# IJEGE-11_BS-Viccione-&-Bovolin

*Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza*

*DOI: 10.4408/IJEGE.2011-03.B-058*

**SIMULATING TRIGGERING AND EVOLUTION**

**OF DEBRIS-FLOWS WITH SPH**

area, the pressure threshold plim and the shear stress

τ

with corresponding Flo 2D results.

**K**

**ey**

**words***: SPH, debris-flow initiation, debris-flow propagation*

**INTRODUCTION**

such as soil, vegetation, debris ranging from clays to boul-

ders. They may represent a threat for people living nearby

such areas and for buildings, i.e. bridges, facilities, etc.

Therefore, understanding the movement mechanism is

of considerable interest, particularly in the evaluation of

potential mitigation policies (t

ics depend on several factors, such as type of weather,

morphology, geology, land use and plant growth. In this

work, we only investigate about the ability of simulat-

ing debris-flow initiation and subsequent movement with

the Smoothed Particle Hydrodynamics (SPH) technique.

Triggering is here settled randomly, making free to move

a particle located in the upper part of the slope being con-

sidered. The others are all initially frozen. Motion of re-

maining particles is related to the achievement of a pres-

sure threshold p

**ABSTRACT**

such as Distinct Element Method (DEM) or Lagrang-

ian Finite Element Method (LFEM). Among the oth-

ers, meshless, Lagrangian numerical method, known

as Smoothed Particle Hydrodynamics (SPH), is here

applied to simulate debris-flow initiation and propaga-

tion over the slope of a mountain located in the city of

Nocera Inferiore (Southern Italy). Debris-flows have

been simulated since long time for hazard mitigation

assessment or deposit evaluation via Eulerian-based

methods. Since they may feature mesh distortion as

the computational domain evolves, heavy grid refine-

ment algorithms are sometimes necessary, especially

for those problems characterized by large deforma-

tions. SPH overcomes such difficulties since no mesh

is needed over the physical domain. Spatial discretiza-

tion is indeed carried out with a collection of parti-

cles without connectivity bonds among them. While

boundary particles are fixed over time, computing

particles are free to move in response of external and

internal forces such as gravity and pressure.

the slope is set free, the others close to it move if a

pressure threshold p

occur, as a domino effect. Runout velocity is control-

led by handling the shear stress τ

*G. VICCIONE & V. BOVOLIN*

*5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011*

ing artificial viscosity model:

neighbouring particles within a short range “r

weighing or kernel function (m

A = 1/π respectively for 2-dimensional (n

*d*

*d*

“j”, or variable (α

term in Π

mum estimate of the velocity field, “v” and “x” repre-

spatial allocation is obtained with a specific mesh gen-

erator, which guarantees a distribution of points form-

ing triangles approximately equilaterals. While some

particles are moving, they may approach others ini-

tially still, to the point for which the relative distance

yields a pressure greater than a threshold value. Once

reached such point, those neighbouring particles, pre-

viously fixed, are then set free to move.

**NUMERICAL APPROACH**

dynamics technique. Introduced three decades ago for

astrophysical applications (G

multi-phase flows (m

*et alii*, 1999;

*et alii*, 1999), high explosive detonation and ex-

*et alii*, 2000),

over the traditional grid-based methods. Among the

others, the most appealing feature is the adaptive na-

ture which means that is not affected by arbitrariness

of particle distribution. Indeed, there is no need to pre-

scribe the connectivity between the moving particles.

With such technique, computing particles carry physi-

cal properties such as velocity or density. Advection

is exactly computed without numerical errors. More

consideration has been subsequently devoted to SPH

as good choice for geomechanical problems.

*Fig. 1 - Neighbour particle destabilization. a) Particle “*i

*”*

*is approaching the neighbour particle “*j

*”. b) De-*

*spite the relative distance “|*r

*ij*

*|” is decreased, par-*

*ticle “*j

*” is still fixed because*p

*ij*

*<*p

*lim*

*. c) Particle*

*“*j

*” is set free to move because the interstitial pres-*

*sure “*p

*ij*

*” has reached the threshold value “*p

*lim*

*”*

**SIMULATING TRIGGERING AND EVOLUTION OF DEBRIS-FLOWS WITH SPH**

*Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza*

of state is assumed (b

tion and “B” is given by:

(m

**DEBRIS FLOW SIMULATION**

slope located in the area of Nocera Inferiore (Italy). The

area, object of study, is shown in the next Figure 4.

ence distance being d

of moving particles has been laid on the upper part

of the slope (blue region in the Figure 5). The total

number of moving and boundary particles are re-

spectively N

the upper part of the slope. Such region is schematically

shown in the above figure with red circles. The subse-

quent mobilization along the slope is subordinated by

the achievement of a particle pressure greater than a lim-

particles are colliding.

is Π

of a special search algorithm (v

*et alii*, 2008).

move with a velocity depending on the average val-

ue of its neighbourhood. This is useful in the case of

high velocity or impact problems, because it avoids

unphysical flow separation.

sure. As a matter of facts, for near incompressible me-

dia, the real equation of state determines time steps

*Fig. 2 - Short range interactions. Properties of particle*

*“i” are computed on the basis of those particles*

*within a cut-off distance “r*

*c*

*” (bold marked). Out-*

*er particles give no contribution*

*Fig. 3 - Smoothing kernel adopted with its gradient*

*Fig. 4 - Map location of the area, object of the investigation*

*G. VICCIONE & V. BOVOLIN*

*5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011*

**CONCLUSIONS**

p

lized become larger when decreasing the isotropic pres-

sure p

ing to the common experience. A comparative analysis

of SPH results with Flo-2D commercial code has been

carried out, obtaining a good agreement in terms of both

mobilized volumes and front propagation.

