The final aim of the present work is to propose a NTHMP-benchmarked numerical tool for landslide-generated tsunami hazard assessment. To achieve this, the novel Multilayer-HySEA model is validated using laboratory experiment data for landslide-generated tsunamis. In particular, this second part of the work deals with granular slides, while the first part, in a companion paper, considers rigid slides. The experimental data used have been proposed by the US National Tsunami Hazard and Mitigation Program (NTHMP) and were established for the NTHMP Landslide Benchmark Workshop, held in January 2017 at Galveston (Texas). Three of the seven benchmark problems proposed in that workshop dealt with tsunamis
generated by rigid slides and are collected in the companion paper

Following the introduction of the companion paper

A set of seven benchmark tests was selected

The present work aims at showing the numerical results obtained with the Multilayer-HySEA model in the framework of the validation effort described above for the case of granular-slide-generated tsunamis for the complete set of the three benchmark problems proposed by the NTHMP. However, the ultimate goal of the present work is to provide the tsunami community with a numerical tool, tested and validated meeting the defined criteria for the NTHMP, for landslide-generated tsunami hazard assessment. This NTHMP acceptance has already been achieved by the Tsunami-HySEA model for the case of earthquake-generated tsunamis

Fifteen years ago, at the beginning of the century, solid block landslide
modeling challenged researchers and was undertaken by a number of authors (see companion paper,

The benchmark problems performed in the present work are based on the laboratory experiments of Kimmoun and Dupont (see

First we consider the Landslide-HySEA model, applied in

System Eq. (

Now, if

In the present study, the governing equations of the landslide motion are derived in Cartesian coordinates. In some cases where steep slopes are involved, landslide models based on local coordinates allow representing the slide motion better. However, when general topographies are considered and not only simple geometries, landslide models based on local coordinates also introduce some difficulties on the final numerical model and on its implementation compromising, at the same time, the computational efficiency of the numerical model. Here, we focus on the hydrodynamic component of the system, and that is one of the reasons for choosing a simple landslide model based on Cartesian coordinates. Of course, the strategies presented here can also be adapted for more sophisticated landslide models. For example, in

The Multilayer-HySEA model implements a two-phase model intended to reproduce
the interaction between the slide granular material (submarine or subaerial)
and the fluid. In the present work, a multilayer non-hydrostatic shallow-water model is considered for modeling the evolution of the ambient water (see

Schematic diagram describing the multilayer system.

The ambient fluid is modeled by a multilayer non-hydrostatic shallow-water system

Figure

Some dispersive properties of system Eq. (

Along the derivation of the hydrodynamic model presented here, the rigid-lid assumption for the free surface of the ambient fluid is adopted. This means that pressure variations induced by the fluctuation on the free surface of the ambient fluid over the landslide are neglected.

The 1D Savage–Hutter model used and implemented in the present work is given by system Eq. (

Note that the slide model can also be adapted to simulate subaerial landslides. The presence of the term (

System Eq. (

The resulting numerical scheme is well balanced for the water-at-rest stationary solution and is linearly

This section presents the numerical results obtained with the Multilayer-HySEA model for the three benchmark problems dealing with granular slides and the comparison with the measured lab data for the generated water waves. In particular, BP4 deals with a 2D submarine granular slide, BP5 with a 2D subaerial slide, and BP6 with a 3D subaerial slide. The description of all these benchmarks can be found in

The model parameters required in each simulation are

The friction angles

With regard to the sensitivity of the model to parameter variation, an appropriate sensitivity analysis can be performed, as is done in

Regarding the parameter denoting the buoyancy effect, for field cases,

We would like to stress the simplicity of the slide model used here as a great advantage regarding parameter setup. Although the end user has to adjust some input parameters of the model, within a range of acceptable value, the simplicity of the proposed numerical model makes this task remain simple – not representing an obstacle to run the model. On the other hand, the efficient GPU implementation of the model allows for performing uncertainty quantification (see

The first proposed benchmark problem for granular slides, BP4 in the list, aims to reproduce the generation of tsunamis by submarine granular slides modeled in the laboratory experiment by means of glass beads. The corresponding 2D laboratory experiments were performed at the École Centrale de Marseille (see

BP4 sketch showing the longitudinal cross section of the IRPHE's precision tank. The figure shows the location of the plane slope, the sluice gate, and the four gages (WG1–WG4).

The one-dimensional domain [0, 6] is discretized with

Numerical time series for the simulated water surface (in blue) compared with lab-measured data (red) at wave gauges

Modeled location of the granular material and water free surface elevation at times

Figure

In the numerical experiments presented in this section, the number of layers was set up to five. Similar results were obtained with a lower number of layers (four or three) but slightly closer to measured data when considering five layers. This justifies our choice in the present test problem. A larger number of layers does not further improve the numerical results. This may indicate that to get better numerical results, it is no longer a question related to the dispersive properties of the model (which improve with the number of layers) but is more likely due to some missing physics.

This benchmark is based on a series of 2D laboratory experiments performed
by

BP5 sketch of the setup for the laboratory experiments.

