In the morning of 23 August 2017, around 3×106 m3 of
granitoid rock broke off from the eastern face of Piz Cengalo, southeastern Switzerland.
The initial rockslide–rockfall entrained 6×105m3
of a glacier and continued as a rock (or rock–ice) avalanche before evolving into a
channelized debris flow that reached the village of Bondo at a distance of
6.5 km after a couple of minutes. Subsequent debris flow surges followed in
the next hours and days. The event resulted in eight fatalities along its
path and severely damaged Bondo. The most likely candidates for the water
causing the transformation of the rock avalanche into a long-runout debris
flow are the entrained glacier ice and water originating from the debris
beneath the rock avalanche. In the present work we try to reconstruct
conceptually and numerically the cascade from the initial rockslide–rockfall to the first debris flow surge and thereby consider two scenarios in
terms of qualitative conceptual process models: (i) entrainment of most of
the glacier ice by the frontal part of the initial rockslide–rockfall
and/or injection of water from the basal sediments due to sudden rise in
pore pressure, leading to a frontal debris flow, with the rear part largely
remaining dry and depositing mid-valley, and (ii) most of the entrained
glacier ice remaining beneath or behind the frontal rock avalanche and
developing into an avalanching flow of ice and water, part of which overtops
and partially entrains the rock avalanche deposit, resulting in a debris
flow. Both scenarios can – with some limitations – be numerically
reproduced with an enhanced version of the two-phase mass flow model
(Pudasaini, 2012) implemented with the simulation software r.avaflow, based
on plausible assumptions of the model parameters. However, these simulation
results do not allow us to conclude on which of the two scenarios is the more
likely one. Future work will be directed towards the application of a
three-phase flow model (rock, ice, and fluid) including phase transitions in
order to better represent the melting of glacier ice and a more appropriate
consideration of deposition of debris flow material along the channel.
Introduction
Landslides lead to substantial damage to life, property, and
infrastructure every year. Whereas they have mostly local effects in hilly
terrain, landslides in high-mountain areas, with elevation differences of
thousands of metres over a few kilometres, may form the initial points of
process chains which, due to their interactions with glacier ice, snow,
lakes, or basal material, sometimes evolve into long-runout debris
avalanches, debris flows, or floods. Such complex landslide events may occur
in remote areas, such as the 2012 Alps rock–snow avalanche in Austria (Preh
and Sausgruber, 2015) or the 2012 Santa Cruz multi-lake outburst event in
Peru (Mergili et al., 2018a). If they reach inhabited areas, such events
lead to major destruction even several kilometres away from the source and
have led to major disasters in the past, such as the 1949 Khait rock
avalanche–loess flow in Tajikistan (Evans et al., 2009b), the 1962 and 1970
Huascarán rockfall–debris avalanche events in Peru (Evans et al.,
2009a; Mergili et al., 2018b), the 2002 Kolka–Karmadon ice–rock avalanche in
Russia (Huggel et al., 2005), the 2012 Seti River debris flood in Nepal
(Bhandari et al., 2012), or the 2017 Piz Cengalo–Bondo rock avalanche–debris
flow event in Switzerland. The initial fall or slide sequences of such process chains are commonly related to a changing cryosphere characterized by glacial debuttressing, the formation of hanging glaciers, or a changing permafrost regime (Harris et al., 2009; Krautblatter et al., 2013; Haeberli and
Whiteman, 2014; Haeberli et al., 2017).
Computer models assist risk managers in anticipating the impact areas,
energies, and travel times of complex mass flows. Conventional single-phase
flow models, considering a mixture of solid and fluid components (e.g.
Voellmy, 1955; Savage and Hutter, 1989; Iverson, 1997; McDougall and Hungr,
2004; Christen et al., 2010), do not serve such a purpose. Instead,
simulations rely on the following:
model cascades, changing from one approach to the next at each process
boundary (Schneider et al., 2014; Somos-Valenzuela et al., 2016) so that each
individual model is tailored for the corresponding process component,
bulk mixture models or two-phase or even multi-phase flow models (Pitman and Le,
2005; Pudasaini, 2012; Iverson and George, 2014; Mergili et al., 2017;
Pudasaini and Mergili, 2019), since two-phase or multi-phase flow models separately
consider not only the solid and the fluid phase but also phase interactions and
therefore allow for considering more complex process interactions such as the
impact of a landslide on a lake or reservoir.
Worni et al. (2014) have highlighted the advantages of the second point for considering
also the process interactions and boundaries.
The aim of the present work is to learn about our ability to reproduce
sophisticated transformation mechanisms involved in complex, cascading
landslide processes with GIS-based tools. For this purpose, we apply the
computational tool r.avaflow (Mergili et al., 2017), which employs an
enhanced version of the Pudasaini (2012) two-phase flow model, to
back calculate the 2017 Piz Cengalo–Bondo landslide cascade in southeastern
Switzerland, which was characterized by the transformation of a rock
avalanche to a long-runout debris flow. We consider two scenarios in terms
of hypothetic qualitative conceptual models of the physical transformation
mechanisms. On this basis, we try to numerically reproduce these scenarios,
satisfying the requirements of physical plausibility of the model
parameters and empirical adequacy in terms of correspondence of the results
with the documented and inferred impact areas, volumes, velocities, and
travel times. Based on the outcomes, we identify the key challenges to be
addressed in future research.
As a result, we rely on the detailed description, documentation, and topographic
reconstruction of this recent event. The event documentation, data used, and
the conceptual models are outlined in Sect. 2. We briefly introduce the
simulation framework r.avaflow (Sect. 3) and explain its parametrization
and our simulation strategy (Sect. 4) before presenting (Sect. 5) and
discussing (Sect. 6) the results obtained. Finally, we conclude with the
key messages of the study (Sect. 7).
The 2017 Piz Cengalo–Bondo landslide cascadePiz Cengalo and Val Bondasca
Val Bondasca is a left-tributary valley to Val Bregaglia in the
canton of Grisons in southeastern Switzerland (Fig. 1). The Bondasca stream joins the
Mera River at the village of Bondo at 823 m a.s.l. It drains part of the
Bregaglia Range, built up by a mainly granitic intrusive body culminating at
3678 m a.s.l. Piz Cengalo, with a summit elevation of 3368 m a.s.l., is
characterized by a steep, intensely fractured northeastern face which has repeatedly
been the scene of landslides and which is geomorphologically connected to
Val Bondasca through a steep glacier forefield. The glacier itself
largely retreated to the cirque beneath the rock wall.
