Numerical simulation

International Conference Vajont, 1963-2013
October 8-10, 2013, Padua, Italy

3D SPH NUMERICAL SIMULATION OF THE
WAVE GENERATED BY THE VAJONT
LANDSLIDE
R. Vacondio*, S. Pagani*, P. Mignosa*, R. Genevois**
* DICATeA – University of Parma, Italy
**Dept. of Geosciences, University of Padua, Italy

OUTLINE OF THE PRESENTATION

1.
2.
3.
4.

Previous works
Data available
Kinematics of the landslide
SPH fundamentals and main characteristics of the
numerical model
5. Numerical simulations and model calibration
6. Results
7. Conclusions

3D SPH numerical simulation of the wave generated by the Vajont landlslide

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PREVIOUS WORKS AN MOTIVATION
Previous works concerning the kinematic of the Vajont slide:
Datei (1969), Hendron & Patton (1985), Semenza & Melidoro (1992),
Zaniboni & Tinti (2013),
Previous works concerning the wave generated by the Vajont slide:
Selli & Trevisan (1964), Viparelli & Merla (1968), Semenza (2001),
Datei (2005).
More recently Bosa & Petti (2010) have simulated the phenomenon by
means of a 2D shallow water model. The slide was schematized as a
moving vertical wall which acted as a «piston» in moving the water of
the Vajont slide.
Motivation:
To overcome the limitations of the SWE through the adoption of a fully
3D numerical model


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DEM USED TO DERIVE THE GEOMETRY OF THE VAJONT VALLEY


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z (m a.s.l.)

LEVEL-VOLUME CURVE OF THE VAJONT LAKE (PRE-SLIDE)

Volume at z=700,42 m a.s.l.:
112 106 m3

volume (106 m3)

Datei (2005)

Present work


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RECONSTRUCTION OF THE SLIDING BODY
Intersection between:
• DEM pre-event , obtained by digitizing maps of Semenza et al. (1965);
• Sliding surface, obtained by Superchi (2011) through seismic sections
and boreholes stratigraphy interpretation)
Vajont valley
Vajont valley

Sliding
Sliding
body
surface

Vajont dam

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KINEMATICS OF THE LANDSLIDE -1
We follow the 2D Datei’s approach extending it to the whole 3D
sliding body
1200
R
1000
800
m a.s.l.

m a.s.l.
CoMpre
CoMpost

800
600
400

The Centers of Mass (CoM) of the sliding body before (CoMpre) and after the
slide (CoMpost) have been calculated.

The following hypoteses have been assumed:
1. The slide moved as a rigid body (Muller, 1961, Selli & Trevisan, 1964) on a
rotational axis normal to the plane containing CoMpre and CoMpost;
2. The CoM trajectory is a circular arc of radius R (to be determined).

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C

For each radius R:
1. the trace of the rotational axis C on the plane
containing both CoM is evaluated;
2. the sliding body is rigidly rotated around C.
The optimal radius R is obtained by minimizing the
L2 norm:
N

L2 ( R)
i 1

zirot

zipost
N

R

CoMpre

2


CoMpost

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Section 1

Section 2


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Section 3

Section 4


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Section 5

Section 6


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Assuming a constant friction coefficient f, from the
second law of dynamics, the following equation of
the CoM can be derived
d2
R 2
dt

g sen

R d
g dt

f cos

R

d
dt

0

f

R (m)
α0 (rad)
α1 (rad)
f( )
vmax (m/s)
Tf (s)

tan

max

R

m ax

1
1

cos
sin

1

CoMpre

gR
g
sin t
cos max
R cos

cos
sin

0

2

With some simplifications (Datei, 1969) and
introducing the b.c. the equation for the velocity
magnitude time history of the CoM is obtained
v

C

CoMpost

max

0
0

800
0.469
0.058
0.27
18.5
27.9


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FUNDAMENTALS OF SPH METHOD
• Meshless spatial interpolation based on kernel functions
• Lagrangian
Water
particles

r’

