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Modelling of fast landslide propagation
M.Pastor, M.M.Stickle, D.Manzanal, P.Mira , J.A.Fernández Merodo
A.Yagüe, S.Moussavi, M.Molinos, A.Furlanetto, A.Longo, P.Dutto
S.Cuomo, L.Cascini, I.Rendina
Li Tong Chun, Liu Xiaoqing, Chuan Lin
ETS de Ingenieros de Caminos
Madrid
[email protected]
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Contents
Introduction
Mathematical Modelling
Rheological Modelling
• 2 phase models
• u-pw models
• 1 phase model
• waves in reservoirs
Depth integrated models:
• 2 phase models
• 1 phase, cupled pwp
• 1 phase
• 2 layers waves in reservoirs
• Classical
• Viscoplastic based models (Perzyna)
• mu(I) based models
SPH techniques
• 2 sets of particles
• Boundary conditions
Examples and applications
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Problems to be solved
Which model?
Granular avalanches
Debris flows, lahars
Flowslides
Single phase
v-pw
vs-vw-pw
Mudflows
Single phase
Landslides and waves
vs-vw
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Contents
Introduction
Mathematical Modelling
Rheological Modelling
• 2 phase models
• u-pw models
• 1 phase model
• waves in reservoirs
Depth integrated models:
• 2 phase models
• 1 phase, cupled pwp
• 1 phase
• 2 layers waves in reservoirs
• Classical
• Viscoplastic based models (Perzyna)
• mu(I) based models
SPH techniques
• 2 sets of particles
• Boundary conditions
Examples and applications
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General Model: 6 Unknowns – 6 equations
s
porosity
, stresses
, velocities
rateof deformation
w
s w
s
n
p
v v
d
Equations
• Balance of mass (soil,water)
• Balance of momentum (soil,water)
• Constitutive or rheological (skeleton)
• Relations velocities – rate of deformations
Soil grains
Pore fluid (water)
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General Model: 6 Unknowns – 6 equations
Comments
• Velocities of solid and fluid phases
are different.
• Non darcinian interaction forces
• Porosity changes
• Pwp included
• Saturated flow
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General Model: material derivatives
Phases
, , 1w sn n n n n
1
s w
s wn n
.grads
T
s
dv
dt t
.gradw
T
w
dv
dt t
.gradw s
T
w s
d dv v
dt dt
Material derivatives following s and w
w sw n v v Averaged velocity
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Depth Integrated Models I. Single phase
Unknowns: , , ,v x y z t
Problems:
• Interfaces (or free surface)
1x
3xh
Unknowns:
1 1 3hv v dx
h
Advantages:
• No interfaces
• Less unknowns (1 dim less)
Z
div , 0v x t
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Depth Integrated Models: Two phases, pwp
Unknowns: 1s
w
w sv
h n h
h nh
v n h
( )
( )
1 1 div 1
div
s
s R
w
w R
dn h n h n e
dt
dn h n h n e
dt
v
v
( )
( )
1 div ' 1 grad
1 1 1
grad
sss
s w b
s s s s R
www
w w b w w w w R
dh n h n h p
dt
n h n h n e
dh n n h p nh n h n e
dt
v
R b v
vR b v
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Depth Integrated Models: Pore pressure evolution
1D consolidation along depth2
33 0 2
3
1w wm v w m
dp x pdhb E d k E
dt dt h x
Edometric modulusmE
0 extra dilatancyvd
permeabilitywk
Use a FD explicit scheme
Depth changes:
Mesh changes too
Total stress and Pwp change
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Coupled model for saturated geomaterials (v-pw)
Balance of momentum
( ) ( )w sd d d
dt dt dt
11
s w
n n
Q K K
div ' grad w
dvp b
dt
1
+div div grad 0ws w w
dpv k p
Q dt
Unknowns : ,
s
w
v
p
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Depth Integrated Models: v-pw
div R
dhh v e
dt
23 3
1grad grad
2b R
dvh h b hb Z e v
dt
1D consolidation along depth2
33 0 2
3
1w wm v w m
dp x pdhb E d k E
dt dt h x
Edometric modulusmE
0 extra dilatancyvd
permeabilitywk
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Problems to be solved
Which model?
Submarine landslides
Waves generated by fast landslides
Approach: 2 Single phases (landslide and water)
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( )
0s
s is
i
dh vh
dt x
( )
0w
w iw
i
dh vh
dt x
Balance of mass
Balance of momentum
( )
2 /
3 3
1 1
2
ww s
w w w s i
w
d vh grad b h b h grad Z h
dt
( )2 /
3 3
1 1 1
2
sw s w
s s s i B s w
s w s
d vh grad b h b h grad Z gh grad h
dt
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Problems to be solved
Which model?
