Predicting potential deposition areas of future debris-flow events is
important for engineering hazard assessment in alpine regions. To this end,
numerical simulation models are commonly used tools. However, knowledge of
appropriate model parameters is essential but often not available. In this
study we use two numerical simulation models, RAMMS–DF (rapid mass movement
system–debris-flow) and DAN3D (dynamic analysis of landslides in three
dimensions), to back-calculate two well-documented debris-flow events in
Austria and to compare the range and sensitivity of input parameters for the
Voellmy flow model. All simulations are based on the same digital elevation
models and similar boundary conditions. Our results show that observed
deposition patterns are best matched with a parameter set of
Debris-flows are mass wasting processes which occur in alpine regions and regularly cause loss of human life and property. It is therefore of great public and private interest to delineate hazardous areas where future debris-flows are expected to occur. For this, various types of simulation models provide useful guidance and are often used in engineering practice. Such models range from purely empirical–statistical approaches (e.g.,, Scheidegger, 1973; Körner, 1976; Rickenmann, 1999; Legros, 2002; Scheidl and Rickenmann, 2010) to more physically based, deterministic approaches, mostly based on depth-averaged flow equations and a simple flow resistance term (e.g., Takahashi, 1991; Hungr, 1995; O'Brien et al., 1993; Medina et al., 2008; Christen et al., 2010a, b).
Independent of the constitutive relation used, a common caveat for all numerical simulation tools remains model calibration (i.e., appropriate choice of flow-resistance parameters). In the case of simple stress–strain relations (e.g., Bingham, Herschel Bulkley model), laboratory experiments have been conducted to derive material parameters for highly concentrated grain–fluid mixtures (e.g., Phillips and Davies, 1991; Major and Pierson, 1992; Contreras and Davies, 2000; Kaitna and Rickenmann, 2007; Kaitna et al., 2007). However, direct application of the results is complicated because scaled experiments together with the simple flow resistance models do not themselves represent full mixture dynamics of a real scale debris-flow (Iverson, 1997, 2003; Ancey, 2006; Kaitna et al., 2014). Therefore, as for conceptual depth-averaged flow resistance approaches (Voellmy model, Coulomb, etc.), model parameterization based on the back-calculation of well-documented past events appears to be preferable for engineering application (e.g., Hungr et al., 2005; Rickenmann et al., 2006; Hürlimann et al., 2008; Christen et al., 2010a).
Comparative studies indicate that the Voellmy model (detailed in Sect. 2), which was originally developed for modeling bulk flow propagation of snow avalanches, is also suitable for modeling other geomorphic processes, including rock avalanches and debris-flows (e.g., Hungr, 1995; Revellino et al., 2004; Naef et al., 2006; Sosio et al., 2008; Deline et al., 2011). For snow avalanches, a reasonable database of model parameters for different types of snow and land cover is available (e.g., Bartelt et al., 2013a). However, there is much less experience in the case of debris-flows.
We therefore present our experiences with back-calculating Voellmy parameters for two well-documented debris-flow events in Austria. We do this using the simulation platforms, RAMMS–DF (rapid mass movement system–debris-flow) and DAN3D (dynamic analysis of landslides in three dimensions). Because a plausible representation of simulation results requires knowledge of the sensitivity of model input parameters, we additionally carried out a comparative sensitivity analysis for both models. Section 2 gives a brief overview of the technical background of RAMMS–DF and DAN3D, the Voellmy model and the application to the two study sites. The best-fit parameters and the sensitivity analyses are presented in Sect. 3 and discussed in Sect. 4.
