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

3D SPH NUMERICAL SIMULATION OF THE
WAVE GENER...
OUTLINE OF THE PRESENTATION

1.
2.
3.
4.

Previous works
Data available
Kinematics of the landslide
SPH fundamentals and m...
PREVIOUS WORKS AN MOTIVATION
Previous works concerning the kinematic of the Vajont slide:
Datei (1969), Hendron & Patton (...
DEM USED TO DERIVE THE GEOMETRY OF THE VAJONT VALLEY

3D SPH numerical simulation of the wave generated by the Vajont land...
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)
...
RECONSTRUCTION OF THE SLIDING BODY
Intersection between:
• DEM pre-event , obtained by digitizing maps of Semenza et al. (...
KINEMATICS OF THE LANDSLIDE -1
We follow the 2D Datei’s approach extending it to the whole 3D
sliding body
1200
R
1000
800...
KINEMATICS OF THE LANDSLIDE -2
C

For each radius R:
1. the trace of the rotational axis C on the plane
containing both Co...
KINEMATICS OF THE LANDSLIDE -3

Section 1

Section 2

3D SPH numerical simulation of the wave generated by the Vajont land...
KINEMATICS OF THE LANDSLIDE -4

Section 3

Section 4

3D SPH numerical simulation of the wave generated by the Vajont land...
KINEMATICS OF THE LANDSLIDE -5

Section 5

Section 6

3D SPH numerical simulation of the wave generated by the Vajont land...
KINEMATICS OF THE LANDSLIDE -6
Assuming a constant friction coefficient f, from the
second law of dynamics, the following ...
FUNDAMENTALS OF SPH METHOD
• Meshless spatial interpolation based on kernel functions
• Lagrangian
Water
particles

r’

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

SPH
discretization

v
1

D i
Dt

p g Θ

...
DISCRETISATION OF SOLID BOUNDARY CONDITIONS
In a SPH framework the discretisation of solid b.c. is still an
open problem. ...
SPH – ADVANTAGES AND DRAWBACKS
• SPH simulations of practical problem is limited by simulation time and
system size
• 3D a...
DualSPHysics – EXAMPLE OF APPLICATION

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

17/25
3D NUMERICAL SIMULATIONS AND MODEL CALIBRATION
Discretization
1. Cubic cells of side x=5 m with a smoothing lenght h=1.5 x...
3D NUMERICAL SIMULATIONS AND MODEL CALIBRATION
Initial conditions: water at rest at z 700,42 m a.s.l.

Dam

Vajont lake

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

link video

3D SPH numerical simulation of the wave ge...
CALIBRATED 3D NUMERICAL SIMULATION – PERSPECTIVE VIEW

link video

3D SPH numerical simulation of the wave generated by th...
CALIBRATED 3D NUMERICAL SIMULATION – MAIN RESULTS
Comparison between historical and calculated maximum run-up of the wave
...
FLOOD WAVE OVERTOPPING THE DAM

Qmax 160·103 m3/s

time (s)

3D SPH numerical simulation of the wave generated by the Vajo...
CONCLUSIONS AND FUTURE WORKS
• The results of a 3D SPH numerical simulation of the wave generated by the
Vajont rockslide ...
Thank you for your attention

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

renato.vacondio@unipr.it

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

Tracimazione diga

Velocità
superiori a
25 m...
SIMULAZIONI NUMERICHE 3D E TARATURA DEL
MODELLO
Tf= 17.2 secondi vmax=30 m/s

t = 10 s

Tracimazione diga

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

t = 20 s

Flusso verso il lago Massalezza

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

t = 30 s

Massima risalita dell’onda

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

t = 40 s

Discesa dell’onda

Mappa delle quo...
BIBLIOGRAFIA














Bosa S., Petti M. & Passaro M. (2010). “Modellazione ai volumi finiti dell’onda ge...
ALGORITHM: WEAKLY COMPRESSIBLE -SPH SCHEME
The artificial viscosity term
v cij

