3D Numerical Modelling of Submerged
and Coastal Landslide Propagation
P. Mazzanti, F. Bozzano, M.V. Avolio, V. Lupiano, and S. Di Gregorio
Abstract The analysis of the propagation phase plays a fundamental role in the
assessment and forecasting of risks related to the occurrence of submerged and coastal
landslides. At present there are few numerical models able to simulate the propagation of such a type of events. This paper presents fully 3D models and approaches
developed by the authors and suitable for the simulation of both completely subaqueous landslides and combined subaerial–submerged ones (i.e. coastal landslides
with a subaerial source which propagate underwater). A Cellular Automata model is
described which has been specifically designed for combined subaerial–submerged
landslides. Moreover, a new approach able to simulate submerged mass movements
using commercial 3D software, originally developed for subaerial landslides, is presented. Calibration and validation of these models upon a real and well constrained
coastal debris flow at Lake Albano (Rome, Italy) is also presented.
Keywords Landslides • propagation • numerical modelling • coastal and submerged landslides
1
Introduction
The analysis of the post-failure stage is a fundamental part in the assessment of landslide
risk. Events like debris flows, rock and debris avalanches usually affect very large
areas during their propagation, whereas they induce limited damage before or during
P. Mazzanti and F. Bozzano ()
Dipartimento di Scienze della Terra, Università di Roma “Sapienza”, P.le Aldo Moro 5,
00185 Roma, Italy
e-mail: paolo.mazzanti@uniroma1.it
M.V. Avolio and S. Di Gregorio
Department of Mathematics, University of Calabria, Arcavacata, 87036 Rende (CS), Italy
V. Lupiano
Department of Earth Sciences, University of Calabria, Arcavacata, 87036 Rende (CS), Italy
D.C. Mosher et al. (eds.), Submarine Mass Movements and Their Consequences,
Advances in Natural and Technological Hazards Research, Vol 28,
© Springer Science + Business Media B.V. 2010
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the failure close to the source area. This is even more valid for coastal and submerged
landslides whose secondary hazard (i.e. tsunami) is closely related to the landslide
behaviour during propagation (velocity, thickness, runout etc.).
The propagation over an irregular morphology of a heterogeneous mixture of
soil and water, which changes frequently its properties (such as volume, shape,
percentage of water etc.) is difficult to be defined and solved in terms of differential
equations and its modelling needs several simplifications. The analytical difficulties
are amplified for phenomena occurring underwater or, still more, for phenomena
which change environment (from air to water) during the propagation.
Laboratory experiments and studies of real events are the basis to improve the
knowledge in this very complex field. As regards the analysis of real landslides in
the last few years, several efforts have been focused on two main directions: empirical approaches based on historical data and approximated numerical methods. The
former, the most common method to predict the runout distances, deals with an
apparent inverse relationship between the volume and the Fahrböschung (Heim
1932) of landslides. Several linear regression equations have been proposed (e.g.,
Scheidegger 1973; Corominas 1996), which are able to predict the landslide runout
and velocity, given the landslide volume. De Blasio et al. (2006) also obtained a
similar plot by comparing different types of subaerial and submerged landslides.
Such an approach, even if extensively used for predictive purposes, has several limitations mainly related to the large variability of landslide features such as topography,
rheology and other peculiarities which a simplified approach is not able to account
for. On the other hand, the analytical and numerical approach is based on the
mechanics of the flow and involves the solution of a system of governing equations
of motion, either in a closed-form or numerically (Hungr et al. 2005).
2
Numerical Modelling of Landslide Propagation:
State of the Art
Due to the high complexity of mechanisms involved in the post-failure stage of an
extremely rapid subaerial landslide (Cruden and Varnes 1996), few models have been
built that try to capture the “real” physics of the flow or part of it (Campbell et al.
1995; Denlinger and Iverson 2004). The most appropriate and commonly used
models adopt a semi-empirical approach based on the principle of the equivalent
fluid, formalized by Hungr (1995). This approach assumes that the flowing mass
behaves like a fluid, whose rheological features cannot be measured through laboratory
or in situ testing, but can only be obtained by the back-analysis of real past events.
The approach is defined as semi-empirical since it uses a numerical model which
accounts for the main physical features of the phenomenon but, at the same time, needs
a large historical record of real events in order to calibrate the parameters.
