1

Prediction of Landslide Runout

Oldrich Hungr and Scott McDougallUniversity of British ColumbiaEarth and Ocean Sciences

α = fahrböschung

α’ = travel angle

Center of gravity

Theoretically, in a frictional material (dry sand, broken rock), the travel angle should equal the angle of friction, φ. The angle α equals approximately α’.If the travel angle is less than φ, pore-pressure is involved

Fahrböschung (travel angle)

2

1x104 1x105 1x106 1x107 1x108 1x109 1x1010 1x1011

VOLUME (m3)

0.1

1

0.2

0.3

0.40.50.60.70.80.9

TAN

a

1x105 1x106 1x107 1x108 1x109 1x1010 1x1011

VOLUME (m3)

0.1

1

0.2

0.3

0.4

0.50.60.70.80.9

TAN

a“Scheidegger plot”(1973)

Center of gravity displacement (Hungr, 1981)

Mobility increases with volume

Corominas (1996)

All landslides

Debris flows

3

University of British ColumbiaLog Initial Volume (m3)

Angle α(deg.)

Travel angle α

Debris flows in Hong Kong

(Wong et al., 1997)

GIS-based susceptibility analysis

Hong Kong, 2003

Delivery paths

4

Empirical Methods• area-volume relationships

for geometrically similar deposits:area ∝ volume(2/3)

1x105 1x106 1x107 1x108 1x109 1x1010 1x1011

VOLUME (m3)

1x104

1x105

1x106

1x107

1x108

AR

EA

(m2 )

(Li 1983; Iverson et al. 1998)

Equivalent Fluid

Dynamic modelling:concept of equivalent fluid

Prototype Model

5

St.Venant Equation, Lagrangian

Acceleration = Gravity – friction + pressure term (P)

MovingCoordinatesystem

dxdHgk

HTg

dtdv α

ρα cossin +−=

(Savage and Hutter, 1988)

H

x

T

P

Dynamic equilibrium of a column

T = resisting stress

Pressure term:

αγ cosHdsdHkP =

k – lateral pressure coefficient

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AvalancheLake runup,Northwest Territories

600 m

0 1000 2000 3000 4000DISTANCE (m)

800

1200

1600

2000

2400

ELE

VA

TIO

N (m

)

0 1000 2000 3000 4000DISTANCE (m)

800

1200

1600

2000

2400

ELE

VA

TIO

N (m

)

“Frictional fluid”

fluid

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Resisting force, TFrictional:

φσ tan)( uT −=

φφ tan)1(tan ub r−=

bT φσ tan=or:

Where Φb is the “Bulk Friction Angle (modified by pore-pressure

Resisting force, T

Plastic:

Viscous:

Bingham:

Voellmy:

τ=T

HVT µ3

=

ξγµσ

2VT +=

Yield stress + viscous effect

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Pseudo-3D (Hungr, 1995)

Simulate path width

Pseudo-3D 3D(Hungr, 1995) McDougall and Hungr, 2004)

Simulate path width

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• the new model ...based on “Smoothed Particle Hydrodynamics”...

DAN 3D

xx x z yx z zx x

v h h eh hg k k vt x y t

ρ ρ σ σ τ ρ ∂ ∂ ∂ ∂ = + − + − + − ∂ ∂ ∂ ∂

yy y z xy z zy y

v h h eh hg k k vt y x t

ρ ρ σ σ τ ρ∂ ∂ ∂ ∂ = + − + − + − ∂ ∂ ∂ ∂

yx vh v eht x y t

∂ ∂ ∂ ∂+ + = ∂ ∂ ∂ ∂

Acceleration =

gravity – friction – pressure - momentum correction(McDougall and Hungr, 2004)

Mass Balance

Momentum equilibrium

Governing equations

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• model testing

DAN3DDAN3D

experiment #1

model

DAN3D Model Verification

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Eaux Froides rock avalanche, Switzerland (courtesy J.-D. Rouiller)

EauxFroides

DAN-WDeposit

DAN-W paths

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Eaux Froides: Voellmy (µ = 0.13, ξ = 450 m/s2)

Left Side Right Side

Voellmy

µ = 0.13

ξ = 450 m/s2

(DAN-W Calibrated)

Eaux

Froides

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Model Calibration:1. Select cases similar to the slide in question2. Compile data on path geometry and character,

debris distribution, velocities3. Run program to obtain requisite runout4. Compare debris thickness, velocity distribution5. Select the “best fit” rheology and parameters6. Use the best fit model and parameters for prediction

e.g.(Hungr et al. 1984)

Forced Vortex Equation (superelevation)

plan x-section

RgvBH2

=∆

Estimation of velocity in the field

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Example back-analysis:Mt. Cayley rock avalanche, 1983

Field observations

0 1000 2000 3000 4000 5000DISTANCE (m)

