technological prediction with models ... - mwcoe

A Technological Appoach to Avalanche Risk ManagementTechnological Prediction with Models:Understanding Mechanisms of Dry Slab Avalanches

2nd Mountain Warfare Congress, 2019NATO Mountain Warfare Centre of Excellence

P.L. Rosendahl · P. Weißgraeber

April 10th, 2019 | Speaker: Dr.-Ing. Weissgraeber | www.2phi.de | 2nd Mountain Warfare Congress, 2019 | MWCOE, Slovenia

The authors

2

2φ MODELINGAPPROACHES

Research campus University Stuttgart

Philipp L. Rosendahl Philipp Weissgraeber

Co-founders of


Why do we need models? – Easter Sunday

3

Easter Sundaymust always

follow the firstfull moon after

the spring equinox.

https://www.statista.com/chart/8959/frequency-of-easter-sunday-by-date-from-1600-to-2099/

Year


Why do we need avalanche models?

4

What are critical conditions for dry-snow slab avalanche release?

▸▸ Dependent and independent input parameters


How do models help?

5

whumpf size ofrelease

critical load

Real-time tool

Our vision

Physically sound

For experts and practitioners

Models can improve ourunderstanding of physics

hcn.org


Models of slab avalanche release

Local stability index (Perla, 1977)

● Stress exceeding strength● A probe could trigger

Shear crack (McClung, 1981)

● No remote triggering● Whumpf only as a

consequence● Assumption of super

weak zones

6

Anticrack – “house of cards” (Heierli, 2008)

● Whumpf and remote triggering explained● Normal displacement within rigid weak layer● Assumption of super weak zones

Finite anticrack initiation (Rosendahl & Weißgraeber, 2018)

● Modern mixed-mode model● No assumptions on defect size● Combination of previous models


Slab avalanche release: from weak layer collapse to crown fracture

7

Failure model Model of system response Failure criterion

crack initiation crack propagation slab fracture slidingundamaged


Finding a suitable failure model

8

linear elastic

visco elastic

...

multi-scale

...

Model of system response

Appropriate failure

criterion

Reality

Prediction

Observations


System of differential equations

Modeling the snowpack: it’s all about the weak layer

9

Schweizer et al. (2003)


Skier-induced stresses in the weak layer

10

FEA: numerical reference solution


Bridging effect

11


h


Propagation saw test

12

Montana avalanche Center (2018)Gauthier et al. (2008)

● Introduction of artificial crack in weak layer● Crack propagation at critical cut length● Resembles fracture mechanical lab test● Determination of fracture mechanical

properties of weak layer● Quantitative field experiment


Energy release rate of anticracks

13

Model results vs. FEA results


Propagation saw test

● Model allows for linking cut length and energy release rate of anticracks


Model validation: comparison to field data

● 93 propagation saw tests (PSTs)● Critical crack length → fracture toughness

Energy release rate of anticracks

14

Model results vs. FEA results



Finding a suitable failure model

15

linear elastic

visco elastic

...

multi-scale

...

Model of system response

Appropriate failure

criterion

Reality

Prediction

Observations


Modeling slab avalanche release

16

present snowpack model

unified failure criterion

critical load and avalanche size

crack initiation crack propagation slab fracture slidingundamaged


Structural integrity: strength

Stress

● Force per unit area● Expresses the internal forces in the material● Tensile, compressive and shear stresses

Strength

● Critical stress a material can sustain● Different strengths in pure tension, pure

compression and pure shear● Failure often caused by mixed loading

(e.g. cornice fracture)

17

Tension

Compression

Shear


Structural integrity: fracture mechanics

Energy release rate (ERR)

● Infinite stresses at crack tip● Change of stored energy because of crack

growth is called energy release rate● ERR determines stability of existing cracks ● Only considers existing cracks

18

Mode I Mode II Mode III

Opening or collapse In-plane shear Out-of-plane shear

= +

Skier loading Compression Shear= +

Fracture toughness

● Critical energy release rate● Different fracture toughnesses for crack

opening, collapse and shear● Crack growth often caused by mixed loading

(e.g. weak layer)


Importance of fracture mechanics: “Liberty” cargo vessels in WW2

19

U.S. WWII Liberty class naval cargo ship

● Low-cost construction● Mass-produced● 2,710 Liberty ships between

1941 and 1945

Embrittlement at cold temperatures

● Colder temperatures led to brittle fracture● Hull and deck cracks● Cracks could propagate in complete hull● 1,200 ships showed fracture● Over 200 ships lost

Failure of moored SS Schenechtady, Jan 17th 1943


Two independent material properties: strength and toughness

Homogeneous stressesStrength-of-materials

20

Carter et al. (2014)

Crack propagationFracture mechanics Crack initiation

strength and fracture toughness

“brutal” crack incrementsEnergy release > toughness

Stress > strength


Coupled stress and energy criterion

21

mechanical model

strengthoverloaded weak layer

fracture mechanicsenergy balance of anticrack

satisfied simultaneouslycrack initiation

1 Leguillon (2002) Eur. J. Mech. A/Sol. 21(1), pp. 61–72.2 Hashin (1996) J. Mech. Phys. Sol. 44(7), pp. 1129–1145.3 Weißgraeber, Leguillon & Becker (2016) Arch. Appl. Mech. 86(1–2), pp. 375–401.

critical loadskier, slab weight

April 10th, 2019 | Speaker: Dr.-Ing. Weissgraeber | www.2phi.de | 2nd Mountain Warfare Congress, 2019 | MWCOE, Slovenia 22

energy release suffices

energy which can be released by a crack

local weak layer loading

overload

weak layer does not collapse despite locally overloaded

critical level

April 10th, 2019 | Speaker: Dr.-Ing. Weissgraeber | www.2phi.de | 2nd Mountain Warfare Congress, 2019 | MWCOE, Slovenia 23

energy release suffices

energy which can be released by a crackoverload

critical level

local weak layer loading

zone of weak layer collapse

weak layer


Evaluation of coupled criterion

24

Physical effects

● Maximum extra load(e.g. skier)

● Effect of slab weight(self-release)

● Slope angle dependence

F


Evaluation of coupled criterion

● Increasing slope angles reduces critical load

● Shear stress in the weak layer increases

● Initial crack lengths increases with transition from normal to shear load

● Longer initial cracks propagate more readily

25


Hazard map

Model chain

26

Geo data

Snowpack data Computational model

Local assessment

Slab avalanche model


Example of hazard mapping

27


Conclusions

What do we have?

● Accurate mechanical model of slab on weak layer

● Physical explanationfor crack initiation

● Unified failure criterion for initiation and growth of cracks in weak layer

● Real-time evaluation

28

What’s to come?

● Layered slab


Vision

29

● Interpret measurements

● Model based hazard mapping for data sparse areas

● Assist experience-based nonformal decision making

● Reduce risk of stability tests in field

30

2φ

technological prediction with models ... - mwcoe

Documents