Study area with the impact area of the 2017 Piz Cengalo–Bondo
landslide cascade. The observed rock avalanche terminus was derived from WSL
(2017).
On 27 December 2011, a rock avalanche with a volume of
1.5×106–2×106 m3 developed out of a rock toppling from the
northeastern face of Piz Cengalo, travelling for a distance of 1.5 km down to the
uppermost part of Val Bondasca (Haeberli, 2013; De Blasio and
Crosta, 2016; Amann et al., 2018). This rock avalanche reached the main
torrent channel. Erosion of the deposit thereafter resulted in increased
debris flow activity (Frank et al., 2019). No entrainment of glacier ice was
documented for this event. As blue ice had been observed directly at the
scarp, the role of permafrost for the rock instability was discussed. An
early warning system was installed and later extended (Steinacher et al.,
2018). Displacements at the scarp area, measured by radar interferometry and
laser scanning, were a few centimetres per year between 2012 and 2015 and
accelerated in the following years. In early August 2017, increased rockfall activity and deformation rates alerted the authorities. A major rockfall event occurred on 21 August 2017 (Amann et al., 2018).
The event of 23 August 2017
The complex landslide which occurred on 23 August 2017 was documented mainly
by reports of the Swiss Federal Institute for Forest, Snow and Landscape
Research (WSL); the Laboratory of Hydraulics, Hydrology and Glaciology (VAW)
of ETH Zurich; and the Amt für Wald und Naturgefahren (Office for
Forest and Natural Hazards) of the canton of Grisons.
At 09:31 local time, a volume of approximately 3×106 m3
detached from the northeastern face of Piz Cengalo, as indicated by WSL (2017),
Amann et al. (2018), and the point cloud we obtained through structure from motion (SfM) using pictures taken after the event. Documented by videos and by
seismic records (Walter et al., 2018), it impacted the glacier beneath the
rock face and entrained approximately 6×105 m3 of ice (VAW,
2017; WSL, 2017), was sharply deflected at an opposite rock wall, and
evolved into a rock (or rock–ice) avalanche. Part of this avalanche immediately
converted into a debris flow which flowed down Val Bondasca. It was
detected at 09:34 LT by the debris flow warning system which had been installed
near the hamlet of Prä, approximately 1 km upstream from Bondo. According to
different sources, the debris flow surge arrived at Bondo between 09:42
(derived from WSL, 2017) and 09:48 LT (Amt für Wald und Naturgefahren,
2017). The rather low velocity in the lower portion of Val Bondasca is
most likely a consequence of the narrow gorge topography and of the viscous
behaviour of this first surge. Whereas approximately 540 000 m3
of material was involved, only 50 000 m3 arrived at Bondo
immediately (data from the canton of Grisons; reported by WSL, 2017). The
remaining material was partly remobilized by six further debris flow surges
recorded during the same day, one on 25 August, and one – triggered by
rainfall – on 31 August 2017. All nine surges together deposited a volume
of approximately 500 000–800 000 m3 in the area of Bondo, less
than half of which was captured by a retention basin (Bonanomi and Keiser,
2017).
The vertical profile of the main flow path is illustrated in Fig. 4. The
total angle of reach of the process chain from the initial release down to
the outlet of Val Bondasca was approximately 17.4∘, computed
from the travel distance of 7.0 km and the vertical drop of approximately 2.2 km.
The initial landslide to the terminus of the rock avalanche showed an angle
of reach of approximately 25.8∘, derived from the travel distance of
3.4 km and the vertical drop of 1.7 km. This value is higher than the
22∘ predicted by the equation of Scheidegger (1973), probably due
to the sharp deflection of the initial landslide. Following the concept of
Nicoletti and Sorriso-Valvo (1991), the rock avalanche was characterized by
channelling of the mass. Only a limited run-up was observed, probably due to
the gentle horizontal curvature of the valley in that area (no orthogonal
impact on the valley slope; Hewitt, 2002). There were eight fatalities,
concerning hikers in Val Bondasca, extensive damage to buildings and
infrastructure, and evacuations for several weeks or even months.
Profile along the main flow path of the Piz Cengalo–Bondo
landslide cascade. The letters A–F indicate the individual zones (Table 1
and Fig. 7), whereas the associated numbers indicate the average angles of
reach along the profile for each zone. The brown number and line show the
angle of reach of the initial landslide (rockslide–rockfall and rock – or rock—ice –
avalanche), whereas the blue number and line show the angle of reach of the
entire landslide cascade. The geomorphic characteristics of the zone (in
black) are indicated along with the dominant process type (in green).
Data and conceptual model
Reconstruction of the rock and glacier volumes involved in the event was
based on an overlay of a 2011 swisstopo digital terrain model (DTM; contract: swisstopo–DV084371), derived through airborne laser scanning in
2011 and available at a raster cell size of 2 m, and a digital surface model
(DSM) obtained through SfM techniques after the 2017
event. This analysis resulted in a detached rock volume of
3.27×106 m3, which is slightly more than the value of
3.15×106 m3 reported by Amann et al. (2018), and an
entrained ice volume of 770 000 m3 (Fig. 5). However, these
volumes neglect smaller rockfalls before and after the large 2017 event
and also glacial retreat. The 2011 event took place after the DTM had been
acquired, but it released from an area above the 2017 scarp. The boundary
between the 2011 and the 2017 scarps, however, is slightly uncertain, which
explains the discrepancies between the different volume reconstructions.
Assuming some minor entrainment of the glacier ice in 2011 and some glacial
retreat, we arrive at an entrained ice volume of approximately
600 000 m3, a value which is very well supported by VAW
(2017).
Reconstruction of the released rock volume and the entrained
glacier volume in the 2017 Piz Cengalo–Bondo landslide cascade. Note that
the boundary between the 2011 and 2017 release volumes is connected to some
uncertainties, explaining the slight discrepancies among the reported
volumes. The glacier volume shown is neither corrected for entrainment
related to the 2011 event nor for glacier retreat in the period 2011–2017.
