Three-dimensional numerical simulation of landslide-induced waves in dams reservoirs (Case study: Siyah bishe dam)

Introduction
Large landslides can cause overtopping and consequently demolish the dams and other substructures and facilities. The landslide stabilization is very costly due to their large size and considerable extent. Hence proper estimation of the wave height because of sliding into the reservoirs in order to determine the risk of overtop is inevitable. In this study, 3D simulation of the SM5 sliding landslide into the upper reservoir of the Siyah Bisheh is conducted to calculate the height of the waves generated by this phenomenon.
Methodology
For landslide modeling, the assumption of rigid mass is assumed and mass motion is considered as a combination of transitional and rotational motion. First, Heinrich's (1992) laboratory model was used to evaluate the performance of the Flow-3D numerical model (calibration and validation). For this purpose, the sliding mass was introduced into the reservoir by prescribed motion and the changes in water level at different points were compared with the experimental results. The results showed that there is an appropriate matching between the experimental and numerical results. The purpose of this comparison was to evaluate the accuracy of the software used to estimate water level. Although in some cases, the trend of changes in water level is significantly different from laboratory results, the maximum level obtained in numerical model is in relevant agreement with laboratory results. In the numerical simulation of the mass movement in the Siyah-Bisheh Dam, the mass range and the shape of the slide circle are first determined. The mass has a volume about 425,000 cubic meters and is about 100 meters long. The slide radius is estimated to be 200 meters. About 250,000 cubic meters of this mass lies beneath the reservoir water level, which 150,000 cubic meters moves during landslide. In this case, the center of mass moved 20 meters downwards and can generate a velocity between 1 to 10 meters per second. For the modeling of motion, different scenarios are considered based on the mass movement velocity. Due to the low width of the river at the mass location (about 60 m), the mass movement is limited at this distance so all masses cannot enter to reservoir. Topography of reservoirs with 1/ 2000 scale were used to model reservoir and SM5 mass. Because of the narrow width of the valley, the mass hits the opposite wall and stops. As mentioned before, mass movement is considered a set of rotations and translations. The main reason of using this type of movement is the lack of ability to consider mass deformation. In terms of mesh size, meshes of 5 and 10 m in plan and 1 and 2 m in height are used. The results of convergence test show that there is no significant difference between the meshes of 5 m in the plan and 2 m in the depth and finer one. Different scenarios with various velocity of mass (velocity of 1, 3, 6 and 10 m / s) are considered for the simulation process. The mass is assumed to have reached maximum speed in a short time and stopped shortly at the end of the opposite wall. Results are presented for the 5 specified points in the reservoir with an appropriate distribution on its surface.
Results and discussion
The results are presented for 90 seconds after the mass enters the reservoir and it has been attempted to take into account the impact of the distance and time when the peak occurred. The wave height near the mass reaches to 10 meters where the mass has 10 meters per second and reaches to around 3 meters as it departs from the entry point. The maximum wave height near the dam site has been obtained around 2.5 m. According to the laboratory results, the wave caused by the landslide moves in the direction of mass entry into the reservoir. The mass direction is perpendicular to the river and parallel to the dam axis and it is expected that the generated wave will hit the opposite wall. The generated wave due to landslide collides to the opposite bank and dispersed. As a result, the height of the generated wave is reduced and therefore the possibility of overtopping falls dramatically. Based on the results, it can be said that the wave height will not exceed 2.5 m near the dam body. However, the maximum wave height produced in the reservoir exceeds 10 m at high velocities. At the end, the surface wave height due to landslide has been calculated using the issue number 53 of Iranian Commission on Large Dams (IRCOLD). In this calculation, the slide mass is estimated to be 150,000 cubic meters and the mass velocity is 13 m/s.
Conclusion
According to the empirical tables and relationships, the wave height is obtained at 400 and 800 m far from the dam body at 2.5 and 1 m respectively. This value is compatible with the results obtained from the numerical model.

Keywords: Landslide, 3D numerical modeling, wave height, overtopping, Siyah Bishe