In recent years, these models have been becoming fully 3D, i.e. are able to simulate
the distribution of the mass in a real topography, and reliable enough to be used in the
assessment of risks related to catastrophic, fast subaerial landslides. Their effectiveness
3D Numerical Modelling of Submerged and Coastal Landslide Propagation
129
is the result of several back-analyses of past phenomena, which allowed us to constrain
the parameters. However, even if these models are calibrated upon real events and
can thus be considered more “practical” than “theoretical”, they are often based, or
at least validated, through laboratory experiments (Bagnold 1954; Savage and Hutter
1989; Iverson and LaHusen 1993).
With regard to landslides occurring underwater, less experimental results are
available (Marr et al. 2001; Ilstad et al. 2004; Breien et al. 2007) and the direct
observation of real phenomena is almost impossible. Furthermore, analysis of landslide deposits is more difficult in the submerged environment, therefore indirect
information is also limited. As a consequence, few rheological and phenomenological constraints are available and, thus, few numerical models have been developed.
Imran et al. (2001) built the bi-dimensional BING model suitable for analyzing
muddy and viscous flow-like mudflows or cohesive debris flows. Fernández-Nieto
et al. (2008) developed a bi-dimensional model which is able to simulate underwater granular flows like rock and debris avalanches, using a Savage–Hutter type
approach. However, few 3D numerical models are available for submerged flowlike mass movements although recently a 3D Cellular Automata model for turbidity
currents has been developed and applied to real cases by Salles et al. (2007).
A further degree of complexity is related to the simulation of combined subaerial–
submerged events since they are characterized by a complicated air–water transition.
In spite of the larger difficulties in the investigation and modelling of submerged
and coastal landslides, an increasing number of case studies will be available in the
near future, thus allowing the constraining and calibration of models or numerical
approaches for such a type of phenomena. Hence, an effort has to be made to build
new and powerful 3D models able to simulate the real distribution of a landslide
over an irregular terrain.
3
Equivalent Fluid Equivalent Medium Approach by DAN3D:
Theory and Example
The first approach here proposed, suitable for the numerical modelling of completely
submerged or subaerial–submerged landslides is named EFEM (Equivalent Fluid
Equivalent Medium) (Mazzanti 2008a). This approach allows for using codes specifically
designed for subaerial landslides to simulate mass movements propagating underwater. In fact, it can account for the interaction between the moving mass and the
surrounding fluid (in the case of submerged movements), through some expedients.
Furthermore, the air to water transition in coastal landslides can be also simulated
by this approach. In greater detail, the following aspects are considered: (1) a sudden change of properties during the air–water transition; (2) the drag forces; (3)
buoyancy forces and (4) peculiar mechanisms like hydroplaning. For example, the
drag force is simulated by using the Voellmy rheology proposed by Hungr (1995)
and increasing the turbulence basal coefficient of friction, which is proportional to
the square of the landslide velocity.
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In addition, a reduction of the landslide unit weight allows one to account for the
Archimedean forces. In this way, the main physical mechanisms which differentiate
subaerial and subaqueous landslides can be reasonably accounted for, thus obtaining reliable results in terms of mass distribution and velocity along the path.
Application of this approach to a real combined subaerial–submerged debris flow
that occurred in 1997 at Lake Albano (Rome, Italy) has been made by DAN3D
model (McDougall and Hungr 2004). This model is an extension of the DAN-W
code (Hungr 1995) since it retains the key features of the original quasi-3D model,
though satisfying the need to consider a complex topography.
