*5.2. Aggregate*

The aggregate content was determined using two methods: in laboratory tests and on the basis of plain optical scanning. General comments on the possibilities of the research techniques used are very similar to those given in Section 5.1. The surface scanning combined with image analysis gives the possibility of obtaining a virtually continuous function of the aggregate content distribution, as well as other morphology measures, characterizing, e.g., grain size (Figures 15 and 16). The laboratory method allowed determining the average values of aggregate content in four layers of the element wall. As in the case of pore analysis, the results of optical scanning had to be averaged within the four layers of equal thickness. Averaged values are presented in blue lines in the graph in Figure 16. In addition, to enable comparison of results from both methods, the volume fraction of aggregate was converted into its content as follows:

$$\mathcal{L}\_{a\%} = \rho\_{a\%} \phi\_{a\%} \tag{11}$$

where *Cagg* is the aggregate content (kg/m3), φ*agg* is the volume of aggregate, and ρ*agg* is the specific density of aggregate.

To apply Equation (11), it is necessary to know the specific density of aggregate ρ*agg* in individual layers. Unfortunately, this value was not explicitly determined as part of the research. Therefore, two approaches were taken to estimate this value. In the first approach (\*), a constant value equal to the average density of the aggregate used for the mixture was assumed, i.e., ρ*agg* = 2710 kg/m3; thus, its segregation (variability in wall thickness) due to centrifugation was not taken into account. In the second approach (\*\*), it was assumed that the specific density of all solid particles is a su fficiently accurate estimation of aggregate density, i.e., ρ*agg* ≈ ρ*cr*. This approach takes into account the variability due to centrifugation, and the estimation error should not be large, because aggregate represents the vast majority of the weight of the solids in the concrete mix (almost 80%); moreover, cement density is similar to aggregate density. Finally, regardless of the adopted estimation, good compliance of laboratory test results and imaging was obtained (Table 6). Relative di fferences in the results obtained using di fferent methods did not exceed a few percent, while the values in individual layers di ffered by up to 20%.

**Table 6.** Comparison of results (aggregate content).


While analyzing the results in Table 6, it should be borne in mind that, in the case of imaging, only the aggregate volume fraction φ*agg* was determined intrinsically. Calculation of mass content in this case required additional data, which could be determined from the recipe for the mixture and physical characteristics of its components, or even on the basis of laboratory test results. However, the obtained compliance indicates that the results of both methods are consistent; the aggregate morphology determined from scanning corresponds to the average values of its content from tests based on physicochemical methods. The results of both test methods used can be considered complementary; they can be used together to analyze spun concrete structure. In particular, thanks to the use of known relationships (e.g., Equation (11)), by creating an appropriate correlation, the image analysis can be used to "extend" point information (in layers) to a continuous functional distribution as a function of the wall thickness.

The content of coarse aggregate decreases toward the inner cross-sectional area. The last inner layer is marked by almost zero aggregate content (Figure 16). It is interesting that the aggregate content as a function of the wall thickness is constant in all layers (Figure 16 and Table 6) except for the very inner layer (layer 1). The results of aggregate distribution as a function of the wall thickness of the cross-section confirm the authors' expectations and macroscopic observations, and they are consistent with the literature [9]. The aggregate content determined using both methods approximately corresponds to the amount of aggregate declared in the mixture recipe given by the manufacturer of spun concrete poles (Table 1).

### *5.3. Cement Content*

From the optical scan, the volume fraction of the cement matrix can be determined. Similarly to the analysis of other concrete components, it is possible to assess the variability of the matrix volume fraction as a function of the wall thickness (see Figure 14). The laboratory test determines the average cement content expressed as the mass of cement used per volume unit of hardened concrete. To determine the relationship between these quantities, both of which in fact show the amount of cement, it is necessary to use some additional information. In order to compare the results obtained using di fferent techniques, the content *Ccem* (kg/m3) was referred to, because the requirements for the minimum value of this parameter are provided by the standard [14]. Cement content can be defined as

$$\mathcal{L}\_{\text{ccm}} = \phi\_{\text{mut}} \cdot \left(1 - \phi\_{\mu p, \text{mut}}\right) \cdot \mathbb{C}^\* \tag{12}$$

where φ*mat* is the volume share of cement matrix (including capillary micropores) according to the estimation made on the basis of optical scanning, φμ*p,ma<sup>t</sup>* is the cement matrix microporosity, and *C*\* is the mass of cement used per volume unit of solid parts of hardened cement matrix (including nonevaporable gel water); according to the relationships given in [31], *C*\* = 1473 kg/m<sup>3</sup> was assumed.