There is still disagreement on the origin of the water that led to the
debris flow, particularly to the first surge. Bonanomi and Keiser (2017)
clearly mention meltwater from the entrained glacier ice as the main source,
whereby much of the melting is assigned to impact, shearing, and frictional
heating directly at or after impact, as is often the situation in
rock–ice avalanches (Pudasaini and Krautblatter, 2014). WSL (2017) has
shown, however, that the energy released was only sufficient to melt
approximately half of the glacier ice. Water pockets in the glacier or a
stationary water source along the path might have played an important role
(Demmel, 2019). Walter et al. (2020) claim that much of the glacier ice was
crushed, ejected, and dispersed (Fig. 3b), whereas water injected into the
rock avalanche due to pore pressure rise in the basal sediments would have
played a major role. In any case, the development of a debris flow from a
landslide mass with an overall solid fraction of as high as ∼0.85 (considering the water equivalent of the glacier ice) requires some
spatio-temporal differentiation of the water and ice content. We consider two
qualitative conceptual models – or scenarios – possibly explaining such a
differentiation:
The initial rockslide–rockfall led to massive entrainment fragmenting, and
melting of glacier ice; mixing of rock with some of the entrained ice and
the meltwater, and injection of water from the basal sediments into the rock
avalanche mass quickly upon impact due to overload-induced pore pressure
rise. As a consequence, the front of the rock avalanche was characterized by
a high content of ice and water, was highly mobile, and therefore escaped as the
first debris flow surge, whereas the less mobile rock avalanche behind it –
still with some water and ice in it – decelerated and deposited mid-valley.
The secondary debris flow surges occurred mainly due to backwater effects.
This scenario largely follows the explanation of Walter et al. (2020) in which
the first debris flow surge was triggered at the front of the rock avalanche
by overload and pore pressure rise, whereas the later surges overtopped the
rock avalanche deposits, as indicated by the surficial scour patterns.
The initial rockslide–rockfall impacted and entrained the glacier. Most of
the entrained ice remained beneath the rock fragments and, after some initial sliding,
developed into an avalanching flow of melting ice behind the rock avalanche.
The rock avalanche decelerated and stopped mid-valley. Part of the
avalanching flow overtopped and partly entrained the rock avalanche deposit
– leaving behind the scour traces observed in the field – and evolved into
the channelized debris flow which arrived at Bondo a couple of minutes
later. The secondary debris flow surges started from the rock avalanche
deposit due to melting and infiltration of the remaining ice and due to
backwater effects. This scenario is similar to the theory developed at the
WSL Institute for Snow and Avalanche Research (SLF), which also did a first
simulation of the rock avalanche (WSL, 2017).
Figure 6 illustrates the conceptual models attempting to explain the key
mechanisms involved in the rock avalanche–debris flow transformation.
Qualitative conceptual models of the rock avalanche–debris flow
transformation. (a) Scenario S1. (b) Scenario S2. See text for the detailed
description of the two scenarios.
The simulation framework r.avaflow
r.avaflow represents a comprehensive GIS-based open-source framework which
can be applied for the simulation of various types of geomorphic mass flows.
In contrast to most other mass flow simulation tools, r.avaflow utilizes a
general two-phase flow model describing the dynamics of the mixture of solid
particles and viscous fluid and the strong interactions between these
phases. It further considers erosion and entrainment of surface material
along the flow path. These features facilitate the simulation of cascading
landslide processes such as the 2017 Piz Cengalo–Bondo event. r.avaflow is
outlined in full detail by Mergili and Pudasaini (2019). The code, a user
manual, and a collection of test datasets are available from Mergili and Pudasaini (2019).
Only the aspects directly relevant to the present work are described in
this section.
Essentially, the Pudasaini (2012) two-phase flow model is employed for
computing the dynamics of mass flows moving from a defined release area
(solid and/or fluid heights are assigned to each raster cell) or release
hydrograph (at each time step, solid and/or fluid heights are added at a
given profile, moving at a given cross-profile velocity) down through a DTM.
The spatio-temporal evolution of the flow is approximated through
depth-averaged solid and fluid mass and momentum balance equations
(Pudasaini, 2012). This system of equations is solved through the total-variation-diminishing (TVD) non-oscillatory central differencing (NOC)
scheme introduced by Nessyahu and Tadmor (1990), adapting an approach
presented by Tai et al. (2002) and Wang et al. (2004). The characteristics
of the simulated flow are governed by a set of flow parameters (some of them
are shown in the Tables 1 and 2).
Descriptions and optimized parameter values for each of the zones
A–F (Figs. 4 and 7). The names of the model parameters are given in the
text and in Table 2. The values provided in Table 2 are assigned to those
parameters not shown. S1 and S2 refer to the corresponding scenarios.
ZoneDescriptionModel parametersInitial conditionsARock zone – northeastern face of Piz Cengalo with rockslide–rockfall release areaδ=20∘ (S1)aδ=13∘ (S2)bCAD=0.2Release volume: 3.2×106 m3, 100 % solidcBGlacier zone – cirque glacier beneath zone A, entrainment of glacier iceaδ=20∘ (S1) δ=13∘ (S2) CE=10-6.5Entrainment of glacier ice and till (Table 3)dCSlope zone – steep, partly debris-covered glacier forefield leading down to ValBondascaδ=20∘ (S1) δ=13∘ (S2) CE=10-6.5 (S1) CE=10-8.0 (S2)Entrainment of injected water in Scenario S1 Entrainment of rock avalanche deposit in Scenario S2DUpper Val Bondasca zone – clearly defined flow channel becoming narrower indownstream directionδ=20–45∘No entrainment allowed, increasing frictionELower Val Bondasca zone – narrow gorgeδ=45∘CFF=0.5No entrainment allowed, high friction due to lateral confinementFBondo zone – deposition ofthe debris flow on the cone ofBondoδ=20∘No entrainment allowed
a Note that in all zones and in
both of the scenarios, S1 and S2, δ is assumed to scale linearly with
the solid fraction. This means that the values given only apply in case of
100 % solid material. b This only applies to the initial landslide, which
is assumed completely dry in Scenario S2. Due to the scaling of δ
with the solid fraction, a lower basal friction is required to obtain
results similar to Scenario S1, where the rock avalanche contains some
fluid. The same values of δ as for Scenario S1 are applied for the
debris flow in Scenario S2 throughout all zones. c This volume is
derived from our own reconstruction (Fig. 5). In contrast, WSL (2017) gives
3.1×106 m3 and Amann et al. (2018) 3.15×106 m3. d In Scenario S2, the glacier is not directly
entrained but instead released behind the rock avalanche. In both
scenarios, ice is considered to melt immediately on impact and included in
the viscous fluid fraction. See text for more detailed explanations.