The 1997 Lake Albano debris flow has been simulated by using a 1 m quare DTLM
(Digital Terrain and Lacustrine Model), obtained by combining a subaerial DTM
(Digital Terrain Model) collected by means of an aerial LiDAR survey (Pietrantonio
et al. 2008) and a high resolution bathymetry (Fig. 1). The pre-landslide morphology
Fig. 1 (a) Aerial photo merged with the actual bathymetry; (b) slope gradient map. White dotted
lines bound the subaerial landslide erosive chute; yellow dashed lines bound a submerged erosive
channel; green full line bounds the subaqueous landslide deposit
3D Numerical Modelling of Submerged and Coastal Landslide Propagation
131
has been reconstructed by using high resolution aerial photos for the subaerial part of
the slope and reshaping the submerged one. The new submerged morphology was
obtained by creating a regular and homogeneous morphology and by considering that
both the submerged channel and deposit were shaped by the 1997 event (Mazzanti et
al. 2007). The initial value of the failed mass used in the simulation was 600 m3, in order
to account for both the initial source (about 300 m3) and a second landslide triggered
along the path (about 300 m3). Different values of entrainment were set in the subaerial
and the submerged part of the slope during the simulations. Specifically, erosion rates
(see McDougall and Hungr 2004 for further details) between 0.007 and 0.004 have
been assumed in the subaerial part while submerged erosion was used only in a few
runs. Several back-analyses have been performed and the best results in terms of areal
and thickness convergence between real and simulated event have been achieved by
using the Voellmy rheology and setting the following parameters:
– Subaerial slope: Unit Weight = 15 kN/m3; Friction Coefficient (m) = 0.1;
Turbulence Coefficient (x) = 500 m/s2; Erosion Rate = 0.007
– Submerged slope: Unit Weight = 15 kN/m3; Friction Coefficient (m) = 0.1;
Turbulence Coefficient (x) = 350 m/s2; Erosion Rate = variable
The achieved final maximum runout and areal landslide distribution are comparable
with the real landslide. Moreover the landslide volume at water impact is similar to
that obtained by comparing pre- and post aerial photos of the subaerial part of the
flow. Best results in terms of final landslide distribution have been achieved by
neglecting submerged erosion and mass entrainment despite evidence of a deep
incised (2–3 m) submerged channel in the continuation of the subaerial one. As a
matter of fact, estimated volume of the submerged deposit is not in accordance with
subaerial and submerged erosion (Mazzanti et al. 2007) so it can be assumed that
the submerged channel is not related to the 1997 event.
The mass reaches the water surface after 25 s after the failure with a volume of
about 10,000 m3. The main flow stops after 80 s when the final deposition area is
reached, while only minor movements are still occurring in the submerged slope.
The width of the flow is quite limited (less than 10 m) in the suberial flow, since it
occurs inside a pre-existing channel, but it spreads more when the submerged slope
is reached. The spreading in the submerged slope occurs even if a pre-existing channel is present and erosion in the submerged slope is neglected. The computed
landslide thickness during the propagation is between 1 and 1.5 m in the subaerial
and in the first part of the submerged pathway, whereas a value up to 2 m is reached
in the final part of the movement before its deposition. Velocity during the overall
propagation is shown in Fig. 2. A rapid initial acceleration of the flow is recorded,
thus reaching values close to 15 m/s after only 12 s; then, such a value is maintained
until plunging into water (at ∼25 s). A maximum velocity close to 17–18 m/s is
obtained just at the shoreline in the frontal part of the flow. In the submerged part,
the velocity of the mass decreases rapidly below 12 m/s until it stops. The reliability
of the achieved results is confirmed by the similarity between simulated velocities
and velocity of similar recorded debris flows events (Berti et al. 1999; Hürlimann
et al. 2003).
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Fig. 2 Time sequence of the landslide velocity distribution during the flow
4
The Cellular Automata Code SCIDDICA SS2:
Theory and Example
SCIDDICA-SS2 model is a Macroscopic Cellular Automaton for simulating subaerial–
subaqueous flow-type landslides specifically developed by some of the authors
(Avolio et al. 2008) as an extension of the model proposed by D’Ambrosio et al.
