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Eduardo E.
ETS de Ingenieros de Caminos, Canales y PuertosUPC, Barcelona
Madrid, 21 de Noviembre de
DINÁMICA DE GRANDES DESLIZAMIENTOS
57th Rankine
(TRIGGERING AND MOTION OF
111
Eduardo E. Alonso
ETS de Ingenieros de Caminos, Canales y PuertosUPC, Barcelona
Madrid, 21 de Noviembre de 2017
DINÁMICA DE GRANDES DESLIZAMIENTOS
Rankine Lecture
AND MOTION OF LANDSLIDES)
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4th Rankine
A. W. Skempton
39th Rankine
S. Leroueil
“Long-term
Residual Factor:
“Natural slopes and cuts
Creep, fatigue, weathering
post-failure…
Rankine Lecture, 1964
Rankine Lecture, 1999
term stability of clay slopes”
Residual Factor: p mob
p r
R−
=−
τ τ
τ τ
cuts: movement and failure mechanism
weathering, infiltration, progressive failure
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PampaneiraPampaneira, Granada
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Pampaneira
penstock
Pampaneira
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Pampaneira
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Expected evolution of slope displacements
Will the “creeping” motion evolve towards failure
How long will the penstock survive?
How to protect it?
Pampaneira
evolution of slope displacements?
Will the “creeping” motion evolve towards failure?
How long will the penstock survive?
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Cortes Landslide, Valencia
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Cortes
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Cortes
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Aznalcóllar
failure
(Sevilla)
April 25th, 1998
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AznalcóllarCentral zone of
Why 40 - 50 m of run
OC brittle
Central zone of failure
50 m of run-out?
(Moya, 2000)
brittle clay
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“Since the analytical and numerical methods available at
present do not usually provide reliable predictions of the
deformation of a natural slope,
limit states should be avoided by one of the following:
— limiting the mobilised shear strength
— observing the movements and
or stop them, if necessary”
Section 11 Overall stability
11.6 Serviceability limit state design
Eurocode 7. November 2004, 2017
the analytical and numerical methods available at
present do not usually provide reliable predictions of the
deformation of a natural slope, the occurrence of serviceability
limit states should be avoided by one of the following:
shear strength;
observing the movements and specifying actions to reduce
11.6 Serviceability limit state design
2004, 2017
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Questions :
IN CASE OF INSTABILITY
- How big?
- How far?
- How fast?
IN CASE OF INSTABILITY
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Contents
1. Creeping landslides
2. Fast landslides
3. Transition from creeping to fast motion
4. Continuum analysis. MPM
5. First time slides
6. THM analysis of landslides
Contents
Transition from creeping to fast motion
Continuum analysis. MPM
THM analysis of landslides
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1. Creeping landslides1. Creeping landslides
St Moritz inclined tower. Courtesy of A. Puz
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1 1,σ ε′
3 3,σ ε′
Laboratory
creeping tests
Toyoura sand(Murayama et al, 1984)
Creeping landslides sandMurayama et al, 1984)
San Francisco bay mud(Lacerda, 1976)
(Kuhn & Mitchell, 1993)
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Assembly of 1002
circular disksKuhn & Mitchell, 1993)
Assembly of 3421
spheres(Kwok & Bolton, 2010)
Creeping landslides
Velocity dependent
contact friction
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• Local contacts deform following a rate process (Arrhenius)
• Velocity of shear deformation of contacts:
E : energy bar
at a shearing rate velocity
decreases the velocity increases
Rate effects on frictionCreeping landslides
c cA A=σ σ
c cA A=τ τc
c
=τ
τ σσ
Local contacts deform following a rate process (Arrhenius)
Velocity of shear deformation of contacts: 1exp( / )v v E RT= −
barrier required to set the contact bonds
at a shearing rate velocity . If the energy barrier
decreases the velocity increases
c iA a=∑
Rate effects on friction
v
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Stress is understood as the energy per unit of volume and the
product: τc × “Active volume of contact bonds (
the energy associated with τc
1 cE E= − ΩτAccept:
Combining equations:
Empirical equation based on friction tests on rock contacts:
f f Aτ
= = + ψ +σ
Basic friction“State”
(healing,
Creeping landslides
= +
Ω Ω τ σ
Stress is understood as the energy per unit of volume and the
“Active volume of contact bonds (Ω)” is a measure of
Empirical equation based on friction tests on rock contacts:
*
*
lnv
f f Av
= = + ψ + (Dieterich,1979;
Ruina,1983)
“State”
(healing, ..)Rate effects
(Rice et al, 2001)1
1
lnc c
E RT v
v
= +
Ω Ω σ σ
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Dynamic equilibrium of a
creeping planar landslide
2
dsin
d
cos cos 0
tan
w w
vW T M
t
W N h
T N
β − =
′β − − γ β =
′= φ
0tan tanφ = φ +
Creeping landslides
1 dtan 1 tan
d
w wh v
D g t
γ β − − φ = γ
ln for
0 for
v ref
ref
v ref
vf A v v
v
f v v
= >
= ≤0 vfφ = φ +
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A landslide creeping
scenario
Creeping
landslides
A=0
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Model response
Rate effects
Creeping landslides
1mm/s
response
No rate effects
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0
6.5º
15.5 m
7.8º
D
β =
=
φ =
Vallcebre
Recorded variation of
ground water level
hw: Variable
Creeping landslides
100m
Vallcebre Landslide, Pyrenees
(Corominas et al, 2011)
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Creeping landslides Vallcebre
(Scoppettuolo, 2016), 2016)
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Rate effects on friction provide a basic explanation
of creeping behaviour at different scales
What happens if the shearing rate increases, say
above 1mm/s?