Model parameters used for the simulations.
SymbolParameterUnitValueρSSolid material density (grain density)kg m-32700ρFFluid material densitykg m-31400aφInternal friction angleDegree27bδBasal friction angleDegreeTable 1νKinematic viscosity of the fluidm2 s-110τYYield strength of the fluidPa10CADAmbient drag coefficient–0.04 (exceptions in Table 1)CFFFluid friction coefficient0.0 (exceptions in Table 1)CEEntrainment coefficient–Table 1
a Fluid is considered here to be a mixture of water and
fine particles. This explains the higher density compared to pure water.
b The internal friction angle φ always has to be larger than
or equal to the basal friction angle δ. Therefore, in the case of
δ>φ, φ is increased accordingly.
The solid and fluid phases have their own mass and momentum balance
equations so that they evolve as independent dynamical quantities while the
phases are still coupled. This means that, in general, the solid and fluid
velocities are different. However, the use of an enhanced drag model
(Pudasaini, 2019) and the consideration of virtual mass forces ensure a
strong coupling between the solid and the fluid phases in the mixture
(Pudasaini, 2012; Pudasaini and Mergili, 2019). Compared to the Pudasaini
(2012) model, some further extensions have been introduced which include (i)
ambient drag or air resistance (Kattel et al., 2016; Mergili et al., 2017)
and (ii) fluid friction, governing the influence of basal surface roughness
on the fluid momentum (Mergili et al., 2018b). Both extensions rely on
empirical coefficients, CAD for the ambient drag and CFF for the
fluid friction. Further, viscosity is computed according to an improved
concept. As in Domnik et al. (2013) and Pudasaini and Mergili (2019), the
fluid viscosity is enhanced by the yield strength. Most importantly, the
internal friction angle φ and the basal friction angle δ of
the solid are scaled with the solid fraction in order to approximate effects
of reduced interaction between the solid particles and the basal surface in
fluid-rich flows.
Entrainment is calculated through an empirical model. In contrast to
Mergili et al. (2017), where an empirical entrainment coefficient is
multiplied by the momentum of the flow, here we multiply the entrainment
coefficient CE (s kg-1 m-1) by the kinetic energy of the
flow:
qE,s=CETs+Tfαs,E,qE,f=CETs+Tf1-αs,E,
where qE,s and qE,f (m s-1) are the solid and fluid entrainment
rates, Ts and Tf (J) are the kinetic energies of the solid and fluid
fractions of the flow, and αs,E is the solid fraction of the
entrainable material. Solid and fluid flow heights and momenta, and the
change of the basal topography, are updated at each time step (see
Mergili et al., 2017, for details).
As r.avaflow operates on the basis of GIS raster cells, its output
essentially consists of raster maps – for all time steps and for the overall
maximum – of solid and fluid flow heights, velocities, pressures, kinetic
energies, and entrained heights. In addition, output hydrograph profiles may
be defined by which solid and fluid heights, velocities, and discharges are
provided at each time step.
Parameterization of r.avaflow
One set of simulations is performed for each of the scenarios, S1 and S2
(Fig. 6), considering the process chain from the release of the rockslide–rockfall to the arrival of the first debris flow surge at Bondo.
Neither triggering of the event nor subsequent surges or distal debris
floods beyond Bondo are considered in this study. Equally, the dust cloud
associated to the rock avalanche (WSL, 2017) is not the subject here.
Initial sliding of the glacier beneath the rock avalanche, as assumed in
Scenario S2, cannot directly be modelled. That would require a three-phase
model, which is beyond the scope here. Instead, release of the glacier ice
and meltwater is assumed in a separate simulation after the rock avalanche
has passed over it. We consider this workaround an acceptable approximation
of the postulated scenario (Sect. 6).
We use the 2011 swisstopo DTM, corrected for the rockslide–rockfall scarp
and the entrained glacier ice by overlay with the 2017 SfM DSM (Sect. 2).
The maps of release height and maximum entrainable height are derived from
the difference between the 2011 swisstopo DTM and the 2017 SfM DSM (Fig. 5;
Sect. 2). The release mass is considered completely solid, whereas the
entrained glacier is assumed to contain some solid fraction (coarse till).
The glacier ice is assumed to melt immediately on impact and is included in
the fluid along with fine till. We note that the fluid phase does not
represent pure water but rather a mixture of water and fine particles (Table 2).
The fraction of the glacier allowed to be incorporated in the process chain
is empirically optimized (Table 3). Based on the same principle, the maximum
depth of entrainment of fluid due to pore pressure overload in Scenario S1
is set to 25 cm, whereas the maximum depth of entrainment of the rock
avalanche deposit in Scenario S2 is set to 1.5 m.
Selected output parameters of the simulations for the scenarios S1
and S2 compared to the observed or documented parameter values. S is solid,
F is fluid, fractions are expressed in terms of volume, and t0 is time
from the initial release to the release of the first debris flow surge.
Reference values are extracted from Amt für Wald und Naturgefahren
(2017), Bonanomi and Keiser (2017), and WSL (2017). *** is empirically
adequate (within the documented range of values). ** is empirically partly
adequate (less than 50 % away from the documented range of values). * is
empirically inadequate (at least 50 % away from the documented range of
values). The arithmetic means of minimum and maximum of each range are used
for the calculations.
