contact with the mold. This is because of the following: first, the concrete showed a wall effect, which led to a greater percentage of the smaller components of the cement paste (filler, cement, and water) in the lateral border. Second, the shrinkage of concrete resulted in a gap between the concrete specimen and molds. This space is initially filled with water and later with air, which can initially be understood as voids, although they cannot be considered 'conventional' voids.

In order to prevent the distortion on the results that can be caused by the voids located in the lateral border of the cylinders, because of the reasons mentioned above, this lateral area was discarded. In particular, the whole cylinder was not studied; instead, only the inner portion of the cylinder was studied, i.e., a cylinder with a diameter that was 90% of the real diameter of the cylinder, i.e., 40.7 mm and 90% of the whole height, i.e., 50 mm (Figure 8).

**Figure 8.** Portion of the concrete to be studied.

In this work, voids with less than three voxels in the largest direction (i.e., 75-μm length, approximately) have been discarded because they are too small, and the CT scan does not provide enough sharpness to clearly identify them. Additionally, pores larger than 10 mm in the largest direction have been discarded, since they are non-representative pores. The results shown in this paper are the average values of the three specimens.

#### **3. Results and Discussion**

Using the naked eye, it is not possible to detect significant differences between the specimens and mixtures, nor the evolution of the specimens with time. Instead, digital image processing (DIP) software needs to be used in combination with homemade routines to deeply analyze the data and extract relevant information. Next, this in-depth analysis is shown, and some interesting conclusions are exposed. The values that are presented correspond to the average of the three specimens belonging to the same mixture.

#### *3.1. Total Volume of Voids and Porosity*

The first studied parameter is the total volume of the voids and the porosity; this last parameter is defined as the ratio between the volume of voids and the volume of the specimen.

Figure 9 shows the variation of the porosity with the age of concrete in the different mixtures.

**Figure 9.** Variation of the porosity with the age of concrete.

Figure 9 shows some interesting conclusions. The first and most striking conclusion is that the porosity is greater in steel fiber-reinforced concrete (SFRC) than in plain concrete (PC). It is concluded that the fibers provoke an increase of the content of entrained air. It is known that the addition of steel fibers to the concrete mixture results in a modification of the properties of fresh concrete, which includes its viscosity, consistency, and porosity, among other properties. To avoid this, usually the concrete mix is corrected a bit in order to mitigate these effects. However, the aim of this work is to analyze how the addition of fibers modifies the evolution of porosity over time, during the first curing week, in the same concrete matrix.

The mixture used in this research is very fluid and, in both cases, a low porosity is observed. This result agrees with the ones obtained in other research, where it is demonstrated that fibers reduce the flowability of the mixture [46,47], hindering the removal of entrained air, and leading to a greater porosity.

Regarding the variation of porosity with time, it can be noticed that SFRC specimens show an increase of the porosity along a seven-day timeline. This is a damped process, since the variation is more intense during the first days, and it decreases with time. In the case of PC, the porosity shows a slight decrease over time.

The porosity of concrete is a dynamic phenomenon and two opposite forces are acting on it. First, the curing process is a water-consuming process. At the beginning of this process, most of the voids are full of water, and the CT scan does not recognize them as voids, since they are not air voids. Over time, because of the hydration process, water is reacting with cement grains to create hydration products. Progressively, water is being consumed and the space is occupied by the air, creating internal voids. The consequence is a progressive increase of the porosity in concrete.

Second, the air entrained inside the pores tends to move up and leave the concrete specimen. In addition, this space tends to be occupied by the cement paste when a collapse of the voids occurs. This second phenomenon implies a progressive decrease of the porosity in concrete. From the macroscopic point of view, this phenomenon is called plastic settlement or initial plastic shrinkage.

The SFRC showed a concrete matrix more consistent than that of the PC because of the presence of fiber. Consequently, in the case of SFRC, the first phenomenon prevails over the second one, so the final result is an overall progressive increase of the concrete's porosity. On the contrary, in the case of PC, both phenomena are balanced, and the final result is that the porosity shows a very slight variation [48].

#### *3.2. Variation of the Total Porosity along the Depth*

Using the Z coordinate of the center of gravity of each void, it is possible to know the variation of the porosity along the depth. Figures 10 and 11 show the variation of the porosity along the depth with the age of concrete in both mixtures. In all cases, the depth is shown in relative terms, i.e., varying from zero to one, where zero belongs to the exposed surface of the specimens, and one belongs to the other end of the specimens.

Figures 10 and 11 show some interesting results. First, it can be noticed that a progressive increase of the porosity with the depth was observed in all cases. This is especially clear in the case of SFRC, but this tendency is not so clear in the case of PC. However, in both cases, the lowest porosity was observed in the first two-tenths of the specimens.

Second, SFRC showed a progressive increase of the porosity with time for all the depths, except for the 10% upper depth, where a slight decrease was observed. In the case of PC, a weak tendency of the porosity with time was observed; if anything, a slight decrease was also observed with time.