**ACKNOWLEDGEMENTS**

jor Hazards (CUGRI ), with special regard to the di-

rector, Prof. Eugenio Pugliese Carratelli. The authors

are also in debt with Ing. Nicola Immediata from the

University of Salerno, for his precious contribution

and for helpful comments concerning this work.

be equal to the artificial viscosity (Eq. 3) introduced by

(m

ing particles and of the parameters above introduced.

area been mobilized. Following a previous study (v

2009) as shown from Figure 17 to Figure 22, willing to

perform a comparison for simulation times t = 50 sec and

t = 100 sec, with the corresponding SPH results shown

in Figure 6 (Simul. N. 1), Figure 11 (Simul. N. 6) and

Figure 14 (Simul. N. 9), showing a good agreement in

terms of both mobilized volumes and front propagation.

*Fig. 5 - Spatial discretization of the study area. Red circles rep-*

*resent the region where a local triggering is imposed*

*Tab. 1 - List of simulations been carried out*

*Fig. 6 - Simul. N.1. Particle trig-*

*gered: PT1, limit pressure*

*p*

*lim*

*= 300 kgf /cm*

*2*

*, viscos-*

*ity coefficient α*

*bed*

*=0.1*

**SIMULATING TRIGGERING AND EVOLUTION OF DEBRIS-FLOWS WITH SPH**

*Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza*

*Fig. 7 - Simul. N.2. Particle triggered:*

*PT1, limit pressure p*

*lim*

*= 200 kgf*

*/cm*

*2*

*, viscosity coefficient α*

*bed*

*=0.1*

*Fig. 8 - Simul. N.3. Particle triggered:*

*PT1, limit pressure p*

*lim*

*= 100 kgf /*

*cm*

*2*

*, viscosity coefficient α*

*bed*

*=0.1*

*Fig. 9 - Simul. N.4. Particle triggered:*

*PT2, limit pressure p*

*lim*

*= 300 kgf*

*/cm*

*2*

*, viscosity coefficient α*

*bed*

*=0.1*

*G. VICCIONE & V. BOVOLIN*

*5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011*

*Fig. 10 - Simul. N.5. Particle triggered:*

*PT2, limit pressure p*

*lim*

*= 200 kgf /*

*cm*

*2*

*, viscosity coefficient α*

*bed*

*=0.1*

*Fig. 11 - Simul. N.6. Particle trig-*

*gered: PT2, limit pressure*

*p*

*lim*

*= 100 kgf /cm*

*2*

*, viscosity*

*coefficient α*

*bed*

*=0.1*

*Fig. 12 - Simul. N.7. Particle*

*triggered: PT3, limit*

*pressure p*

*lim*

*= 300*

*kgf /cm*

*2*

*, viscosity co-*

*efficient α*

*bed*

*=0.1*

**SIMULATING TRIGGERING AND EVOLUTION OF DEBRIS-FLOWS WITH SPH**

*Fig. 13 - Simul. N.8. Particle trig-*

*gered: PT3, limit pressure*

*p*

*lim*

*= 200 kgf /cm*

*2*

*, viscosity*

*coefficient α*

*bed*

*= 0.1*

*Fig. 14 - Simul. N.9. Particle*

*triggered: PT3, limit*

*pressure p*

*lim*

*= 100 kgf*

*/cm*

*2*

*, viscosity coeffi-*

*cient α*

*bed*

*= 0.1*

*Fig. 15 - Simul. N.10. Particle trig-*

*gered: PT3, limit pressure*

*p*

*lim*

*= 200 kgf /cm*

*2*

*, viscosity*

*coefficient α*

*bed*

*= 1*

*G. VICCIONE & V. BOVOLIN*

*Fig. 16 - Simul. N.10. Particle*

*triggered: PT3, limit*

*pressure p*

*lim*

*= 200*

*kgf /cm*

*2*

*, viscosity co-*

*efficient α*

*bed*

*=10*

*Fig. 17 - Comparison between Simul. N.1. and*

*Flo-2D results for t =50 secs*

*Fig. 18 - Comparison between Simul. N.1.*

*and Flo-2D results for t =100 secs*

**SIMULATING TRIGGERING AND EVOLUTION OF DEBRIS-FLOWS WITH SPH**

*Fig. 19 - Comparison between Simul. N.6. and Flo-*

*2D results for t =50 secs*

*Fig. 20 - Comparison between Simul. N.6. and*

*Flo-2D results for t =100 secs*

*Fig. 21 - Comparison between*

*Simul. N.9. and Flo-2D*

*results for t =50 secs*

*G. VICCIONE & V. BOVOLIN*

*Fig. 22 - Comparison between Simul. N.9. and*

*Flo-2D results for t =100 secs*

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