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
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
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
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
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)
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
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
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
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
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
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
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
Problems to be solved
Which model?
Submarine landslides
Waves generated by fast landslides
Approach: 2 Single phases (landslide and water)
( )
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
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
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
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.
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)
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
Infinite landslide: Perzyna
x
y
Velocity Profile
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
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
Runout depends on volume of granular avalanches
argeLV
SmallV
tan Small argetan L
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
Crushing (Douadji and Hicher, Casini and Springman…)
0d dB
1/
0 0.5 1/ 0.4d dB
b
udt
h
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
I
J
k h
' ' , 'x x W x x h dx
SPH discretization of Integral Approximations (Functions)
Introduce Nodes
(Particles)
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
SPH interactions. 1 phase (mudflows, avalanches)
I
J
k h
soil
Interactions:
soil –soil I-J
I
J
k h
2 sets of nodes: w and s
WaterSolid
SPH interactions. 2 phases (DFs without pwp)
I
J
k h
soil
water
Interactions:
soil –soil I-J
soil-water I-K
KK
WaterSolid
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
SPH interactions. 1 phase with pwp (flowslides)
I
J
k h
soil
FD mesh
(pwp)
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
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
SPH: Absorbing boundary conditions
SPH: Vn=0 boundary conditions
: 0nn v
SPH: Vn=0 boundary conditions
Boundary nodes
SPH: Inflow conditions (hydrograms, flow trough weirs,…etc)
SPH: Inflow conditions (hydrograms, flow trough weirs,…etc)
“Pool”Domain
(Vacondio et al 2011, C.Lin et al 2018)
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
Frank avalanche: Overall view
Rock avalanche involving 36 million m3
- Dimensions:
- Length: 2 Km
- Width: 1.7 Km
- Mean Thickness of deposit: 18 m
Overall view of the landslide
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
Avalanche path
t= 0 s t= 14 s
t= 31 s t= 71 s
Movie 01 of the avalanche
Model predictions versus real event
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
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
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
Runout obtained with a pure frictional law
Runout obtained with Hatano law
Runout obtained with Gray law
Comparison of the final deposition profile of
the three calibrated cases
Gray
Height profile at different
time step (Hatano with
crushing)
Diameter variation along
profile (Hatano with
crushing)
0d dB
0d dB
1/
0 0.5 1/ 0.4d dB
b
udt
h
Tip of a loose colliery
waste
200 m above of Aberfan
slope 25º100000 m3
(144 dead)
Benchmarks: Flowslide at Aberfan (21 Oct 1966)
Flow slides
(Aberfan, 1966)
t = 0 s
t = 6 s
t = 10 s
t = 15 s
t = 20 s
t = 30 s
0wpP
Rake
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
17t s
0wpP
0wpP
Detail of pore water distribution
in the proximity of the rack at t = 17 s
Detail of pore water distribution
in the proximity of the rack at t = 20 s
Sham Tseng San Tsuen
debris flow,
Hong Kong 1999
h (m) t = 5 s h (m) t = 10 s
h (m) t = 60 s h (m) t =120 s
h water (m) t = 5 s h water (m) t = 10 s
h water (m) t = 60 s h water (m) t = 120 s
porosity t = 5 s porosity t = 10 s
porosity t = 60 s porosity t = 120 s
In collaboration with
Prof. Rainer Poisel
Waves generated by landslides
Aknes: Terrain Model
Aknes Sc01: data
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
Run PFC3D up to the instant of entering the water
Aknes Sc01 Tsunami formation and propagation
Aknes Sc01 Tsunami formation and propagation
t = 0 s t = 6 s t = 16 s
t = 20 s t = 30 s t = 42 s
Aknes Sc01 Tsunami formation and propagation
Aknes Sc01 : Situation of control points
C2
C1
C0
C-1
C-2
R1L1
L-1 R-1
Aknes scenario 1: water elevation
at centerline control points
C2
C1
C0
C-1
C-2
Thanks for your attention