Granular avalanches
Debris flows, lahars
Flowslides
Single phase
v-pw
vs-vw-pw
Mudflows
Single phase
Landslides and waves
vs-vw
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Contents
Introduction
Mathematical Modelling
Rheological Modelling
• 2 phase models
• u-pw models
• 1 phase model
• waves in reservoirs
Depth integrated models:
• 2 phase models
• 1 phase, cupled pwp
• 1 phase
• 2 layers waves in reservoirs
• Classical
• Viscoplastic based models (Perzyna)
• mu(I) based models
SPH techniques
• 2 sets of particles
• Boundary conditions
Examples and applications
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Which models are we using?
Newtonian (viscous)
Bingham (cohesive-viscous)
3B
v
h
vp
v
z
B
z
x
h
2
1 26
B Y Y
B B
v h
???B
Frictional
( ) tanzz tanb z
Non-consistent
0B
v
h
Tchebichev approx.
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Which models are we using?
Frictional-viscous (consistent)
2
( ) tanz CF
vz
z
Law of similar structure than Voellmy’s
2
tanb z
vg
2
2
25tan
4b z CF
v
h
Frictional-viscous (Perzyna based)
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Infinite landslide: Perzyna, Von Mises Model
x
y
E 8.e7 Pa
Poiss 0.3
Dens 2000 Kg/m3
Yield 0.285 e5 Pa
gamma 0.1
delta 1.
Slope 1:4
Shear zone
Plug
Velocity Profile
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Infinite landslide: Perzyna
x
y
Velocity Profile
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Infinite landslide: Perzyna, Cam Clay Model
x
y
E 1.5 e7 Pa
Poiss 0.3
Dens 1500 Kg/m3
Mg 1.1
Lambda 0.51 k 0.09
Pc0 0.285 e5 Pa
gamma 0.1
delta 1.
Slope 1:4
Shear zone
Velocity Profile
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Infinite landslide: Perzyna Cam Clay
Note: Sigma x = Sigma y within shear zone!
Cam Clay Perzyna
0
20000
40000
60000
80000
100000
120000
140000
160000
0 5 10 15
Y
Str
ess Sxx
Syy
Tauxy
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Runout depends on volume of granular avalanches
argeLV
SmallV
tan Small argetan L
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Rheology (Pouliquen, da Cruz, Hatano, Gray…) I
/ P
ud
zIP
Inertia number
grain diameter
pressure
density P
P
d
I
2
01 /
ss
I I
n
s aI
ˆ/ P
ud
FrzIP d
ˆ /
/r
d d h
F u gh
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Crushing (Douadji and Hicher, Casini and Springman…)
0d dB
1/
0 0.5 1/ 0.4d dB
b
udt
h
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Contents
Introduction
Mathematical Modelling
Rheological Modelling
• 2 phase models
• u-pw models
• 1 phase model
• waves in reservoirs
Depth integrated models:
• 2 phase models
• 1 phase, cupled pwp
• 1 phase
• 2 layers waves in reservoirs
• Classical
• Viscoplastic based models (Perzyna)
• mu(I) based models
SPH techniques
• 2 sets of particles
• Boundary conditions
Examples and applications
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I
J
k h
' ' , 'x x W x x h dx
SPH discretization of Integral Approximations (Functions)
Introduce Nodes
(Particles)
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I
J
k h
' ' , 'x x W x x h dx
1
,N
I I J J I JhJ
x x W x x h
Summation extended
to nodes within kh
1
,Nh
I J J I J
J
x W x x h
Numerical Integration
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SPH interactions. 1 phase (mudflows, avalanches)
I
J
k h
soil
Interactions:
soil –soil I-J
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I
J
k h
2 sets of nodes: w and s
WaterSolid
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SPH interactions. 2 phases (DFs without pwp)
I
J
k h
soil
water
Interactions:
soil –soil I-J
soil-water I-K
KK
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SPH interactions. 2 phases (DFs with pwp)
I
J
k h
soil
water
FD mesh
(pwp)
Interactions:
soil –soil I-J
soil-water I-K
K
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SPH interactions. 1 phase with pwp (flowslides)
I
J
k h
soil
FD mesh
(pwp)
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SPH interactions. 2 phases (avalanche in a water body)
I
J
k h
soil
water
Interactions:
soil - soil I-J
soil - water I-K
K
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SPH: Absorbing boundary conditions
2 SLh
Boundary
Method: Impose along the outer normal n Riemann invariant = 0
n(1) (1)
02R c v R
c gh
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SPH: Absorbing boundary conditions
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SPH: Vn=0 boundary conditions
: 0nn v
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SPH: Vn=0 boundary conditions
Boundary nodes
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SPH: Inflow conditions (hydrograms, flow trough weirs,…etc)
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SPH: Inflow conditions (hydrograms, flow trough weirs,…etc)
“Pool”Domain
(Vacondio et al 2011, C.Lin et al 2018)
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Contents
Introduction
Mathematical Modelling
Rheological Modelling
• 2 phase models
• u-pw models
• 1 phase model
• waves in reservoirs
Depth integrated models:
