The impact of an avalanche in a reservoir induces impulse waves, which pose a threat to population and infrastructure. For a good approximation of the generated wave height and length as well as the resulting overtopping volume over structures and dams, formulas, which are based on different simplifying assumptions, can be used. Further project-specific investigations by means of a scale model test or numerical simulations are advisable for complex reservoirs as well as the inclusion of hydraulic structures such as spillways.

This paper presents a new approach for a 3-D numerical simulation of the avalanche impact in a reservoir. In this model concept the energy and mass of the avalanche are represented by accelerated water on the actual hill slope. Instead of snow, only water and air are used to simulate the moving avalanche with the software FLOW-3D. A significant advantage of this assumption is the self-adaptation of the model avalanche onto the terrain. In order to reach good comparability of the results with existing research at ETH Zürich, a simplified reservoir geometry is investigated. Thus, a reference case has been analysed including a variation of three geometry parameters (still water depth in the reservoir, freeboard of the dam and reservoir width). There was a good agreement of the overtopping volume at the dam between the presented 3-D numerical approach and the literature equations. Nevertheless, an extended parameter variation as well as a comparison with natural data should be considered as further research topics.

Avalanches are dangerous natural events that can threaten
settlements, roads or other infrastructure objects in mountainous regions

Once the avalanche reaches the water surface of the reservoir, the complete
impacting process can be divided into two parts: (a) the generation and the
movement of the avalanche and (b) the impact into the reservoir with the
propagation of the impulse wave. Different types of special numerical
software are available to simulate the first part
(Sect.

Based on the characteristics of the avalanche-induced impulse waves, the
process within the reservoir can be divided into three phases: (a) the wave
generation including the impact of the sliding mass, (b) the wave propagation
in connection with lateral propagation including the progressive frequency
dispersion and (c) the last phase, which is the run-up on the (opposite)
shore. The transition between these three phases is smooth. If the distance
between impact spot and the accumulation areas is very small, the propagation
phase of avalanche-induced impulse waves can sometimes be neglected

The formation and movement of avalanches can be simulated using several
existing software solutions. One commonly applied numerical tool is the RAMMS
(rapid mass movement system) software, which is used by the WSL (Swiss
Federal Institute for Forest, Snow and Landscape Research) Institute for
Snow and Avalanche Research SLF

The investigation of avalanche impact and the thereby generated impulse
wave in a reservoir can not be simulated with the numerical tools presented
in Sect.

The build-up of a scale model test is a very reliable but also cost-intensive
way to evaluate the danger of impulse waves in reservoirs caused by
avalanches. In addition to general scale effects

In recent years, extensive basic research in the field of avalanche- and
landslide-induced impulse waves in reservoirs has been carried out at ETH
Zürich. Within these laboratory tests, different granulates and solid
bodies were used. In the following section a brief overview is given, leading
to approaches to calculate the impulse wave (behaviour, height, length) and
the overflow volume depending on the actual dam structure
(Sect.

Different studies have accurately shown the impact phase of wave generation
using scale model tests

The above-mentioned experiments at ETH Zürich

The overtopping volume per metre crest length

The formulas are based on different generalisations and simplifications. To
use them for a specific adaptation on a complex bathymetry or the
consideration of wave reflection, the applicability of these formulas has to
be carefully checked

In addition to (existing) scale model tests, more and more numerical models
are used, for which free surface modelling (interaction of water and air) is
a standard application.

Examples for existing 2-D simulations of scale model tests can be found in

A 3-D numerical approach should be used especially for complex terrain,
smaller reservoirs and if the effect of spillways or other structures should
be considered. While conducting a broad scale model test of a weir and intake
structure,

For both modelling concepts (scale model test and numerical simulation), two
assumptions are frequently used: (a) the impacting avalanche is homogeneous
and (b) the impact is limited to a specific location in the reservoir.
Depending on the used modelling concept for the avalanche, this latter
assumption can lead to very different results. If for example simple solid
slide is used, it results in a single, big impact at a defined place on the
water surface. A good adaptation of the model avalanche to an actual terrain
can be achieved by using granulates

Based on third-party-funded research at the Unit of Hydraulic Engineering at
the University of Innsbruck, different concepts were studied. The starting
point was the use of moving objects, which represent the avalanche as a solid
with a defined velocity. These bodies and also the particles were accelerated
in a chute. The main goal was to reproduce an existing scale model test,
which would be focused on the concentrated impact and the conditions at
a weir structure

An avalanche study that has been conducted with a suitable software
(examples for these kinds of software are mentioned in
Sect.

Based on the results of the avalanche simulation, a mass-equivalent amount
of water is placed in the starting zone of the avalanche, for which the
chosen water depth should be adjusted in relation to the distribution of the
snow heights. In general, the slide density

At the control section, the kinetic energy or rather the momentum (product of the mass and velocity) of the incoming water is compared to the previously simulated avalanche in step 1 over the entire impact time. In general, the water has a higher density than snow and so the water avalanche is too fast.

To correct this effect, a restart simulation on the existing simulation is
conducted. After some simulated seconds, the complete water body of the
avalanche model is used as an initial condition for a restart. The thereby
chosen time is only a first assumption and lasts typically 2–4 s. The only
difference between the original simulation and the restart is, that the
velocity is set to 0 at the beginning of the restart simulation
(Fig.

