# Investigating the Poisson Ratio of 3D Printed Concrete
## 3 Results
### Void Topology  
The results from the \(\mu\)-CT scans of the four specimen configurations were plotted comparing the void diameter to the void length in each Cartesian direction. The void diameter refers to the largest dimension present in the void, while the void length refers to the longest measurement for each of the x, y and z Cartesian directions. The x-direction denotes the printing direction, y the lateral dimension, and z the vertical dimension or height of the void. Linear regression was applied to the data as a means of distinguishing between averages toward deriving conclusions. These graphs are depicted in Figures 9-12 for all the specimen configurations.  
Figure 8: Sphericity and compactness means of all specimen groups obtained from \(\mu\)-CT scanning. Error bars indicate standard deviation. Values are unitless; however, a value of 1 equals an ideal spherical pore space.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Specimen** & & & & & \\
**Characteristics** & **Unit** & **CAST-CM** & **CAST-3 DPC** & **3 DPCOIB** & **3 DPCOIT** \\ \hline Voxel & Voxel & 19,188,360 & 21,931,200 & 59,887,344 & 35,192,596 \\ Proj. area (yz) & mm\({}^{2}\) & 960.37 & 2166.47 & 3375.27 & 2873.17 \\ Volume & mm\({}^{3}\) & 204.31 & 233.52 & 637.68 & 374.73 \\ Proj. area (xz) & mm\({}^{2}\) & 1015.22 & 2339.31 & 3878.10 & 2771.90 \\ Surface area & mm\({}^{2}\) & 6028.75 & 12,937.23 & 23,833.75 & 17,764.57 \\ Proj. area (xy) & mm\({}^{2}\) & 1080.25 & 2362.37 & 4502.17 & 3350.73 \\ \hline Material volume & mm\({}^{3}\) & 12,495.13 & 12,425.50 & 10,599.98 & 13,780.40 \\ Defect volume & mm\({}^{3}\) & 204.32 & 233.52 & 637.68 & 374.73 \\ Defect ratio/porosity & \% & 1.61 & 1.84 & 5.67 & 2.65 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Porosity characteristics of all specimen groups obtained from \(\mu\)-CT scanning.  
Figure 10: CAST-3 DCP void topology from \(\mu\)-CT scanning. The coefficients of determination (R\({}^{2}\)) for x, y and z linear regression are 0.84, 0.85 and 0.83, respectively.  
Figure 9: CAST-CM void topology from \(\mu\)-CT scanning. The coefficients of determination (R\({}^{2}\)) for x, y and z linear regression are 0.91, 0.92 and 0.87, respectively.  
Table 6 gives a summary of the analysed data presented in Figures 9-12. It is evident from the normalised regression model gradients, as well as the normalised variances, that the CAST-CM specimen has the most spherical void topology. The CAST-3 DCP specimen's voids are slightly narrower than those of CAST-CM due to the pumping and extrusion  
Figure 11: 3 DCPOIB void topology from \(\mu\)-CT scanning. The coefficients of determination (R\({}^{2}\)) for x, y and z linear regression are 0.9, 0.89 and 0.74, respectively.  
Figure 12: 3 DCPOIT void topology from \(\mu\)-CT scanning. The coefficients of determination (R\({}^{2}\)) for x, y and z linear regression are 0.92, 0.91 and 0.86, respectively.  
process. The 3D printed specimen's voids are considerably flatter due to the printing process, with the flattest voids present in the 3 DCPOIB specimen. These results corroborate the findings presented in the previous section and confirm that oblate voids are present in this study's 3D printed specimens.