Creeping landslides
Rate effects on friction provide a basic explanation
at different scales
What happens if the shearing rate increases, say
Creeping landslides
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2. Fast landslides
Vajont landslide
(Valdés y Díaz
Caneja, 1964)
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Collected cases
of landslide
evolution
Fast landslides
100 m
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Rotary shear tests. v = 0.1 Fast landslides
(Di Toro et al, 2011) Nature
= 0.1 – 2.6 m/s. 300 tests reviewed
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1400 watts thermal pulse applied during 40 secondsSaturated specimens before heating
A laboratory heating experiment in a microwave oven
Opalinus clay: soft clayey rock
(K =10-12 to 10-13 m/s; n= 4%-12%)
Fast landslides
1400 watts thermal pulse applied during 40 secondsSaturated specimens before heating
heating experiment in a microwave oven
A porous stone
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After heating
Fast landslides
A laboratory heating experiment in a microwave oven
Opalinus clay: soft clayey rock
(K =10-12 to 10-13 m/s; n= 4%-12%)
After heating (Tests performed by J. Pineda
heating experiment in a microwave oven
A porous stone
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Recorded
temperature
during
experiments
Fast landslides
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Thermal volumetric strains
Pore pressure generation
Fast landslides Thermal volumetric strains
generation:
ww
vol ww
ss
vol ss
dVd d
V
dVd d
V
ε = − = −β θ
ε = − = −β θ
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Habib (1967)PioneeringRomero & Molina (1974)
Voigt & Faust (1982) Deformation concentrates
band. Mass, energy and
formulated. One dimensional
and pore water pressure
Vardoulakis (2000, 2002)
Veveakis et al (2007)
Vardoulakis & Veveakis (2010)
Goren & Aharonov (2007)
Goren & Aharonov (2009)
Pinyol & Alonso (2010a)
Pinyol & Alonso (2010b)
Goren et al (2010)
Cecinato et al (2011)
Cecinato & Zervos (2012)
al (2015)
Pioneering contributions Planar
Vertical slices
concentrates in a saturated shear
and momentum balances
dimensional model for heat
pressure dissipation
Planar
Slip circle
Planar
Planar
Planar
Planar
Two interacting wed
Evolving geometr
Planar
Planar and slip circ
Planar
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Fast landslides
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Equations to be solved
Upper block (shear band)
Lower block (shear band)
o Solid +
INSIDE
o Solid
Overall equilibrium o Dynamic
interacting
Fast landslides
o Solid +
INSIDE
o Solid
Solid + water balance + heat generation
INSIDE shear band
Solid + water balance OUTSIDE shear band
Dynamic equilibrium of two
interacting wedges
(1
(2
(3
(4
(5
Solid + water balance + heat generation
INSIDE shear band
Solid + water balance OUTSIDE shear band
UpperUpper
Lower
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Scaled Vajont (x1/10). Effect of shear band Fast
landslides
2e = 2.5 mm
Run out: 50 m
Effect of shear band permeability
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Fast landslides
Shear band thickness: 0 mm to 10 mm
Maximum
velocity. Effect
of permeability
Two
wedges
Shear band thickness: 0 mm to 10 mm
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Unsafe
Fast landslides
Shear band thickness: 0 mm to 10 mm
Maximum
velocity. Effect
of permeability Planar
Two
wedges
Unsafe
Safe
Shear band thickness: 0 mm to 10 mm
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Fast landslides
2e = 50cm
Maximum
velocity. Effect
of permeability
Shear band thickness: 0 mm to 10 mm
UnsafePlanar
Two
wedges
Shear band thickness: 0 mm to 10 mm
Unsafe
Safe
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Thermal pressurization of water explains high
velocity
Controlling variables:
Landslide geometry (planar; interacting wedges..)
Shear band permeability
Shear band thickness (but limited effect for 2e
from 0 to 10 mm)
Fast landslides in clayey materials
Thermal pressurization of water explains high
Landslide geometry (planar; interacting wedges..)