Reiselehnrinne Creek is located in the Pitztal Valley, southwest of
Innsbruck, Tyrol, Austria (
The second study area is the densely forested fan of Festeticgraben Creek,
situated in the Gesäuse National Park, Styria, Austria
(
Within this study, the numerical simulation tools RAMMS–DF (developed at the WSL Institute for Snow and Avalanche Research SLF and the Swiss Federal Institute for Forest, Snow and Landscape Research WSL) and DAN3D (developed at the Department of Earth, Ocean and Atmospheric Sciences at the University of British Columbia UBC) were applied to replicate the deposition patterns of two well-documented debris-flow events. Both simulation tools use the equivalent fluid concept (Hungr, 1995) and assume constant density and incompressibility of the flowing media as well as the validity of the shallow water approximation (i.e., negligible slope, normal accelerations). Mass and momentum balance is provided by solving the depth-averaged flow equations in a Lagrangian reference framework for DAN3D (Hungr and McDougall, 2009) and with a fixed Eulerian coordinate system for RAMMS (Christen et al., 2010b). A number of studies can be found in literature in which similar depth-averaged equations were derived, such as Iverson and Denlinger (2001) and Pastor et al. (2002) for Eulerian forms, and e.g., Savage and Hutter (1989) and Gray et al. (1999) for Lagrangian forms.
RAMMS uses the total variation diminishing (TVD) finite volume scheme (FVM)
applied on 3D terrain (Christen et al., 2005; Graf and McArdell, 2008). By
this method, averaged cell values are calculated for each place in a grid by
the means of the edge fluxes from the neighboring cells (Toro, 1999).
Detailed information on the discretization technique and the numerical
background of RAMMS can be found in Christen et al. (2008, 2010a, b). The
frictional behavior in
Contrary to RAMMS, DAN3D is based on smoothed particle hydrodynamics (SPH) (Lucy, 1977; Gingold and Monaghan, 1977) to solve the governing equations resulting in flow depths, velocities and erosion thickness. Here the equations are solved in the center of reference columns and these mass particles are in the flow and progressed to a new position for each time step individually (Monaghan, 1989; Benz, 1990; Sosio et al., 2008). The SPH method uses the Langrangian reference frame and does not need a computational grid. DAN3D allows a selection of different types of resistance laws, including a laminar, turbulent, plastic, Bingham, frictional or Voellmy rheology (Hungr, 1995 and Hungr and McDougall, 2009 and references therein). For comparative reasons, in this study we only focused on the Voellmy rheology.
From theoretical reasoning, Voellmy (1955) divided total resistance of the
flowing media into two parts: a Coulomb-type friction (coefficient
In both simulation tools, modeling of internal pressure gradients is guided
by Rankine's earth pressure theory, as similarly applied by Savage and Hutter
(1989) (Bartelt et al., 1999; Hungr, 2008a). Here an internal friction angle
controls the resulting stresses of longitudinal straining. A minimum value of
the pressure coefficient
In engineering applications, the uncertainties are not only connected to the
choice of flow resistance parameters
As an initial condition, RAMMS–DF and DAN3D use a block release of source
material of a predefined volume. RAMMS–DF additionally offers the
possibility to define an inflow hydrograph at an arbitrary position in the
channel. To keep boundary conditions consistent, we used a mass block release
(e.g., an instantaneous landslide release) as the initial condition in both
codes. Based on indications from aerial images, we assumed source areas in
the upper part of catchments, with release heights of
Because we do not have any reliable information on flow parameters in the
transit reach during the events (i.e., flow depth, flow velocity), the
evaluation of model performance focused solely on the deposition pattern.
Since the event at Reiselehnrinne Creek as well as first simulation runs
showed limited spreading of the material, the runout length of the simulated
debris-flow deposits appeared to be the most useful evaluation criteria.
Observed debris-flow material of the Festeticgraben Creek event in 2006
overtopped the channel and widely spread over the fan in form of tongues or
lobes. We therefore compared observed and simulated deposition areas by using
a similar approach to Carranza and Castro (2006) and Scheidl and Rickenmann
(2010). For this, subareas
Superposition of the simulated area with the observed area of
recently deposited debris-flow material at the Festeticgraben debris
fan
First back-calculations of the event at the Reiselehnrinne Creek with both
models led to differences to observed deposition patterns. Specifically, most
of the material left the channel close to the distal limit of the fan and ran
out straight into the forest instead of following the channelized path to the
orographic right section of the fan (see dashed lines in Fig. 3a and c). To
overcome this problem, we assigned an area with increased roughness
For the second study site (Festeticgraben, Gesäuse) we differentiated
between the roughness within the channel (
Best-fit simulations of RAMMS–DF and DAN3D for both study areas,
the Reiselehnrinne (
Variation of the Voellmy parameters (0.03–0.16 for
A sensitivity analysis was performed for
In the case of the Festeticgraben Creek, the evaluation parameter
First simulation runs did not match the observed deposition pattern for both
investigation areas. In the case of the Reiselehnrinne, most of the material
left the channel before it reached the proximal limit of the fan. This was
not observed after the event in 2009. This discrepancy is most likely due to
(1) the use of an outdated or insufficiently precise DEM,
(2) erosion/deposition processes during the event itself, or (3) an
overestimation of simulated flow depth. We have no data to quantify these
effects, but we can make qualitative assessments. The grid size of the DEM
used in this study was set to 2 m to reduce the calculation time and yet
provide simulation results with a relatively high spatial resolution.
