A cellular automaton for the factor of safety field in landslides modeling

Landslide inventories show that the statistical distribution of the area of recorded events is well described by a power law over a range of decades. To understand these distributions, we consider a cellular automaton to model a time and position dependent factor of safety. The model is able to reproduce the complex structure of landslide distribution , as experimentally reported. In particular, we investigate the role of the rate of change of the system dynamical variables, induced by an external drive, on landslide mod-eling and its implications on hazard assessment. As the rate is increased, the model has a crossover from a critical regime with power-laws to non power-law behaviors. We suggest that the detection of patterns of correlated domains in monitored regions can be crucial to identify the response of the system to perturbations, i.e., for hazard assessment. Introduction As for earthquakes and forest fires, there is a compelling evidence that the landslide frequency-size distributions are power-law functions of the area [Turcotte et al., 2002]. The presence of these broad distributions has crucial consequences on both the basic understanding of these phenomena and the practical and relevant purposes, such as the evaluation of natural hazards. Here, we introduce a cellular automaton that is aimed at modeling the general features of landslides, and is focused on the dynam-ical evolution of a space and time dependent factor of safety field. This model is very simple, but it is able to give a comprehensive picture of the avalanching phenomena and to reproduce some well-known properties of landslide distributions. Several authors invoked the paradigm of self-organized criticality (SOC) [Bak et al.though the " critical " nature of the present phenomenon is not yet assessed and many authors believe that deviations from power-law appear to be systematic for small land-regional landslide inventories records show robust power-law distributions of large events with an exponent around α ∼ 2.5 [Turcotte et al., 2002], ranging approximately from α ∼ 1.75 for rockfalls to α ∼ 2.8 for mixed landslides (see [Dussauge et al., 2003; Faillettaz et al., 2004] and references therein). The universality of such an exponent is still debated (see [Turcotte et al. and references above), and its reported values are far from the one in the original " sandpile model " [Bak et al., 1987], where α ∼ 1.0. Recently, the reported values of α have been obtained by introducing two-thresholds mechanisms in models that …