Shear band permeability
Shear band thickness (but limited effect for 2e
Fast landslides in clayey materials
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3. Transition
from creeping
to fast motion
Canillo giganticgigantic creeping landslide. Andorra
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External
“loading”
Landslide velocity increases
Friction increases (rate effects)
Heat generated in shear band
Pore water pressure increases
and dissipates
Changes in landslide geometry
Equilibrium?YES
New creeping velocity
Creep - Fast
Time
Landslide velocity increases
Friction increases (rate effects)
Heat generated in shear band
Pore water pressure increases
and dissipates
in landslide geometry
Equilibrium?NO
Thermal feedback mechanism
∆u: ++ “Blow-up”
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Balance equations (water+energy
Inside shear band
Outside shear band
Dynamic equilibrium
Basic THM formulation
Creep - Fast
β
v
D
z
2e
0tan tan
ln for
0 for
v
v ref
ref
v ref
f
vf A v v
v
f v v
φ = φ +
= >
= ≤
water+energy)
Friction law
+
hw
![Page 44: DINÁMICA DE GRANDES DESLIZAMIENTOS · Ruina,1983)..) Rate effects 1 (Rice et al, 2001) 1 ln c c E RT v σ σ v. Dynamic equilibrium of a creeping planar landslide 2 d sin d cos cos](https://reader034.vdocuments.us/reader034/viewer/2022050606/5fad2d651c8068248439a4dd/html5/thumbnails/44.jpg)
Dimensionless formulation
ˆz
zD
=
ˆt gD
tD
=
( )( )
0
,ˆ ˆˆ,
z tz t
θθ =
θ
( )(
ˆˆ ˆ,w
w
u z tu z t
gD=
ρ
( )( )
ˆˆv t
v tgD
=
Coordinate
Time
Temperature
Excess pwp
Sliding velocity
Creep - Fast Dimensionless formulation
),u z t
gD
β
v
D
h
z
2e
![Page 45: DINÁMICA DE GRANDES DESLIZAMIENTOS · Ruina,1983)..) Rate effects 1 (Rice et al, 2001) 1 ln c c E RT v σ σ v. Dynamic equilibrium of a creeping planar landslide 2 d sin d cos cos](https://reader034.vdocuments.us/reader034/viewer/2022050606/5fad2d651c8068248439a4dd/html5/thumbnails/45.jpg)
Dimensionless coefficients
( )m
c D gD
ΓΘ =
ρ
( )
2
0
( )
2m
D gD
c e
ρ=
ρ θ
0soil
soilm gD
β θ=
ρ
w soil
K
m D gD=
γ
Thermal dissipation: combines thermal conduction, heat
storage, a reference dimension and a reference
Ratio between the kinetic energy of the moving mass
and the initial heat stored in the shear band (30
Ratio of the thermal e
with respect to its mechanical compressibility (0.1
“Consolidation coefficient”: confined compressibility and the sliding depth
Creep - Fast Dimensionless coefficients
Thermal dissipation: combines thermal conduction, heat
storage, a reference dimension and a reference velocity (fixed
Ratio between the kinetic energy of the moving mass
and the initial heat stored in the shear band (30 - 1800)
al expansion of the saturated porous mediu
with respect to its mechanical compressibility (0.1 - 10)
“Consolidation coefficient”: combines permeability,
confined compressibility and the sliding depth (10-12 – 10-1)
(Alonso, Zervos & Pinyol, 2015)
![Page 46: DINÁMICA DE GRANDES DESLIZAMIENTOS · Ruina,1983)..) Rate effects 1 (Rice et al, 2001) 1 ln c c E RT v σ σ v. Dynamic equilibrium of a creeping planar landslide 2 d sin d cos cos](https://reader034.vdocuments.us/reader034/viewer/2022050606/5fad2d651c8068248439a4dd/html5/thumbnails/46.jpg)
=25m
0 =11.05m
= 9.8°
= 12°
2e = 2.5mm
mv = 1.5·10-9 Pa-1
K = 10-9 m/s
θ0 = 10 °C
A = 0.014
vref = 10-5 m/s
Rate effects
on friction
Creep - FastAn illustrative example
2e
Rate effects
on friction
An illustrative example
![Page 47: DINÁMICA DE GRANDES DESLIZAMIENTOS · Ruina,1983)..) Rate effects 1 (Rice et al, 2001) 1 ln c c E RT v σ σ v. Dynamic equilibrium of a creeping planar landslide 2 d sin d cos cos](https://reader034.vdocuments.us/reader034/viewer/2022050606/5fad2d651c8068248439a4dd/html5/thumbnails/47.jpg)
Velocity
Creep - FastSlope
Friction angle
response
![Page 48: DINÁMICA DE GRANDES DESLIZAMIENTOS · Ruina,1983)..) Rate effects 1 (Rice et al, 2001) 1 ln c c E RT v σ σ v. Dynamic equilibrium of a creeping planar landslide 2 d sin d cos cos](https://reader034.vdocuments.us/reader034/viewer/2022050606/5fad2d651c8068248439a4dd/html5/thumbnails/48.jpg)
Slope
Temperature
Creep - Fastresponse
Excess pore pressure
![Page 49: DINÁMICA DE GRANDES DESLIZAMIENTOS · Ruina,1983)..) Rate effects 1 (Rice et al, 2001) 1 ln c c E RT v σ σ v. Dynamic equilibrium of a creeping planar landslide 2 d sin d cos cos](https://reader034.vdocuments.us/reader034/viewer/2022050606/5fad2d651c8068248439a4dd/html5/thumbnails/49.jpg)
The relevance
w soil
