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)

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

PampaneiraPampaneira, Granada

Pampaneira

penstock

Pampaneira

Pampaneira

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?

Cortes Landslide, Valencia

Cortes

Cortes

Aznalcóllar

failure

(Sevilla)

April 25th, 1998

AznalcóllarCentral zone of

Why 40 - 50 m of run

OC brittle

Central zone of failure

50 m of run-out?

(Moya, 2000)

brittle clay

“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

Questions :

IN CASE OF INSTABILITY

- How big?

- How far?

- How fast?

IN CASE OF INSTABILITY

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

1. Creeping landslides1. Creeping landslides

St Moritz inclined tower. Courtesy of A. Puz

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)

Assembly of 1002

circular disksKuhn & Mitchell, 1993)

Assembly of 3421

spheres(Kwok & Bolton, 2010)

Creeping landslides

Velocity dependent

contact friction

• 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

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

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 +

A landslide creeping

scenario

Creeping

landslides

A=0

Model response

Rate effects

Creeping landslides

1mm/s

response

No rate effects

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)

Creeping landslides Vallcebre

(Scoppettuolo, 2016), 2016)

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

2. Fast landslides

Vajont landslide

(Valdés y Díaz

Caneja, 1964)

Collected cases

of landslide

evolution

Fast landslides

100 m

Rotary shear tests. v = 0.1 Fast landslides

(Di Toro et al, 2011) Nature

= 0.1 – 2.6 m/s. 300 tests reviewed

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

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

Recorded

temperature

during

experiments

Fast landslides

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

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

Fast landslides

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

Scaled Vajont (x1/10). Effect of shear band Fast

landslides

2e = 2.5 mm

Run out: 50 m

Effect of shear band permeability

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

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

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

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

3. Transition

from creeping

to fast motion

Canillo giganticgigantic creeping landslide. Andorra

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”

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

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

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)

=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

Velocity

Creep - FastSlope

Friction angle

response

Slope

Temperature

Creep - Fastresponse

Excess pore pressure

The relevance

w soil

K

m D gD=

γ

Creep - Fast

345

1

Ψ =

Π =

of rate effects

Creep-THM Creep - Fast

Planar

slide

Time for blow

THM creep

THM interactions

blow-up and rate effects

creep velocity

Creep - Fast

Planar

slide

Creep-THM

Time for blow

THM creep

THM interactions

blow-up and rate effects

creep velocity

Creep - Fast

Planar

slide

Creep-THM

Time for blow

THM creep

THM interactions

blow-up and rate effects

creep velocity

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

4. Continuum

analysis

(MPM)Vajont. Del Ventisette et al. (2015)

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)

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

Three-Phase MPM

Phase MPM

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

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

5. First time

slides

Sabadell slide

First time AznalcóllarAznalcóllar dam failure

First time.

AznalcóllarModel domain and and construction stages

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

Modelling foundationFirst time.

Aznalcóllar

1m x 1m

cell

foundation clay

(Zabala & Alonso, 20

First time. Aznalcóllar

Equivalent plastic deviatoric strainstrain contours (1% - 5%). K0=1

First time. Aznalcóllar

Equivalent plastic deviatoric strainstrain contours (1% - 5%). K0=1

First time. Aznalcóllar

Equivalent plastic deviatoric strainstrain contours (1% - 5%). K0=1

(Courtesy of J. M. Rodríguez Ortiz

First time.

Aznalcóllar

Courtesy of J. M. Rodríguez Ortiz)

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)

MPM analysis 6 years later. Geometry and mesh

First time. Aznalcóllar

years later. Geometry and mesh

First time. Aznalcóllar

Long alluvial terrace

Short alluvial terrace

First time. Aznalcóllar

0 0.5

Shear strain

Long alluvial terrace

Short alluvial terrace

Time: 3 s

First time. Aznalcóllar

Time: 10 s0 0.5

Shear strain

Long alluvial terrace

Short alluvial terrace

0 0.

Shear strain

First time. Aznalcóllar

First time. Aznalcóllar

Level of tailings

Failure of

Selborne

experimental

slope

First time. Selborne

(Cooper, 1996; Cooper et al, 1998)

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)

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°

Instability process

First time. Selborne

Instability process

Progressive failureFirst time. Selborne

Progressive failure

(Cooper, 1996)

First time. Selborne

* / failuret t t=

First time. Selborne

First time. Selborne

0.845

First time. Selborne

First time. Selborne

First time. Selborne

First time. Selborne

First time. Selborne

Instability

process

First time. Selborne

Instability

process

First time. Selborne

Surface movementsFirst time. Selborne

Field data by

Grant (1996)

Surface movements

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)

(?)

6. THM analysis

of landslides

Alcántara-Ayala, 2008

San Juan de Grijalva

Ayala, 2008

San Juan de Grijalva landslide, Mexico

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& &

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

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)

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)

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]

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]

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

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

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

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

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]

THM

Embedded shear bands. Effect of mesh size on runEmbedded shear bands. Effect of mesh size on run-out

K = 10-11 m/s

THM

∆Temperature

Embedded Band thickness , LB= 1cm

0 4 8 12 16 20

[10-3 ºC]

Temperature in bands

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]

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]

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

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

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

Run-

THM. Vajont

-out

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

THM. Vajont

The

motion

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)

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

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!

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

Thank

for your

you very much

your attention!