Numerical modeling and Numerical modeling and sensitivity analysis of sensitivity analysis of

landslide tsunami: Lituya Bay landslide tsunami: Lituya Bay and La Palmaand La Palma

Josh TaronJosh Taron

Miller, 1960

The Setting: Lituya Bay

Modified from Fritz et al., 2001

The Stage: Gilbert Inlet

The Numerical Recipe: Level-The Numerical Recipe: Level-SetSet• Indicator Functions and Smooth HeavisideIndicator Functions and Smooth Heaviside

• Demarcating Physical PropertiesDemarcating Physical Properties

• Dimensionless Navier-StokesDimensionless Navier-Stokes

• Advection-Diffusion of IndicatorsAdvection-Diffusion of Indicators

T

2

u( u+ u ) (u )u

o o

dp

t u d u

F

0t

u

( ) ( ) 1a w a s w w aP P P P H P P H P P H H

1 tanh( )( )

2H

if 0( )

- if 0H

Numerical Recipe: LandslideNumerical Recipe: Landslide

• FEMLAB’s Full Stress TensorFEMLAB’s Full Stress Tensor

• Iverson et al (1985)Iverson et al (1985)

I u uT

p

1 1 / 2

1

cos sin2 4 D

D

c pII D

II

No slip boundaries with bulk density 1610 kg/m3

Slip boundary - same conditions

ValidationValidation• Maximum Landslide VelocityMaximum Landslide Velocity

• Wave HeightWave Height

tan tan 2 sin tan cosv gl

Newmark, 1965Dynamic FOS

Maximum Velocity

Slingerland et al., 1979 Noda, 1970

/hv gd 3 2maxlog / log 0.5 / / /s wd a b V d v gd

1610 kg1610 kg

30.6 Mm30.6 MmFEMLABFEMLAB Slingerland et alSlingerland et al

(using 48 m/s)(using 48 m/s)NodaNoda Max Vel.Max Vel.

HeightHeight 158m158m 100m100m 125m125m ----

velocityvelocity 48m/s48m/s ---- ---- 55 m/s55 m/sSlide path length = 358m, slide height, h, = 90m

a = -1.25 b=0.71

Parametric AnalysisParametric Analysis

DensityDensity SlopSlope e AnglAnglee

Slide Slide VolumeVolume

Slide Slide VelocitVelocityy

Wave Wave HeighHeightt

16101610 4040 30.6 Mm330.6 Mm3 48 m/s48 m/s 158m158m

16101610 4040 51.6 Mm351.6 Mm3 56 m/s56 m/s 203m203m

27002700 4040 30.6 Mm330.6 Mm3 66 m/s66 m/s 208m208m

16101610 4545 30.6 Mm330.6 Mm3 52 m/s52 m/s 178m178m

Slip Slip BoundaryBoundary

16101610 4040 30.6 Mm330.6 Mm3 57 m/s57 m/s 228m228m

ReferencesReferences• Iverson, R., 1985. A constitutive equation for mass movement Iverson, R., 1985. A constitutive equation for mass movement

behavior. Journal of Geology, 93: 143-160.behavior. Journal of Geology, 93: 143-160.• Miller, D.J., 1960. A timely account of the nature and possible Miller, D.J., 1960. A timely account of the nature and possible

causes of certain giant waves, with eyewitness reports causes of certain giant waves, with eyewitness reports of of their destructive capacity, Geological survey their destructive capacity, Geological survey professional professional paper 354-C, U.S. Department of the Interior, paper 354-C, U.S. Department of the Interior, Washington.Washington.

• Fritz, H.M., Hager, W. H., and Minor, H. -E., 2001. Lituya Bay Fritz, H.M., Hager, W. H., and Minor, H. -E., 2001. Lituya Bay case: case: Rockslide impact and wave run-up. Science of Tsunami Rockslide impact and wave run-up. Science of Tsunami

Hazards, 19(1): 3-22.Hazards, 19(1): 3-22.• Newmark, N.M., 1965. Effects of earthquakes on dams and Newmark, N.M., 1965. Effects of earthquakes on dams and

embankments. Geotechnique, 15(2): 139-160.embankments. Geotechnique, 15(2): 139-160.• Noda, E., 1970. Water waves generated by landslides: Noda, E., 1970. Water waves generated by landslides:

Proceedings Proceedings of the American Society of Civil Engineers. of the American Society of Civil Engineers. Journal Waterways Journal Waterways Harbors Div, 96(4): 835-855.Harbors Div, 96(4): 835-855.

• Slingerland, R.L., and Voight, B., 1979. Occurences, Slingerland, R.L., and Voight, B., 1979. Occurences, properties, and properties, and predictive models of landslide-predictive models of landslide-generated water waves. In: generated water waves. In: Developments in Geotechnical Developments in Geotechnical Engineering 14B: Rockslides and Engineering 14B: Rockslides and Avalanches, 2, Avalanches, 2, Engineering Sites., Voight, B., ed.(Elsevier Engineering Sites., Voight, B., ed.(Elsevier Scientific Scientific Publishing Company): 317-397.Publishing Company): 317-397.

Thanks

To be continued with La Palma…