K
m D gD=
γ
Creep - Fast
345
1
Ψ =
Π =
of rate effects
![Page 50: DINÁMICA DE GRANDES DESLIZAMIENTOS · Ruina,1983)..) Rate effects 1 (Rice et al, 2001) 1 ln c c E RT v σ σ v. Dynamic equilibrium of a creeping planar landslide 2 d sin d cos cos](https://reader034.vdocuments.us/reader034/viewer/2022050606/5fad2d651c8068248439a4dd/html5/thumbnails/50.jpg)
Creep-THM Creep - Fast
Planar
slide
Time for blow
THM creep
THM interactions
blow-up and rate effects
creep velocity
![Page 51: DINÁMICA DE GRANDES DESLIZAMIENTOS · Ruina,1983)..) Rate effects 1 (Rice et al, 2001) 1 ln c c E RT v σ σ v. Dynamic equilibrium of a creeping planar landslide 2 d sin d cos cos](https://reader034.vdocuments.us/reader034/viewer/2022050606/5fad2d651c8068248439a4dd/html5/thumbnails/51.jpg)
Creep - Fast
Planar
slide
Creep-THM
Time for blow
THM creep
THM interactions
blow-up and rate effects
creep velocity
![Page 52: DINÁMICA DE GRANDES DESLIZAMIENTOS · Ruina,1983)..) Rate effects 1 (Rice et al, 2001) 1 ln c c E RT v σ σ v. Dynamic equilibrium of a creeping planar landslide 2 d sin d cos cos](https://reader034.vdocuments.us/reader034/viewer/2022050606/5fad2d651c8068248439a4dd/html5/thumbnails/52.jpg)
Creep - Fast
Planar
slide
Creep-THM
Time for blow
THM creep
THM interactions
blow-up and rate effects
creep velocity
![Page 53: DINÁMICA DE GRANDES DESLIZAMIENTOS · Ruina,1983)..) Rate effects 1 (Rice et al, 2001) 1 ln c c E RT v σ σ v. Dynamic equilibrium of a creeping planar landslide 2 d sin d cos cos](https://reader034.vdocuments.us/reader034/viewer/2022050606/5fad2d651c8068248439a4dd/html5/thumbnails/53.jpg)
Transition creeping
Highly non-linear interactions (and numerical difficulties)
Blow-up conditions are very sensitive to strain rate effects
Increasing strain rate effects on friction
permeability between slow-fast
Thermal effects enhance creeping velocity
If blow-up conditions develop, rate effects and landslide
geometry become irrelevant
Transition creeping – fast motion
linear interactions (and numerical difficulties)
conditions are very sensitive to strain rate effects
Increasing strain rate effects on friction reduces the threshold
fast regimes
Thermal effects enhance creeping velocity
up conditions develop, rate effects and landslide
![Page 54: DINÁMICA DE GRANDES DESLIZAMIENTOS · Ruina,1983)..) Rate effects 1 (Rice et al, 2001) 1 ln c c E RT v σ σ v. Dynamic equilibrium of a creeping planar landslide 2 d sin d cos cos](https://reader034.vdocuments.us/reader034/viewer/2022050606/5fad2d651c8068248439a4dd/html5/thumbnails/54.jpg)
4. Continuum
analysis
(MPM)Vajont. Del Ventisette et al. (2015)
![Page 55: DINÁMICA DE GRANDES DESLIZAMIENTOS · Ruina,1983)..) Rate effects 1 (Rice et al, 2001) 1 ln c c E RT v σ σ v. Dynamic equilibrium of a creeping planar landslide 2 d sin d cos cos](https://reader034.vdocuments.us/reader034/viewer/2022050606/5fad2d651c8068248439a4dd/html5/thumbnails/55.jpg)
Numerical Methods
Finite Element (FEM)
Finite Difference (FDM)
Arbitrary Lagrangian
Coupled Eulerian
Material Point Method (MPM)
Smooth Particle Hydrodynamics (SPH)
Particle Finite Element Method (PFEM)
FEM + Lagrangian integration points (FEMLIP)
Element-free
for Landslide analysis
Finite Element (FEM)
Finite Difference (FDM)
Lagrangian-Eulerian (ALE)
Coupled Eulerian-Lagrangian (CEL)
Point Method (MPM)
Smooth Particle Hydrodynamics (SPH)
Particle Finite Element Method (PFEM)
integration points (FEMLIP)
free Galerkin (EFG)
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It is a continuum method. Constitutive
Incorporates FE methodologies
Statics + Dynamics + large deformations
Background mesh facilitates application of boundary
conditions
“Multiple layer” formulation
to be solved (solid-water interactions;
external erosion; flow through preferential
MPM in landslide analysisMPM
Constitutive equations
FE methodologies
deformations
Background mesh facilitates application of boundary
tions open the class of problems
water interactions; internal and
through preferential paths)
MPM in landslide analysis
Soga et al. (201
![Page 57: DINÁMICA DE GRANDES DESLIZAMIENTOS · Ruina,1983)..) Rate effects 1 (Rice et al, 2001) 1 ln c c E RT v σ σ v. Dynamic equilibrium of a creeping planar landslide 2 d sin d cos cos](https://reader034.vdocuments.us/reader034/viewer/2022050606/5fad2d651c8068248439a4dd/html5/thumbnails/57.jpg)
Three-Phase MPM
Phase MPM
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Sulsky et al.
