Some Critical Comments on the Landslides Modelling

8/13/2019 Some Critical Comments on the Landslides Modelling

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SOME CRITICAL COMMENTS ON THE

LANDSLIDES MODELLING

DENYS DUTYKH1

Senior Research Fellow UCD & Charge de Recherche CNRS

1University College DublinSchool of Mathematical Sciences

UCD Wave Group Seminar
http://www.denys-dutykh.com/http://www.denys-dutykh.com/http://www.denys-dutykh.com/http://www.denys-dutykh.com/http://www.denys-dutykh.com/http://www.denys-dutykh.com/http://find/http://goback/


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ACKNOWLEDGEMENTS

ICT, NOVOSIBIRSK, RUSSIA:

Prof. Leonid Chubarov [CKS11]

Prof. Gayaz Khakimzyanov[KS10]

Sonya Beisel [BCK11]

Nina Shokina[BCS11]

RECENT DEVELOPMENTS:

Dimitrios Mitsotakis (UC Merced, CA, USA) [DMBS12]

Henrik Kalisch (University of Bergen, Norway)[DK11]
http://www.ict.nsc.ru/indexen.phphttp://www.ict.nsc.ru/indexen.phphttp://find/http://goback/


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OUTLINE

WHAT IS A LANDSLIDE?

WHAT YOU WILL NOT LEARN. . .

Solid mechanics based approaches (DEM)Subaerial processes

Two-phase models

WHAT YOU WILL LEARN

Some constructive critics

Simple classical mechanics-based method
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WHAT IS A LANDSLIDE?SOURCE: ENCYCLOPDIA BRITANNICA, NOT WIKIPEDIA!

DEFINITION (FROM BRITANNICA):

Landslide, also calledlandslip, the

movement downslope of a mass ofrock, debris, earth, or soil (soil being

a mixture of earth and debris).

Landslides occur when gravitational

and other types of shear stresses

within a slope exceed the shearstrength (resistance to shearing) of

the materials that form the slope.

FIGURE: La Conchita, CA
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TYPES OF LANDSLIDES
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LANDSLIDES IN COASTAL AREAS

subaerial / partially submerged /underwater landslide

generation/ propagation / run-up
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EXPERIMENTS ON SUBAERIAL LANDSLIDESCREDIT: PHD OF VALENTIN HELLER, VAW ETH ZURICH (2007)
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EXISTING MODELING APPROACHES - IDISCRETE ELEMENT METHOD (CREDIT: PAUL W. CLEARY(CSIRO, AUSTRALIA)
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EXISTING MODELING APPROACHES - IILANDSLIDE MODELING IN WATER WAVE COMMUNITY

Two-layer shallow water models Rheology is unknown Shallow water approximation for the slide is questionable Uncertainties in data!

Sevilla [FNBB+08], Paris XIII [BSS10], Paris 6 [MCVB+03]

Since geophysical uncertainties are important, we will

simplify the model
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CENTER OF MASS-BASED MODELSWE SHOULD SIMPLIFY, BUT NOT TOO MUCH!

Our assumptions:

Landslide is a solid quasi-deformable body:

(x, t) =0(x xc(t))

Shape is prescribed

Mass and volume are conserved

CONCLUSION:It is sufficient to determine thetrajectory of the barycenter

x=xc(t)to know the motion of the whole body.

THREE APPROACHES FORxc(t): Trajectory isprescribed[RS10]

Trajectory is measured

Trajectory ismodeled
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EXPERIMENTS ON CONSTANT SLOPESEXPERIMENTAL MEASUREMENT OF THE LANDSLIDE TRAJECTORY: [EG07]

Experimental set-up of

Enet & Grilli (2007)

[EG07]:

S
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SIMPLE MODEL OF THE BARYCENTER MOTIONWE USE THE 2ND NEWTON LAW

NATURAL ARC-LENGTH PARAMETRIZATION:

s=L(x) =

xx0

1 + (h0())

2 d.

WE APPLY THENEWTON LAWS TO WRITE:

md2s

dt2 =F(t)

F(t) =Fg+sign

dsdt

Fd: tangential component of forces actingon the moving submerged body

m= (+cww)V: the total mass

Fg(t) = ( w)WgR(x, t) sin

(x)

dx: gravity and

buoyancy force

D
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DISSIPATIVE FORCESFRICTION AND DISSIPATION HAVE TO BE ACCOUNTED FOR!

Water resistance to the motion:

Fr = 1

2cdwAW

dsdt

2

Friction force: Ff = cfN(x, t)

N(x, t) =gW

R

(x, t) cos(x)

dx+

( w)W

R

(x, t)(x)ds

dt

2dx.

(x) = h0(x)

1+ (h0(x))2 3

2

.

N(x, t): Normal (reaction) force

(x): signed curvature of the bottom

GO G Q A O
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GOVERNING EQUATIONJUST A 2ND ORDER OD E TO SOLVE!

