Modeling 

Generation and 

Propagation of 

Landslide 

Tsunamis

Patrick J. Lynett

University of Southern California
Modeling Generation and Propagation of 

Landslide Tsunamis - OUTLINE

Approaches for Generating Waves Directly from Landslide Motion

• Modeling the slide mass (types of failures, types of rheology)

• Modeling the waves generated (shallow water models, dispersive models, nonlinearity)

• Establish the (wide) range of slide dynamics, and the proper hydrodynamics to capture wave physics

General Approach for Site Safety Assessment for New Nuclear Reactor Applications 

• Work done with Nuclear Regulatory Commission (NRC) & USGS over past 4 years

• Highly conservative, Probable Maximum Tsunami (PMT) – attempt to select the “worst” wave that might 

be generated from the wide range of slide dynamics

Probabilistic Approach for the Waves Generated by a Specified Landslide

• Given a specific slide geometry and slide failure mechanism, can we capture the distribution of possible 

generated wave heights? 

• Specify some parameter distribution / uncertainty (e.g slide speed, slide “coherency”, etc)

• Quantify how the generated wave height reacts to this uncertainty -> probability of exceedence curve 

for H
Approaches for Generating Waves 

Directly from Landslide Motion

Types of 

Failures

Mass 

movements 

can take a 

wide variety 

of forms, and 

each will 

have different 

tsunamigenic

efficiency 

and potential
Approaches for Generating Waves 

Directly from Landslide Motion

Types of 

Failures

Mass 

movements 

can take a 

wide variety 

of forms, and 

each will 

have different 

tsunamigenic

efficiency 

and potential Mass movements that are “shallow” (horizontal length scale much 

greater than local depth), “coherent” (fails as a single mass, not a 

group of smaller pieces), “fast” (time scale on the order of the 

generated wave period), and involve strong VERTICAL 

ACCELERATION will be the most tsunamigenic sources
Approaches for Generating Waves 

Directly from Landslide Motion

Types of 

Failures

Mass 

movements 

can take a 

wide variety 

of forms, and 

each will 

have different 

tsunamigenic

efficiency 

and potential Mass movements that are “shallow” (horizontal length scale much 

greater than local depth), “coherent” (fails as a single mass, not a 

group of smaller pieces), “fast” (time scale on the order of the 

generated wave period), and involve strong VERTICAL 

ACCELERATION will be the most tsunamigenic sources

 Rotational slides (slumps)
Approaches for Generating Waves 

Directly from Landslide Motion

Types of slide motion & rheology

Most (or at least many) existing studies assume the slide translates down slope following solid body 

motion

• Slide speed is dependent on 

material density, drag 

coefficient, added mass 

coefficient, interface friction

• There is variation in these 

properties – can 

distributions be generated??

• Shape of slide controls the 

drag and added mass 

coefficient, but also the 

generated wave properties 
Approaches for Generating Waves 

Directly from Landslide Motion

Types of slide motion & rheology

Most (or at least many) existing studies assume the slide translates down slope following solid body 

motion

• Slide speed is dependent on 

material density, drag 

coefficient, added mass 

coefficient, interface friction

• There is variation in these 

properties – can 

distributions be generated??

• Shape of slide controls the 

drag and added mass 

coefficient, but also the 

generated wave properties 

• Time history of ground 

movement

– numerical 

Slope implementation

rotates 

CCW

Wedge 

Translates 

away from 

slope
Approaches for Generating Waves 

Directly from Landslide Motion

Types of slide motion & rheology

Most (or at least many) existing studies assume the slide translates down slope following solid body 

motion

• Slide speed is dependent on 

material density, drag 

coefficient, added mass 

coefficient, interface friction

• There is variation in these 

properties – can 

distributions be generated??

• Shape of slide controls the 

drag and added mass 

coefficient, but also the 

generated wave properties 
Approaches for Generating Waves 

Directly from Landslide Motion

Types of slide motion & rheology

Most (or at least many) existing studies assume the slide translates down slope following solid body 

motion

• Slide speed is dependent on 

material density, drag 

coefficient, added mass 

coefficient, interface friction

• There is variation in these 

properties – can 

distributions be generated??

• Shape of slide controls the 

drag and added mass 

coefficient, but also the 

generated wave 

properties 
Approaches for Generating Waves 

Directly from Landslide Motion

Types of slide motion & rheology

A increasing number of studies attempt to model the slide mass as a viscous continuum, described by 

various stress laws

• Simplest is to model the slide as a highly viscous Newtonian fluid (honey slide)

 Allows for deformation of the slide mass, have to tune viscosity

 Initial wave generation often most important stage, is this a proper model at this time?