(1994)
Zabala & Alonso
Jassim et al. (2013)
Bandara
Abe et al. (2014)
One phaseDry
Two phasesSaturated
Single
layer
Multiple
layer
MPM
& Alonso (2011)
et al. (2013)
Bandara (2013)
Abe et al. (2014)
Yerro et al. (2015)
?
phasesSaturated
Three phasesUnsaturated
Soli
Liqu
Air
![Page 59: DINÁMICA DE GRANDES DESLIZAMIENTOS · Ruina,1983)..) Rate effects 1 (Rice et al, 2001) 1 ln c c E RT v σ σ v. Dynamic equilibrium of a creeping planar landslide 2 d sin d cos cos](https://reader034.vdocuments.us/reader034/viewer/2022050606/5fad2d651c8068248439a4dd/html5/thumbnails/59.jpg)
1) Dynamic equilibrium Liquid
2) Dynamic equilibrium Gas
3) Dynamic equilibrium Mixture
4) Mass balance Solid
5) Mass balance Water
6) Mass balance Air
7) Constitutive equations
Governing equations
l l l l s lρ ρv v v b&
g g g g s gρ ρ= ∇ − − +v v v b&
(1s s l l l g g g mρ ρ ρ ρ− + + = ∇ ⋅ +
( w w w w
g g g l l l g lS n S nt
ω ρ ω ρ∂
+ + ∇⋅ + =∂
( a a a a
g g g l l l g lS n S nt
ω ρ ω ρ∂
+ + ∇⋅ + =∂
( )(1 ) (1 ) 0s s sn nt
ρ ρ∂
− + ∇ ⋅ − =∂
MPM Governing equations
( )l ll l l l s l
l
nSp
k
µρ ρ= ∇ − − +v v v b&
( )g g
g g g g s g
g
nSp
k
µρ ρ= ∇ − − +v v v b
)1s s l l l g g g mn nS nSρ ρ ρ ρ− + + = ∇ ⋅ +v v v σ b& & &
) ( ) 0w w w w
g g g l l l g lS n S nω ρ ω ρ+ + ∇⋅ + =j j
) ( ) 0a a a a
g g g l l l g lS n S nω ρ ω ρ+ + ∇⋅ + =j j
( )(1 ) (1 ) 0s s sn nρ ρ− + ∇ ⋅ − =v
( ), ,s l gv v v formulation
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5. First time
slides
Sabadell slide
![Page 61: DINÁMICA DE GRANDES DESLIZAMIENTOS · Ruina,1983)..) Rate effects 1 (Rice et al, 2001) 1 ln c c E RT v σ σ v. Dynamic equilibrium of a creeping planar landslide 2 d sin d cos cos](https://reader034.vdocuments.us/reader034/viewer/2022050606/5fad2d651c8068248439a4dd/html5/thumbnails/61.jpg)
First time AznalcóllarAznalcóllar dam failure
![Page 62: DINÁMICA DE GRANDES DESLIZAMIENTOS · Ruina,1983)..) Rate effects 1 (Rice et al, 2001) 1 ln c c E RT v σ σ v. Dynamic equilibrium of a creeping planar landslide 2 d sin d cos cos](https://reader034.vdocuments.us/reader034/viewer/2022050606/5fad2d651c8068248439a4dd/html5/thumbnails/62.jpg)
First time.
AznalcóllarModel domain and and construction stages
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Brittle clay. Strain Softening Mohr
( )' ' ' 'peq
r p rc c c c e−ηε
= + −
( )' ' ' 'peq
r p r e−ηε
ϕ = ϕ + ϕ − ϕ
Softening
rules
Yield
function'cos ' 'sin 'q c p= ϕ + ϕ
' , 'r pc c
' , 'r pϕ ϕp
eqε
η
First time
residual and peak effective cohesion
residual and peak effective friction angle
deviatoric plastic strain
shape factor
Softening Mohr-Coulomb
peq−ηε
peq−ηε
cohesion
residual and peak effective friction angle
![Page 64: DINÁMICA DE GRANDES DESLIZAMIENTOS · Ruina,1983)..) Rate effects 1 (Rice et al, 2001) 1 ln c c E RT v σ σ v. Dynamic equilibrium of a creeping planar landslide 2 d sin d cos cos](https://reader034.vdocuments.us/reader034/viewer/2022050606/5fad2d651c8068248439a4dd/html5/thumbnails/64.jpg)
Modelling foundationFirst time.