ParameterDocumentation and observationScenario S1Scenario S2Entrained ice (m3)600 000a––Entrained S (m3)–60 00060 000bEntrained F (m3)–305 000240 000Duration of initial landslide (s)60–90c100–120**100–120**Travel time to O2 (s)90–120d140**t0+120***Travel time to O3 (s)210–300e280***t0+240***Travel time to O4 (s)630–1020f700***t0+640***Debris flow volume at O2 (m3)540 000530 000** (43 % S)430 000** (45 % S)Debris flow volume at O4 (m3)50 000265 000* (34 % S)270 000* (24 % S)
a Not all the
material entrained from the glacier was relevant to the first debris flow
surge (Fig. 6); therefore lower volumes of entrained S (coarse till; in
Scenario S2 also rock avalanche deposit) and F (molten ice and fine till; in
Scenario S1 also pore water) yield the empirically most adequate results.
The F volumes originating from the glacier in the simulations represent
approximately half of the water equivalent of the entrained ice,
corresponding well to the findings of WSL (2017). b This value does
not include the 145 000 m3 of solid material remobilized
through entrainment from the rock avalanche deposit in Scenario S2. c
WSL (2017) states that the rock avalanche came to rest approximately 60 s after
release, whereas the seismic signals ceased 90 s after release. d A
certain time (here, we assume a maximum of 30 s) has to be allowed for the
initial debris flow surge to reach O2, located slightly downstream of the
front of the rock avalanche deposit. e WSL (2017) gives a travel time
of 3.5 min to Prä, roughly corresponding to the location of O3. It
remains unclear whether this number refers to the release of the initial
rockslide–rockfall or (more likely) to the start of the first debris flow
surge. Bonanomi and Keiser (2017) give a travel time of roughly 4 min
between the initial release and the arrival of the first surge at the sensor
of Prä. f Amt für Wald und Naturgefahren (2017) gives a time
span of 17 min between the release of the initial rockslide–rockfall
and the arrival of the first debris flow surge at the “bridge” in Bondo.
However, the bridge that this number refers to is not indicated. WSL (2017),
in contrast, gives a travel time of 7–8 min from Prä to the “old
bridge” in Bondo, which, in sum, results in a shorter total travel time as
indicated in Amt für Wald und Naturgefahren (2017). Depending on the
bridge, the reference location for these numbers might be downstream from
O4. In the simulation, this hydrograph shows a slow onset – travel times
refer to the point when 5 % of the total peak discharge is reached.
The study area is divided into six zones, labelled A–F (Figs. 4 and 7; Table 1).
Each of these zones represents an area with particular geomorphic
characteristics and dominant process types, which can be translated into
model parameters. Due to the impossibility of directly measuring the key
parameters in the field (Mergili et al., 2018a, b), the parameters
summarized in Tables 1 and 2 are the result of an iterative
optimization procedure, where multiple simulations with different parameter
sets are performed in order to arrive at one “optimum” simulation for each
scenario. It is thereby important to note that we largely derive one single
set of optimized parameters which is valid for both of the scenarios.
Optimization criteria are (i) the empirical adequacy of the model results
and (ii) the physical plausibility of the parameters. Therefore, the empirical
adequacy is quantified through comparison of the results with the documented
impact area; the travel times to the output hydrograph profiles O2, O3, and
O4 (Fig. 7); and the reported volumes (Amt für Wald und Naturgefahren,
2017; Bonanomi and Keiser, 2017; WSL, 2017). The physical plausibility of
the model parameters is evaluated on the basis on the parameters suggested
by Mergili et al. (2017) and on the findings of Mergili et al. (2018a, b).
The values of the basal friction angle (δ), the ambient drag
coefficient (CAD), the fluid friction coefficient (CFF), and the
entrainment coefficient (CE) are differentiated between and within the
zones (Table 1), whereas global values are defined for all the other
parameters (Table 2). It is further important to note that δ scales
linearly with the solid fraction – this means that the values given in
Table 1 only apply for 100 % solid material.
Overview of the heights and entrainment areas as well as the
zonation performed as the basis for the simulation with r.avaflow. Injection
of pore water only applies to Scenario A. The zones A–F represent areas
with largely homogeneous surface characteristics. The characteristics of the
zones and the model parameters associated to each zone are summarized in
Table 1 and Fig. 4. O1–O4 represent the output hydrograph profiles. The
observed rock avalanche terminus was derived from WSL (2017).
Durations of t=1800 s are considered for both scenarios. At this point in
time, the first debris flow surge largely passed and left the area of
interest, except for some remaining tail of fluid material. Only heights
≥0.25 m are taken into account for the visualization and evaluation of
the simulation results. A threshold of 0.001 m is used for the simulation
itself, keeping the loss due to numerical diffusion within a range of
<1 %–4 % until the point when the flow first leaves the area of
interest. Taking into account the size of the event, a cell size of 10 m is
considered the best compromise between capturing a sufficient level of
detail and ensuring an adequate computational efficiency and is therefore
applied for all simulations.
Figure 8 illustrates the distribution of the simulated maximum flow heights,
maximum entrained heights, and deposition area after t=1800 s, when most
of the initial debris flow surge has passed the confluence of the Bondasca
stream and the Maira River. The comparison of observed and simulated impact
areas results in a critical success index (CSI) of 0.558, a distance to perfect
classification (D2PC) of 0.167, and a factor of conservativeness
(FoC) of 1.455. These performance indicators are derived from the confusion
matrix of true positives, true negatives, false positives, and false
negatives. CSI and D2PC measure the correspondence of the observed and simulated
impact areas. Both indicators can range between 0 and 1, whereby values of
CSI close to 1 and values of D2PC close to 0 point to a good correspondence. FoC
indicates whether the observed impact areas are overestimated
(FoC > 1) or underestimated by the simulation (FoC < 1).
More details are provided by Formetta et al. (2016) and by Mergili et al. (2017, 2018a).
Maximum flow height and entrainment derived for Scenario S1.
RA is rock avalanche; the observed RA terminus was derived from WSL (2017).