In Table 7, a comparison of obtained results is given. Due to the lack of detailed information on the microporosity of the matrix, an upper and lower estimation was made, assuming the following as the limit assumptions: (1) an even distribution of porosity within the matrix and aggregate and (2) full tightness of the aggregate, i.e., that all micropores are located in the cement matrix. The microporosity of the matrix corresponding to such assumptions φμ*p,ma<sup>t</sup>* can be estimated from the following inequalities:

$$\frac{\phi\_{p,tot} - \phi\_{p,m}}{\phi\_{mut} + \phi\_{n\xi\xi}} \le \phi\_{\mu p, mut} \le \frac{\phi\_{p,tot} - \phi\_{p,m}}{\phi\_{mut}} \tag{13}$$

where φ*p,tot* is the total porosity (from the laboratory test), φ*p,m* is the macroporosity (based on scanning, average value in the layer), φ*mat* is the volume fraction of cement matrix, and φ*agg* is the volume fraction of the aggregate.


**Table 7.** Comparison of results (cement content).

The specified ranges in Table 7 are quite wide; however, in terms of quality, cement content is "well rendered", i.e., the smallest values are in the middle layers (No. 2 and 3), and the highest value is in the inner one (Layer 1) (see Figure 20).

**Figure 20.** Estimation of cement content *Ccem* (kg/m3) in particular layers of the element's wall.

The conclusion concerning the applied research methodology is similar to the previous analyses. The results are comparable and consistent; they complement each other. Imaging naturally results in geometrical relationships, i.e., a description of the cement matrix morphology, which is important information from the point of view of determining the effective parameters of concrete as composite using micromechanics tools or the theory of homogenization [21,32–34]. Information on the structure of concrete obtained from laboratory methods is limited to average values of cement content in arbitrarily separated layers. This information directly refers to the practical aspects of design and construction, related, for example, to the formulation of a recipe and control of the composition of concrete mix.

The description of the cement distribution as a function of the wall thickness of the cross-section obtained by means of both methods allows for straightforward qualitative description of this distribution. Optical scanning allowed determining the volume fraction of the cement matrix (Figure 12), with the cement matrix being segmented as a homogeneous component, although in fact it may contain a certain amount of the finest aggregate fraction. However, the laboratory study determined the average cement content expressed as the mass of cement used per volumetric unit of hardened concrete (Table 2). To determine the relationship between these quantities, some additional information was necessary. Due to the lack of detailed data on the microporosity of individual components (aggregate and matrix), a final estimation on the basis of the method of image analysis was made for the lower and upper cement content bounds in individual layers of the element wall (Table 7 and Figure 20). The obtained results show that the cement distribution was relatively constant as a function of the wall thickness, and an increase in its quantity was observed only in the inner layer of the cross-section (2 mm thick) (Figure 14 and Table 7). These research results coincide almost exactly with Marquardt's conclusions [4].

Cement content in individual layers determined by the laboratory method (Table 2) and by the image analysis method (lower estimate, Table 7) was lower than the amount of cement declared in the recipe by the manufacturer of spun concrete poles (Table 1). It can also be stated that, in the outer layer, the amount of cement, as a result of the centrifugation process, was reduced from 400 kg/m<sup>3</sup> (Table 1) to about 308 kg/m<sup>3</sup> (according to the laboratory method, Table 2) and to about 292 kg/m<sup>3</sup> (according to the lower estimation from the image analysis method, Table 7). Due to the durability of power poles made of spun concrete exposed to direct influence of atmospheric factors, described by standard [14] class XC4 (cyclically wet and dry concrete surfaces exposed to contact with water), and for structures located near motorways class XF2 (vertical concrete surfaces exposed to freezing and de-icing agents), the minimum cement content in the outer layer should not be less than 300 kg/m3.

### *5.4. General Remarks*

It was expected that, during concrete centrifugation, air and water would be squeezed out more from the outer, more compressed layers. Approaching the inner surface of the concrete section, less water would be squeezed out. From the inner layer of the concrete section, where the radial

pressure is close to zero, water would not be removed at all. Following laboratory tests, it was observed that the total porosity of the inner layer (No. 3) increases (Table 2) compared to the porosity of other layers. This result confirmed the authors' expectations and previous research [5,7–9], in which it was found that the total porosity of concrete is greater for the inner layers than the outer layers. The other observation made in [7–9] was confirmed using image analysis methods. It was observed (Figure 21) that the pores (mostly in layer No. 3) were usually located next to the edges of large grains of aggregate on its outer side. Furthermore, the cement matrix had distinctly fewer aggregate inclusions in these locations compared to the other ones. Therefore, water and air were blocked there from being moved toward the inside of the cross-section as imposed by the centrifugal forces. Such a picture of the porosity and fine aggregate arrangemen<sup>t</sup> next to large aggregate grains indicates that the speed and spinning time of concrete in the pole were probably incorrectly selected, preventing the escape of excess air and water from the concrete mixture.

