the 1963 landslide and flood at vaiont reservoir italy. a tsunami

ABSTRACT

We apply the recently developed «tsunami ball» method to con-struct a physics-based simulation of the 1963 Vaiont Reservoir land-slide and flood disaster. Previous tsunami ball applications restrictedattention to landslide-generated sea waves and local runup. For thefirst time, we expand the approach to include overland flows andfloods in a dam-break like situation. The Vaiont landslide was not adebris avalanche, but rather a semi-coherent slump. The slump ver-sus avalanche distinction is embodied with a 2-D variation of a par-ticulate landslide model. With proper adjustment of landslide para-meters, we find that a slump of dimension and volume consistentwith observations can indeed slip from the south slope of the reser-voir, splash water ~200 m up on the north slope, spill 30 million m3

of water over the dam and flood the valley below – all as wererecorded in that day’s events. Incorporating runup and flood infor-mation with geological data provides additional insight into thekinematics of the landslide. The observed distribution of inundationrequires that the eastern part of the landslide begin to move beforethe western part, so trapping and pushing more water over the dam

than would otherwise have been the case. As aids for visualization,this paper includes links to Quicktime movies of the simulations,including a three dimensional «fly by».

KEY WORDS: Landslide, Tsunami, Flood.

REVIEW OF THE 1963 EVENT

The October 9, 1963 landslide and flood at VaiontReservoir in northeast Italy (fig. 1) is a famous engineer-ing disaster caused by the failure to manage the effects ofreservoir filling upon the stability of Monte Toc, just tothe south. The disaster was unusual in that dam collapsedid not trigger the ensuing flood. Rather, a catastrophiclandslip from the slope of Monte Toc (figs. 1 and 2)pushed ~1/5 of the water in the newly created reservoirovertop and around the dam. The 2.6×108 m3 slide massflung down 30 million cubic meters of water to flood thePiave Valley below. The slump itself occurred quickly. Aseismic record from a station north of Vaiont as well aseyewitness accounts, imply that less than 45 secondselapsed from the start of the slide’s movement until itsleading face impacted the opposite wall of the gorge.Afterwards, water drained over the dam for severaldozens of minutes, although the bulk of the volumeejected in the first three or four.

Even though the dam remained intact, over 2000 peo-ple perished in villages and towns overwhelmed by theflood as it descended the Piave River Valley. Because thedisaster was attributed to mismanagement of the reser-voir construction and filling process, years of legal actionensued. Voluminous geological and geotechnical investi-gations (notably MULLER, 1964, 1968; SEMENZA, 1965;HENDRON & PATTON, 1985; SEMENZA & MELIDORO, 1992;SEMENZA & GHIROTTI, 2000) make the Monte Toc slopefailure one of the most intensively studied in history. Incontrast to the landslide itself however, the run up ofreservoir water onto the north slope and the subsequentflow over and around the dam has received less attention.In this paper we show how run up and flood informationhelps to constrain the kinematics of landslide movementbetter than geological and geotechnical data alone.

One of the ironies of the Vaiont disaster is that theattractiveness of the site for a reservoir stems in part froma major paleo-landslide that co-located there. ModernVaiont valley is a broad glacial trough along much of itslength that narrows to a deep gorge near its junction withthe Piave Valley. The construction of a narrow but high(over 260 m) dam in the gorge could thus impound an

(*) Institute of Geophysics and Planetary Physics. Earth andMarine Sciences Building. University of California, Santa Cruz,CA 95064 USA - [email protected]; http://es.ucsc.edu/~ward.

(**) Aon Benfield UCL Hazard Research Center, UniversityCollege London.

The 1963 Landslide and Flood at Vaiont Reservoir Italy.A tsunami ball simulation

STEVEN N. WARD (*) & SIMON DAY (**)

Ital.J.Geosci. (Boll.Soc.Geol.It.), Vol. 130, No. 1 (2011), pp. 16-26, 9 figs. (DOI: 10.3301/IJG.2010.21)

Fig. 1 - Location map of the Vaiont Dam region showing the landslideexcavation zone, limit of deposit (purple); limit of wave trim line(red) and inundation limit in Piave Valley (orange).

