## 3 Case Studies
### Acheron Rock Vvalanche
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter (Symbol)** & **GeoFlow-SPH** & **ravaflow** \\ \hline Density of the of solid particle (\(\rho_{s}\)) & 2700 kg/m\({}^{3}\) & 2700 kg/m\({}^{3}\) \\ Density of the of water particle (\(\rho_{w}\)) & 1000 kg/m\({}^{3}\) & 1000 kg/m\({}^{3}\) \\ Mixture density (\(\rho\)) & 2350 kg/m\({}^{3}\) & - \\ Internal friction angle (\(\delta\)) & - & 35\({}^{\circ}\) \\ Basal friction angle (\(\phi_{B}\)) & 17\({}^{\circ}\) & 17\({}^{\circ}\) \\ Virtual mass force coefficient (\(C\)) & - & 0.5 \\ Terminal velocity (\(V_{T}\)) & 0.01 m/s & 0.01 m/s \\ Parameter related to drag resistance (\(P\)) & - & 0.5 \\ Particle Reynolds number (\(Re_{p}\)) & - & 1 \\ Exponent for drag -1 D linear, 2 D quadratic- (\(m\)) & 1 & 1 \\ Quasi-Reynolds numbers (\(N_{R}\)) & - & 30,000 \\ Mobility number (\(N_{R_{A}}\)) & - & 1000 \\ Viscous shearing coefficient for fluid (\(X\)) & - & 0 \\ Solid concentration distribution with depth (\(\xi\)) & - & 0 \\ Ambient drag coefficient (\(C_{AD}\)) & - & 0 \\ Manning’s coefficient (\(C_{FF}\)) & 0 s/m\({}^{1/3}\) & 0 s/m\({}^{1/3}\) \\ Entrainment coefficient (\(E_{s}\)) & \(5\times 10^{-5}\) m\({}^{-2}\) & \(10^{-7}\) kg\({}^{-1}\) \\ Elastic volumetric stiffness (\(k_{p}\)) & \(4\times 10^{8}\) N/m\({}^{2}\) & - \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Material parameters used in the analysis of the avalanche. sets of code gave relatively similar deposit distributions, velocities, runout distances, and final deposition thickness values. Both sets of code show the traveling of small portions of the volume in the wrong direction (northern). It should be recalled that the event is an ancient rock avalanche, and perhaps there exist some unrecognizable deposition volumes in the field. Figure 5: A comparison between two sets of code: the results on the left side were obtained with Geoglow and on the right side with ravaflow. They show the flow propagation path, with the numerical results of flow-depth and maximum velocity at different times: (**a**) 0 s, (**b**) 20 s, (**c**) 40 s, (**d**) 60 s, (**e**) 100 s, and (**f**) 230 s.  
The deposition volume was considered to be the field deposit estimate of \(8.9\times 10^{6}\) m\({}^{3}\) for both sets of code using the back-calculated erosion rate given in Table 1. As described in Sections 2.2 and 2.3, the erosion laws implemented in both sets of code are of empirical type. During the propagation stage, a significant difference was observed in the numerical results of maximum height evolutions. However, the ravaflow and GeoFlow-SPH sets of code had similar results regarding the shape of the final deposit and depositional height distribution. The maximum deposit thicknesses calculated by ravaflow and GeoFlow-SPH sets of code were 31.8 and 27.3 m, respectively. As shown in Figure 5, both sets of code reached a satisfactory approximation of the depositional area shape. However, the ravaflow code gave a larger lateral mass spread than GeoFlow-SPH. The excessive lateral spreading might be solved by choosing appropriate combinations of internal friction angle \(\delta\) and basal friction angel \(\phi_{B}\). The GeoFlow-SPH code successfully modeled the final deposit, although an isotropic state of stress was assumed, and the earth pressure coefficient (k-value) was considered equal to 1. Lateral spreading also depends on the evolution of pore-water pressure, which the GeoFlow-SPH is capable of considering. As depicted in Figure 6a, the r.avaflow code overestimated the height values with respect to the GeoFlow-SPH code until 95 s (time of reach). After that, the numerical result of maximum deposit thickness obtained by the ravaflow decreased during the lateral spreading of the flowing mass until the numerical results of both sets of code became relatively close in terms of the shape of the final deposit and depositional height distribution.