## 3 Case Studies
### Sham Tseng San Tsuent Debris Flow  
This debris flow took place in Hong Kong on 23 August 1999. This case was proposed as a benchmarking exercise by the Hong Kong Geotechnical Office with the objective of evaluating the precision of numerical and constitutive models [41]. They also provided a detailed digital map of terrain elevation, including the mobilized mass's original position and the reservoir's final position. The event took place after heavy rain. During the 24 h before the event, the precipitation was 479 mm. The debris flow consisted of 600 m\({}^{3}\) of channeled material, according to the report. It originated from three shallow landslides, of which one was much larger than the others. In fact, the data provided included only this main source. The debris traveled downhill along an incised rocky stream course with negligible debris entrainment, and it destroyed several one-story buildings at the end of the canal. Figure 7 represents a map of the terrain showing the position of landslide A, the track, Sham Tseng San Tsuent village's location, and the house labeled as \"No. 38\", which was destroyed. More information can be found in a geotechnical report provided by [PERSON] et al. (2005) [42]. This simulation aimed to consider excess pore-water pressures in the two-phase model implemented in GeoFlow-SPH. In the previous simulation, it was assumed that the permeability was very large, and the excess pore pressure terms were neglected. Densities of soil particles, pore fluid, and mixture were taken as 2400 Kg/m\({}^{3}\), 1000 Kg/m\({}^{3}\), and 2000 Kg/m\({}^{3}\). The drag laws that have been implemented in both sets of code were based on the Anderson and Jackson law [27] model. In this case, the terminal velocity (\(V_{T}\)) and \(m\) were taken as 10\({}^{-4}\) ms\({}^{-1}\) and 1, respectively. According to the report [42], the triaxial tests show that the material did not present cohesion, and the friction angle varied from 37\({}^{\circ}\) to 38\({}^{\circ}\), for which we found \(\tan\phi_{B}=0.75-0.78\). Interestingly, the report states that \"the distal end of the debris deposition had a travel angle of about 24\({}^{\circ}\)\", which is much smaller than the friction angle found in laboratory tests. For the two-phase model developed by [PERSON] (2021) [26], the values of the friction angle and travel angle coincided well with those obtained in the reports by using the following equation:  
\[\tan\phi_{app}=\left(\frac{\rho_{s}-\rho_{w}}{\rho_{s}}\right)\tan\phi_{B}= \left(\frac{2400-1000}{2400}\right)\tan 37\rightarrow\phi_{app}=24^{\circ} \tag{19}\]  
where \(\phi_{B}\) is the friction angle and \(\phi_{app}\) the travel angle. The rest of the parameters were similar to those in the previous case study. Figure 8 presents the propagation predicted by the ravaflow (right) and GeoFlow-SPH (left) programs at different time steps. In Figure 8, we can observe the larger velocities of the model simulated in the GeoFlow-SPH code, capable of considering excess pore-water pressures. The main reason for these differences was the pore-water pressure's evolution in the GeoFlow-SPH code. As described in Section 2.3, the consolidation equation was employed in the two-phase modeling of debris flow to compute the quantity of excess pore-water pressure, which has been implemented in the balance of momentum equation. Besides, the frictional rheological equation implemented in the numerical code is capable of considering the effects of the pore pressure dissipation and generation. As can be seen in Equation (11), the generation of pore-water pressure is similar in effect to reducing the friction angle, and the dissipation of pore-water pressure is equivalent to increasing the friction angle. To obtain similar numerical results, it is necessary to use a lower value of basal friction angel in the ravaflow code. Therefore, improvements to the numerical results obtained by the ravaflow code can be achieved by modifying the values of rheological parameters.