# Granular collapse into water: toward tsunami landslides

Sylvain Viroulet, Alban Sauret, Olivier Kimmoun, Christian Kharif

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Sylvain Viroulet, Alban Sauret, Olivier Kimmoun, Christian Kharif. Granular collapse into water: toward tsunami landslides. Journal of Visualization, 2013, 16 (3), pp.189-191. 10.1007/s12650-013-0171-4. hal-00948389

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Submitted on 4 May 2023

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# Granular collapse into water: toward tsunami landslides

S. Viroulet, A. Sauret, O. Kimmoun, C. Kharif

## 1 Introduction

Modeling of granular flow is a key issue in many geophysical and industrial applications. Since the seminal work of Bagnold (1954), a huge number of studies have considered the dynamics of dry granular flow in various situations (Jop et al. 2006; Forterre and Pouliquen 2008; Lagrée et al. 2011). Underwater granular events are more complicated to describe as the presence and the influence of the surrounding fluid modifies the rheology of the flow (Rondon et al. 2011; Topin et al. 2012). It becomes even more challenging, but also important, to predict the impact of a granular media from the air into a fluid and the subsequent wave generated by the impact. This situation constitutes a model for subaerial deformable landslide and have many implications to forecast the generation of tsunamis. Recent experimental studies considered the generation of impulse wave, in water of depth $H$, by subaerial landslides (Mohammed and Fritz 2012). However, these experiments focused on a Froude number at the impact $Fr = v_s/\sqrt{gH}$, i.e., the ratio of the slide velocity $v_s$ to the gravitational wave velocity, larger than one. Therefore, the dynamic of a dry granular flow during the collapse into water remains largely unknown, especially at Froude number smaller than unity which would be of crucial importance for cliffs failure into water. In this work, we study such a situation in an experimental setup designed to characterize both the wave generated by the impact and also the granular flow after its penetration into the water.

## 2 Experimental setup

The experimental setup is shown in Fig. 1. It consists of a wave tank of 2.20 m long, 0.40 m high, and 0.20 m wide and a slope with glass beads stuck on it to suppress slipping of particles on the surface. The initial water depth is $H = 14.8$ cm. A vertical gate is used to delimitate the initial reservoir of granular materials located just above the undisturbed free surface. The gate is opened vertically using a 20-kg mass and pulley. The particles used are glass beads of diameter $d = 1.5$ mm and density $\rho_s = 2,500$ kg.m$^{-3}$. The evolution of the generated wave and of the granular flow are recorded with a high speed camera (Phantom Cinemag II). The amplitude and the propagation of the generated wave are also measured with four resistive gauges located at 0.45, 0.75, 1.05, and 1.35 m from the lifting gate. In addition, a PIV measurement system is used to estimate the velocity field in the water.

S. Viroulet (✉) · A. Sauret · O. Kimmoun · C. Kharif
IRPHE, CNRS UMR7342, Ecole Centrale de Marseille, Aix-Marseille University-AMU, Marseille, France
E-mail: viroulet@irphe.univ-mrs.fr
Tel.: +33-4-13552068

A. Sauret
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
## 3 Results and perspectives

Experiments were performed varying the initial mass of the granular media in the range $m \in [0.5; 4.5]$ kg and the slope angle $\theta \in [35^\circ; 60^\circ]$. Figure 2 shows a sequence of snapshots of the granular collapse process and the generation of the wave. The shape of the granular front just after the opening of the gate remains vertical. During the collapse, a vortex is generated at the interface of the granular flow and the water which may be induced by a shear instability. The time evolution of the free surface and the granular flow are represented in Fig. 3a, every 1/50 s. The free-surface evolution at each probe is represented in Fig. 3b.

<figure><img src="image_2.png" /><figcaption>Fig. 1 Schematic view of the experimental setup</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>Fig. 2 Sequence of snapshots showing the granular collapse and the generated wave for a slope angle of 45° and 3.00 kg of beads. At time $a\ t = 230$ ms, $b\ t = 410$ ms, and $c\ t = 520$ ms. PIV field are also represented</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>Fig. 3 a Evolution of the free-surface and the granular flow during the collapse and b elevation of the free surface at each probe for the parameters used in Fig. 2</figcaption></figure>
Sufficiently far from the collapse, i.e., in far field, the leading wave amplitude decreases as $t^{-1/3}$ during the propagation (see Viroulet et al. 2013).

Despite the complexity of this phenomenon, the experiments reported in this article provide first insights into the collapse of a dry granular flow into water and the generated wave. A more detailed analysis is in progress to quantify and model the interactions between the landslide and the wave. The derivation of scaling laws to relate the experimental parameters such as size or density of the granular media to real landslides would be of crucial importance to forecast tsunami generated by cliffs failure.

## References

* Bagnold RA (1954) Experiments on a gravity-free dispersion of large solid spheres in a Newtonian fluid under shear. Proc R Soc A 225:49–63

* Forterre Y, Pouliquen O (2008) Flows of dense granular media. Ann Rev Fluid Mech 40:124

* Jop P, Forterre Y, Pouliquen O (2006) A constitutive law for dense granular flows. Nat Biotechnol 441:727–730

* Lagrée P-Y, Staron L, Popinet S (2011) The granular column collapse as a continuum: validity of a Navier–Stokes model with a $\mu(I)$-rheology. J Fluid Mech 686:378–408

* Rondon L, Pouliquen O, Aussillous P (2011) Granular collapse in a fluid: role of the initial volume fraction. Phys Fluids 23:073301

* Topin V, Monerie Y, Perales F, Radja F (2012) Collapse dynamics and runout of dense granular materials in a fluid. Phys Rev Lett 109:188001

* Mohammed F, Fritz HM (2012) Physical modeling of tsunamis generated by three-dimensional deformable granular landslides. J Geo Res Oceans 117:C11015. doi: 10.1029/2011JC007850

* Viroulet S, Cebron D, Kimmoun O, Kharif C (2013) Shallow water waves generated by subaerial solid landslides. Geophys J Int 193(2):747–762. doi:10.1093/gji/ggs133