A(r)

j
r r’ i
2h

Ai
j

j

AjWij

Compact support
of kernel

r

A r' W r r' , h dr'
mj

W(r r’, h)

Radius of
influence

A' (r)

A r' W ' r r' , h dr'
mj

'
i

A

j

AjWij'

j


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ALGORITHM: WEAKLY COMPRESSIBLE – SPH SCHEME
Navier – Stokes
Equations
D
Dt
Dv
Dt

SPH
discretization

v
1

D i
Dt

p g Θ

Dv i
Dt

m j vi

vi

Wi , j

j

mj

pj

pi

2
j

2
i

j

Lagrangian particles motion:
Dx i
Dt

vj

i, j

Wi , j

g

Stiff equation of state:
pi

2
c0

0

i

1

7

0


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DISCRETISATION OF SOLID BOUNDARY CONDITIONS
In a SPH framework the discretisation of solid b.c. is still an
open problem. Several options are available
Type

Sketch
Interior fluid
particles

Time consuming, not
suitable for complex
geometry

Mirror Particles
Boundary

Characteristics

Mirror (ghost) particles

Repulsive Force
(Lennard –Jones
molecular model,
Monaghan, 1994)

Dynamic boundaries

Empirical

Suitable for complex
geometry, good
accuracy and efficiency


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SPH – ADVANTAGES AND DRAWBACKS
• SPH simulations of practical problem is limited by simulation time and
system size
• 3D applications have been limited until now by the maximum number
of particles in order to perform simulations within reasonable
computational time.
• Two options are available to overcome this issue:
Supercomputers
GP-GPUs

DualSPHysics code exploits the computing capability of GPUs (x 100
speedup)

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DualSPHysics – EXAMPLE OF APPLICATION


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3D NUMERICAL SIMULATIONS AND MODEL CALIBRATION
Discretization
1. Cubic cells of side x=5 m with a smoothing lenght h=1.5 x

Data available for calibration:
1. Historical (Semenza et al, 1965) maximum run-up of the wave;
2. Water level at rest on the residual lake after the event (712,5 m a.s.l.).
Calibration parameters:
1. Main: friction factor f maximum velocity vmax;
2. Minor: model resolution, kernel type and smoothing lenght, artificial
viscosity;

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3D NUMERICAL SIMULATIONS AND MODEL CALIBRATION
Initial conditions: water at rest at z 700,42 m a.s.l.

Dam

Vajont lake

Landslide
body


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CALIBRATED 3D NUMERICAL SIMULATION – PLANE VIEW
f=0.14 vmax=30 m/s

link video


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CALIBRATED 3D NUMERICAL SIMULATION – PERSPECTIVE VIEW

link video


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CALIBRATED 3D NUMERICAL SIMULATION – MAIN RESULTS
Comparison between historical and calculated maximum run-up of the wave
Historical (Semenza et al., 1965)
Numerical

Dam

Water level at rest on the residual lake after the event:
Calculated: 710 m a.s.l.. Historical 712,5 m a.s.l.

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FLOOD WAVE OVERTOPPING THE DAM

Qmax 160·103 m3/s

time (s)


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CONCLUSIONS AND FUTURE WORKS
• The results of a 3D SPH numerical simulation of the wave generated by the
Vajont rockslide are presented.
• The slide was modeled as a rigid body on a rotational axis normal to the plane
containing CoMpre and CoMpost
• The water volume before the slide was discretized by means of about 1.7
millions of liquid particles, thanks to the CUDA parallelization of the opensource DualSPHysics code.
• The sensitivity analysis of the numerical model has shown that the main
parameter is the friction factor f (which influence the total duration of the fall).
In order to correctly reproduce the maximum historical run-up a friction factor
f=0.14 was necessary.
• The comparison between the results of the numerical simulation and the data
available in literature shows that the numerical scheme is able to reasonably
reproduce, the maximum run-up and level in the residual lake after the event.
• The peak of the flood wave overtopping the dam was estimated at about 160 103
m3/s;
• The numerical results can be adopted in future works as upstream b.c. to
simulate the propagation of the wave in the Vajont gorge, downstream the dam
and in the Piave valley.

