Gianluca Martelloni - Università di Firenze #
Comparison between simulation results of 2D and 3D models for 
deep-seated landslide #
 We propose 2D and 3D models for deep-seated landslide triggered by 
rainfall. Our models are based on interacting particles or grains and 
describes the behavior of a fictitious granular material along a slope 
with a wide thickness. The triggering of the landslide is caused by the 
passing of two conditions: a threshold speed and a condition on the 
static friction of the particles, the latter based on the Mohr-Coulomb 
failure criterion according to the infiltration processes. In our scheme 
the positive pure pressures, that have local value, should be simply 
interpreted as a perturbation of the rest state of each grain, i.e., the 
pore pressure function can be interpreted as a time-space dependent 
scalar field acting on the particles. The resulting numerical method, 
similar to that of molecular dynamics (MD), is based on the use of an 
interaction potential between the particles, similar to the 
Lennard-Jones one. Moreover by means of this type of force we can also 
simulate a compressed state of the particles, according to a stress 
state of the slope material. Although the models proposed are still 
quite schematic, our results encourage the investigations in this 
direction. The results are consistent with the behavior of real 
landslides induced by rainfall and an interesting behavior emerges from 
the dynamical and statistical points of view. Emerging phenomena such as 
fractures, detachments and arching can be observed (Martelloni et al., 
2012; Martelloni et al., 2013). In particular, the models reproduce well 
the energy and time distribution of avalanches, analogous to the 
observed Gutenberg-Richter and Omori power law distributions for 
earthquakes. We observe a power law distribution also considering the 
number of the particles in motion. We note that other natural hazards 
(landslides, earthquakes and forest fires) also exhibit similar 
distributions (Malamud et al., 2004; Turcotte 1997), characteristic of 
self-organized critical systems (Turcotte and Malamud 2004). From 
statistical point of view we observe an interesting characteristic of 
this type of systems, i.e., a transition of the mean energy increment 
distribution from a Gaussian to a power law after decreasing the 
viscosity coefficient up to zero. This behavior is compatible with the 
corresponding velocity increase, i.e., such cross-over in the 
distribution means that we pass from a relative slow movement to a 
relative fast slow movement. This results is obtained also within a 
single simulation for fixed viscosity coefficient (also for zero value 
of this parameter), i.e., if we consider the distribution of kinetics 
increment in an initial phase of movement of the system we observe a 
Gaussian distribution (all particles have similar velocity), while, 
continuing the simulation, a power law is detected due the presence of 
particles at higher velocity. Actually, we observe a characteristic 
velocity and energy pattern typical of a stick-and-slip dynamics, 
similar to real landslides behavior (Sornette et al., 2004). We have 
also shown that it is possible to apply the method of the inverse 
surface displacement velocity for predicting the failure time (Fukuzono 
1985). Then we achieve a complete sensibility analysis of the 2D model 
parameters considering also the fluctuations necessary to take into 
account the variability of the soil. Moreover the simulations are 
achieved considering both initial regular configuration of the grains 
and random configuration ones where each particle is shifted from 
equilibrium state according to a Gaussian distribution of the position 
shifts. In conclusion the results of 2D and 3D models are similar, but 
the three-dimensional scheme allow a better stability concerning the 
observed kinetics energy and velocity that can become very high for some 
particles, during the slip, due to the effect of the repulsive forces, 
obviously equal values of the potential parameters.   
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<b>References</b>
<br/>
Fukuzono T (1985) A new method for predicting the failure time of a 
slope. Proc. 4th Int. Conf. Field Workshop Landslides, 145-150. 
Tokyo: Jpn. Landslide Soc.
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Malamud BD, Turcotte DL, Guzzetti F, Reichenbach P (2004) Landslide 
inventories and their statistical properties. Earth Surface Processes 
and Landforms, 29: 687-711
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Martelloni G, Bagnoli F, Massaro E (2012) A computational toy model for 
shallow landslides: Molecular Dynamics approach. Communications in 
Nonlinear Science and Numerical Simulation 
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Martelloni G., Bagnoli F. (2013) Infiltration effects on a 
two-dimensional molecular dynamics model of landslides. In NHAZ (Natural 
Hazards). 
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Sornette D, Helmstetter A, Grasso JR, Andersen JV, Gluzman S, Pisarenko 
V (2004) Towards Landslide Predictions: Two Case Studies. Physica A, 
338: 605-632
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Turcotte DL (1997) Fractals and chaos in geology and geophysics. 
Cambridge University Press, Cambridge, (2nd Edition)
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Turcotte DL, Malamud BD (2004) Landslides, forest fires, and 
earth-quakes:examples of self-organized critical behavior. Physica A, 
340: 580-589