## 2 Overview
### Marchetti Dilatometer: Conceptualization
#### 3.1.6 Relative Density  
The type of soil is important for determining the best method for calculating the degree of compaction (Dr) and the degree of saturation (S). Therefore, it is important to become familiar with the conditions of the study area, such as the geology, stratigraphy, and hydrology [31]. Although consideration was given to finding the specific gravity of the recovered samples, several mishaps made this task so difficult that it could not be performed in the laboratory. In the first place, the scarcity of material required that it be prioritized in the most important tests. In addition, the material, due to its consistency, when submerged in the pycnometers, would have remained suspended without settling on the base, which would lead to erroneous results. It was advisable to find the specific gravity of the organic content and similar separately since these were the ones that tended to be lighter than water, and to use pycnometers with an automatic helium gas injection to obtain more accurate results [3].  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Depth (m)** & **Moisture (\%)** & **LL** & **PL** & **PI** & **Organic** & **Ash Content** & **Organic Content** & **Soil Type** \\ \hline
0–1 & 60.66 & 68.45 & 47.38 & 21.07 & Yes & 93.09 & 6.91 & OH, Organic Sandy Silt \\
1–2 & 264.02 & 238.17 & 129.85 & 108.32 & Yes & 83.08 & 16.92 & OH, Organic Sandy Silt \\
2–3 & 351.01 & 164.97 & 84.94 & 80.03 & Yes & 78.26 & 21.74 & OH, Organic Sandy Silt \\
3–4 & 207.70 & 289.37 & 135.46 & 153.91 & Yes & 86.01 & 13.99 & OH, Organic Sandy Silt \\
4–5 & 240.76 & 207.29 & 98.65 & 108.64 & Yes & 85.39 & 14.61 & OH, Organic Sandy Silt \\
5–6 & 257.50 & 212.69 & 118.99 & 93.7 & Yes & 85.47 & 14.53 & OH, Organic Sandy Silt \\
6–7 & 346.91 & 257.74 & 107.2 & 150.54 & Yes & 82.02 & 17.98 & OH, Organic Sandy Silt \\
7–8 & 249.88 & 258.11 & 152.72 & 105.39 & Yes & 79.49 & 20.51 & OH, Organic Sandy Silt \\
8–9 & 129.01 & 100.74 & 65.26 & 35.48 & Yes & 89.78 & 10.22 & OH, Organic Sandy Silt \\
9–10 & 282.83 & 219.32 & 157.88 & 61.44 & Yes & 83.66 & 16.34 & OH, Organic Sandy Silt \\ \hline \hline \end{tabular}
\end{table}
Table 7: Summary of results for the fourth borehole.  
Figure 11: Variation of density values of each borehole about depth.  
Despite the above, it was decided to use the following Equation (1) to obtain the specific gravity values for our material using its ash content [32].  
\[G=\frac{(2.7*1.4)}{(2.7-1.4)*\left(1.04*\frac{N}{100}-0.04\right)+1.4} \tag{1}\]  
where:  
\(G\): specific gravity.  
\(N\): ignition loss (%).  
Figure 12 shows that the specific gravity of soils ranges between 1.45 and 1.75. These values were validated with the research developed by [PERSON] et al. (2020) [33], using the following expression:  
\[G_{\mathrm{s}}=\frac{3.74}{N*1.42+1.35} \tag{2}\]  
where:  
\(G_{\mathrm{s}}\): specific gravity.  
\(N\): ignition loss (%).  
Figure 13 shows that the specific gravity of soils ranges between 1.40 and 1.70.  
Figure 12: Relationship between the specific gravity of the soil and its ash content, using equation 1.  
Figure 13: Relationship between the specific gravity of the soil and its ash content, using equation 2.