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Thank you for your attention

paolo.mignosa@unipr.it
rinaldo.genevois@unipd.it

renato.vacondio@unipr.it


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SIMULAZIONI NUMERICHE 3D E TARATURA DEL
MODELLO
Tf= 17.2 secondi vmax=30 m/s

vmax=20 m/s
vmax=35 m/s

Formazione
del lago
Massalezza

Evoluzione temporale della distribuzione del modulo della velocità dell’onda nella valle del Vajont

MODELLO

Tracimazione diga

Velocità
superiori a
25 m/s

Flusso prevalente in
sinistra idraulica
Evoluzione temporale della distribuzione del modulo della velocità dell’onda in prossimità della diga

MODELLO

t = 10 s

Tracimazione diga

Mappa delle quote idriche a diversi istanti temporali

MODELLO

t = 20 s

Flusso verso il lago Massalezza


MODELLO

t = 30 s

Massima risalita dell’onda


MODELLO

t = 40 s

Discesa dell’onda


BIBLIOGRAFIA
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Bosa S., Petti M. & Passaro M. (2010). “Modellazione ai volumi finiti dell’onda generata dalla frana del
Vajont”. XXXII Convegno Nazionale di Idraulica e Costruzioni Idrauliche, Palermo.
Bosa S. & Petti M. (2012). “A numerical model of the wave that overtopped the Vajont dam in 1963”.
Università di Udine, Udine.
Caloi P. (1966). “L’evento del Vajont nei suoi aspetti geodinamici“. Istituto Nazionale di Geofisica,
Roma.
Ciabatti M. (1964). “La dinamica della frana del Vajont”. Giornale di Geologia, 32, 139-160.
Datei C. (1969). “Su alcune questioni di carattere dinamico relative ad un eccezionale scoscendimento
di un ammasso roccioso”. Memorie della Accademia Patavina, 89-108, Padova
Datei C. (2005). “Vajont. La storia idraulica”. Cortina, Padova.
Genevois R. & Ghirotti M. (2005). “The 1963 Vaiont Landslide”. Giornale di Geologia Applicata, 1, 41–
52.
Giudici F. & Semenza E. (1960). “Studio geologico del serbatoio del Vajont”. Report for S.A.D.E.,
Venezia.
Semenza E., Rossi D. & Giudici F. (1965). “Carte geologiche del versante settentrionale del Monte Toc
e zone limitrofe, prima e dopo il fenomeno di scivolamento del 9 ottobre 1963”. Scala 1:5000. Istituto di
Geologia dell’Università di Padova, Padova.
Selli R. & Trevisan L. (1964). “Caratteri e interpretazione della Frana del Vajont”. Giornale di Geologia,
32, 1-154.
Semenza E. (2001). “La storia del Vajont raccontata dal geologo che ha scoperto la frana”.
Tecomproject Editore Multimediale, Ferrara.
Superchi L. (2011). “The Vajont rockslide: new techniques and tradizional method to re-evaluate the
catastrophic event”. Tesi di dottorato XXIV ciclo, PhD School in Earth Sciences, Università di Padova.
Viparelli M. & Merla G. (1968). “L'onda di piena seguita alla frana del Vajont”. Atti dell’Accademia
Pontaniana, 15.

ALGORITHM: WEAKLY COMPRESSIBLE -SPH SCHEME
The artificial viscosity term
v cij

is defined as follows:
v ij

vj

0

rij

ri r j

v ij rij

0

with

0

cij

0.5 ci

ij

hv ij rij
rij2

vi

v ij rij

ij

i, j

ij

ij

i, j

2

2

0. 5

cj
i

j

0.01h 2

Artificial viscosity v must prevent instabilitiy and
spurious oscillations. For violent phenomena has little
influence on the main characteristics of the flow (Crespo
et al., 2011). The value v=0.2 was assumed in this work

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Numerical simulation

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