Program
February, 3

       10h30-11h00 Registration / Coffee

       11h00-11h50 Didier Bresch,  Avalanches: Mixture and/or non-newtonian PDEs?

In this talk, I  will present recent nonlinear hypocoercivity
for PDEs used to modelize mixtures including powder-snow avalanches.
This property shows explicitly that two-velocity hydrodynamics may
be encoded in such models even if the system concerns a priori
only a single mass density and a velocity field. In a second part
I will also present recent mathematical results related to
non-newtonian compressible fluid systems that may occur in
dense snow avalanches modeling.
 
       12h15-13h45 Lunch
      
       14h00-14h50 Oana Lupascu, Branching processes for the fragmentation equation: applications to avalanches


We investigate branching properties of the solution of the fragmentation
equation and we properly associate a continuous time cadlag Markov process
on the space of all fragmentation sizes of J. Bertoin. We give an application to
a stochastic model for the avalanches. The talk is based on joint works with
L. Beznea and M. Deaconu.

       15h00-15h50 Thierry Goudon, Simulation of non homogeneous flows and application to powder snow avalanches

We are interested in hydrodynamic models of mixture that involve unusual
constraints relating the divergence of the velocity to derivatives of the density.
We discuss numerical method for the simulation of such models, based on a
hybrid Finite Volume/Finite Element method. This approach is validated by
comparison to analytical solutions, numerical solutions and experimental data.
The scheme works on unstructured meshes and it can be advantageously
coupled to mesh refinements strategies in order to follow fronts of high density
variation. We explore numerically the role of the leading coeffecients that
characterize the flow and grade the numerical difficulty: the Froude, the Reynolds
and the Schmidt numbers.

       16h00-16h30 Coffee break
 
       16h30-17h20 Nicolas Eckert, Snow avalanche long term risk assessment

Evaluating risk to extreme avalanches realistically is a crucial question for land
use planning and the design of appropriate defense structures in mountainous
areas.Legal thresholds are defined using high return levels, which are by essence
probabilistic concepts. To determine them on the basis of observations, the use of
univariate extreme value theory is natural, but remains cumbersome because the
most critical variable, the travelled distance, strongly depends on topography. Also,
different damageable quantities (travelled distance, impact pressure, flow depth,
deposit volumes) have to be considered and, for these, field data are generally not
available, making the use of multivariate extreme value models practically impossible.
The existing alternative is the combination of a mechanical model for flow propagation
with a stochastic model describing the variability of the different inputs/outputs.
High avalanche magnitude and frequency are modeled independently, leading to a
sort of multivariate Peak Over Threshold (POT) model where the correlation between
the different magnitude variables is constrained by the physical rules describing
avalanche propagation.The inference challenge can be solved under the Bayesian
paradigm using MCMC techniques. However, the consistency of such an approach with
extreme value theory in terms of attraction domain and asymptotic dependence for
the different variables is not guaranteed, making the validation of model predictions a
critical issue. Also, in practice, return period/level approaches, purely hazard-oriented,
have the drawback to not considering elements at risk explicitly (buildings, people
inside, etc.), and to neglect possible budgetary constraints. To overcome these, risk
based zoning methods and cost-benefit analyses have emerged recently. They
combining hazard distribution and vulnerability relations (damage susceptibility
functions) for various elements at risk. Here as well, computations can be made
with standard extreme value models, or with a statistical numerical model, with
advantages / drawbacks for each option. In this talk, these points are discussed
with referenceto real case studies in the French Alps for which different kind of
data are available.


        20h00 Conference Dinner
 



February, 4

       9h30-10h20 Ioan R. Ionescu, Shallow viscoplastic modeling of dense avalanches: from the onset to the dynamic flow


We investigate the  shallow  flow of a viscoplastic fluid over a general basal
topography. A  Saint-Venant  model  and   a new depth integrated theory is
presented.  The curvature of the bottom surface is included in the model  in
the expression of the differential operators  as well as in  the frictional terms.
To model  the avalanche onset we  introduce  a simple criterion  to distinguish
if an avalanche  occurs or not.  This criterion, relating the yield limit (material
resistance)  to the distribution of the external forces, is deduced from  an
optimization problem,  called limit load analysis.  To prove the existence of an
onset  velocity field (collapse flow) the appropriate  functional space consists of
bounded tangential deformation functions.  We propose  a numerical strategy
to solve the limit load problem and to get the onset flow field.  A mesh free 
method, called the discontinuous velocity domain splitting   (DVDS),  is adapted
and illustrated  by solving  several safety factor problems.
For the dynamic flow a mixed Finite-Element and Discontinous Galerkin strategy is
developed using a decomposition-coordination formulation coupled with the
augmented lagrangian method. The DG method makes use of an upwind strategy
in the choice of the flux.  A couple of boundary value problems, modeling shallow
dense avalanches, for different viscoplastic laws are selected  to
illustrate the predictive capabilities of the model:  spreading a Drucker-Prager dome
on a talweg and   the role of barriers in stopping a viscoplastic avalanche.