The granular material was confined in triangular subaerial cavities and composed of dry glass beads of diameter

The granular material is initially retained by a vertical gate on the dry slope. The gate is suddenly lowered, and in the numerical experiments, it should be assumed that the gate release velocity is large enough to neglect the time it takes the gate to withdraw. The front face of the granular slide touches the water surface at

For the present benchmark, two cases are considered. Case 1 is defined by the following setup:

The same model configuration as in the previous benchmark problem is used here. The vertical structure is reproduced using three layers in the present case. The one-dimensional domain is given by the interval [0, 2.2], and it is discretized using a step

Figure

Numerical time series for the simulated water surface (in blue) compared with lab-measured data (red). Case 1 at gauges

Numerical time series for the simulated water surface (in blue) compared with lab-measured data (red). Case 2 at gauges

Two things can be concluded from the observation of Figs.

Finally, Fig.

Modeled water free-surface elevation and granular slide location at times

This benchmark problem is based on the 3D laboratory experiment of

Schematic picture of the computational domain. Plan view in panel

The landslide material is deployed using a box measuring 2.1 m

Initially, the slide box is driven using four pneumatic pistons. Here we provide comparisons for the case where the pressure for the pneumatic pistons generating the slide is

BP6 cross section at

Simulated (solid blue lines) time series compared with measured (dashed red lines) free-surface waves for the nine wave gauges considered at (

The benchmark problem proposed consists of simulating the free-surface elevation at some wave gauges. In the present study, we include the comparison for the nine wave gauges displayed in Fig.

Location of the nine waves gauges referenced to the toe's slope.

Before comparing time series, we first check the simulated landslide velocity at impact with the measured one. The slide impact velocity measured in the lab experiment is

Figure

Time series comparing numerical run-up (solid blue) at the four run-up gauges with the measured (dashed red) data at (

Wall-clock times in seconds for the hydrostatic shallow-water Savage–Hutter system (SWE-SH) and the non-hydrostatic GPU implementations. The ratios are with respect to the SWE-SH model implementation.

Table

Numerical models need to be validated prior to their use as predictive tools. This requirement becomes even more necessary when these models are going to be used for risk assessment in natural hazards where human lives are involved. The current work aims at benchmarking the novel Multilayer-HySEA model for landslide-generated tsunamis produced by granular slides, in order to provide the tsunami community with a robust, efficient, and reliable tool for landslide tsunami hazard assessment in the future.

The Multilayer-HySEA code implements a two-phase model to describe the interaction between landslides (aerial or subaerial) and water body. The upper phase describes the hydrodynamic component. This is done using a stratified vertical structure that includes non-hydrostatic terms in order to include dispersive effects in the propagation of simulated waves. The motion of the landslide is taken into account by the lower phase, consisting of a Savage–Hutter model. To reproduce these flows, the friction model given in

The implemented numerical algorithm combines a finite-volume path-conservative scheme for the underlying hyperbolic system and finite differences for the discretization of the non-hydrostatic terms. The numerical model is implemented to be run in GPU architectures. The two-layer non-hydrostatic code coupled with the Savage–Hutter used here has been shown to run at very efficient computational times. To assess this, we compare with respect to the one-layer SWE/Savage–Hutter GPU code. For the numerical simulations performed here, the execution times for the non-hydrostatic model are always below 4.66 times the times for the SWE model for a number of layers up to three. We can conclude that the numerical scheme presented here is very robust, is extremely efficient, and can model dispersive effects generated by submarine/subaerial landslides at a low computational cost considering that dispersive effects and a vertical multilayer structure are included in the model. Model results show a good agreement with the experimental data for the three benchmark problems considered, in particular for BP5, but this also occurs for the other two benchmark problems. In general, a better agreement for the hydrodynamic component, compared with its morphodynamic counterpart, is shown, which is more challenging to reproduce.

The numerical code is currently under development and only available to close collaborators. In the future, we will provide an open version of the code as we already do for Tsunami-HySEA. This version will be available from the website

All the data used in the present work and necessary to reproduce the setup of the numerical experiments as well as the laboratory-measured data to compare with can be downloaded from

JM led the HySEA codes benchmarking effort undertaken by the EDANYA group, wrote most of the paper, reviewed and edited it, and assisted in the numerical experiments and in their setup. CE implemented the numerical code and performed all the numerical experiments; he also contributed to the writing of the manuscript. JM and CE did all the figures. MC significantly contributed to the design and implementation of the numerical code.

The authors declare that they have no conflict of interest.

The authors are indebted to Diego Arcas (PMEL/NOAA) and Victor Huérfano (PRSN) for supporting our participation in the 2017 Galveston workshop and to the MMS of the NTHMP for kindly inviting us to that event.

This research has been supported by the Spanish Government–FEDER (project MEGAFLOW) (grant no. RTI2018-096064-B-C21) and the Junta de Andalucía–FEDER (grant no. UMA18-Federja-161).

This paper was edited by Maria Ana Baptista and reviewed by two anonymous referees.