WSL Institute for Snow and Avalanche Research SLF

Johan Gaume and Chenfanfu Jiang

A Material Point Method

for snow and avalanche mechanics

GRAPHYS, Grenoble, 26-27 October 2019

Acknowledgments

Dr. Ted Gast

Prof. Joseph Teran

Prof. Chenfanfu Jiang

Dr. Alec van Herwijnen

Stephanie Wang

Dr. Xingyue Li

Lars Blatny

Bertil Trottet

Princess Elsa of

Arendelle

ContextProcesses of dry-snow slab avalanche release

Flow

Adapted from Schweizer et al., (2016)

ContextProcesses of dry-snow slab avalanche release

Flow

DEM

FBM

FEM FEM

FV

Adapted from Schweizer et al., (2016)

DEM

FEM

DEM

CAM

?

ContextProcesses of dry-snow slab avalanche release

Flow

Adapted from Schweizer et al., (2016)

NO UNIFIED APPROACH

DEM

FBM

FEM

FV

DEM

FEM

DEM

CAM

?

FEM

Context: Another challengeVolumetric collapse of the weak layer

Field experiments:

The Propagation Saw Test (PST)

van Herwijnen, Gaume, Bair, Reuter, Birkeland, Schweizer (2016).

Journal of Glaciology

Context: Another challengeVolumetric collapse of the weak layer

2D DEM modeling: onset and

dynamics of crack propagation

Field experiments:

The Propagation Saw Test (PST)

Gaume et al. (2015) – Gaume et al. (2017). The Cryosphere

van Herwijnen, Gaume, Bair, Reuter, Birkeland, Schweizer (2016).

Journal of Glaciology

Context: Another challengeVolumetric collapse of the weak layer

2D DEM modeling: onset and

dynamics of crack propagation

Field experiments:

The Propagation Saw Test (PST)

Gaume et al. (2015) – Gaume et al. (2017). The Cryosphere

van Herwijnen, Gaume, Bair, Reuter, Birkeland, Schweizer (2016).

Journal of Glaciology

NO RELEVANT CONSTITUTIVE

MODEL INCLUDING “COLLAPSE”

Gaume et al., (2018). Dynamic anticrack propagation in snow.

Nature Communications. 9(1), 3047

How does it work?We need 3 ingredients:

How does it work?We need 3 ingredients:

1. A hybrid

numerical method

How does it work?We need 3 ingredients:

2. A snow

model

1. A hybrid

numerical method

How does it work?We need 3 ingredients:

2. A snow

model

3. A weak layer

model

1. A hybrid

numerical method

© ASARC

A hybrid numerical methodThe Material Point Method (hybrid Eulerian-Lagrangian)

Momentum balance equation

Adapted from Stomakhin et al. (2013), SIGGRAPH and

Gaume et al. (2018). Nature Communications, 9(1), 3047

A hybrid numerical methodThe Material Point Method (hybrid Eulerian-Lagrangian)

Momentum balance equation

Adapted from Stomakhin et al. (2013), SIGGRAPH and

Gaume et al. (2018). Nature Communications, 9(1), 3047

A snow mechanical modelWhat do we want?

1. A mixed-mode yield surface (tension, shear, compression)

2. Hardening in compression (promoting compaction)

3. Softening in tension (promoting fracture)

► Fracture

(softening)

► Compaction

(hardening)

A snow mechanical model1. A mixed-mode yield surface: our model

q

elastic

non admissible

Gaume et al., (2018). Dynamic anticrack propagation in snow.

Nature Communications. 9(1), 3047

𝝉 = 𝐶: 𝝐

p

Yield surface:

Stress invariants:

Associative flow rule:

Simo and Meschke 1993

elastic right Cauchy-Green

strain tensorLie derivative plastic right Cauchy-Green

strain tensor

A snow mechanical model1. A mixed-mode yield surface: our model

Gaume et al., (2018). Dynamic anticrack propagation in snow.

Nature Communications. 9(1), 3047

p0

• p0: compressive strength

q

p

A snow mechanical model1. A mixed-mode yield surface: our model

Gaume et al., (2018). Dynamic anticrack propagation in snow.

Nature Communications. 9(1), 3047

-bp0 p0

• p0: compressive strength

• bp0: tensile strength (COHESION)

q

p

A snow mechanical model1. A mixed-mode yield surface: our model

Gaume et al., (2018). Dynamic anticrack propagation in snow.

Nature Communications. 9(1), 3047

-bp0 p0

M

• p0: compressive strength

• bp0: tensile strength (COHESION)

• M: slope of the Critical State Line (FRICTION)

q

p

A snow mechanical model2. Hardening in compression

Gaume et al., (2018). Dynamic anticrack propagation in snow.

Nature Communications. 9(1), 3047

q

p

Hardening rule:

A snow mechanical model2. Hardening in compression

Gaume et al., (2018). Dynamic anticrack propagation in snow.

Nature Communications. 9(1), 3047

HARDENING IN

COMPRESSION

q

p

Hardening rule:

A snow mechanical model2. Hardening in compression

Gaume et al., (2018). Dynamic anticrack propagation in snow.

Nature Communications. 9(1), 3047

HARDENING IN

COMPRESSION

q

p

Hardening rule:

A snow mechanical model2. Hardening in compression

Gaume et al., (2018). Dynamic anticrack propagation in snow.