Interpreting these values as indicators for a reasonably good correspondence
between simulation and observation in terms of impact area, we now consider
the dimension of time, focussing on the output hydrographs OH1–OH4 (Fig. 9;
see Figs. 7 and 8 for the location of the corresponding hydrograph
profiles O1–O4). Much of the rock avalanche passes the profile O1 between
t=60 s and t=100 s. OH2 (Fig. 9a; located in the upper portion of Val
Bondasca) sets on before t=140 s and quickly reaches its peak, with a
volumetric solid ratio of approximately 30 % (maximum 900 m3 s-1
of solid and 2200 m3 s-1 of fluid discharge). Thereafter,
this first surge quickly tails off. The solid flow height, however,
increases to around 3 m and remains so until the end of the simulation,
whereas the fluid flow height slowly and steadily tails off. Until
t=1800 s the profile O2 is passed by a total of
221 000 m3 of solid and 308 000 m3 of
fluid material (the fluid representing a mixture of fine mud and water with
a density of 1400 kg m-3; see Table 2). The hydrograph profile O3 in
Prä, approximately 1 km upstream of Bondo, is characterized by a surge
starting before t=280 s and slowly tailing off afterwards. Discharge at
the hydrograph OH4 (Fig. 9b; O4 is located at the outlet of the canyon to
the debris fan of Bondo) starts at around t=700 and reaches its peak of
solid discharge at t=1020 s (167 m3 s-1). Solid discharge
decreases thereafter, whereas the flow becomes fluid-dominated with a fluid
peak of 202 m3 s-1 at t=1320 s. The maximum total flow
height simulated at O4 is 2.53 m. This site is passed by a total of
91 000 m3 of solid and 175 000 m3 of fluid
material, according to the simulation – an overestimate, compared to the
documentation (Table 3).
Output hydrographs OH2 and OH4 derived for the scenarios S1 and
S2. (a) OH2 for Scenario S1. (b) OH4 for Scenario S1. (c) OH2 for Scenario
S2. (d) OH4 for Scenario S2. See Figs. 7 and 8 for the locations of the
hydrograph profiles O2 and O4. Hs is solid flow height,
Hf is fluid flow height, Qs is solid discharge, and
Qf is fluid discharge.
Figure 10 illustrates the travel times and the frontal velocities of the rock
avalanche and the initial debris flow. The initial surge reaches the
hydrograph profile O3 – located 1 km upstream of Bondo – at t=280 s
(Fig. 10a; Fig. 9c). This is in line with the documented arrival of the
surge at the nearby monitoring station (Table 3). Also the simulated travel
time to the profile O4 corresponds to the existing – though uncertain –
documentation. The initial rock avalanche is characterized by frontal
velocities >25 m s-1, whereas the debris flow largely moves at
10–25 m s-1. Velocities drop below 5 m s-1 in the lower part of the valley
(Zone E; Fig. 10b).
Spatio-temporal evolution and velocities of the event obtained
for Scenario S1. (a) Travel times, starting from the release of the initial
rockslide–rockfall. (b) Frontal velocities along the flow path, shown in
steps of 20 s. Note that the height of the velocity graph does not scale
with flow height. White areas indicate that there is no clear flow path.
Scenario S2 – debris flow surge by overtopping and entrainment of rock
avalanche
Figure 11 illustrates the distribution of the simulated maximum flow heights,
maximum entrained heights, and deposition area after
t=t0+1740 s, where t0 is the time between the release of the
initial rock avalanche and the mobilization of the entrained glacier. The
simulated impact and deposition areas of the initial rock avalanche are also
shown in Fig. 11. However, we now concentrate on the debris flow, triggered
by the simulated entrainment of 145 000 m3 of solid
material from the rock avalanche deposit. Flow heights – as well as the
hydrographs presented in Fig. 9c and d and the temporal patterns illustrated
in Fig. 12 – only refer to the debris flow developing from the entrained
glacier and the entrained rock avalanche material. The confusion matrix of
observed and simulated impact areas reveals partly different patterns of
performance than for Scenario S1: CSI = 0.590, D2PC = 0.289, and
FoC = 0.925. The lower FoC value and the lower performance in terms of D2PC reflect
the missing initial rock avalanche in the simulation results. The output
hydrographs OH2 and OH4 differ from the hydrographs obtained through
Scenario S1 but also show some similarities (Fig. 9c and d). Most of the
flow passes through the hydrograph profile O1 between
t=t0+40 s and t0+80 s and through O2 between
t=t0+100 s and t0+180 s. The hydrograph OH2 is
characterized by a short peak of 3500 m3 s-1 of solid and
4500 m3 s-1 of fluid material, with a volumetric solid fraction of
0.44, and quickly decreasing discharge afterwards (Fig. 9c). In contrast to
Scenario S1, flow heights drop steadily, with values below 2 m from
t=t0+620 s onwards. The hydrograph OH3 is characterized by a
surge starting around t=t0+240 s. Discharge at the hydrograph OH4
(Fig. 9d) sets at around t=t0+600 s, and the solid peak of
240 m3 s-1 is simulated at approximately
t=t0+780 s. The delay of the peak of fluid discharge is more
pronounced when compared to Scenario S1 (310 m3 s-1 at
t=t0+960 s). Profile O4 is passed by a total of
65 000 m3 of solid and 204 000 m3 of fluid
material. The volumetric solid fraction drops from above 0.60 at the very
onset of the hydrograph to around 0.10 (almost pure fluid) at the end. The
maximum total flow height at O4 is 3.1 m.
Maximum flow height and entrainment derived for Scenario S2.
RA is rock avalanche; the observed RA terminus was derived from WSL (2017).
Figure 12 illustrates the travel times and the frontal velocities of the rock
avalanche and the initial debris flow. Assuming that t0 is in the range
of some tens of seconds, the time of arrival of the surge at O3 is in line
with the documentation also for Scenario S2 (Fig. 12a; Table 3). The
frontal velocity patterns along Val Bondasca are roughly in line with those
derived in Scenario S1 (Fig. 12b). However, the scenarios differ among
themselves in terms of the more pronounced but shorter peaks of the
hydrographs in Scenario S2 (Fig. 9). This pattern is a consequence of the
more sharply defined debris flow surge. In Scenario S1, the front of the
rock avalanche deposit constantly releases material into Val Bondasca,
providing supply for the debris flow also at later stages. In Scenario S2,
entrainment of the rock avalanche deposit occurs relatively quickly, without
material supply afterwards. This type of behaviour is strongly coupled to
the value of CE and the allowed height of entrainment chosen for the
rock avalanche deposit.
