Prediction of the water waves generated by a potential semisubmerged landslide in La Yesca reservoir, Mexico

Abstract

This paper presents a study of the effects of a potential landslide in La Yesca Reservoir, Jalisco-Nayarit, Mexico. The main purpose of the paper is to predict the maximum wave amplitude, wave run-up, and dam overtopping. The landslide is formed by an unstable slope of more than 24 Mm³ that is partially submerged for the range of the reservoir operation levels. The dynamics of the sliding mass were obtained in detail considering that it moves over a pair of failure surfaces with the potential rupture of a third surface. The paper presents results of a physical model of the reservoir based on Froude similitude (scale 1:200). Impulse waves are produced with a solid wedge shape slide as it moves on rails. The movement was calibrated to reproduce the dynamics of the landslide. Also, numerical modelling of the event was performed with a 2D implicit model that solves the two-dimensional shallow water equations. In this case, the impulse waves were generated at each time increment with the variation of the ground elevation (obtained from the dynamics of the landslide) for the mesh points where the landslide passes. The results of both studies are similar.

Appendix

There are several empirical expressions available for obtaining wave characteristics. Most of them were formulated for subaerial landslides, as those of Kamphuis and Bowering (1970), Fritz et al. (2004), Di Risio (2005), Zweifel et al. (2006), Ataie-Ashtiani and Nik-Khah (2008a), Heller (2007), Slingerland and Voight (1982), and Mohammed and Fritz (2012). The use of these equations is questionable for semisubmerged landslides as is the case studied here mainly because the wave generation is different: the impulse and impact of the slide on the water body are definitive for the wave generation. The same can be said about the expressions for submerged blocks as those of Watts (1998), Watts and Grilli (2003), Ataie-Ashtiani and Nik-Khah (2008a) (Ataie-Ashtiani and Nik-Khah, 2008b) and Enet and Grilli (2007). Di Risio et al. (2009) commented that in submerged landslides, the wave generation is dominated by the water movement filling the space left by the block as it moves; the wave starts in a trough that determines the wave crest afterwards.

Huber and Hager (1997) performed a series of experiments for subaerial slides, as is of interest here. These experiments were for granular material. The expressions of Walder et al. (2003) and Panizzo et al. (2005) are for subaerial rigid blocks. The latter expressions require the time of underwater motion, T _s (that can be obtained from the dynamics of the landslide, Eq. 1). A summary of the equations for subaerial slides is given in Table 2.

The relative maximum wave amplitude is a _M /h and relative wave height H(x)/h to a relative propagation distance X = x/h (where x is the perpendicular direction to the landslide). In 3D experiments, R = r/h (with an angle γ and a distance r). The parameters of the block are as follows: specific gravity G = ρ _s /ρ _w (water density ρ _w ), landslide volume per unit area $Vo{l}_T^{*}=Vo{l}_T/b{h}^2,$ and landslide grain volume per unit area $Vo{l}_g^{*}=Vo{l}_g/b{h}^2$; the relation between the granular landslide volume and the total volume is Vol _g  = (1 − n)Vol _T and ρ _g  = ρ _s /(1 − n), after Fritz (2002).