*4.1. Theoretical Assumptions*

Research on the morphology of the spun concrete microstructure was divided into two parts due to the method of image acquisition: flat optical scanning and three-dimensional (3D) imaging in X-ray microcomputed tomography (μCT). Regardless of the method of obtaining the image, the analysis is aimed at characterizing selected morphology measures of the considered microstructure components: pores, aggregate, and cement matrix. In both cases, the following stages of research can be distinguished:


In the conducted analyses, it was assumed that, due to the axial symmetry of the spun elements, the properties of the obtained material do not depend on the angular coordinate. Thus, at a fixed pole height (i.e., for a fixed coordinate value along the axis of rotation of the element), the parameters of the microstructure change only along the radius. The identified values were, therefore, referred to coordinate *R* in the radial direction (perpendicular to the axis of rotation of the spun concrete element). Coordinate *R* increases from *R* = 0 on the outer edge of the element toward the center of the cross-section in accordance with Figure 3.

The mathematical morphology methods were used to describe the distribution of concrete components (i.e., macropores, cement matrix, and aggregate) over the wall of the spun column. The theoretical foundations for these tools, based mainly on works [21–23], were described in more detail in the previous work of the authors [12].

On the basis of the analyses carried out, selected morphological statistical measures were determined: component volume fraction and so-called local thickness. The average volume fraction of the selected component is defined as the number of pixels in the component divided by the total number of pixels (in a selected area of the image). To describe the variability of the volume of the component as a function of *R*, a series of image subareas was selected, which are narrow circumferential bands of the concrete pole wall. The volume fraction φ(*R*) (dependent on coordinate *R*) is calculated in the band with the center line corresponding to coordinate *R* and the width Δ *R*. The method of selecting the aforementioned band is shown in Figure 4a. It is worth mentioning that, in the case of cross-section analysis as in [12], the shape of the band is annular (see Figure 4b).

**Figure 4.** Selection of peripheral band: (**a**) in longitudinal section; (**b**) in cross-section [12].

Local structure thickness is a scalar field, defined only in the area occupied by the considered constituent. The procedure for determining the local element thickness generally consists of filling the area occupied by the considered constituent with circles of the largest possible diameter [24]. Then, the thickness of the element at a given point *x* is defined as the largest diameter of the circle, which entirely fits within the constituent under consideration and, at the same time, contains point *x* in its interior. This is schematically illustrated in Figure 5.

**Figure 5.** Element thickness at point *x* as the maximum diameter of the inscribed circle.

The calculations are performed first for the entire image, resulting in a map of the local thickness of the constituent under consideration. Then, to describe the variation of local thickness as a function of the wall thickness of the concrete element (i.e., relative to coordinate *R*), a procedure analogous to that for the volume fraction was used; specifically, the average in the appropriate circumferential band was determined as in Figure 4.

### *4.2. Two-Dimensional (2D) Imaging in an Optical Scanner*

The research procedure used is based on the procedure given in [12]. It consists of the following consecutive actions:


Staining the pores first and then the matrix (with a different color), after etching it with acid, allowed quantifying the morphology of the following components: air voids (macro-pores), cement matrix, and aggregate. Thus, the scope of analyses was expanded compared to the analysis presented

in [12], where only aggregate morphology was described. To perform calculations as a part of the analysis of the morphology of individual components, the author's own procedure written in the Mathematica program was used. Selected image transformations were carried out in GIMP, ImageJ (Fiji distribution), and CTAn programs.

The first stage of sample preparation for scanning was to level the cut surface in such a way that it was as flat, even, and smooth as possible. For this purpose, a Struers LaboPol 5 grinding and polishing machine with an MD Piano grinding disc was used. The result of the optical scan of the surface of the test sample prepared in this way (before staining) is shown in Figure 6. The scan was performed using a standard o ffice scanner with a resolution of 600 dpi, which, calculated using the pixel size, gives 42.33 μm/pix.

The pores were stained green by applying acrylic ink to the entire surface of the sample, which was then ground again. After this procedure, the sample was rescanned Figure 7.

Then, after etching the matrix with hydrochloric acid, it was stained yellow (Figure 8). The method of staining was analogous to that for pores; only the ink color changed.

To enable comparison of scans at individual stages of staining, all images were superimposed and matched to each other by appropriate rotation and shift. The pictures presented below show already "matching" images, for which the dimensions in pixels are the same and the position of the analyzed sample is the same. To exclude the background from the analysis, as well as inadequately polished fragments, edges jagged during cutting, and reinforcing bars, further analysis focused on the area of the image showing the correctly prepared surface of the concrete sample. This area is called the region of interest (ROI). The complement of ROI was not included in the analysis. For this part of the image, a white mask was applied. The image of the stained sample, limited by the aforementioned mask to ROI, is presented in Figure 9. By using ROI, most of the polishing marks, which were stained as pores, were eliminated from the analysis.

**Figure 6.** Raw scan of the tested sample.