• A number of rheological models have been proposed, including Bingham, Herschel-Bulkley, and bilinear 

rheologies of viscoplastic fluids (muddy flows, silts & clays, debris flows)

• Can the threshold shear strength be well defined? Can a distribution be developed?
Approaches for Generating Waves 

Directly from Landslide Motion

Modeling the Generated Waves

• It is natural to try to model landslide waves with the “traditional” nonlinear shallow water wave 

equations. 

 However, both the slide-water column coupling and the generated wave propagation can be (and 

often is) characterized as a dispersive (short wave) problem

dL

For the process to be properly described 

by the shallow water model:

dL>>local water depth

(practically speaking dL>~25*h)

*Note that the above dL represents a 

characteristic horizontal length scale, it 

does not necessary mean the front or 

slide half-length. There can be 

numerous important length scales for an 

irregular mass (think spectrally).

Difficult to satisfy for an arbitrarily 

deforming mass
Approaches for Generating Waves 

Directly from Landslide Motion

Modeling the Generated Waves

• It is natural to try to model landslide waves with the “traditional” nonlinear shallow water wave 

equations. 

 However, both the slide-water column coupling and the generated wave propagation can be (and 

often is) characterized as a dispersive (short wave) problem

dL

For the process to be properly described 

by the shallow water model:

dL>>local water depth

(practically speaking dL>~25*h)

Best to use a dispersive model (e.g. 

Boussinesq), or even better a fully 

3D non-hydrostatic model. For 

near vertical fronts, the latter 

would be REQUIRED.
Approaches for Generating Waves 

Directly from Landslide Motion

Modeling the Generated Waves

• For a DETERMINISTIC coupled slide+waves forecast, one would need to:

1. Decide on the geometry of the mass movement – not just volume, but 2D slip surface as well

2. Choose a mass movement failure mechanism (e.g. rotational, translational) and/or choose a 

slide material behavior model (e.g. solid body motion, Bingham)

3. Choose the coefficients that govern the material behavior model (e.g. drag coefficient, threshold 

shear stress formulation coefficients)

4. Based on geometric properties of slide (throughout its evolution) choose an appropriate 

hydrodynamic model to accurately model the “important” wave frequencies

5. Develop a bathy / topo grid for propagation of the waves away from the source, and choose a 

still water level (high tide, sea level rise)

6. Specific a bottom friction factor (probably spatially variable) to account for energy dissipation 

during shallow and overland tsunami flow

• For a PROBABILISITC forecast, a branching decision tree of the above steps is needed, with parameter 

distributions for all the “important” empirical factors involved in the simulation
Approach for Site Safety Assessment for 

New Nuclear Reactor Applications 

Develop a hierarchal approach

 Identify any earthquake or 

landslide source that could 

conceivably impact the site

 For earthquakes, use the 

maximum earthquake that the fault 

could produce (not based on local 

historical precedent)
Approach for Site Safety Assessment for 

New Nuclear Reactor Applications 

Develop a hierarchal approach

 Identify any earthquake or landslide source that could conceivably impact the site

 For landslides, use existing bathymetry data to map the dimensions of the failure

 Following the previous discussion, most of the uncertainty is in the landslide motion, 

so we conservatively assume the slide failed all at once and quickly, such that the 

generated tsunami has an initial amplitude equal to the slide scarp depth (slide thickness)

 For local slides, start with 1HD simulations (equivalent to the entire offshore shelf 

failing simultaneously)
Approach for Site Safety Assessment for 

New Nuclear Reactor Applications 

Develop a hierarchal 

approach

 For runup & 

inundation, start 

with assuming the 

entire land area is 

hydraulically 

smooth
Approach for Site Safety Assessment for 

New Nuclear Reactor Applications 

Develop a hierarchal approach

 If this condition floods the inland location of interest, then perform a 1HD simulation with 

“realistic” friction, and perform a 2HD simulation to quantify radial spreading effects
Approach for Site Safety Assessment for 

New Nuclear Reactor Applications 

Develop a hierarchal 

approach

 If this condition floods 

the inland location of 

interest, then perform a 1HD 

simulation with “realistic” 

friction, and perform a 2HD 

simulation to quantify radial 

spreading effects, and local 

refraction/diffraction 

focusing effects
Approach for Site Safety Assessment for 

New Nuclear Reactor Applications 

Develop a hierarchal approach

 If either of these conditions impact the inland site, then the 

time-history of the landslide motion should be modeled, using 

conservative and realistic slide motions

 If these impact the site, then that particular tsunami source 

is a candidate for the PMF (probably maximum flood – the 

constraining design condition)

Approach is very useful for tsunami hazard assessment of nuclear 

facilities

 Start with the most conservative approach, and remove 

levels of conservatism if needed

 Measures of uncertainty or probability are not included in 

the analysis; using expert judgment to define a highly 

conservative result
Probabilistic Approach for the Waves 

Generated by a Specified Landslide

Example approach to generate a probability distribution for the waves 

generated by a submarine

 Given a specific slide geometry and slide failure mechanism, can we 

capture the distribution of possible generated wave heights? 

