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Prediction of Landslide Runout - IPGPstep.ipgp.fr/images/c/c1/05_05_Runout_Analysis.pdf ·...
Transcript of Prediction of Landslide Runout - IPGPstep.ipgp.fr/images/c/c1/05_05_Runout_Analysis.pdf ·...
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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)
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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)
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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
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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
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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
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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
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2400
ELE
VA
TIO
N (m
)
0 1000 2000 3000 4000DISTANCE (m)
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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)
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ELE
VAT
ION
(m)
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ELE
VAT
ION
(m)
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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
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DISTANCE (m)
0
100
200
300
PAT
H W
IDTH
(m
)
300400500600700800900
ELEV
ATIO
N (
m)
WIDTH
EROSION
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DISTANCE (m)
0
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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