In order to calibrate the velocity of the model avalanche at the moment of impact, it is evaluated at the control section (identical to step 3) and, if necessary, the time of the restart is changed accordingly. Depending on the terrain and the avalanche characteristics, with approximately three to four iterations a good avalanche model in FLOW-3D can be built up, which should be comparable in expansion and fragmentation to the original simulated avalanche (step 1).

After this process, the impacting mass, shape and velocity of the model
avalanche is comparable to the avalanche computed in step 1. The main
difference is the reduced slide thickness

Exemplary results of a simulation with FLOW-3D (including added
original stl-geometry) of a stopped and restarted avalanche model at

The result of the shown process is a model avalanche based on water, which is the boundary condition for the impulse wave in the reservoir. By use of the 3-D numerical simulation, the complex reflection and interaction of the impulse wave can be calculated. Furthermore, spillways or other structures, such as bridges or wave breaker, can be implemented in the 3-D numerics.

In addition to the self-adaptation of the thereby generated model avalanche
onto the given terrain, another advantage is the mass conservation. Both
characteristics can not be easily implemented in a solid body concept with
a fixed moving part. The difference in density between snow and water is
compensated by correcting the used bulk slide volume

Figure

The numerical calculations are performed with FLOW-3D. This 3-D numerical
software is a good solution for flow calculation with a free surface and is
based on the Reynolds-averaged Navier–Stokes equations in combination
with the volume of fluid (VOF) technique

In case of a sharp interface, FLOW-3D calculates, based on the VOF, the
surface slope in each cell. As a result of the used modelling concepts, only
the velocities of the water (fluid 1) have to be computed and the second
fluid (in general air) is not considered. The solver is very accurate and
stable for free-surface simulations. Various validation experiments showed
the capacity of FLOW-3D. As examples, the software was successfully used for
the investigation of a combined sewer overflow

The basic scale model tests at ETH Zürich base on investigations
conducted in a channel with a length to width ratio

The reference geometry is shown in Fig.

Input parameter for the reference geometry based on the water slide.

Reference geometry including the initial condition at time

The origin of the coordinate system is defined in the middle of the bottom
line of the upstream dam. The

The simulations with the software FLOW-3D are based on one single mesh block
with a homogeneous cell size of 1

At the upper end of the slope, a water block with a chosen volume

Exemplary results of the reference case. Left column

The impact of the avalanche at time

The investigation of the impulse wave shows that the primary wave front is
nearly parallel to the dam and orthogonal to the wall. This is comparable to
the laboratory tests at ETH Zürich (Sect.

To classify the impact behaviour, the Froude number of the inflowing water is
analysed with FLOW-3D. Depending on the location and time, the Froude number
is approximately in the range of 7–8 (–) for the chosen set-up. According
to

The resulting impulse wave in the reservoir is best described as a solitary
wave. It is characterised by large mass transport, no wave through and an
approximate wave length of

The overflow process at the dam is described in detail by

Accumulation of the overtopping volume

The Excel tool based on

Based on this mentioned input parameter and the assumption of a 2-D case, the
Excel tool calculates an overtopping volume

A larger run-up height

The same overtopping volume

The 3-D numerical simulation monitors the resulting overtopping volume over
1000

The input parameters for the computation of the overtopping volume

In the formulas presented in Sect.

Overtopping volume

Overtopping volume

Input parameters for the variation and the results (run-up height

A higher freeboard

Overtopping volume

Initial condition for simulation with

Overtopping volume

The Excel tool based on

The results of overtopping volume

As mentioned in Sect.

The paper presents a new approach for simulating the impact of
an avalanche in a reservoir with the 3-D numerical software FLOW-3D. Water
is placed in the release zone and only accelerated by gravity. The volume of
the used water is identical to the melted snow (mass conservation) and the
flow behaviour is also comparable to the avalanche simulation. Restarts of
the model avalanche, for which the velocity of the inflowing water is set to
0, are used to calibrate the velocities with which the water reaches the
reservoir (Sect.

The advantages of this modelling concept are the limitation on two fluids (water and air) to simulate such an impact as well as the good adaptation of the avalanche onto the terrain. The latter can be a critical point, if simplified solid bodies are used to generate the impulse wave. By using 3-D numerical simulations in general, complex terrains and reservoirs including spillways or other structures can be included in the investigation. Furthermore, reflections and interactions of the impulse waves can be simulated as well as resulting influences on the downstream area of the dam.

The long-standing research at ETH Zürich in the field of impulse waves
led to generalised formulas to compute such an impact
(Sect.

The comparison of the 3-D numerical approach and the used formulas provided
by ETH Zürich showed similar overtopping volumes for the investigated
reference case and the conducted parameter studies. Hence, the presented
model concept can help to quantify the impulse wave and its consequence for
actual (complex) projects based on FLOW-3D. The extension of the parameter
study (including the assumption that the slide thickness

The presented work is mainly based on third-party-funded research. The authors want to thank different Austrian hydro power producers and FLOW-3D Germany for the support. The authors are grateful to the editor Thomas Glade and the two anonymous reviewers for their valuable comments. Edited by: T. Glade Reviewed by: two anonymous referees