Spatio-temporal evolution and velocities of the event obtained
for Scenario S2. (a) Travel times, starting from the release of the initial
rockslide–rockfall. Therefore t0 (s) is the time between the release of
the rockslide–rockfall and the mobilization of the entrained glacier. (b)
Frontal velocities along the flow path, shown in steps of 20 s. Note that
the height of the velocity graph does not scale with flow height. White
areas indicate that there is no clear flow path.
Discussion
Our simulation results reveal a reasonable degree of empirical adequacy and
physical plausibility with regard to most of the reference observations.
Having said that, we have also identified some important limitations which
are now discussed in more detail. First of all, we are not able to decide on
the more realistic of the two scenarios, S1 and S2. In general, the melting
and mobilization of glacier ice upon rockslide–rockfall impact are hard to
quantify from straightforward calculations of energy transformation, as
Huggel et al. (2005) have demonstrated on the example of the 2002
Kolka–Karmadon event. In the present work, the assumed amount of melting
(approximately half of the glacier ice) leading to the empirically most
adequate results corresponds well to the findings of WSL (2017), indicating
a reasonable degree of plausibility. It remains equally difficult to
quantify the amount of water injected into the rock avalanche by overload of
the sediments and the resulting pore pressure rise (Walter et al., 2020).
Confirmation or rejection of conceptual models with regard to the physical
mechanisms involved in specific cases would have to be based on better-constrained initial conditions and the availability of robust parameter
sets.
We note that with the approach chosen we are not able (i) to adequately
simulate the transition from solid to fluid material and (ii) to consider
rock and ice separately with different material properties, which would
require a three-phase model and is thus not within the scope here. Therefore, entrained
ice is considered viscous fluid from the beginning. A physically better-founded representation of the initial phase of the event would require an
extension of the flow model employed. Such an extension could build on the
rock–ice avalanche model introduced by Pudasaini and Krautblatter (2014).
Also, the vertical patterns of the situation illustrated in Fig. 5 cannot be
modelled with the present approach, which (i) does not consider melting of
ice and (ii) only allows one entrainable layer at each pixel. The
assumption of fluid behaviour of entrained glacier ice therefore represents
a necessary simplification which is supported by observations (Fig. 3b) but
neglects the likely presence of remaining ice in the basal part of the
eroded glacier, which melted later and so contributed to the successive
debris flow surges.
Still, we currently consider the Pudasaini (2012) model – and the extended
multi-phase model (Pudasaini and Mergili, 2019) – to be best practice, even
though other two-phase or bulk mixture models do exist. Most recently,
Iverson and George (2014) presented an approach that has been solved with an
open-source software, called D-Claw (George and Iverson, 2014), and compared it
to large-scale experiments considering dense debris materials (Iverson et
al., 2000, 2010). The Iverson and George (2014) model can be
useful for flow-type landslides, or bulk motion, where the solid particles
and fluid molecules move together. However, the Pudasaini (2012) model is
better suited for the simulation of cascading mass flows for the following
reasons: (i) solid and fluid velocities are considered separately, which is
important for complex, cascading mass flows; (ii) pore fluid diffusion is
included, whereas the model of Iverson and George (2014) is limited to pore
pressure advection and source terms associated with dilation; (iii)
interfacial momentum transfers, such as the drag force, virtual mass force,
and buoyancy between the solid and fluid phases are fully included; and (iv)
viscous shear stress and dynamical coupling between the pore fluid pressure
evolution and the bulk momentum equations are considered.
The initial rockslide–rockfall and the rock avalanche are simulated in a
plausible way, at least with regard to the deposition area. Whereas the
simulated deposition area is clearly defined in Scenario S2, this is to a
lesser extent the case in Scenario S1, where the front of the rock avalanche
directly transforms into a debris flow. Both scenarios seem to overestimate
the time between release and deposition compared to the seismic signals
recorded – an issue also reported by WSL (2017) for their simulation. We
observe a relatively gradual deceleration of the simulated avalanche,
without clearly defined stopping, and note that also in Scenario S2,
there is some diffusion after the considered time of 120 s so that the
definition of the simulated deposit is somehow arbitrary. The elaboration of
well-suited stopping criteria, going beyond the very simple approach
introduced by Mergili et al. (2017), remains a task for the future. However,
as the rock avalanche has already been successfully back calculated by WSL
(2017), we focus on the first debris flow surge: the simulation input is
optimized towards the back calculation of the debris flow volumes entering
the valley at the hydrograph profile O2 (Table 3). The travel times to the
hydrograph profiles O3 and O4 are reproduced in a plausible way in both
scenarios, and so are the impact areas (Figs. 8 and 11). Exceedance of the
lateral limits in the lower zones is attributed to an overestimate of the
debris flow volumes there and to numerical issues related to the narrow
gorge: the steep walls of the gorge, in combination with the low number of
raster cells representing the width of the flow, challenge the correct
geometric representation of the flow in the topography-following coordinate
system. Further, application of the TVD NOC scheme results in numerical
diffusion which becomes particularly evident in this situation. The
introduction of adaptive meshes – which would help to locally increase the
spatial resolution while maintaining the computational efficiency – could
alleviate this type of issue in the future. The same is true for the fan of
Bondo. The solid ratio of the debris flow in the simulations appears
realistic, ranging from around 40 % to 45 % in the upper part of the debris flow
path and from around 30 % to 35 % and lower (depending on the cut-off time of the
hydrograph) in the lower part. This means that solid material tends to stop
in the transit area rather than fluid material, as can be expected.
Nevertheless, the correct simulation of the deposition of debris flow
material along Val Bondasca remains a major challenge (Table 3). Even though
a considerable amount of effort was put into reproducing the much lower
volumes reported in the vicinity of O4, the simulations result in an
overestimate of the volumes passing through this hydrograph profile. This is
most likely a consequence of the failure of r.avaflow to adequately
reproduce the deposition pattern in the zones D and E. Whereas some material
remains there at the end of the simulation, more work is necessary to
appropriately understand the mechanisms of deposition in viscous debris
flows (Pudasaini and Fischer, 2016). Part of the discrepancy, however,
might be explained by the fact that part of the fluid material – which does
not only consist of pure water but also consists of a mixture of water and fine mud –
left the area of interest in the downstream direction and was therefore not
included in the reference measurements. That lower part of the process chain
was not subject of the present work.