 Look at a simple case of a translational slide moving down a linear 

slope

 Allow the initial slide mass to failure in different segments, staggered 

in time. The motion of each slide is governed by solid body motion.
Deterministic Inputs:

 Nc – Number of detached pieces (Nc=3 in figure)

 b – slide width along slope to thickness ratio

 doI – depth above slide center to thickness ratio

 slope – bottom slope

 delay–dimensionless factor scaling failure duration

b

Probabilistic Approach for the Waves 

Generated by a Specified Landslide
Parameters randomized with normal distributions:

Specific 

weight (γ)

μ=2.65, 

σ=12%

Drag 

Coefficient (Cd)

μ=0.8, σ=56%

Added-mass 

Coefficient (Ca)

μ=1.0, σ=20%

Probabilistic Approach for the Waves 

Generated by a Specified Landslide
The relative width of each slide “piece” is randomized

The time interval between motion initialization of 

each “piece” is randomized

Velocity evolution and displacement for each piece 

are

Water depth function for each piece is

*

c tanh ds ds u dt = +

c t

o

t ts

u u

t

  − =    

1 ( ) ( ) ( , ) ( ) 1 tanh 1 tanh

4

l r

o R

x xt x xt hxt h x m h

S S

 −    −   = − ∆+       −          

Probabilistic Approach for the Waves 

Generated by a Specified Landslide
Nc=1 doI=6 b=50 1/10 

slope

delay= 

UnDefined

Probabilistic Approach for the Waves 

Generated by a Specified Landslide
Nc=3 doI=6 b=50 1/10 

slope delay=10

Probabilistic Approach for the Waves 

Generated by a Specified Landslide
Nc=50 doI=6 b=50 1/10 

slope delay=10

Probabilistic Approach for the Waves 

Generated by a Specified Landslide
Nc=5 doI=10 b=40 1/5 slope delay=3

Probabilistic Approach for the Waves 

Generated by a Specified Landslide
Various Nc

2,000 MC 

simulations 

for each 

curve

H50% for Nc=1

∆h

slope=1/5

b/∆h=40

doI/∆h

=10

Delay/(doI/

g)0.5

=10

Probabilistic Approach for the Waves 

Generated by a Specified Landslide
Probabilistic Approach for the Waves 

Generated by a Specified Landslide
Modeling Generation and Propagation 

of Landslide Tsunamis - Conclusions

“Worst Conceivable Tsunami” approach used for 

safety assessment at nuclear sites

 Provides an upper-bound on tsunami impact, singularly 

useful for this particular application

Landslide Tsunami Height Distribution

 Allows for the estimation of:

Statistical Wave Height (e.g. H50%,H2%)

Associated wave period & number of waves

 Can compare with single-body, deterministic runs, to 

provide a measure of the conservatism

 Need much more geophysical information about existing 

slides

Can a distribution for Nc be created?

Info will tend to be very local, site-specific
Conclusions

Need much more geophysical information about existing slides

Can a distribution for Nc be created?

Info will tend to be very local, site-specific

Example use – What would be needed as inputs for a given location:

Deterministic/Probabilistic Inputs:

Slide Slope

Slide Thickness

Time scales 

Duration of failure initiation: downslope (translational)

Duration of failure initiation: lateral (translational)

Duration of slumping (rotational)

Measure of slide mass cohesion (Nc distribution)

Failure “patchiness”, a fraction of failure in the lateral direction
Conclusions

Need much more geophysical information about existing slides

Can a distribution for Nc be created?

Info will tend to be very local, site-specific

Example use – What would be needed as inputs for a given location:

Deterministic/Probabilistic Inputs:

Slide Slope

Slide Thickness

Time scales 

Duration of failure initiation: downslope (translational)

Duration of failure initiation: lateral (translational)

Duration of slumping (rotational)

Measure of slide mass cohesion (Nc distribution)

Failure “patchiness”, a fraction of failure in the lateral direction

Outputs:

Probabilistic distribution of Height, Period, # of Waves
Nc=3 doI=6 b=50 1/10 

slope delay=20

Probabilistic Approach for the Waves 

Generated by a Specified Landslide