Program

February, 3

10h30-11h00 Registration / Coffee

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

12h15-13h45 Lunch

14h00-14h50 Oana Lupascu, Branching processes for the fragmentation equation: applications to avalanches

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

20h00 Conference Dinner

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.

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.

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 avalanchesequation 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.

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 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.

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.

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

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

12h15-13h45 Lunch

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

15h00-15h50 Mikhail Lebyodkin, Avalanche phenomena in crystal
plasticity

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 breaktopography. 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.

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.

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.

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.

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.

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.