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Moreover, the complexity of the problem resides both in the difficulty of
managing irregular ground topography and in complications of the equations, that
must also be able to account for flows that can range, rheologically, from nearly
Newtonian fluids to brittle solids by means of water loss.
Some authors proposed CA or CA -like models for flow type landslides.
Barca et al. [10] designed 3-dimensional CA models with a cellular space divided
in cubic cells, but computational high complexity and costs did not permit to apply
the model to the simulation, except for few cases of small and simple landslides.
Sassa [11] adopted CA -like numerical method to finite differences for a simplified
solution of debris flow equations and applied it to the M. Ontake landslide. His
approach accounts for the physics of the phenomenon, but the simulation suffered
because of cell dimension, too large to obtain an accurate description of the event.
Di Gregorio et al. [9] developed a simple 2-dimensional CA model (first release of
SCIDDICA) and validated it by simulating the Mt. Ontake landslide.
Segre & Deangeli [12] presented a 3-dimensional numeric model, based on CA ,
for debris flows, using difference equations. The model was validated on the M.
XiKou landslide, capturing its main characteristics.
SCIDDICA was further improved, introducing correlating empirical parameters of
the model to physical ones, and applied again to the M. Ontake landslide [13].
Avolio et al. [14] applied a modified release of SCIDDICA to the Tessina
landslide, also performing a risk analysis for the threatened area.
Malamud & Turcotte [15] presented a very simple CA “sand pile” model to be
applied to landslides from a statistical viewpoint in order to forecast the frequency-
area distribution of landslides triggered by earthquakes.
Clerici & Perego [16] simulated the Corniglio landslide using a simple CA model
in order to capture the blockage mechanisms for that type of landslide.
Finally, a preliminary extension of SCIDDICA was developed in order to capture
the characteristics of the extremely complex landslides of Sarno [17].
3.2 The Hexagonal Model SCIDDICA
The latest hexagonal release of SCIDDICA is a significant extension of the models
applied successfully to the landslides of Tessina and Mount Ontake. Such extension
involves new substates, new procedures, new parameters because of the landslides of
Sarno appear to be a more complex phenomenon, especially for their avalanche effect
in soil erosion during the phenomenon evolution.
The hexagonal CA model SCIDDICA is the quintuple
SCIDDICA= <R, X, Q, P,
>
R is the set of regular hexagons covering the finite region, where the phenomenon
evolves.
X identifies the geometrical pattern of cells, which influence any state change of the
central cell (the central cell itself and the six adjacent cells):
Q is the finite set of states of the ea ; it is equal to the Cartesian product of the sets of
the considered substates:
Q = Q a
Q o 6
Q i 6
Q th
Q r
Q d
Q m
where:
o
Q a is the cell altitude
Q th is the thickness of landslide debris
o
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