Aznalcóllar
1m x 1m
cell
foundation clay
(Zabala & Alonso, 20
![Page 65: DINÁMICA DE GRANDES DESLIZAMIENTOS · Ruina,1983)..) Rate effects 1 (Rice et al, 2001) 1 ln c c E RT v σ σ v. Dynamic equilibrium of a creeping planar landslide 2 d sin d cos cos](https://reader034.vdocuments.us/reader034/viewer/2022050606/5fad2d651c8068248439a4dd/html5/thumbnails/65.jpg)
First time. Aznalcóllar
Equivalent plastic deviatoric strainstrain contours (1% - 5%). K0=1
![Page 66: DINÁMICA DE GRANDES DESLIZAMIENTOS · Ruina,1983)..) Rate effects 1 (Rice et al, 2001) 1 ln c c E RT v σ σ v. Dynamic equilibrium of a creeping planar landslide 2 d sin d cos cos](https://reader034.vdocuments.us/reader034/viewer/2022050606/5fad2d651c8068248439a4dd/html5/thumbnails/66.jpg)
First time. Aznalcóllar
Equivalent plastic deviatoric strainstrain contours (1% - 5%). K0=1
![Page 67: DINÁMICA DE GRANDES DESLIZAMIENTOS · Ruina,1983)..) Rate effects 1 (Rice et al, 2001) 1 ln c c E RT v σ σ v. Dynamic equilibrium of a creeping planar landslide 2 d sin d cos cos](https://reader034.vdocuments.us/reader034/viewer/2022050606/5fad2d651c8068248439a4dd/html5/thumbnails/67.jpg)
First time. Aznalcóllar
Equivalent plastic deviatoric strainstrain contours (1% - 5%). K0=1
![Page 68: DINÁMICA DE GRANDES DESLIZAMIENTOS · Ruina,1983)..) Rate effects 1 (Rice et al, 2001) 1 ln c c E RT v σ σ v. Dynamic equilibrium of a creeping planar landslide 2 d sin d cos cos](https://reader034.vdocuments.us/reader034/viewer/2022050606/5fad2d651c8068248439a4dd/html5/thumbnails/68.jpg)
(Courtesy of J. M. Rodríguez Ortiz
First time.
Aznalcóllar
Courtesy of J. M. Rodríguez Ortiz)
![Page 69: DINÁMICA DE GRANDES DESLIZAMIENTOS · Ruina,1983)..) Rate effects 1 (Rice et al, 2001) 1 ln c c E RT v σ σ v. Dynamic equilibrium of a creeping planar landslide 2 d sin d cos cos](https://reader034.vdocuments.us/reader034/viewer/2022050606/5fad2d651c8068248439a4dd/html5/thumbnails/69.jpg)
Run-
Rigid body motion
The total displacement allows calibration of the model
Unknown aspects (velocity, acceleration) may be derived
First time. Aznalcóllar-out
calibration of the model
Unknown aspects (velocity, acceleration) may be derived
(Alonso & Gens, 2011)
![Page 70: DINÁMICA DE GRANDES DESLIZAMIENTOS · Ruina,1983)..) Rate effects 1 (Rice et al, 2001) 1 ln c c E RT v σ σ v. Dynamic equilibrium of a creeping planar landslide 2 d sin d cos cos](https://reader034.vdocuments.us/reader034/viewer/2022050606/5fad2d651c8068248439a4dd/html5/thumbnails/70.jpg)
MPM analysis 6 years later. Geometry and mesh
First time. Aznalcóllar
years later. Geometry and mesh
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First time. Aznalcóllar
Long alluvial terrace
Short alluvial terrace
![Page 72: DINÁMICA DE GRANDES DESLIZAMIENTOS · Ruina,1983)..) Rate effects 1 (Rice et al, 2001) 1 ln c c E RT v σ σ v. Dynamic equilibrium of a creeping planar landslide 2 d sin d cos cos](https://reader034.vdocuments.us/reader034/viewer/2022050606/5fad2d651c8068248439a4dd/html5/thumbnails/72.jpg)
First time. Aznalcóllar
0 0.5
Shear strain
Long alluvial terrace
Short alluvial terrace
Time: 3 s
![Page 73: DINÁMICA DE GRANDES DESLIZAMIENTOS · Ruina,1983)..) Rate effects 1 (Rice et al, 2001) 1 ln c c E RT v σ σ v. Dynamic equilibrium of a creeping planar landslide 2 d sin d cos cos](https://reader034.vdocuments.us/reader034/viewer/2022050606/5fad2d651c8068248439a4dd/html5/thumbnails/73.jpg)
First time. Aznalcóllar
Time: 10 s0 0.5
Shear strain
Long alluvial terrace
Short alluvial terrace
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0 0.
Shear strain
![Page 75: DINÁMICA DE GRANDES DESLIZAMIENTOS · Ruina,1983)..) Rate effects 1 (Rice et al, 2001) 1 ln c c E RT v σ σ v. Dynamic equilibrium of a creeping planar landslide 2 d sin d cos cos](https://reader034.vdocuments.us/reader034/viewer/2022050606/5fad2d651c8068248439a4dd/html5/thumbnails/75.jpg)
First time. Aznalcóllar
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First time. Aznalcóllar
Level of tailings
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Failure of
Selborne
experimental
slope
First time. Selborne
(Cooper, 1996; Cooper et al, 1998)
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0 m
-4.0
-9
-17.0
Soliflucted deposits
Upper weathered Gault Clay
Lower weathered Gault
Unweathered Gault Clay
Lower Greensand
First time. Selborne
Recharge zone
2:1 slopeClay
Clay
Clay
Recharge wells (20)
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Geotechnical parameters
based on published
laboratory testing(Cooper et al, 1998)
∆pl = 110 kPa
15 m
18 m 18 m
First time. Selborne
Parameter
Effective
cohesion
Effective
friction
18 m 20 m
6 m
Weathered Gault Clay
Unweathered Gault Clay
Parameter Weathered Unweathered
Effective
cohesion
13/4.7 kPa
(peak/residual)
25/1 kPa
Effective
friction24.5°/13.5° 26°/15°
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Instability process
First time. Selborne
Instability process
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Progressive failureFirst time. Selborne
Progressive failure
(Cooper, 1996)
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First time. Selborne
* / failuret t t=
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First time. Selborne
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First time. Selborne
0.845
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First time. Selborne
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First time. Selborne
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First time. Selborne
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First time. Selborne
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First time. Selborne
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Instability
process
First time. Selborne
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Instability
process
First time. Selborne
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Surface movementsFirst time. Selborne
Field data by
Grant (1996)
Surface movements
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Accelerated motion starts when last point in
shear band reaches peak
Kinematics are well captured by MPM modelling
Static and dynamic behaviour can be explained
by a single set of constitutive parameters
First time failures (Aznalcóllar
motion starts when last point in
shear band reaches peak strength
Kinematics are well captured by MPM modelling
and dynamic behaviour can be explained
by a single set of constitutive parameters
Aznalcóllar, Selborne)
(?)