The simulation results are strongly influenced by the initial conditions and
the model parameters. Parameterization of both scenarios is complex and
highly uncertain, particularly in terms of optimizing the volumes of
entrained till and glacial meltwater and injected pore water. In general,
the parameter sets optimized to yield empirically adequate results are
physically plausible. Reproducing the travel times to O4 in the present
study requires the assumption of a low mobility of the flow in Zone E. This
is achieved by increasing the friction (Table 1), accounting for the narrow
flow channel, i.e. the interaction of the flow with the channel walls, which
is not directly accounted for in r.avaflow. Still, the high values of
δ given in Table 1 are not directly applied, as they scale with the
solid fraction. This type of weighting has to be further scrutinized. We
emphasize that also reasonable parameter sets are not necessarily physically
true, as the large number of parameters involved (Tables 1 and 2) create a
lot of space for equifinality issues (Beven et al., 1996). The higher values
of δ in the lower portion of the channel are based on the assumption
that δ of the solid material would somehow depend on the momentum or
energy of the flow, which – due to the relatively low velocity – is much
less in the zones D and, particularly, E. While this assumption, in our
opinion, is justified by fluidization and lubrication effects often observed
– or inferred – for very rapid mass flows, it remains hard to consider
those effects by a well-justified numerical relationship. Until such a
relationship (which definitely remains an important subject of future work)
has been proposed, we rely on empirically based zonation of friction
parameters.
We have further shown that the classical evaluation of empirical adequacy,
by comparing observed and simulated impact areas, is insufficient in the
case of complex mass flows: travel times, hydrographs, and volumes involved
can provide important insight in addition to the quantitative performance
indicators used, for example, in landslide susceptibility modelling
(Formetta et al., 2016). Further, the delineation of the observed impact
area is uncertain, as the boundary of the event is not clearly defined
particularly in Zone C. Also, the other reference data are not exact.
Therefore, we allow a broad margin (50 % deviation of the observation) for
considering the model outcomes as empirically adequate.
The present work is seen as a further step towards a better understanding of
the challenges and the parameterization concerning the integrated simulation
of complex mass flows. More case studies are necessary to derive guiding
parameter sets facilitating predictive simulations of such events (Mergili
et al., 2018a, b). A particular challenge of case studies consists of the
parameter optimization procedure: in principle, automated methods do exist
(e.g. Fischer et al., 2015). However, they have been developed for optimizing
globally defined parameters (which are constant over the entire study area)
against runout length and impact area, and such tools do a very good job for
exactly this purpose. However, they cannot directly deal with spatially
variable parameters, as they are defined in the present work. With some
modifications they might even serve that purpose – but the main issue is that
optimization should also consider shapes and maximum values of hydrograph
discharges or travel times at different places of the path. It would be a
huge effort to trim optimization algorithms for this purpose and to make
them efficient enough to prevent excessive computational times – we
consider this to be an important task for the future which is out of the scope of
the present work. Therefore, we have used a stepwise expert-based
optimization strategy.
Conclusions
We have back calculated the 2017 Piz Cengalo–Bondo landslide cascade in
Switzerland, where an initial rockslide–rockfall of approximately
3×106 m3 entrained a glacier, continued as a rock
avalanche, and finally converted into a series of debris flows, reaching the
village of Bondo at a total distance of 6.5 km. The water causing the
transformation into a debris flow might have originated from entrained
glacier ice or from water injected from the debris beneath the rock
avalanche. Considering the event from its initiation to the first debris
flow surge, we have evaluated not only the possibilities but also the challenges in
the simulation of such complex landslide events, employing the two-phase
model of the software r.avaflow.
Both of the investigated scenarios, S1 (debris flow developing through
injected water at the front of the rock avalanche) and S2 (debris flow
developing through melted ice at the back of the rock avalanche, overtopping
the deposit), lead to empirically reasonably adequate results when back
calculated with r.avaflow using physically plausible model parameters. Based
on the simulations performed in the present study, final conclusions on the
more likely of the mechanisms sketched in Fig. 6 can therefore not be drawn
purely based on the simulations. The observed jet of glacial meltwater
(Fig. 3b) points towards Scenario S1. The observed scouring of the rock
avalanche deposit, in contrast, rather points towards Scenario S2 but could
also be associated to subsequent debris flow surges. Open questions include
at least (i) the interaction between the initial rockslide–rockfall and
the glacier, (ii) flow transformations in the lower portion of Zone C
(Fig. 7), leading to the first debris flow surge, and (iii) the mechanisms
of deposition of 90 % of the debris flow material along the flow channel
in Val Bondasca. Further research is therefore urgently needed to shed
more light on this extraordinary landslide cascade in the Swiss Alps. In
addition, improved simulation concepts are required to better capture the
dynamics of complex landslides in glacierized environments: this would
particularly have to include a three-phase model, where ice – and melting
of ice – are considered in a more explicit way. Finally, more case studies
of complex mass flows have to be performed in order to derive guiding
parameter sets serving for predictive simulations.
Code and data availability
The r.avaflow code, including a detailed manual, is available for download
at https://www.avaflow.org/ (Mergili and Pudasaini, 2019).
The study is largely based on the 2011 swisstopo digital terrain model (DTM; contract: swisstopo–DV084371) and derivatives thereof. Unfortunately, the
authors are not entitled to make these data publicly available.
Author contributions
MM contributed to the conceptualization and methodology of the research;
designed the software; and performed the formal analysis, visualization,
validation, and most of the writing of the original draft. MJ was involved
in the conceptualization, investigation, and supervision as well as in the
review and editing of the paper. JP contributed to the
investigation, visualization, and review and editing. SPP provided input
in terms of methodology and review and editing of the paper.
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
We are grateful to Sophia Demmel and Florian Amann for valuable discussions as well as to Matthias Benedikt for comprehensive technical assistance.
Financial support
This research has been supported by the Herbette Foundation,
the German Research Foundation (DFG; grant nos. PU 386/5-1 and PU 386/3-1), and the Austrian Science Fund (FWF; grant no. I 1600-N30).
Review statement
This paper was edited by Margreth Keiler and reviewed by Brian McArdell and one anonymous referee.
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