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Assessment of landslide run-out by Monte Carlo simulations
Évaluation de la dynamique des glissements de terrain par des simulations de Monte-Carlo
Cepeda J., Quan Luna B., Nadim F.
Norwegian Geotechnical Institute – NGI and International Centre for Geohazards - ICG, Oslo, Norway.
ABSTRACT: Landslides run-out models are based on theoretical descriptions of mass motion which attempt to model the complex
behaviour of the actual flow phenomenon. To reproduce the general features of the mass motion, these models simplify the problem
by using parameters that account for complex aspects, which are not explicitly included. This simplification results in model
parameters that cannot be related to a specific physical process, and therefore cannot be directly measured. In order to analyse the
effect of uncertainties in the input parameters, a probabilistic procedure based on a Monte Carlo simulation for run-out modelling was
considered. The framework is based on a dynamic model (MassMov2D), which is combined with an explicit representation of the
different parameter uncertainties. The main goal with the proposed methodology is to present a framework to obtain potentially
expected run-out extents and intensities in areas where it is not possible to determine the rheological parameters on the basis of back-
analyses. The outlined procedure provides a useful approach for experts to produce hazard or risk maps in cases where historical
records are either poorly documented or completely lacking, as well as to derive confidence limits on the proposed zoning.
RÉSUMÉ : Les modèles de la dynamique des glissements de terrain sont basés sur des formulations mathématiques qui tentent de
théorétiser les phénomènes d'écoulement réels, par nature très complexes. Afin de simuler les caractéristiques générales du
mouvement, ces modèles utilisent des paramètres qui représentent et simplifient les aspects complexes du problème, sans pour autant
les prendre en compte explicitement. Il en résulte une simplification des paramètres du modèle: ceux-ci ne sont donc plus liés à un
processus physique réel, et ne peuvent par conséquent pas être mesurés directement. Afin d'analyser l'effet des incertitudes entourant
ces paramètres, une approche probabiliste, basée sur la méthode de Monte Carlo, a été employée. Celle-ci se base sur un modèle
dynamique (MassMov2D) ainsi que sur une représentation explicite des incertitudes des différents paramètres. L'objectif principal de
cette méthode est de proposer une approche générale dans le but de prédire la taille et l’amplitude des glissements de terrain dans des
zones où il n’est normalement pas possible de déterminer les paramètres rhéologiques par méthode arrière. La méthode décrite ici
propose une approche pratique afin d’établir des cartes de risque dans les cas où la documentation est limitée, voire inexistante, ainsi
que pour estimer les limites de confiance des zonages proposés.
KEYWORDS: Landslides, run-out, Monte Carlo, Bingham rheology, Voellmy rheology, quantitative risk assessment.
1 INTRODUCTION
Dynamic run-out models for landslides are able to simulate the
spatial distribution of depth and velocity of the moving mass,
which is essential for a quantitative evaluation of hazard and
risk at a specific site. Another advantage of the application of
dynamic models is that they can simulate the effect of variations
in the release volume as well as in the rheological parameters
for different scenarios including ones that have no historical
evidences.
In practice, a substantial degree of uncertainty characterizes
the definition of the deterministic model parameters. This is due
to the lack of experimental data and the poor knowledge of the
mechanical behaviour of the moving flows. Consequently all
models, either those widely used in practical applications or
those more recently developed, are based on simplified
theoretical descriptions of mass motion which try to capture the
complex rheology of the flow phenomenon. This results in a
generalization of all models to attempt to reproduce the general
features of the moving mass through the use of parameters
(mostly for evaluating base shear) which account for aspects not
explicitly described or oversimplified. The outcome is that the
model parameters cannot be related to a specific physical
process, and therefore directly measured, but need to be
calibrated. At the moment, a relatively complete and well-
established calibration for most of the run-out models is still
lacking or not reliable enough to be applied in practical
applications. This is connected with one of the basic limitations
with the use of dynamic run-out models, which are significantly
sensitive to the parameters controlling the base shear (Revellino
et al. 2004, Hurlimann et al. 2007, Hungr & McDougall 2009).
Inherent uncertainties in the specification of the input data for
models are well acknowledged but usually not explicitly
incorporated into the analyses. Such uncertainties are normally
addressed through conservative estimate of parameters, or in
some cases, by a sensitivity analysis. These approaches do not
integrate objectively the estimation of uncertainties, and thus
may be impractical and lead to either conservative or
underestimated hazard levels.
In order to analyze the effect of the uncertainty of input
parameters, a probabilistic framework based on a Monte Carlo
simulation for run-out modelling is considered as an alternative
approach. Monte Carlo analysis is a method that uses statistical
sampling techniques of input parameters to derive the
probability distributions of solutions for mathematical equations
or models. The Monte Carlo analysis was initially developed in
the 1940’s and it has been applied to a wide variety of problems
for addressing the uncertainty of data and models (Metropolis
1987).
2 METHODOLOGY
The dynamic model used in this study was MassMov2D
(Beguería et al. 2009), which solves the equations of
conservation of mass and momentum averaged over the depth
of the landslide mass using an Eulerian scheme scripted in
PCRaster, a GIS modelling environment (Karssenberg et al.
2001). In the equation of conservation of momentum, the shear
stress at the bed contact (base of the analysed differential
column) is calculated using a rheological model (a relation
coupling stresses and strain rates) that should be physically
consistent with the overall behaviour of the landslide. In this
particular case, two models are used for describing frictional
and cohesive-like dominated behaviours, namely the Voellmy
and the Bingham models. Simplified formulations of these
models are presented in Equations (1) and (2), respectively:
