Modelling of fast landslide propagation · Li Tong Chun, Liu Xiaoqing, Chuan Lin ETS de Ingenieros de Caminos Madrid manuel.pastor@upm.es. Contents Introduction Mathematical Modelling

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

manuel.pastor@upm.es

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