Resulting simulated maximum flow depths between 5 and 10 m are plausible for
both model results. However, the DEM used in our calculations was derived by
air-borne laser scanning 3 years before the event occurred and therefore does
not account for potential morphological changes in the meantime. In an
earlier study, Kogelnig-Mayer et al. (2011) reconstructed debris-flows and
snow avalanches back to 1868 by tree ring analysis. The results showed that
no debris-flow events were detectable between 2006 and 2009. Therefore
morphological changes in the channel are expected to be mainly due to fluvial
processes. For practical engineering applications, there are several ways to
direct the flow in a certain direction, including modification of the DEM
(adding a dam structure or changing the height in the original grid of the
DEM), change of resistance parameters of the flowing mass along the channel
(thereby altering the shape of the hydrograph), or localized increase of
roughness of one channel bank. We chose the latter approach and increased the
left channel bank roughness to
Sensitivity of the dimensionless
For the second study site at the Festeticgraben Creek we assumed that the
forested fan has considerably influence on the deposition behavior of
debris-flows and separated
Though we used the same input parameters for both models, there are several
differences between the simulation programs leading to the results (Table 1).
The main differences arise from different stopping criteria, calculation of
the pressure term, and the numerical solution schemes of the mass and
momentum conservation equations. For quantifying the effect of the different
stopping criteria, we conducted some additional simulations to evaluate the
repeatability and relative sensitivity of the outcomes. RAMMS–DF stops
calculation at a user-defined percentage value of the total mass momentum (or
it can be stopped manually or after a user-defined run duration). In this
study we consistently used a value of 15 %. Changing this stopping
criteria to other plausible values (5, 10 and 20 %), indicates that the
overall sensitivity can be similar to that of the variation in
Comparison of model input conditions within our study. Grids, triggering conditions, excluded erosion, rheology and the governing equations are identical, whereas the numerical solution, the reference system as well as the stopping of the simulations are different.
Another difference between RAMMS and DAN3D is the effect of vertical pressure
gradients on the internal stress state in the 2-D momentum balance equations,
which is modeled by a proportionality coefficient
Variations of stopping criteria using the RAMMS–DF model for the Reiselehnrinne Creek case study. Outlines of the simulations are presented in black; observed deposits are given in red.
Besides these differences in program code, there are also other factors that may influence model output, like the question of DEM and calculation resolution (Rickenmann et al., 2006; Hungr, 2008b; Christen et al., 2010a; Bühler et al., 2011), or erosion along the path (e.g., Hungr, 1995; McDougall and Hungr, 2005; Christen et al., 2010b; Berger et al., 2011). Effects of both were not investigated in this study.
A general observation is that for both programs, changing the friction
parameter
For the simulation of our small alpine debris-flow events, the best-fit
Voellmy parameter sets of RAMMS–DF and DAN3D are in the range of
Voellmy resistance parameter sets from back-calculation of different
events with RAMMS (
Two documented debris-flow events in Austria were
back-calculated with two different simulation tools, the RAMMS–DF code and
the DAN3D code: the Reiselehnrinne Creek (Pitztal) event in 2009, which
released a total volume of
This project received financial support from the Climate and Energy Fund and is carried out within the framework of the “ACRP” Program. The authors would like to thank Oldrich Hungr for providing the DAN3D code to perform our simulations within this study and for helpful discussion. Edited by: F. Guzzetti Reviewed by: C. Huggel and one anonymous referee