Numerical characterisation of landslide-tsunamis in idealised and real water bodies

Landslide-tsunamis are caused by mass movements such as landslides and rockfalls impacting into a water body. This phenomenon has caused catastrophes in recent history that significantly affected both human lives and the economies of countries. Landslide-tsunamis also need to be assessed in high risk countries such as China with 87000 reservoirs. For this reason, reliable hazard assessment methods are required. Next to landslides generating the tsunamis, two additional water body characteristics affect their propagation before reaching the shore. These are: the water body geometry affecting the landslide-tsunami energy spread, and the bathymetry affecting phenomena such as shoaling and reflection. Landslide-tsunamis research under idealised conditions, is essentially based on the two idealised water body geometries (i) wave flume (2D, laterally confined wave propagation) and (ii) wave basin (3D, unconfined wave propagation). The wave heights in 2D and 3D can differ by over one order of magnitude in the far field and the wave characteristics in intermediate geometries are currently not well understood. Further, under idealised conditions, the majority of the studies use a uniform water depth to better isolate other effects. However, it has been demonstrated that also the bathymetry can considerably affect tsunami propagation via shoaling and other depth and shore related effects. This study focuses on how these two described aspects affect landslide-tsunami propagation. The numerical model SWASH, based on the non-hydrostatic non-linear shallow water equations, was used to simulate approximate linear, Stokes, cnoidal and solitary waves. The effect of the water body geometry was investigated in 6 different idealised water body geometries including 2D, 3D and intermediate geometries with water body side angles of θ=7.5°, 15°, 30° and 45° at uniform water depths. The effect of the bathymetry was mainly studied in 2D using a wide range of potential conditions representing real cases namely beach, positive and negative Gaussian and positive and negative step bathymetries. This resulted in a total of 184 numerical tests. In addition, the combined effect of the water body geometry and bathymetry was investigated in selected bathymetries with wave conditions spanning from deep to shallow water. The wavefront length, i.e. the arc length of the circle sector formed by the wave front, e.g. a semi-circle in 3D, was found to be an excellent parameter to correlate the wave decay along the slide axis in all investigated geometries in agreement with Green's law and diffraction theory in 3D. Semi-theoretical equations to predict the wave magnitude of the idealised waves at any desired point in the water bodies are also presented. Further, simulations of experimental landslide-tsunami time series were performed in 2D to quantify the effect of frequency dispersion. This process may be negligible for solitary- and cnoidal-like waves for initial landslide-tsunami hazard assessment but results in approximations in deeper waters. The results of landslide-tsunami propagation over different bathymetries showed that shoaling on beaches follows either Green's law or the Boussinesq's adiabatic approximation up to wave breaking with an error of -7% to +10% for cnoidal and solitary waves. The results were then analysed with an Artificial Neural Network (ANN) and a regression analysis to find the transformed wave characteristics downwave of the investigated bathymetries with the first showing better performance. In addition, the combined effects of the water body geometry and bathymetry were studied revealing that relations derived for a 2D geometry result in under-predictions of the wave characteristics for deep-water waves while they are more appropriate for shallow-water when θ>0°. The 2014 Lake Askja case, Iceland, was used to validate and define a prediction procedure to calculate the wave characteristics for a real case with variable geometry and bathymetry. The derived semi-theoretical equations resulted in an error of 10% for the wave height and 1.5% for the amplitude when compared with the detailed numerical simulations of Gylfadóttir et al. (2017). This is under the condition that only the effect of the water body geometry is relevant. When both the effect of the water body geometry and bathymetry are relevant then additional prediction methods were employed with the ANN resulting in the best performance with errors of 23.4% and 1.0% for the wave height and amplitude, respectively. Note that the lower agreement found when combining the two effects can be attributed to non-linear superposition effects which are highly dependent on the wave type. The findings herein are expected to significantly improve the reliability of preliminary landslide-tsunami hazard assessment in water body geometries between 2D and 3D and with variable bathymetries. However, the combined effect showed that the water body geometry and bathymetry play an important role. Therefore, future developments should investigate this combined effect for both idealised and real cases using numerical simulations and laboratory experiments. Also, the impact on defense structures and buildings should be investigated by using inundation models to improve design equations to mitigate future risks