## 3 Results and Discussion
### Air Pycnometer Test Results  
Figure 3a,b show the experimental data obtained with the air pycnometer device for all six consecutive groups of specimens. The presence of strong variability in the solid particle densities within each tested group of specimens is noticeable in both subfigures. The observed variability can be explained by the strong heterogeneous nature of the tested waste. Clearly, contrary to what might be expected, the treatment process did not significantly reduce the heterogeneity of the tested waste material. The percentage ranges within which the solid particle densities varied for each consecutive group were 19%, 20%, 6%, 13%, 9%, and 21%, respectively. Consequently, the void ratio of each consecutive group also varied within the similar percentage limits. The obtained percentage ranges notably differed among the tested groups, indicating that each tested group had different levels of heterogeneity. The obtained SD values of the solid particle density and void ratio (Figure 3a) revealed that group #3 contained the fewest heterogenous specimens, whereas groups #1 and #2 consisted of the most heterogeneous specimens. Moreover, it is interesting to observe that, even though groups #1 and #6 shared similar solid particle density SD values, the corresponding void ratio SD values significantly differed. Clearly, the SD void ratio value of group #6 was much smaller than the SD void ratio value of group #1. This finding indicates that a strong variation in the solid particle density does not necessarily provide a strong variation in the corresponding void ratio. However, further research is necessary to better understand this anomaly. In addition, Figure 3a also presents the theoretical curve obtained with Equation (3), with a constant solid particle density set to 1600 kg/m\({}^{3}\). Clearly, these particular specimens,for which the measured solid particle densities lie close to 1600 kg/m\({}^{3}\), strongly resemble the theoretical curve. These results are a strong indication that, for waste materials, a set of \(\rho_{d}\) vs. \(e\) hyperbolic curves, in which each curve is defined with a unique solid particle density value, do exist. Figure 3b shows the measured \(\rho_{s}\) vs. \(e\) relationship of each consecutive group of specimens. The presented results confirm that, for the tested waste material, a strong positive linear correlation between the solid particle density and void ratio under constant dry density, does exist. Clearly, the obtained gradients presented in Figure 3b correspond to dry density values. During the experiment, the mass and total volume (\(V=V_{v}+V_{s}\)) of all the specimens were kept constant. Therefore, the increase in the solid particle density was conditioned exclusively by the decrease in the solid particle volume (\(V_{s}\)). This implies that the size, shape, and orientation of individual solid particles also played a significant role in the formation of the waste specimen skeleton and its total volume. Figure 3: (**a**) Hyperbolic \(\rho_{d}\) vs. \(e\) relationship under constant solid particle densities. (**b**) Linear \(\rho_{s}\) vs. \(e\) relationship under constant dry densities. Variability in the Solid Particle Density Caused by Waste Heterogeneity and Its Influence on the Estimation of The Initial Void Ratio  
In practice, it is not so uncommon that the solid particle density of waste material is estimated based on the values obtained from the available literature. This approach is the legacy from soil mechanics, in which it is customary to estimate the solid particle density of soils. However, because the solid particle density of soils varies within the small range of values, the estimated value does not introduce significant errors into the further calculations. With respect to the waste materials, such an approach should be avoided. Table 1 presents the solid particle densities of MBT waste gathered from the published literature. As expected, the collected values lie in a very wide range from 1260 kg/m\({}^{3}\) to 2210 kg/m\({}^{3}\).