**Figure 21.** Arrangement of pores (white), aggregate (gray), and cement matrix (black) in the section of the element wall.

### **6. Summary and Conclusions**

The aim of the article was to compare different methods for determining porosity, as well as cement and aggregate content, in the layered structure of spun concrete. The variability of these parameters considered as a function of the thickness of the concrete wall determines the macroscopic properties such as durability, load capacity, and rigidity of spun concrete poles. The article compares the results obtained using two methodologically different approaches: laboratory determinations based on chemical and/or physical methods and image analysis. In general, mass content per unit volume is obtained in laboratory tests, and the volume fraction of individual concrete components is obtained using image analysis methods. If the specific density of the component under consideration is known, conversion of one quantity to another becomes easy.

The main advantage of the methods based on image analysis is the possibility of obtaining a practically continuous function of the content of the considered concrete components as a function of the wall thickness of a spun pole. In this context, the main limitation of chemical/physical methods is the ability to determine only the average value for a few, arbitrarily separated layers of the concrete wall of a spun pole. In turn, the main limitation of image analysis methods is the pixel/voxel size and image quality, particularly due to sample preparation and image acquisition method.

In terms of concrete porosity, it should be stated that the attempt to validate the results obtained from imaging the structure of concrete using laboratory techniques (determining the composition of hardened concrete on the basis of physical and chemical methods) was only partially successful. The results obtained cannot be directly compared due to the fact that porosities are described on different scales. The methods based on image analysis allowed describing the structural porosity (i.e., macroporosity) of concrete, while the laboratory methods enabled describing total and open porosity (capillary microporosity). Quite importantly, imaging methods give the opportunity to analyze the macropore morphology. In particular, it was possible to visualize the location of air voids in relation to the other concrete components (Figure 21), which may have a direct impact on the assessment of the centrifugation process in terms of centrifugation parameters selection such as speed and time.

In terms of the description of aggregate distribution as a function of the wall thickness of the cross-section, very good compatibility of both methods was obtained. The image analysis method allowed determining the volume fraction of aggregate φ*agg*. Calculation of aggregate mass content per unit volume in this case required additional information about the density of the aggregate, which could be determined either from the recipe for the concrete mixture and the physical characteristics of its components or from laboratory tests. The obtained consistency of the results from both methods shows that the methods are consistent, and the aggregate morphology determined by scanning corresponds to the average values of its content coming from research based on physicochemical methods.

Very good qualitative and quantitative compatibility of both methods in the field of aggregate morphology as a function of the wall thickness of the element was obtained. Thanks to the positive validation of laboratory methods and the method based on image analysis, it can be safely stated that optical scanning is a cheap, relatively fast, and e ffective method of assessing aggregate segregation as a function of the wall thickness of a spun concrete element.

The description of cement distribution as a function of the wall thickness of the element cross-section obtained using both methods allows for straightforward qualitative description of this distribution. However, full validation success was not achieved because the results based on optical scanning allow obtaining quantitative results only after taking into account additional calculations and information from laboratory tests. Thus, in this case, to ge<sup>t</sup> full information about the distribution of cement as a function of the wall thickness of the element, both methods must complement each other. Nevertheless, the information obtained as a result of testing with any of methods used allows assessing the cement content, which determines the requirement for durability of columns made of spun concrete.

An attempt to validate the imaging method with the use of laboratory techniques based on physical and chemical methods showed that optical scanning methods are relatively e ffective, and they can be a significant complement to the research methods used so far. The analyses also showed that there is a further need to conduct research in the area of spun concrete structure, with particular emphasis on the distribution of concrete porosity and cement content as a function of the wall thickness of the ring-shaped cross-section. The research methods presented in the work can be used to improve the production process of poles made of spun concrete as an e ffective tool for testing its structure.

**Author Contributions:** Conceptualization, J.M.; methodology, J.M. and M.S.; software, M.S.; validation, J.M. and M.S.; formal analysis, J.M. and M.S.; investigation, J.M. and M.S.; resources, J.M. and M.S.; data curation, J.M. and M.S.; writing—original draft preparation, J.M. and M.S.; writing—review and editing, J.M. and M.S.; visualization, J.M. and M.S.; supervision, J.M. and M.S.; project administration, J.M. and M.S.; funding acquisition, J.M. and M.S. All authors read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.