02 (10-10) WARD 16-26_GEOLOGIA 18/02/11 09.15 Pagina 16

unusually large volume reservoir in relation to the size ofthe dam. The gorge formed by re-incision of the VaiontRiver through the 200 m thick toe of a paleo-landslidethat had slid from Monte Toc and blocked the valley. Thepaleo-slide mass consisted primarily of limestone,interbedded with weaker clay layers upon which themovement initiated. The bulk of the paleo-rock mass noteroded by the river remained relatively intact andappeared stable to engineers. In modern times, submerg-ing the Vaiont valley to form the reservoir destabilizedthe weak layers of crushed rock and clay beneath the pre-historic landslide. Almost from the first day of filling in1960, slow movements of the slope began – first at theeastern side of the slide mass then propagating to thewest (KILBURN & PETLEY, 2003 and references therein).Concern heightened after a small rockslide fell into thereservoir from the steep cliffs at the front of the old land-slide on November 4th, 1960. Once these creeping move-ments had been recognized, further geological investiga-tions revealed the full extent and limited stability of theancient landslide (SEMENZA & GHIROTTI, 2000). Respond-ing to these warning signs, engineers partially drained thereservoir in early 1961. This appeared to stabilize theslope; but subsequent refilling during 1963 led to arenewal of slow but accelerating deformations, capped onthe evening of October 9th by the catastrophic failure.

The exact mechanism by which reservoir fillingcaused the initial slow creep of the ancient landslide andthen its sudden acceleration remain controversial (KIL-BURN & PETLEY 2003; HENDRON & PATTON, 1985). Mostlikely, increasing pore pressure within the weak clay andcrushed rock (mylonite) layers at the base of the prehis-toric landslide re-activated the mass as a high velocityslump. Although intensively fractured and partly disinte-grated, the 1963 slump retained a degree of cohesion. Itcame to a halt against the north wall of the Vaiont valleyas a thick mass (fig. 2b) rather than changing directionand spreading out as a debris avalanche eastward to lowerelevations. The slump-like behavior of the Vaiont landslidecontrasts other historical examples that we have investi-gated, such as the May 18th 1980 Mount St. Helens vol-cano collapse (WARD & DAY, 2006) and the July 9th 1958Lituya Bay fjord rock avalanche and proglacial sedimentfailure (WARD & DAY, 2010). The particulate landslidemodel employed in these earlier works needs certain mod-ifications to mimic slump-like versus avalanche-like cases.

TSUNAMI BALL APPROACH

This article closely follows WARD & DAY (2010) andWARD (2010) who simulated wave runup and inundationfrom the 1958 Lituya Bay Alaska and the 1889 John-stown, Pennsylvania disasters. While those papers supplyfull mathematical details, Appendix A provides a shortsummary. Simply, tsunami balls are pencil-like columnsof water gravitationally accelerated over a 3-D surface.That part of the 3-D surface within the excavation anddeposition zones of a landslide varies in time thus drivingthe motion of the water. The volume density of tsunamiballs at any point equals the thickness of the water col-umn there. Tsunami balls care little if they find them-selves on parts of the surface originally under water or onparts originally dry. Such indifference is made-to-orderfor flood-like inundations.

As do the Lituya Bay models, the Vaiont simulationinvolves two stages. The first stage computes a landslidehistory. The second stage feeds landslide history into the

THE 1963 LANDSLIDE AND FLOOD AT VAIONT RESERVOIR ITALY 17

Fig. 2 - (top) Pre-landslide view looking east over the dam in foreground.(middle) Post-slide view also looking east. Slide mass and scouredterrain show as the lighter tone. (bottom) North-looking view of thePiave Valley after the flood. Vaiont gorge runs off to the right.


tsunami ball calculation to distort the 3-D surface andinduce water waves on the reservoir and the subsequentflood. Primary outputs of the simulation include the his-tory and shape of the landslide and water waves, theirkinetic and potential energies, and the extent of on- andover-land inundation.

1963 LANDSLIDE SIMULATION

Slide Distribution: To begin constructing the landslidesimulation, we need three sets of topography: (1) thepost-slide topography Tpost (x); (2) the pre-slide topogra-phy Tpre (x); and (3), the basal surface topography underthe landslide Tbase (x). Outside of the slide’s excavationand deposition zones Tpre (x) = Tpost (x) = Tbase (x). Withinthe excavation zone, the basal surface topography isTpre (x) less the initial slide thickness H0 (x). The post-slide topography derives from a 10 m DEM (TARQUINI etalii, 2007) down-sampled to 20 m spacing. Within theexcavation and deposition zones, pre-slide topographyfrom SEMENZA’S (1965) map sampled at 100 m intervals(with additional points defining key features and thegorge axis) was interpolated onto the 20 m post topogra-phy grid. The shape, area (2.1×106 m3), total volume(260×106 m3) and mean thickness (125 m) of the land-slide are well constrained (fig. 1). Because the base of theslide is not well exposed however, the thickness distribu-tion of the material H0 (x) is less certain. To fix the basalsurface and initial slide thickness H0 (x) within the exca-vation, we took the following tack:

(1) A trial basal surface Tbasetrial (x) was fixed to emerge

along the base of the pre-historic slide – near the moderncanyon floor at an elevation of 550 m. From there, rampsupward toward the south at a low angle.

(2) On the cleanly exposed cliffs above 950 m eleva-tion (fig. 2b), we suppose that Tbase

trial (x) coincided withTpost (x), hence H0 (x) is known above there.