(+cw)Sd2s

dt2 = ( 1)g

I1(t) cf(t)I2(t)

(t)

cfI3(t) +1

2cdA

dsdt

2 cvS

ds

dt cb

ds

dt

ds

dt

,

I1(t) =

R

(x, t) sin(x)

dx,

I2(t) = R

(x, t) cos(x) dx,

I3(t) =

R

(x, t)(x) dx.

WE CAN SOLVE IT EASILY NUMERICALLY!

See one Matlab example.

3D LANDSLIDE EXAMPLE
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3D LANDSLIDE EXAMPLECREDIT: ICT TSUNAMI GROUP ( H TTP://TSUNAMI.ESEMC.NSC.RU/)

3D LANDSLIDE EXAMPLE
http://tsunami.esemc.nsc.ru/http://tsunami.esemc.nsc.ru/http://tsunami.esemc.nsc.ru/http://tsunami.esemc.nsc.ru/http://tsunami.esemc.nsc.ru/http://tsunami.esemc.nsc.ru/http://tsunami.esemc.nsc.ru/http://tsunami.esemc.nsc.ru/http://tsunami.esemc.nsc.ru/http://tsunami.esemc.nsc.ru/http://tsunami.esemc.nsc.ru/http://find/


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3D LANDSLIDE EXAMPLECREDIT: ICT TSUNAMI GROUP ( H TTP://TSUNAMI.ESEMC.NSC.RU/)

CONCLUSIONS
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CONCLUSIONS

Initial problem is too complex

Lack of data (initial location. . . )

Many parameters even aftersimplification

Identify most importantparameters

Experimental campaign tomeasure their values

Go beyond quasi-deformableassumption Shape evolution equation?

THANK YOU FOR YOUR ATTENTION!
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THANK YOU FOR YOUR ATTENTION!

REFERENCES I
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REFERENCESI

S. A. Beisel, L. B. Chubarov, and G. S. Khakimzyanov.

Simulation of surface waves generated by an underwaterlandslide moving over an uneven slope.

Russian Journal of Numerical Analysis and Mathematical

Modelling, 26(1):1738, 2011.

S. Beisel, L. Chubarov, and Yu. Shokin.

Some features of the landslide mechanism of surface

waves generation in real basins.

In E. Krause et Al., editor,Notes on Numerical Fluid

Mechanics and Multidisciplinary Design, pages 137148.

Springer Verlag, Berlin, Heidelberg, 2011.F. Benkhaldoun, S. Sahmim, and M. Sead.

A two-dimensional finite volume morphodynamic model on

unstructured triangular grids.

Int. J. Num. Meth. Fluids, 63(11):12961327, 2010.

REFERENCES II
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REFERENCESII

L. B. Chubarov, G. S. Khakimzyanov, and N. Yu. Shokina.Numerical modelling of surface water waves arising due to

movement of underwater landslide on irregular bottom

slope.

InNotes on Numerical Fluid Mechanics and

Multidisciplinary Design: Computational Science and High

Performance Computing IV, pages 7591. Springer-Verlag,

Berlin, Heidelberg, vol. 115 edition, 2011.

D. Dutykh and H. Kalisch.

Boussinesq modeling of surface waves due to underwaterlandslides.

http://hal.archives-ouvertes.fr/hal-00654386/, 2011.

REFERENCES III
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REFERENCESIII

D. Dutykh, D. Mitsotakis, S. Beisel, and N. Yu. Shokina.

Dispersive waves generated by an underwater landslide.In M. E. Vazquez-Cendon, editor,Numerical Methods for

Hyperbolic Equations: Theory and Applications,

http://hal.archives-ouvertes.fr/hal-00637102/, 2012.

F. Enet and S. T. Grilli.Experimental study of tsunami generation by

three-dimensional rigid underwater landslides.

J. Waterw. Port C-ASCE, 133:442454, 2007.

E. D. Fernandez-Nieto, F. Bouchut, D. Bresch, M. J.

Castro-Diaz, and A. Mangeney.

A new Savage-Hutter type models for submarine

avalanches and generated tsunami.

J. Comput. Phys., 227(16):77207754, 2008.

REFERENCES IV
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REFERENCESIV

G. S. Khakimzyanov and N. Y. Shokina.

Numerical modelling of surface water waves arising due to

a movement of the underwater landslide on an irregular

bottom.

Computational technologies, 15(1):105119, 2010.

A. Mangeney-Castelnau, J.-P. Vilotte, M. O. Bristeau,B. Perthame, F. Bouchut, C. Simeoni, and S. Yerneni.

Numerical modeling of avalanches based on Saint-Venant

equations using a kinetic scheme.

J. Geophys. Res., 108:2527, 2003.

E. Renzi and P. Sammarco.

Landslide tsunamis propagating around a conical island.

J. Fluid Mech, 650:251285, March 2010.
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Some Critical Comments on the Landslides Modelling

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