**Figure 10.** Variation of the porosity in steel fiber-reinforced high-performance concrete (SFRC) according to the depth and age.

**Figure 11.** Variation of the porosity in plain concrete (PC) according to the depth and age.

Using the data of the porosity with time, the best fitting line was obtained at each depth, and its slope was extracted. This represents the average value of the porosity variation speed during the first seven days. Figure 12 shows the variation of this parameter along the depth for both mixtures.

**Figure 12.** Variation of the porosity variation speed along the depth.

Figure 12 reveals that SFRC specimens showed a progressive increase of the porosity with time for almost all of the depths, except for the upper tenth, where a slight decrease was observed. In the case of PC, a slight decrease was observed for almost all the depths.

Again, the two different mechanisms regarding the void generation can be used to explain the behavior shown in Figure 12. Inside the specimen, when it is not close to the exposed surface, the loss of water is mainly due to hydration. In this case, the progressive reduction of free water, and in consequence, the progressive appearance of voids is strongly related to the creation of the cement matrix. In the case of SFRC, fibers provide extra stiffness to the cement matrix, which prevent the collapse of the voids. On the contrary, the cement matrix of PC specimens is less stiff, and the collapse of the voids happens more easily.

On the other side, close to the exposed surface, the loss of water is mainly due to evaporation, and the risk of a collapsing void increases. In this case, since the specimens are kept in a moisture curing room, the evaporation is almost null, and in consequence, this phenomenon can be observed only really close to the exposed surface.

In the case of SFRC, the average porosity variation speed is approximately 0.02%/day. On the contrary, in the case of PC, the average porosity variation speed is approximately −0.01%/day.

In all cases, the specimens show a slight different behavior around their middle height, i.e., at a relative depth of approximately 0.5. This is because the molds were filled in twice, and a horizontal joint appeared.

#### *3.3. Porosity and Porosimetric Curves*

Using the DIP software, it is possible to know the exact geometry of each void. At this point, it is interesting to obtain the volume of each void and its length, which is defined as the maximum distance between two voxels belonging to the same void.

Using this information, it is possible to obtain the pore volume curves and the porosimetric curves. A pore volume curve is defined as the graph correlating the length of the void and the total pore volume of the voids with a length equal to or less than this one. On the other hand, the porosimetric curve is defined as the graph correlating the length of the void and the relative pore volume of the voids with a length equal to or less than this one.

Figures 13 and 14 show the pore volume curves of the mixtures at the different ages. On the other side, Figures 15 and 16 show the porosimetric curves of the mixtures at the different ages. In all cases, the maximum length is limited to 10 mm, since larger voids are residual.

**Figure 13.** Pore volume curves of SFRC.

**Figure 14.** Pore volume curves of PC.

**Figure 15.** Porosimetric curves of SFRC.

**Figure 16.** Porosimetric curves of PC.

Figures 13 and 14 reveal that, in general, the pore volume curves show small variations with the age of concrete. In the case of SFRC, the curves belonging to the first days are placed below the ones belonging to the last days, being, in general, homothetic. This means that a progressive increase of the pore volume occurs with time, and it happens for all of the pore sizes.

In the case of PC, the curves belonging to the first days are placed over the ones belonging to the last days, being, in general, homothetic again. This means that a progressive decrease of the pore volume occurs with time, and it also happens for all of the pore sizes.

Figure 15 shows that, in general, the porosimetric curves belonging to the first days are placed over the ones belonging to the last days. This means that SFRC tends to increase the pore size with time.

In the case of PC (Figure 16), this tendency is not so clear. This means that PC tends to keep the pore size constant with time.

An interesting parameter that can be obtained through the porosimetric curves is the nominal maximum pore size (NMPS), which can be defined, similarly to the well-known nominal maximum aggregate size (NMAS), as the pore length corresponding to a cumulative pore volume of 90%. This is a representative value of the pore size distribution, since the remaining 10% of the pore volume belongs to an extremely low number of individual pores (less than 0.05% of the pores, on average). Figure 17 show the variation of the NMPS in both mixtures with time.

Figure 17 reveals that the NMPS is greater in SFRC than in PC at all ages. This means that SFRC not only shows a greater pore volume (as can be observed in Figure 9), but also that the pores are bigger. In the case of SFRC, there is a progressive increase of the NMPS, which agrees with there being a progressive increase of the pore size with the age of concrete (Figure 15). On the contrary, in the case of PC, the curve shows a horizontal tendency, which means that there is not a variation (neither increase nor decrease) of the NMPS.

**Figure 17.** Variation of the nominal maximum pore size (NMPS) with the age.

Both the pore volume curves (Figures 13 and 14) and porosimetric curves (Figures 15 and 16) reveal that, in the case of SFRC, the curves shows an initial part substantially straight up to a pore length of approximately 3 mm. This means that below a 3-mm pore length, there is a substantially uniform volume distribution. Beyond this critical pore length, the slope of the curves decreases drastically, becoming horizontal very quickly. The PC curves show a similar behavior, although the critical pore length can be established at 1 mm.