is defined as follows:
v ij

vj

0

rij

r...
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Numerical simulation

  1. 1. 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
  2. 2. 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 2/25
  3. 3. 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 3D SPH numerical simulation of the wave generated by the Vajont landlslide 3/25
  4. 4. DEM USED TO DERIVE THE GEOMETRY OF THE VAJONT VALLEY 3D SPH numerical simulation of the wave generated by the Vajont landlslide 4/25
  5. 5. 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 3D SPH numerical simulation of the wave generated by the Vajont landlslide 5/25
  6. 6. 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 3D SPH numerical simulation of the wave generated by the Vajont landlslide 6/25
  7. 7. 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). 3D SPH numerical simulation of the wave generated by the Vajont landlslide 7/25
  8. 8. KINEMATICS OF THE LANDSLIDE -2 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 3D SPH numerical simulation of the wave generated by the Vajont landlslide CoMpost 8/25
  9. 9. KINEMATICS OF THE LANDSLIDE -3 Section 1 Section 2 3D SPH numerical simulation of the wave generated by the Vajont landlslide 9/25
  10. 10. KINEMATICS OF THE LANDSLIDE -4 Section 3 Section 4 3D SPH numerical simulation of the wave generated by the Vajont landlslide 10/25
  11. 11. KINEMATICS OF THE LANDSLIDE -5 Section 5 Section 6 3D SPH numerical simulation of the wave generated by the Vajont landlslide 11/25
  12. 12. KINEMATICS OF THE LANDSLIDE -6 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 3D SPH numerical simulation of the wave generated by the Vajont landlslide 12/25
  13. 13. 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 3D SPH numerical simulation of the wave generated by the Vajont landlslide 13/25
  14. 14. 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 3D SPH numerical simulation of the wave generated by the Vajont landlslide 14/25
  15. 15. 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 3D SPH numerical simulation of the wave generated by the Vajont landlslide 15/25
  16. 16. 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) 3D SPH numerical simulation of the wave generated by the Vajont landlslide 16/25
  17. 17. DualSPHysics – EXAMPLE OF APPLICATION 3D SPH numerical simulation of the wave generated by the Vajont landlslide 17/25
  18. 18. 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; 3D SPH numerical simulation of the wave generated by the Vajont landlslide 18/25
  19. 19. 3D NUMERICAL SIMULATIONS AND MODEL CALIBRATION Initial conditions: water at rest at z 700,42 m a.s.l. Dam Vajont lake Landslide body 3D SPH numerical simulation of the wave generated by the Vajont landlslide 19/25
  20. 20. CALIBRATED 3D NUMERICAL SIMULATION – PLANE VIEW f=0.14 vmax=30 m/s link video 3D SPH numerical simulation of the wave generated by the Vajont landlslide 20/25
  21. 21. CALIBRATED 3D NUMERICAL SIMULATION – PERSPECTIVE VIEW link video 3D SPH numerical simulation of the wave generated by the Vajont landlslide 21/25
  22. 22. 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. 3D SPH numerical simulation of the wave generated by the Vajont landlslide 22/25
  23. 23. FLOOD WAVE OVERTOPPING THE DAM Qmax 160·103 m3/s time (s) 3D SPH numerical simulation of the wave generated by the Vajont landlslide 23/25
  24. 24. 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. 3D SPH numerical simulation of the wave generated by the Vajont landlslide 24/25
  25. 25. Thank you for your attention paolo.mignosa@unipr.it rinaldo.genevois@unipd.it renato.vacondio@unipr.it 3D SPH numerical simulation of the wave generated by the Vajont landlslide 25/25
  26. 26. 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
  27. 27. SIMULAZIONI NUMERICHE 3D E TARATURA DEL MODELLO Tf= 17.2 secondi vmax=30 m/s 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
  28. 28. SIMULAZIONI NUMERICHE 3D E TARATURA DEL MODELLO Tf= 17.2 secondi vmax=30 m/s t = 10 s Tracimazione diga Mappa delle quote idriche a diversi istanti temporali
  29. 29. SIMULAZIONI NUMERICHE 3D E TARATURA DEL MODELLO Tf= 17.2 secondi vmax=30 m/s t = 20 s Flusso verso il lago Massalezza Mappa delle quote idriche a diversi istanti temporali
  30. 30. SIMULAZIONI NUMERICHE 3D E TARATURA DEL MODELLO Tf= 17.2 secondi vmax=30 m/s t = 30 s Massima risalita dell’onda Mappa delle quote idriche a diversi istanti temporali
  31. 31. SIMULAZIONI NUMERICHE 3D E TARATURA DEL MODELLO Tf= 17.2 secondi vmax=30 m/s t = 40 s Discesa dell’onda Mappa delle quote idriche a diversi istanti temporali
  32. 32. BIBLIOGRAFIA              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.
  33. 33. 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 3D SPH numerical simulation of the wave generated by the Vajont landlslide 33/25

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