3d numerical modelling of submerged and coastal landslide...

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 propaga-tion 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 sub-aqueous 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 pre-sented. 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 sub-merged 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, Italye-mail: [email protected]

M.V. Avolio and S. Di GregorioDepartment of Mathematics, University of Calabria, Arcavacata, 87036 Rende (CS), Italy

V. LupianoDepartment of Earth Sciences, University of Calabria, Arcavacata, 87036 Rende (CS), Italy

D.C. Mosher et al. (eds.), Submarine Mass Movements and Their Consequences, 127Advances in Natural and Technological Hazards Research, Vol 28,© Springer Science + Business Media B.V. 2010

128 P. Mazzanti et al.

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: empiri-cal 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 limita-tions 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 land-slide deposits is more difficult in the submerged environment, therefore indirect information is also limited. As a consequence, few rheological and phenomenologi-cal 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 underwa-ter granular flows like rock and debris avalanches, using a Savage–Hutter type approach. However, few 3D numerical models are available for submerged flow-like 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 under-water. 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 sud-den 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.


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 obtain-ing 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


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 chan-nel 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).


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 corre-sponds 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

Fig. 2 Time sequence of the landslide velocity distribution during the flow


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 com-putation step is performed simultaneously for all the cells and considers the follow-ing 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 mini-mise differences in height (kinetic energy is also considered); their shift is deduced by simple motion equations accounting for slope, friction, turbulence effects, eventu-ally water resistance and buoyancy effect. Detrital cover erosion is computed pro-portionally 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


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 pre-existing 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


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

Fig. 5 Maximum values of (a) thickness, (b) velocity and (c) erosion during the overall simulation


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 differen-tial equations of motion is used in DAN3D; (b) a Cellular Automata method, dis-crete 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 deposi-tion 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 diffi-cult 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 geomorpho-logical 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).


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 simula-tion 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 reason-able 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 suita-ble 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 origi-nally 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 com-pletely 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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