SFRC shows porosimetric curves flatter than the ones belonging to PC. This can be explained in terms of the stiffness of the cement matrix. In the case of SFRC, fibers provide additional stiffness to the cement paste, and they prevent the voids from collapsing. The greater the void, the greater the instability of the concrete. As a consequence, SFRC is able to withstand a greater percentage of larger voids than PC.

#### *3.4. Variation of the Porosity and Porosimetric Curves along the Depth*

Voids are not uniformly distributed along the depth. The distance to the exposed surface, where the loss of water occurs, has a strong influence on the pore size distribution. Next, the porosimetric curves of all the days at the different depths are shown (Figures 18 and 19).

In the case of SFRC (Figure 18), it can be observed that in the first two tenths of the depth, there is an intense variation of the porosity with the age of concrete. This is because of the water interchange with the environment (mainly evaporation). This activity starts to decrease beyond day four, showing almost identical graphs beyond this day.

Something similar can be observed at the middle height of the specimens. This is because the molds were filled in two parts, creating a small horizontal joint in this area.

**Figure 18.** Porosimetric curves of SFRC at different ages and depths.

**Figure 19.** Porosimetric curves of PC at different ages and depths.

Similarly to what happens in Figure 15, in the case of SFRC, all the curves are substantially bilinear. The first part is approximately a straight line with a big slope up to a critical pore length. Beyond

this value, the slope of the curve decreases drastically. In all cases, lines belonging to the first part of the curve show a similar slope. However, the critical pore length varies with the depth, from 2 to 3 mm. This means that the percentage of greater pores decreases with the depth. It can be explained in terms of the hydrostatic pressure of fresh concrete, which increases with the depth. There is an inverse relation between the hydrostatic pressure of fresh concrete and the maximum stable void volume. Voids smaller than this critical volume are stable, but voids greater than that tend to collapse, becoming several smaller voids.

In the case of PC, a relevant temporary variation around the middle height of the specimens is observed. However, this phenomenon is not observed in the upper tenths. Except for the first day (where voids are full of free water and they are not detected by a CT scan), the tendency is toward a progressive reduction of the greater pores.

In this case, almost all of the curves are substantially straight. The slope of the curve is significantly greater than that in the case of SFRC, which is directly related to the viscosity and stiffness of the cement paste [46,47]. In this case, the lower stiffness of the cement paste of the PC causes the large pores to be much more unstable than in the case of SFRC, and they tend to collapse, becoming several smaller voids.

#### *3.5. Shape Factor of the Voids*

As explained before, the data provided by the CT scan and the DIP software lead us to know the volume and the length of each void. Using these two data, it is possible to obtain the shape factor of each pore, which is defined as the quotient between the volume of the void and the volume of the sphere circumscribed to the void, as shown in Equation (1) [49]:

$$SF = \frac{V\_p}{\frac{1}{6} \cdot \pi \cdot L\_p^{\ast 3}} \tag{1}$$

where *Vp* is the pore volume and *Lp* is the pore length.

Figures 20 and 21 show the histograms of the shape factor of the different mixtures.

**Figure 20.** Histogram of the shape factor of SFRC.

**Figure 21.** Histogram of the shape factor of PC.

Figures 20 and 21 reveal interesting results. First, it can be observed that in both cases, the voids are far from the spheres since in all of the cases, the shape factor is far from one.

SFRC shows smaller shape factors than PC, showing a mode value between 0.10–0.15, as well as more than 90% of the voids showing a shape factor below 0.30.

PC shows slightly greater shape factors, with a mode value between 0.15–0.25, as well as more than 90% of the voids showing a shape factor below 0.40.

Pores are the less stiff components of the cement paste, and they tend to occupy the space that is not occupied by the rest of the components of the cement paste. These 'free' spaces do not show spherical shapes; instead, they are flaky or elongated. In the case of SFRC, these spaces become even more elongated because of the fibers. Again, fibers modify the pore morphology.

The shape factor shows relevant variations along the depth. Figures 22 and 23 show the histograms of the shape factor at different ages of concrete and at different depths for both SFRC and PC.

**Figure 22.** *Cont*.

**Figure 23.** *Cont*.

**Figure 23.** Histograms of the shape factors of PC at different depths and ages.

Figures 22 and 23 reveal that in general, the shape of the histograms remains constant with the age of the concrete, which demonstrates that the shape of the voids does not vary with time.

However, a substantial variation of the shape of the histograms at different depths is observed. When the depth increases, the histograms moves toward the right. This phenomenon can be observed on all the days, although it is more intense at the earliest ages. This is because the increase of the hydrostatic pressure of the fresh concrete promotes more spherical voids, which are more stable under higher hydrostatic pressure values.

This variation cannot be clearly shown in the case of PC because of the collapse of the voids due to the lower stiffness of the cement paste, which redraws the shape of the voids. This can be clearly observed on day four, when a substantial increase of the elongated voids was observed.
