## 3 Results and Discussion
### Air Pycnometer Test Results
Clearly, a significant scatter of solid particle density values among the various types of MBT waste can be anticipated. Moreover, although Table 1 shows the solid particle densities of MBT waste, none of the collected values are an exact match for the solid particle density of the waste material considered within this research. This finding clearly reveals that the estimation of the solid particle density of MBT waste material based on published data is not feasible. Such an approach will most certainly end up with an incorrect estimate of the solid particle density, and consequently lead to the incorrect prediction of the initial void ratio. In addition, Figure 3a,b reveal that even in single MBT waste material, strong variability in the solid particle density among the tested specimens can be anticipated. For example, the measured solid particle density of group #1 was in the range from 1666 kg/m\({}^{3}\) to 2055 kg/m\({}^{3}\). Such a wide range of solid particle density values will have a significant influence on the initial void ratio estimate because, as Figure 3b clearly demonstrates, the increase in the solid particle density is followed by a corresponding increase in the initial void ratio. Thus, the solid particle density of any kind of waste material under consideration has to be established experimentally. In the case of the necessity to estimate the solid particle density of waste material, the authors recommend using Equation (4), as proposed by [2]:  
\[\rho_{s}=\frac{1}{\sum_{i}\frac{\mu_{i}}{\rho_{si}}} \tag{4}\]  
where \(\rho_{si}\) and \(\mu_{i}\) are the solid particle density and mass fraction of each waste component (\(i\)), respectively. For a precise estimation of the solid particle density in accordance with \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Ref.** &
\begin{tabular}{c} \(\rho_{s}\) \\ [kg/m\({}_{3}\)] \\ \end{tabular} & **Measurement Method** & **Additional Information** \\ \hline
[9] & 1580–1980 & Capillary pycometer & Various waste mixtures \\ \hline
[16] & 2210 & - & Particle size \(\leq\) 25 mm; waste was treated together with sewage sludge in a two-step process over a period of \textgreater{}20 weeks. \\ \hline
[17] & 880–1300 & - & The waste was processed using the DANO technique prior to testing. The evolution of the solid particle density with the vertical load. The vertical stress range went from 34 to 463 kPa. \\ \hline
[18] & 1900 & Water pycometry & MSW compost, test method NBR 7181/1984 (ABNT (a), 1984). \\ \hline
[19] & 1690 & Gas jar method & 0–10 mm fraction size, average value. \\ \cline{2-4}  & 1930 & Gas jar method & 0–20 mm fraction size, average value. \\ \hline
[20] & 1630 & Gas jar method & BS1377-2 \\ \hline
[21] & 2150 & Water pycometry & D 854-02, maximum particle size was 4.75 mm. \\ \hline
[22] & 1260 & \
\begin{tabular}{c} Density bottle method and \\ pycometer method \\ \end{tabular} & Mechanically and biologically treated compost reject collected from the \\ \cline{2-4}  & 1580 \(\pm\) 60 &
\begin{tabular}{c} MBT waste, Tianziling landfill, Hangzhou, China—winter specimen. \\ \end{tabular} \\ \cline{2-4}
[23] & 1380 \(\pm\) 80 & Water pycometry & MBT waste, Tianziling landfill, Hangzhou, China—summer specimen. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Solid particle densities of the MBT waste collected from the published literature. Equation (4), a thorough compositional analysis of waste has to be conducted. In addition, the accurate values of the solid particle densities of each waste component must also be known. More details about the solid particle density of the individual waste components can be found in [3,24].