Some Critical Comments on the Landslides Modelling
Transcript of 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]
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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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EXPERIMENTS ON SUBAERIAL LANDSLIDESCREDIT: PHD OF VALENTIN HELLER, VAW ETH ZURICH (2007)
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EXPERIMENTS ON SUBAERIAL LANDSLIDESCREDIT: PHD OF VALENTIN HELLER, VAW ETH ZURICH (2007)
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EXPERIMENTS ON SUBAERIAL LANDSLIDESCREDIT: PHD OF VALENTIN HELLER, VAW ETH ZURICH (2007)
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EXPERIMENTS ON SUBAERIAL LANDSLIDESCREDIT: PHD OF VALENTIN HELLER, VAW ETH ZURICH (2007)
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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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