(2003). It consists of a finite matrix of identical hexagonal cells. Each cell corresponds to a portion of that real surface, involved in the landslide. A list of values
(of substates) is assigned to each cell, accounting for the local features relevant to
the development of the phenomenon: elevation, depth of erodible soil cover,
attributes of superficial material (average thickness, co-ordinates of its mass center,
kinetic head), attributes of outflows crossing hexagon’s edges (co-ordinates of their
3D Numerical Modelling of Submerged and Coastal Landslide Propagation
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mass center, kinetic energy, velocity). A computation unit (a finite automaton) is
embodied in each cell; it computes (computation step) the variation of the cell
substates that occurred in a fixed time interval, on the basis of the substates’ values
of the current cell and its adjacent cells. The time interval depends on the cell
dimension and the maximum possible flow speed (an outflow may not overcome
the adjacent cell); it ranges between hundredths of seconds and minutes. The computation step is performed simultaneously for all the cells and considers the following physical processes in sequence. Debris outflows are computed from determination
of mass quantities, to be distributed from a cell to adjacent cells in order to minimise differences in height (kinetic energy is also considered); their shift is deduced
by simple motion equations accounting for slope, friction, turbulence effects, eventually water resistance and buoyancy effect. Detrital cover erosion is computed proportionally to the kinetic energy of the mass overtaking a threshold value
(empirically defined) with corresponding variation of cell elevation, flow thickness
and kinetic energy. Air–water transition involves computation of mass loss (finer
components), energy dissipation by water resistance at the impact and buoyancy
effect. Composition of matter inside the cell (remaining matter plus inflows) and
determination of new thickness mass center, co-ordinates and kinetic energy are all
computed at the end. The complexity of the phenomenon emerges from the simple
computations of the interacting cells step by step updating of the substates. The
same DTLM with a 1 m cell used for DAN3D simulations has been set as input
topography. Two source areas have been considered which correspond respectively
to the scar located in the upper part of the channel and to a further scar, located
along the slope, which is activated when it is reached by the flow. Figure 3 shows
the best simulation in terms of areal fit between real and simulated event. The most
effective parameters used in the simulation are listed below:
– Subaerial slope: Density = 15 g/cm3; Friction Coefficient = 0.08; Energy dissipation
by turbulence = 0.005; Energy dissipation by erosion = 0.3
– Submerged slope: Density = 15 g/cm3; Friction Coefficient = 0.1; Energy dissipation
by turbulence = 0.006; Energy dissipation by erosion = 0.1
The best fit value, that considers a normalised value between 0 (simulation
completely failed) and 1 (perfect simulation), is computed by the function
Ö( (RÇS)/(RÈS) ), where R is the set of cells affected by the landslide in the real
Fig. 3 Intersection between the real event and the simulated event
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event and S the set of cells affected by the landslide in the simulation. In this case,
the achieved result is 0.83 which is considered a quite good value for the simulation
of such a complex phenomenon.
Figure 4 shows the time history of the first 2 min of simulation in terms of velocity
distribution of the flow. As it can be seen, the mass reaches the water surface about
24 s after the failure with a volume of few thousands of cubic meters. The main flow
stops after 2–3 min when the final deposition area is reached and only minor
flows are still occurring in the submerged slope. The area affected by the landslide
is quite narrow (less than 10 m) on the subaerial slope since it occurs inside a preexisting channel, while it experiences a larger spreading when the submerged slope
is reached.
In Fig. 5 the final results in terms of landslide thickness, velocity and erosion,
are reported, respectively. The maximum values of thickness during the whole
simulation are computed in the subaerial part of the flow where a value up to 10 m
Fig. 4 Time sequence of the landslide velocity distribution during the flow
3D Numerical Modelling of Submerged and Coastal Landslide Propagation
135
Fig. 5 Maximum values of (a) thickness, (b) velocity and (c) erosion during the overall simulation
is reached. Such a high value corresponds to the shoreline and this is probably due
to the slope break and the sudden reduction of velocity during the first stages of the
underwater flow.
Figure 5b points out that the value of 15 m/s is reached in the subaerial part whereas
underwater the velocity decreases below 10 m/s immediately after submergence. Concerning
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the erosion (Fig. 5c), values up to 3–4 m are computed in the subaerial slope whereas
underwater only a very limited erosion (less than 1 m) is obtained.
5
A Comparative Analysis of Codes
Both SCIDDICA SS2 and DAN3D can be considered fully 3D models based on the
equivalent fluid approach but, apart from these common characteristic, they are
characterized by different features. First of all, they use a dissimilar numerical
approach: (a) the SPH method (Monaghan 1992) based on the solution of differential equations of motion is used in DAN3D; (b) a Cellular Automata method, discrete in time and space, with transition functions based on proper equations of
motion is used in SCIDDICA SS2.
Furthermore, other important aspects which differentiate the two models, are
briefly listed below:
– SCIDDICA SS2 is a model specifically developed for combined subaerial–
subaqueous landslides whereas DAN3D is a model developed for subaerial
landslides and its application to coastal landslides is carried out through the
EFEM approach.
