Physica A: Statistical Mechanics and its Applications
Towards landslide predictions: two case studies
Introduction
There is a growing interest in understanding and predicting catastrophic phenomena, such as floods, earthquakes and avalanches, which are characterized by their rarity and intermittence, often leading to disastrous consequences for their environment [1]. Notwithstanding their large societal impacts, the scientific community is only beginning to develop the concepts and tools to model and predict this class of events. The prediction of catastrophes is often considered to be essentially impossible either due to intrinsic mechanisms inherent to systems [2] or from the existence of enormous practical barriers [3]. Several groups have however found evidence of a degree of predictability of certain catastrophes [4], such as financial crashes [5] and earthquakes [6].
Here, we address the question of the predictability of landslides which constitute a major geologic hazard of strong concern in most parts of the world. Landslides occur in a wide variety of geomechanical contexts, geological and structural settings, and as a response to various loading and triggering processes. They are often associated with other major natural disasters such as earthquakes, floods and volcanic eruptions.
Derived from the civil-engineering methods developed for the safety of human-built structures, including dams and bridges, the standard approach to slope instability is to identify the conditions under which a slope becomes unstable [7]. By their nature, standard stability analysis cannot account for acceleration in slope movement [8]. The problem is that this modeling strategy gives a nothing-or-all signal. In this view, any specific landslide is essentially unpredictable, and the focus is on the recognition of landslide prone areas. This approach is very similar to the practice in seismology called “time-independent hazard” where earthquake-prone areas are located in association with active faults for instance, while the prediction of individual earthquake is recognized to be much more difficult if not unattainable. This “time-independent hazard” essentially amounts to assume that landslides are a random (Poisson) process in time, and uses geomechanical modeling to constrain the future long-term landslide hazard. The approaches in terms of a safety factor do not address the preparatory stage leading to the catastrophic collapse, if any. In contrast, “time-dependent hazard” would accept a degree of predictability in the process, in that the landslide hazard varies with time, maybe in association with varying external forcing (rain, snow, earthquake, volcano). The next level in the hierarchy would be “landslide forecasting”, which require significant better understanding to allow for the prediction of some of the features of an impending landslide, usually on the basis of the observation of precursory signals. Practical difficulties include identifying and measuring reliable, unambiguous precursors, and the acceptance of an inherent proportion of missed events or false alarms.
Our purpose is to extend the model of a slider-block with state- and velocity-dependent friction introduced in our companion paper [9] for the analysis of two landslides. Here, we examine how one could have perhaps predicted these landslides in advance. By studying these two cases, we hope to develop a methodology that could be useful in the future as well as to determine the limits of predictability. For the Vaiont landslide, our model provides good predictions with a precision of about one day of the critical time of failure up to 20 days before the collapse. Tests are also presented on the prediction of the time of the change of regime for La Clapière landslide. Re-examining the calibration of the model of a slider-block with state- and velocity-dependent friction, we cannot exclude that La Clapière might also belong to the unstable velocity weakening regime; its deceleration observed after 1988 may then be interpreted as a change of either the surface properties or of the sliding interface that modifies the friction law parameters.
Section snippets
Phenomenological power law acceleration
Accelerating displacements preceding some catastrophic landslides have been found empirically to follow a time-to-failure power law, corresponding to a finite-time singularity of the velocity v∼1/(tc−t) [10]. Controlled experiments on landslides driven by a monotonic load increase have been quantified by a scaling law relating the surface acceleration to the surface velocity according towhere A and α are empirical constants [11]. For α>1, this relationship predicts a
Prediction of the Vaiont landslide
On October 9, 1963, a wide landslide initiating at an elevation of 1100–, that is 500– above the valley floor, on the Mt Toc slope in the Dolomite region in the Italian Alps about north of Venice, ended up 69.8 days later in a run-away of about of rocks sliding into a dam reservoir. The high velocity of the slide triggered a water surge within the reservoir, overtopping the dam and killing 2000 people in the villages downstream. For a synthesis of its history and
Prediction of the aborted 1986–1987 peak acceleration of La Clapière landslide
We now report results on another case which exhibited a transient acceleration which did not result in a catastrophic failure but re-stabilized. This example provides what is maybe an example of the m=B/A<1 stable slip regime as interpreted within the friction model.
Let us recall for the sake of completeness some salient facts (see [9] for more details). La Clapière landslide is located at an elevation between 1100 and on a slope high. The volume of mostly gneiss rocks implied in
Discussion and conclusion
We have extended the quantitative analysis of our companion paper [9] on the displacement history for two landslides, Vaiont and La Clapière, to explore their potential predictability. Using a variety of techniques, we have tried to go beyond the time-independent hazard analysis provided by the standard stability analysis to include time dependent predictions. While our present inversion methods provide a single estimate of the critical time tc of the collapse for each inversion, a better
Acknowledgements
We thank C. Scavia and Y. Guglielmi for key supports to capture archive data for Vaiont and La Clapière landslide, respectively. We are very grateful to N. Beeler, J. Dieterich, Y. Guglielmi, D. Keefer, J.P. Follacci, J.M. Vengeon for useful suggestions and discussions. AH and JRG were supported by INSU French Grants, Gravitationnal Instability ACI. SG and DS acknowledge support from the James S. Mc Donnell Foundation 21st century scientist award/studying complex systems.
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