Nature Communications. 9(1), 3047

HARDENING IN

COMPRESSION

q

p

Hardening rule:

A snow mechanical model2. Hardening in compression

Gaume et al., (2018). Dynamic anticrack propagation in snow.

Nature Communications. 9(1), 3047

stress

strain

HARDENING IN

COMPRESSION

q

p

A snow mechanical model3. Softening in tension

Gaume et al., (2018). Dynamic anticrack propagation in snow.

Nature Communications. 9(1), 3047

SOFTENING

q

p

Hardening rule:

A snow mechanical model3. Softening in tension

Gaume et al., (2018). Dynamic anticrack propagation in snow.

Nature Communications. 9(1), 3047

SOFTENING

q

p

Hardening rule:

A snow mechanical model3. Softening in tension

Gaume et al., (2018). Dynamic anticrack propagation in snow.

Nature Communications. 9(1), 3047

SOFTENING

q

p

Hardening rule:

A snow mechanical model3. Softening in tension

Gaume et al., (2018). Dynamic anticrack propagation in snow.

Nature Communications. 9(1), 3047

SOFTENING

stress

strain

q

p

A good snow mechanical model2. Snow simulations

Ref: Gaume, Gast, Teran, van Herwijnen, Jiang. Dynamic anticrack propagation in snow

using large strain continuum elastoplasticity. Under review

A weak layer mechanical modelWhat do we want?

1. A mixed-mode yield surface (tension, shear, compression)

2. Softening and collapse under mixed-mode shear-compression loading

3. Frictional behavior after collapse

© ASARC

1. A mixed-mode yield surface: our model

Gaume et al., (2018). Dynamic anticrack propagation in snow.

Nature Communications. 9(1), 3047

-bp0 p0

M

• p0: compressive strength

• bp0: tensile strength (COHESION)

• M: slope of the Critical State Line (FRICTION)

A weak layer mechanical model

q

p

2. Softening

Gaume et al., (2018). Dynamic anticrack propagation in snow.

Nature Communications. 9(1), 3047

SOFTENING IN

COMPRESSION

A weak layer mechanical model

q

p

Hardening rule:

2. Softening

Gaume et al., (2018). Dynamic anticrack propagation in snow.

Nature Communications. 9(1), 3047

A weak layer mechanical model

SOFTENING IN

COMPRESSION

q

p

Hardening rule:

2. Softening

Gaume et al., (2018). Dynamic anticrack propagation in snow.

Nature Communications. 9(1), 3047

A good weak layer mechanical model

SOFTENING IN

COMPRESSION

q

p

Hardening rule:

2. Softening

Gaume et al., (2018). Dynamic anticrack propagation in snow.

Nature Communications. 9(1), 3047

A good weak layer mechanical model

stress

strainSOFTENING IN

COMPRESSION

3. Collapse and frictional behaviour

Gaume et al., (2018). Dynamic anticrack propagation in snow.

Nature Communications. 9(1), 3047

HARDENING

WITHOUT COHESION

A good weak layer mechanical model

q

p

Gaume et al., (2018). Dynamic anticrack propagation in snow.

Nature Communications. 9(1), 3047

HARDENING

WITHOUT COHESION

A good weak layer mechanical model3. Collapse and frictional behaviour

q

p

Gaume et al., (2018). Dynamic anticrack propagation in snow.

Nature Communications. 9(1), 3047

HARDENING

WITHOUT COHESION

A good weak layer mechanical model3. Collapse and frictional behaviour

q

p

Gaume et al., (2018). Dynamic anticrack propagation in snow.

Nature Communications. 9(1), 3047

HARDENING

WITHOUT COHESION

stress

strain

A good weak layer mechanical model3. Collapse and frictional behaviour

q

p

Application to avalanche releasePropagation Saw Test on a 37°slope

Application to avalanche releasePropagation Saw Test on the flat

Application to avalanche releasePropagation Saw Test with crack branching

2D remote avalanche triggering

2D remote avalanche triggering

slab fractures

crack tip in

the weak layer

« shooting cracks »

2D remote avalanche triggering

Crack propagation speed

3D remote avalanche triggering

Crack propagation speed

3D remote avalanche triggering

Crack propagation speed

More recent – preliminary work

MPM simulations of snow microstructure

PhD Thesis of

Lars Blatny

More recent – preliminary work

Crack propagation

PhD Thesis of

Bertil Trottet

More recent – preliminary work

Crack propagation

PhD Thesis of

Bertil Trottet

More recent – preliminary work

Avalanche dynamics

PostDoc

research of

Dr. Xingyue Li

More recent – preliminary work

Avalanche dynamics

M(1+b) = 0.5

M(1+b) = 0.65

M(1+b) = 1.95

M(1+b) = 3

More recent – preliminary work

Avalanche dynamicsM(1+b) = 0.225 M(1+b) = 0.75 M(1+b) = 0.945

More recent – preliminary work

Avalanche dynamics

ConclusionFlow

Avalanche

dynamics

4

Slab releaseCrack propagationFailure initiation

Sliding of the

slab

Dynamic crack

propagation

Onset of crack

propagationCrack

formationDamage

process

microscale (mm – dm) mesoscale (dm – 1 m) macroscale (10 m – 100 m) scale

adapted from Schweizer et al. (2016)

OutlookCurrent work

Snow-tire

interaction by Stephanie Wang

(collab. SLAB x UCLA x UPenn)

Glacier calving

(collab SLAB x UPenn x UZH)

Do you have any questions?

Thanks for your attention!