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6. THM analysis
of landslides
Alcántara-Ayala, 2008
San Juan de Grijalva
Ayala, 2008
San Juan de Grijalva landslide, Mexico
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Add Energy Balance equation
[ ] [ ]( ) ( )m w w m S
Dc c c H
Dtρ θ + ⋅ −Γ θ + ⋅ ρ θ + ρ θ =∇ ∇ ∇∇ ∇ ∇∇ ∇ ∇∇ ∇ ∇
Stored heat Heat
conduction
(: :p pH p′= = −σ ε σ m ε& & &
THM
equation to HM formulation
[ ]( ) ( )m w w m S
c c c Hρ θ + ⋅ −Γ θ + ⋅ ρ θ + ρ θ =q v &∇ ∇ ∇∇ ∇ ∇∇ ∇ ∇∇ ∇ ∇
Convective heat transfer
Supplied energy
): :L
p pH p= = −σ ε σ m ε& &
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φ’ = 28°
c’ = 2 kPa
13 m
10 m
0.5 m
0.5 m
THM
kPa 1 kPa (failure)
13 m8 m
6 m
4 m
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13 m
10 m
0.25 m
0.25 m
THM
φ’ = 28°
c’ = 2 kPa
13 m8 m
6 m
4 m
kPa 1 kPa (failure)
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13 m
10 m
0.125 m
0.125 m
THM
φ’ = 28°
c’ = 2 kPa
13 m8 m
6 m
4 m
kPa 1 kPa (failure)
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0.5 m
0.5 m
0.25 m
0.25 m
0.125 m
0.125 m
K = 10-11 m/s
K = 10-11 m/s
K = 10-11 m/s
THM
0 0.5 1.0 1.5 2.0 2.5
0 0.5 1.0 1.5 2.0 2.5
0 0.5 1.0 1.5 2.0 2.5
∆Pore Pressure [kPa]
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0.5 m
0.5 m
0.25 m
0.25 m
0.125 m
0.125 m
K = 10-11 m/s
K = 10-11 m/s
K = 10-11 m/s
THM
0 0.5 1.0 1.5 2.0 2.5
0 0.5 1.0 1.5 2.0 2.5
0 0.5 1.0 1.5 2.0 2.5
Displacement [m]
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THM Embedded shear
Shear bands activate when
Strains localize in shear bands
Heat generates in shear bands
Dissipation processes (heat and
liquid pressure) between band
and matrix are formulated at loca
level
p
devε
shear bands
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THM Embedded shear
Reference
volumeLocal liquid flow rate:
( )B M B M
L L L Lf p p− = ψ −
Local heat flow rate:
( )B M B Mf −
θ θ= ψ θ − θ
shear bands
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Energy Balance
Mass Balance of Liquid
Effective stress
( ) ( )M M
m w w m S
Dc c c
Dt ρ θ + ⋅ −Γ θ + ⋅ ρ θ + ρ θ = ψ θ − θ ∇ ∇ ∇∇ ∇ ∇∇ ∇ ∇∇ ∇ ∇
(( )B B M B
m
Dc H
Dtθ
ρ θ = −ψ θ − θ +
MM B ML
m L S L L L L
D Dpn p p
Dt Dt β θ + α + ∇ ⋅ + ∇ ⋅ = ψ −
1B
B B MLm L L L L
L
D Dpn p p
Dt Dt β θ + α = − ψ − ρ
( )max ,B M
L Lp p= −′ mσ σ
L
THM Embedded shear
(( ) ( )M M M B M
m w w m Sc c c θ ρ θ + ⋅ −Γ θ + ⋅ ρ θ + ρ θ = ψ θ − θ q v∇ ∇ ∇∇ ∇ ∇∇ ∇ ∇∇ ∇ ∇
Local source
)B B M Bc Hρ θ = −ψ θ − θ + &
Supplied Energy
( )1M B M
m L S L L L L
L
n p pβ θ + α + ∇ ⋅ + ∇ ⋅ = ψ −ρ
v q
Local source term
( )1B B M
m L L L L
L
n p pβ θ + α = − ψ −ρ
m
( : )ref p
B
L
L′σ ε&
shear bands
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Band thickness, LB= 1cm K = 10-11 m/s
K = 10-11 m/s
K = 10-11 m/s
0.5 m
0.5 m
0.25 m
0.25 m
0.125 m
0.125 m
THM
0 10 20 30 40 50
0 10 20 30 40 50
0 10 20 30 40 50
∆Pore Pressure in Bands [k
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K = 10-11 m/s
K = 10-11 m/s
K = 10-11 m/s
0.5 m
0.5 m
0.25 m
0.25 m
0.125 m
0.125 m
THM
Band thickness, LB= 1cm
0 1.4 2.8 4.2 5.6 7
0 1.4 2.8 4.2 5.6 7
0 1.4 2.8 4.2 5.6 7
Displacement [m]
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THM
Embedded shear bands. Effect of mesh size on runEmbedded shear bands. Effect of mesh size on run-out
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K = 10-11 m/s
THM
∆Temperature
Embedded Band thickness , LB= 1cm
0 4 8 12 16 20
[10-3 ºC]
Temperature in bands
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K = 10-3 m/s
No Heat
K = 10-5 m/s
Effect of
permeability on
run-out
THM
Band thickness, LB= 1cm
0 2 4 6 8 10
0 2 4 6 8 10
0 2 4 6 8 10
Displacements [m]
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K = 10-11 m/s
K = 10-9 m/s
K = 10-7 m/s
Effect of
permeability on
run-out
THM
