Towards landslide predictions: two case studies

doi:10.1016/j.physa.2004.02.065

Physica A: Statistical Mechanics and its Applications

Volume 338, Issues 3–4, 15 July 2004, Pages 605-632

https://doi.org/10.1016/j.physa.2004.02.065 Get rights and content

Abstract

In a previous work (J. Geophys. Res. (2004)), we have proposed a simple physical model to explain the accelerating displacements preceding some catastrophic landslides, based on a slider-block model with a state- and velocity-dependent friction law. This model predicts two regimes of sliding, stable and unstable leading to a critical finite-time singularity. This model was calibrated quantitatively to the displacement and velocity data preceding two landslides, Vaiont (Italian Alps) and La Clapière (French Alps), showing that the former (resp. later) landslide is in the unstable (resp. stable) sliding regime. Here, we test the predictive skills of the state- and velocity-dependent model on these two landslides with a variety of techniques using (i) a finite-time singularity power law, (ii) the state- and velocity-dependent friction law and (iii) resummation methods extrapolating from early times. For the Vaiont landslide, our model provides good predictions of the critical time of failure up to 20 days before the collapse. Tests are also presented on the predictability of the time of the change of regime for La Clapière landslide.

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/(t_c−t) [10]. Controlled experiments on landslides driven by a monotonic load increase have been quantified by a scaling law relating the surface acceleration $d δ ̇ / d t$ to the surface velocity $δ ̇$ according to $d δ ̇ / d t=A δ ̇^{α},$ where A and α are empirical constants [11]. For α>1, this relationship predicts a

Prediction of the Vaiont landslide

On October 9, 1963, a $2 km$ wide landslide initiating at an elevation of 1100– $1200 m$ , that is 500– $600 m$ above the valley floor, on the Mt Toc slope in the Dolomite region in the Italian Alps about $100 km$ north of Venice, ended up 69.8 days later in a $20 m/s$ run-away of about $0.3 km^{3}$ 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 $1800 m$ on a $3000 m$ 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 t_c 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.

References (36)

C Ziehmann et al.
Phys. Lett. A
(2000)
A. Bunde, J. Kropp, H.-J. Schellnhuber (Eds.), The Science of Disasters, Springer, Berlin,...
R.J Geller et al.
Science
(1997)
W.J Karplus
The heavens are Falling: The Scientific Prediction of Catastrophes in our Time
(1992)
D Sornette
Proc. Nat. Acad. Sci. USA
(2002)
D Sornette
Why Stock Markets Crash: Critical Events in Complex Financial Systems
(2003)
V.I. Keilis-Borok, A.A. Soloviev (Eds.), Nonlinear Dynamics of the Lithosphere and Earthquake Prediction, Springer, New...
E. Hoek, J.W. Bray, Rock Slope Engineering, 3rd Edition (rev), Institution of Mining and Metallurgy and E&FN Spon,...
E. Hoek, E.T. Brown, Underground Excavation in Rock, Institution of Mining and Metallurgy, London,...
A. Helmstetter, D. Sornette, J.-R. Grasso, J. Andersen, S. Gluzman, V.F. Pisarenko, Slider-block friction model for...

B Voight

Nature

(1988)

T. Fukuzono, Method for predicting the failure time of a slope, Proceedings of the Fourth International Conference and...

R.K. Bhandari, Some lessons in the investigation and field monitoring of landslides, in: C. Bonnard, (Ed.) Proceedings...

J Dieterich

Pure Appl. Geophys.

(1978)

A.L Ruina

J. Geophys. Res.

(1983)

C.H Scholz

Mechanics of Earthquakes and Faulting

(2002)

J McCloskey

Geophys. J. Int.

(1993)

J Schmittbuhl et al.