         10h30-11h00 Coffee break
 
       11h00-11h50 Cesar Vera Valero, New methods in avalanche modelling: The influence of thermal temperature on snow avalanche dynamics

Snow avalanche dynamics models are used for hazard mapping and to study
mitigation measures.  They are widely applied in snow engineering practice.  In
this talk, we present several new trends in avalanche dynamics modelling. 
These include: (1) the inclusion of thermal temperature to model wet snow
avalanches, (2) lubrication effects induced phase changes, (3) entrainment
of thermal energy by snowcover erosion and (4) avalanche fluidization and the
formation of powder snow avalanches from cold snow.  As the avalanche core
is modelled as a granular system, the fluctuation energy of the granules is
considered.  Avalanche flow regimes are governed by degree of fluctuation
energy which is controlled by snow temperature.  The evolution of the avalanche
is therefore governed by two time scales:  one time scale is defined by the
friction in the slope parallel direction, the other time scale is defined by the
decay time of fluctuation energy dissipation.  Fluctuation energy dissipates
rapidly in wet flows leading to dense-type, slow moving avalanches.  Phase
changes, however, introduce liquid water into the flow, modifying the friction
on the basal boundary.  Runout distances can be extreme. With this approach
we are able to simulate many features (runout, velocity, depositions) of wet
snow avalanches.  Examples are presented
.

                     


       12h15-13h45 Lunch

       14h00-14h50 Anne Mangeney, How seismic waves can be used to constrain landslide dynamics and rheology

Gravitational instabilities such as landslides or avalanches play a key role in erosion
processes on the Earth surface and represent one of the major natural hazards
threatening life and property in mountainous, volcanic, seismic and coastal areas.
The unpredictable nature and destructive power of landslides make fast and
reliable in situ measurements of their properties extremely difficult. Consequently,
remote seismic monitoring proves to be a unique tool for quantification of such
phenomena and for monitoring gravitational activity. Over and above event
detection, seismic signals can provide important information on the
characteristics of the source (e.g. volume, duration, location) and even on its
dynamics and mechanical behaviour (velocity, friction coefficient, etc.). However,
inferring information from the seismic signal to characterize the “landslide source”
(landquake) suffers from uncertainties related to the respective role of topography,
mass involved, flow dynamics and wave propagation on the recorded signal. We show
here that coupled numerical modeling of landslide and generated seismic waves
provides a new tool to address these issues. Modeling of different landquakes shows
that the main features of the low frequency seismic signal are reproduced by the
simulation. Topography effects on the flowing mass have a major impact on the
generated seismic signal. Simulation of the seismic signal makes it possible to
discriminate between possible alternative scenarios for flow dynamics and to provide
first estimates of the rheological parameters during the flow. Granular flow modeling
and analysis of the seismic signals of hundreds of rockfalls within the Dolomieu
crater in La Reunion island show that similar scaling laws can be defined between
the seismic energy and the signal duration on one hand, and between the difference
in the potential energy released during the event and the flow duration on the other
hand. The ratio R between the seismic energy and the release of potential energy
is shown to be almost constant (R=10-4). Based on these observations, we propose
a simple method to estimate the volume of rockfalls from their seismic signal. As
andquakes are continuously recorded by seismic networks, our results provide a
new way to collect data on the dynamics and rheology of natural flows and to study
he spatio-temporal change of gravitational activity in relation with volcanic, seismic
or climatic activity.
    
      15h00-15h50  Mikhail Lebyodkin, Avalanche phenomena in crystal plasticity


Investigations of crystal plasticity during last two decades proved that the ensemble
of crystal defects represents a nonlinear dynamical system characterized by
self-organization phenomena. Examples of the collective dynamics include localization
and propagation of deformation bands, deterministic chaos, intermittency associated
with a power-law statistics of jumps of the local strain rate, and so on. Avalanche-like
behaviour was first identified for various mechanisms of the so-called plastic
instability giving rise to macroscopic intermittency visible on stress-strain curves.
Due to the development of high-frequency measurement techniques, e.g., based
on the acoustic emission (AE), these ideas were later confirmed in a more general
case of macroscopically smooth plastic flow, albeit on finer scales. More specifically,
power-law statistics of AE were found during smooth deformation of pure crystals,
which led to a conclusion that plastic flow is an inherently intermittent scale-invariant
process. The talk will briefly outline some milestones of the studies of self-organization
in  plasticity. It will also present recent data of AE investigations under conditions of
plastic instability, which aim at establishing the relationships between the mesoscopic
 scales related to self-organization of crystal defects and the macroscopic scale
relevant to the continuous approach of plasticity. This study is done in collaboration
witg T.A. Lebedkina.