– DAN3D accounts for the inner earth pressures (Pirulli et al. 2007) of the moving
mass using active and passive stresses differently from SCIDDICA SS2 which
considers, at present, only adjusted hydrostatic and isotropic earth pressures.
– SCIDDICA SS2 is able to simulate the erosion accounting for both the consequent
loss of energy and increase of the mass due to entrainment; DAN3D computes the
entrainment only by a pre-defined value of erosion rate.
– SCIDDICA SS2 updates the morphology step by step when erosion and deposition occur; on the contrary, DAN3D uses the original topography during the whole
simulation.
– In SCIDDICA SS2, different sources can be set occurring at pre-defined time,
whereas only one source can be set in DAN3D.
With regard to the 1997 Lake Albano debris flow, results achieved by using the
two codes are quite similar in several respects. First of all, the similar deposit
distribution suggests that the use of adjusted hydrostatic pressure (in SCIDDICA
SS2) is suitable for debris flows and hyper-concentrated flows. Concerning
erosion, the simulation performed by SCIDDICA SS2 shows that it is quite difficult to produce a deeply incised channel in the subaqueous slope (comparable with
the real one discussed in Mazzanti et al. 2007) due to the low energy available in
the 1997 event. Following both SCIDDICA simulation results and the geomorphological evidence of a limited submerged deposit, DAN3D simulations have been
performed with and without setting underwater erosion; the best back-analysis has
been obtained neglecting the entrainment. These combined results suggest that the
subaqueous channel should be not related to the 1997 event. This is also consistent
with the small volume of final deposit detected by the high resolution bathymetry
(5,000–7,000 cubic meters).
3D Numerical Modelling of Submerged and Coastal Landslide Propagation
137
Moreover, the small submerged deposit (whose volume is lower than the material
reaching the shoreline) suggests that part of the material was transformed into a
turbidity current after the impact, moving separately from the main debris flow.
This effect cannot be simulated using DAN3D but has been considered, in a
straightforward way, in SCIDDICA SS2, by setting an instantaneous loss of mass
at the water level.
However, some differences in the results obtained with the two models have
been observed; for example, the maximum thickness of the flow is up to 3 m with
DAN3D and up to 10 m in SCIDDICA SS2. The peak value in SCIDDICA SS2 has
been computed at the shoreline and could result from the sudden reduction of
velocity at the impact with water.
Apart from the different value at the shoreline, the mass thickness during the flow
is quite comparable between the simulation performed by DAN3D and SCIDDICA
SS2 and this is particularly true in the submerged part of the slope. Even the simulation time sequences are quite similar; the mass plunges into water after 24 and 25 s
from the beginning of the flow using SCIDDICA SS2 and DAN3D, respectively.
Slightly different velocities are computed in the submerged path between the two
models (a bit lower with SCIDDICA SS2); nevertheless, both values seem reasonable for this type of event.
6
Conclusions and Outlook
In spite of the increasing evidence of submerged landslide instabilities and of their
large mobility, few numerical models are available which can be considered suitable for the simulation of underwater or coastal mass movements’ propagation over
a real 3D topography. In this paper a new approach for the simulation of coastal and
submerged landslides has been proposed which allows us to use 3D models originally developed for subaerial landslides. Furthermore, a new 3D Cellular Automata
model (SCIDDICA SS2), specifically developed for combined subaerial–submerged
flow-like landslides has been presented. The two approaches have been tested by
simulating in back-analysis a coastal debris-flow at Lake Albano. Both models
have been able to reproduce the real event in terms of runout distance and areal
distribution of the mass. Reasonable values of landslide velocity have been also
computed, which represent input needed for the analysis of induced tsunamis.
Further back-analyses of real submerged landslides by the proposed methods will
allow to better constrain the parameters of the codes. The future development of
this research aims to obtain useful numerical tools for forecasting analyses related
to the propagation of both combined subaerial/submerged landslides and completely subaqueous ones.
Acknowledgments The authors wish to thank Prof. O. Hungr for giving a research license of
DAN3D. Professor O. Hungr and Dr. D. Leynaud are also acknowledged for useful revisions and
suggestions.
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