## 4 Engineering-Geological Model
### Rock Mass Rheological Behavior  
Starting from the characteristics of the intact rock and considering the jointing conditions as they have been surveyed, the properties of the rock mass were determined by exploiting the main correlations present in literature studies. In addition to the physical characteristics, the main parameters concerning a visco-plastic behavior were determined. The entire rock mass was previously portioned into several zones characterized by homogeneous properties. Regarding the structural setting of the slope, a cataclastic zone with extension as observed in the field was considered for each longitudinal normal fault reported in the cross-section. The rock mass was characterized through an equivalent continuum approach, as previously carried out by several authors e.g., [17; 23; 43]. Such an approach transposes the rock mass in a continuous equivalent medium, endowed with a single constitutive law deriving from the characteristic of all the elements that characterize it [43; 44; 45; 46; 47]. The equivalent continuum approach is applicable to slope of considerable dimensions and is therefore widely used for the study of DSGSDs [2; 12; 14; 16; 19; 20; 23; 31]. The unit weight was determined through the equations provided by [PERSON] et al. [48], considering the intact rock properties and the rock mass structure. The unit weight \(\gamma_{m}\) of jointed rocks was calculated through the following equation: \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Specimen** & **Lithology** & \begin{tabular}{c} **Unit** \\ **Weight** \\ \end{tabular} & \begin{tabular}{c} **UCS** \\ **Strength** \\ \end{tabular} & \begin{tabular}{c} **Young** \\ **Modulus** \\ \end{tabular} & \begin{tabular}{c} **Poisson** \\ **Ratio** \\ \end{tabular} \\ \hline - & - & \(\gamma\) & \(\sigma_{c}\) & \(E\) & \(v\) \\ - & - & \(\text{kN}/\text{m}^{3}\) & \(\text{MPa}\) & \(\text{MPa}\) & - \\ \hline C\_1 & \begin{tabular}{c} Intact \\ limestone \\ \end{tabular} & 26.1 & 71.88 & 47,736 & 0.20 \\ C\_2 & \begin{tabular}{c} Intact \\ limestone \\ \end{tabular} & 26.3 & 92.83 & 72,356 & 0.28 \\ \hline C\_3 & \
\begin{tabular}{c} Limestone with \\ calcite veins \\ \end{tabular} & 25.6 & 40.56 & 29,088 & 0.24 \\ C\_4 &
\begin{tabular}{c} Limestone with \\ calcite veins \\ \end{tabular} & 26.4 & 9.30 & 6670 & 0.24 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Synthesis of physical and mechanical parameters derived from the laboratory tests. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Lithology** & \begin{tabular}{c} **Unit** \\ **Weight** \\ \end{tabular} & \begin{tabular}{c} **UCS** \\ **Strength** \\ \end{tabular} & \begin{tabular}{c} **Young** \\ **Modulus** \\ \end{tabular} & \begin{tabular}{c} **Poisson** \\ **Ratio** \\ \end{tabular} & \begin{tabular}{c} **UCS/E** \\ **Ratio** \\ \end{tabular} & \
\begin{tabular}{c} **Viscosity** \\ **Viscosity** \\ \end{tabular} \\ \hline - & \(\gamma\) & \(\sigma_{c}\) & \(E\) & \(v\) & \(\sigma_{c}\)/\(E\) & \(\mu\) \\ - & \(\text{kN}/\text{m}^{3}\) & \(\text{MPa}\) & \(\text{MPa}\) & - & - & \(\text{Pa}\)-\(\text{s}\) \\ \hline \hline \end{tabular}
\begin{tabular}{c} Intact limestone \\ Limestone with \\ calcite veins \\ \end{tabular} & 26.2 & 82.36 & 60,046 & 0.24 & 0.001394 & \(2.00\times 10^{19}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Synthesis of physical and mechanical parameters of the intact rock constituting the mass affected by the Luco dei Marsi DSGSD.