Band thickness, LB= 1cm
Displacements [m]
0 2 4 6 8 10
0 2 4 6 8 10
0 2 4 6 8 10
Displacements [m]
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field evidence has clearly demonstrated
was characterized by a stepped pattern
and marly limestone strata, clay interbeds
THM. Vajont
demonstrated that the basal detachment surfa
pattern involving various materials (limeston
interbeds, clay lenses, angular gravel, etc.)”
(Simplified from Paronuzzi et al, 2013
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Clay
(K=10-11 m/s)
Rock
(K=10-5 m/s)
Geometry
THM. Vajont
260 m
Rock
Water
(no strength, incompressible)
100 m
Geometry
260 m
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Material properties
Hendron and Patton, 1985)
Rock
Porosity
Young modulus
Density
Poisson’s coefficient
Cohesion (peak
Friction angle
Residual friction of
clay layer
Embedded band thickness in clay, L
Embedded band thickness in rock, L
THM. Vajont
11′φ = o
Material properties
Rock Parameter Value
0.2
modulus 5000 MPa
2700 kg/m3
coefficient 0.33
peak/residual) 2800/200 kPa
angle (peak/residual) 43/34°
, LB = 2.5 cm
rock, LB = 5 cm
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Run-
THM. Vajont
-out
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9 s after impoundment
Equivalent
plastic
shear strain
THM. Vajont Initial: self weight
40 s after impoundment
0 0.2 0.4
s after impoundment
0 0.025 0.05
Initial: self weight
0 1 2
40 s after impoundment
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THM. Vajont
The
motion
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Pwp increment at t = 40s
THM. Vajont
Temperature increment at t = 40s
0 5 10at t = 40s
0 25 50
Temperature increment at t = 40s
(MPa)
(°C)
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Main ideas
Rate effects on friction: a basic component of creep
Thermal effects are believed to be widespread
Blow-up conditions are mainly controlled by permeability
Subtle interaction between creep and fast sliding
Rate effects on friction reduce blow
Lagrangian-Eulerian methods offer a good promise
A novel procedure to include thermal effects in general
computational tools: embedded
Main ideas
Rate effects on friction: a basic component of creep
Thermal effects are believed to be widespread
up conditions are mainly controlled by permeability
Subtle interaction between creep and fast sliding
Rate effects on friction reduce blow-up risk
Eulerian methods offer a good promise
A novel procedure to include thermal effects in general
ded shear bands and local dissipation
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Advancing current knowledge
Geotechnical description
Failure and post-failure observations
Understanding
Improved computational tools
Well documented failure events
Bon courage!
Advancing current knowledge
Geotechnical description before events
failure observations
Improved computational tools
Well documented failure events
Bon courage!
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Acknowledgements
Dr. N. M. Pinyol, UPC
Dr. A. Yerro, UPC
Eng. M. Alvarado, UPC
Eng. M. Sondon, UPC
o Prof.
o Prof.
o Dr. A.
o Dr. A.
Prof. J. Corominas, UPC
Prof. A. Gens, UPC
Prof. J. Gili, UPC
Prof. A. Lloret, UPC
Dr. A. Ramon, UPC
o Prof.
o Dr. J. Moya,
o Prof.
o Prof.
o Prof.
MPM Research Community: Deltares
UPC, U of Padova, TU Delft, U of California Berkeley
Acknowledgements
. S. Olivella, UPC
Prof. F. Zabala, U. de S. Juan, Argentin
A. Zervos, U. of Southampton
A. Rohe, Deltares, Delft
Prof. E. Romero, UPC
J. Moya, UPC
Prof. A. Puzrin, ETH Zürich
Prof. L. Picarelli, U. Federico2. Napoli
Prof. L. Cascini, U. Salerno
Deltares, U of Cambridge, TU Hamburg
, TU Delft, U of California Berkeley
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Thank
for your
you very much
your attention!