• 2 phase models
• 1 phase, cupled pwp
• 1 phase
• 2 layers waves in reservoirs
• Rheology vs plasticity
•Infinite landslide based models
• Viscoplastic (Perzyna) models
SPH techniques
• 2 sets of particles
• Boundary conditions
Examples and applications
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Frank avalanche: Overall view
Rock avalanche involving 36 million m3
- Dimensions:
- Length: 2 Km
- Width: 1.7 Km
- Mean Thickness of deposit: 18 m
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Overall view of the landslide
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Model Predictions
Input parameters :
- tan Φ = 0.22
2
2
25' tan
4b CF
vp
h 3 2tan 0.218 0.1510 .CF Pa s
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Avalanche path
t= 0 s t= 14 s
t= 31 s t= 71 s
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Movie 01 of the avalanche
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Model predictions versus real event
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Rheology (Pouliquen, da Cruz, Hatano, Gray…) I
/ P
ud
zIP
Inertia number
grain diameter
pressure
density P
P
d
I
2
01 /
ss
I I
n
s aI
ˆ/ P
ud
FrzIP d
ˆ /
/r
d d h
F u gh
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Crushing (Douadji and Hicher, Casini and Springman…)
0d dB
1/
0 0.5 1/ 0.4d dB
b
udt
h
0d dB
1/
0 0.5 1/ 0.4d dB
b
udt
h
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Dependence of the final deposition angle β
on volume of the landslide: Hatano rheol.
Law
Dependence of the final deposition
angle βdep on volume of the
landslide: Gray rheol. Law
n
s aI
2
01 /
ss
I I
ˆ
FrI
d
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Runout obtained with a pure frictional law
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Runout obtained with Hatano law
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Runout obtained with Gray law
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Comparison of the final deposition profile of
the three calibrated cases
Gray
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Height profile at different
time step (Hatano with
crushing)
Diameter variation along
profile (Hatano with
crushing)
0d dB
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0d dB
1/
0 0.5 1/ 0.4d dB
b
udt
h
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Tip of a loose colliery
waste
200 m above of Aberfan
slope 25º100000 m3
(144 dead)
Benchmarks: Flowslide at Aberfan (21 Oct 1966)
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Flow slides
(Aberfan, 1966)
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t = 0 s
t = 6 s
t = 10 s
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t = 15 s
t = 20 s
t = 30 s
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10.t s
15t s
20t s
27t s
Profiles (amplification factor 4)
with rackoriginal
10.t s
15t s
20t s
27t s
34t s
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17t s
0wpP
0wpP
Detail of pore water distribution
in the proximity of the rack at t = 17 s
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Detail of pore water distribution
in the proximity of the rack at t = 20 s
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Sham Tseng San Tsuen
debris flow,
Hong Kong 1999
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h (m) t = 5 s h (m) t = 10 s
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h (m) t = 60 s h (m) t =120 s
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h water (m) t = 5 s h water (m) t = 10 s
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h water (m) t = 60 s h water (m) t = 120 s
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porosity t = 5 s porosity t = 10 s
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porosity t = 60 s porosity t = 120 s
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In collaboration with
Prof. Rainer Poisel
Waves generated by landslides
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Aknes: Terrain Model
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Methodology
Run PFC3D up to the instant of entering the water
Transform the 3D output of DEM into
depth integrated magnitudes (height and velocities)
Run the SPH solid avalanche – water code
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Run PFC3D up to the instant of entering the water
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Aknes Sc01 Tsunami formation and propagation
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Aknes Sc01 Tsunami formation and propagation
t = 0 s t = 6 s t = 16 s
t = 20 s t = 30 s t = 42 s
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Aknes Sc01 Tsunami formation and propagation
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Aknes Sc01 : Situation of control points
C2
C1
C0
C-1
C-2
R1L1
L-1 R-1
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Aknes scenario 1: water elevation
at centerline control points
C2
C1
C0
C-1
C-2
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Thanks for your attention