J. Geophys. Res. (Solid Earth)

(1996)

Cited by (69)

Landslide susceptibility evaluation in Alpine environment: 2. Thermo-hydro-mechanical modeling for the response to climate-related variables
2023, Geomechanics for Energy and the Environment
This paper is Part 2 of two companion papers, proposing a multidisciplinary approach to assess stability and velocity evolution of a large landslide located in the Central Italian Alps (upper Valtellina region): the Ruinon landslide. Part 1 of this work presented a 3D stress–strain finite element analysis, which assessed the morphological and geomechanical predisposition of the slope to gravitational instabilities and defined the current stress state along the slope. In this paper, a thermo-hydro-mechanical (THM) numerical analysis is applied to the landslide shear zone, to assess the link between landslide driving factors and the shear band material response. Data used as input for the model were pore pressure, reference stresses and initial temperature at the sliding surface, as well as the monitored velocity of the landslide body, assumed to move as a rigid block. The shear band material was modeled as a visco-plastic medium with thermal softening and velocity hardening, thus thermal- and load-rate sensitivity of the material were estimated through laboratory testing. To this end, triaxial compression tests with thermal control were performed on rock samples representative of the shear band. To constrain the model, results of the analysis presented in Part 1 were used to define the stress state at the sliding surface and the relationship between pore pressure and shear stresses. Then, pore pressure data from in-situ piezometers relevant to the period 2014–2018 were introduced and a best fitting between modeled and monitored landslide velocities was obtained. Finally, velocities were forecasted for the period 2018–2020 and a process of validation was performed using field displacement data. The outputs of the model adequately simulate the measured landslide velocity, reproducing the sliding behavior and its relationship with pore pressure. The presented approach may be applied to further case studies, aimed at defining a novel physics based early warning strategy for landslides.
Bayesian machine learning-based method for prediction of slope failure time
2022, Journal of Rock Mechanics and Geotechnical Engineering
The data-driven phenomenological models based on deformation measurements have been widely utilized to predict the slope failure time (SFT). The observational and model uncertainties could lead the predicted SFT calculated from the phenomenological models to deviate from the actual SFT. Currently, very limited study has been conducted on how to evaluate the effect of such uncertainties on SFT prediction. In this paper, a comprehensive slope failure database was compiled. A Bayesian machine learning (BML)-based method was developed to learn the model and observational uncertainties involved in SFT prediction, through which the probabilistic distribution of the SFT can be obtained. This method was illustrated in detail with an example. Verification studies show that the BML-based method is superior to the traditional inverse velocity method (INVM) and the maximum likelihood method for predicting SFT. The proposed method in this study provides an effective tool for SFT prediction.
Prediction and Forecasting of Mass-Movements
2022, Treatise on Geomorphology
In the attempt of mitigating landslide risks, the capability of quantitatively assessing hazard, that is the probability of occurrence of a possibly damaging event in time and space, is fundamental. In this chapter, we will briefly review the main operational methods for the prediction and the forecasting of the time of occurrence of mass movements and present some relevant examples concerning different landslide typologies and hazard settings. We differentiate between slope scale and basin scale approaches, and between process-based and empirically-based methods. In this framework, we distinguish three main approaches in the way the prediction is made: methods to predict failure based on slope displacement monitoring, methods based on triggering monitoring and methods based on numerical modelling. Furthermore, we hint that prediction may concern different physical variables, such as failure time, factor of safety estimation, thresholding of a signal or of a given initiation process. Although we will mainly focus on the prediction of failure time, alternative methods will be discussed also for cases where such estimation is difficult or impossible. This chapter will not treat the prediction of the failure location that is left to a specific section.
Creep of clayey soil induced by elevated pore-water pressure: Implication for forecasting the time of failure of rainfall-triggered landslides
2022, Engineering Geology