0102030405060708090

100

VE

LOC

ITY

(m/s

)

Voellmy, 0.1,500Voellmy, 0.2, 1500FrictionalBingham

Frictional: fi=30, ru=0.45Bingham: tau=18kPa, viscosity=1 kPa.s

1000 2000 3000 4000DISTANCE (m)

1000

1200

1400

1600

1800

2000

ELE

VAT

ION

(m)

1000 2000 3000 4000DISTANCE (m)

1000

1200

1400

1600

1800

2000

ELE

VAT

ION

(m)

1000 2000 3000 4000DISTANCE (m)

1000

1200

1400

1600

1800

2000

ELE

VAT

ION

(m)

Debris distribution (Frank Slide)

Frictional

Voellmy

Bingham

Magnified 5x

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Frank Slide debris

Velocity comparison(23 rock avalanches Hungr and Evans, 1996)

0 20 40 60 80 100FIELD VELOCITY (m/s)

0

20

40

60

80

100

CA

LCU

LATE

D (m

/s)

Voellmy

Frictional

Bingham

“Opportunistic” field velocity estimates

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0 5000 10000 15000ACTUAL RUNOUT (m)

0

5000

10000

15000C

ALC

ULA

TED

RU

NO

UT

(m)

FIDAZ

TURBID CK.

SHERMAN

ONTAKE

Voellmy model with fixed parametersfirst – order prediction for rock avalanches

µ = 0.1

ξ = 500 m2/s

Sarno, 1998 (courtesy, F.Guadagno)

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Map of Sarno area

Sarno: DAN back-analyses

f=0.07

Ksi=200(Revellino et al.,2002)

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Summary of Calibration results1) Small, “dry” rock avalanches - frictional, Φb=30º

(e.g. Strouth et al., 2005)

2) Campania debris avalanches - Voellmy, µ = 0.07, ξ = 200 m/sec2

(Revellino et al., 2002)

3) “Normal” waste dump flow slides - frictional, Φb=20º(Hungr et al., 2002)

4) Debris avalanches in Hong Kong - frictional, Φb=20º(Ayotte and Hungr, 2001)

5) Typical rock avalanches - Voellmy, µ = 0.1, ξ = 500 m/sec2

(Hungr and Evans, 1996)

6) Large rock avalanches involving ice - Voellmy, µ = 0.05, ξ = 1000

7) Landslides involving clay - Bingham Model (Geertsema et al., 2006)

Material entrainment (Sassa, 1985)

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Nomash Slide, Vancouver Island, B.C.

(Photos D.Ayotte)

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ROCK SLIDE

COARSE DEBRIS AVALANCHE

DEPOSITION

0 400 800 1200 1600 2000 2400

DISTANCE (m)

200

400

600

800

1000

ELEV

ATIO

N (

m)

0 400 800 1200 1600 2000 2400

DISTANCE (m)

-1500-1000

-5000

50010001500

YIEL

D R

ATE

(m3 /

m)

ROCKDEBRISEROSION

0 400 800 1200 1600 2000 2400

DISTANCE (m)

0100000200000300000400000500000600000700000

VOLU

ME

PAS

SIN

G (

m3 ) ROCK

DEBRISTOTAL

DEPOSITS

Nomash River

Profile

Yield rate(m3/m)

Volume balance

0 500 1000 1500 2000 2500

DISTANCE (m)

0

100

200

300

PAT

H W

IDTH

(m

)

300400500600700800900

ELEV

ATIO

N (

m)

WIDTH

EROSION

0 500 1000 1500 2000 2500

DISTANCE (m)

0

10

20

30

40

VELO

CIT

Y (m

/s)

FRONTTAIL

Model with material entrainmentNomash River slide, 1999 (Hungr and Evans, 2004)Source volume: 370 000 m3Entrained debris: 400 000 m3

Frictional Voellmy (0.05, 400)

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0m 1000m

measured trimline

simulated source slide

simulated entrainment zone

Nomash River rock slide – debris avalanche

Nomash River rock slide – debris avalancheSimulation with entrainment(McDougall and Hungr, 2005)

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Real case, 2D analysis:

Real case: estimate flow energy at x=390 m

Calibration

tanΦ

b

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Real case, 3D:

New location

Real case, 3D:

b) with proposed berma) existing conditions

protected areaberm

1) influence of a proposed berm

• berm could potentially be effective

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Another real case, Indonesia

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Factory, Switzerland

Conclusions:1. Landslides are complex, but predictions are possible2. Our approach is to concentrate on the external aspects

of behaviour. We consider the micro-mechanics intractable.

3. We should be open-minded about the rheologicalcharacter of landslide motion

4. Analysis must consider the character of material forming the path

5. Material entrainment should be considered6. Model verification and calibration are essential