Many models have been proposed to forecast the time of failure of landslides, among them the Voight model ( $\ddot{Ω} = A {\dot{Ω}}^{α}$ ) has been widely used. Values for controlling parameters of α and A, defined by accelerating movement, are representative of kinematic behavior prior to material failure. Nevertheless, due to the unknowns in the key parameters (α and A), failure-time forecast using this model remains elusive. To examine the nature of these two parameters and their physical background, we conducted ring-shear tests on clayey soil to reproduce tertiary creep through two different approaches: a pore-water pressure-controlled approach to simulate the initiation process of landslides resulting from elevated pore-water pressure during rainfall, and a shear-stress-controlled approach often used in studies of the creep behavior of clayey soils. By examining the creeping behavior observed in the pore-water pressure-controlled tests, we found a 3-stage log-linear relationship between velocity and acceleration. The sample showed drastic dilation with short shear displacement in the first stage, and the dilation decreased in the subsequent two stages with further progress of shear displacement. The smaller value of α in the first stage increased to another value which was larger in the third stage. This variation might result from changes in the dominant shear mechanisms, i.e., in the first stage the observed creeping displacement results from pervasive grain realignment within a relatively wide shear zone, while in the following two stages, it may arise from more localized grain slip within a narrowing domain of shear zone along the sliding surface. In contrast, no evident variations in α value or sample height were found in the shear-stress-controlled tests. The effects of increasing rate of pore-water pressure or shear stress on the value of α were not pronounced in our tests. These results provide further information for understanding the progressive failure process and the Voight model of failure-time forecast. The failure-time forecast of rainfall-triggered landslides could be fundamentally difficult because of a changeable α value with the intricate volumetric variation and a diverse range of operating shear mechanisms involved.
Material failure and caldera collapse: Insights from the 2018 Kilauea eruption
2021, Earth and Planetary Science Letters
Citation Excerpt :
The introduction of the failure forecast method (FFM; e.g., Voight, 1988; Voight and Cornelius, 1991) has led to a variety of attempts to predict sudden catastrophic failure events, such as landslides (e.g., Federico et al., 2012; Carlà et al., 2017) and volcanic eruptions (e.g., Kilburn and Voight, 1998; Tárraga et al., 2008). The study of material failure can also be used to gain more insight into the processes involved in failing systems and why not all failing systems end in a catastrophic material failure (e.g., Cornelius and Scott, 1993; Sornette et al., 2004; Gershenzon, 2019). Material failure laws have been applied to different geophysical parameters related to strain and energy release.
The Failure Forecast Method (FFM) was introduced as an empirical model for forecasting catastrophic material failures related to natural hazards, such as landslides and volcanic eruptions, with mixed success. During the 2018 eruption of Kilauea volcano, Hawaii, the draining of the summit magma reservoir into the Lower East Rift Zone resulted in the formation of a new caldera at the summit. I tested the applicability of the FFM to caldera collapse by analyzing the cyclical earthquake swarms and ground deformation that occurred between 62 sudden major caldera collapse events. The progression of both the cumulative moment release of the cyclical earthquakes and the GNSS displacement show a major change in mid-June. In late May through early June, the progression of the parameters is consistent with strain localization or creep progression related to the development or activation of the ring fault system. From late June until the end of the eruption, parameter progression is roughly steady with initial accelerating increases in cumulative moment and displacement that shift to approximately linear progression. Analysis of repeating earthquake families in the cyclical swarms showed that the behavior of the repeaters was consistent with that of the cyclical swarms as a whole and suggested that each family undergoes its own progression of activation to termination. While the FFM analysis identified the system change in mid-June, it did not demonstrate an ability to forecast collapse events or the end of the eruption.
Probabilistic prediction of slope failure time
2020, Engineering Geology
The inverse velocity method is widely used for slope failure time prediction. In practice, the presence of factors like measurement error, environmental noise, and modeling assumptions may make the predicted failure time different from the actual failure time. While the traditional inverse velocity method can provide useful information about the probable failure time, it does not furnish an estimate about the reliability of the prediction. In this paper, the uncertainties in slope failure time forecast are divided into two categories, i.e., observational uncertainty and model uncertainty. A method is suggested to assess the effect of observational uncertainty on slope failure time prediction through site-specific data based on the maximum likelihood principle. The model uncertainty associated with the inverse velocity method is calibrated based on a database containing 50 landslides with known failure time. A procedure is suggested to predict the probability density function of the slope failure time considering both uncertainties. Two illustrative examples are provided to show that the outcome from the probabilistic method suggested in this paper can be more informative for rational decision making.

View all citing articles on Scopus

View full text