(3) Where the trial basal surface emerges near thecanyon floor, the trial slide thickness H0

trial (x) was givena value Hbase(x) that tapered to zero at the easternand western edges of the slide zone. Toward the south,H0

trial (x) also tapered so that it matched its known valueat 950 m elevation.

(3) If Tpre(x) – H0trial (x) > Tbase

trial (x), then the final slidethickness H0 (x) equals H0

trial (x) and Tbase (x) is set toTpre (x) – H0 (x). If not, then Tbase (x) equals Tbase

trial (x) andH0 (x) is set to Tpre (x) – Tbase (x)

(4) Finally, Hbase was increased or decreased suchthat the total volume of the slide filled out to 260 millioncubic meters.

The four panels in the top row of fig. 3 picture the ini-tial slide distribution so determined. As you can see, theslide is thicker toward the middle, its top surface coin-cides with Tpre (x) and its bottom surface coincides withTpost (x) above 950 m elevation.

Slide Mechanics: With the initial slide mass estab-lished, the next step brings it down. One of the main goalsis to let the material sandwiched between the basal andpre-slide surfaces accelerate through the forces of gravityand friction and hopefully, deposit such to replicate post-slide topography (black lines, fig. 3). While the simulationdirectly incorporates pre-slide and basal surfaces, post-slide topography is not a direct constraint. Trial and erroradjustments guide the model deposit to a configurationresembling the actual deposit. WARD & DAY (2010) pre-sent the governing equations for the landslide particles,but suffice to say that the primary adjustable dynamicparameters are the slide’s basal and dynamic frictional

18 S.N. WARD & S. DAY

Fig. 3 - Landslide Simulation at T=0:00, 0:31 and 2:03. The three map view panels at the left contour landslide thickness and correspondingcolor bar at bottom. In this simulation, the slide initiated about ¾ of the distance along length of the slide from the dam (middle panel left).The panels to the right show south to north landslide cross sections along west, central and east transects. The blue and black lines are thepre- and post- slide topography respectively. Tick marks above are at 100 m spacing. The blue color in this fig. indicates initial lake level only,not the history of fluid motion. The letters (L, P, C etc.) abbreviate the village names listed in fig. 1.


coefficients, Cb and Cd. Primary adjustable kinematicparameters define the sequence of slide release and defor-mation style.

As mentioned earlier, geological evidence suggeststhat the Vaiont landslide was more slump than avalanche.Slumps generally run-out less than their along-sectionlength, whereas avalanches can run-out many times theirlength. Slumps also maintain internal integrity more thandisintegrating avalanches. To embody slump-like featuresto the Vaiont slide, volumes in slices aligned with the slid-ing direction (in-section) were conserved. Specifically,evolving slumps deforming in response to the drivingforces, do so in-section only. To implement a slumpwithin our particulate landslide code, we zero-out thecomponent of particle acceleration perpendicular to asupposed sliding direction – North in this case. With noout-of-section forces acting, slide bits always stay in-sec-tion and conserve in-section volume. All of the fig. 3 viewsare in-section.

Clues to the slide’s basal and dynamic frictional coef-ficients are gleaned from the top row of fig. 3. You cansee that the height to which slump material runs up onthe north wall does not correlate well its initial height onthe south wall. In particular, the steep slide at the eastruns up less than does the initially shallower sloped mate-rial in the middle. To reproduce this, the landslide bitstook on a spatially variable basal drag coefficient Cb. Thecenter 750 m of slide took a coefficient of Cb=0.05whereas the ~600 m on the east and west flanks took on avalue of 0.14. The east-to-west progression in the onset ofprecursory deformation during 1960 to 1962 hints at acomplex basal slide surface with a weaker central portion.Variable basal friction might reflect directly mechanicalproperties of the basal surface, e.g. variable contactingmaterials or fluid presence. Variable basal friction mightalso reflect geometrical properties of the basal surface,e.g. variable roughness. Dynamic drag (velocity squaredfriction) Cd coefficient was 5×10-4/m for slide bits on landand 20×10-4/m for slide bits in water. The idea here is that itis harder to push landslide material through water than air.

Pre- and Post-slide topography alone do not speakdirectly toward landslide kinematics – i.e. how materialtraveled from start to finish. Curiously, it is in thisaspect where run up and flood information help out.Firstly, a successful simulation needs some 30 millioncubic meters of water to run past the dam. This is tricky.When the slump begins its fall, water displaces bothwestward toward the dam and eastward into the unaf-fected section of the reservoir. If the landslide sequenceis incorrect, too much or too little water passes the dam.Secondly, the well mapped inundation limit or «trim-line» around the reservoir can not be exceeded signifi-cantly. We found that to satisfy these requirements,landslide release must happen in stages. All-at-oncereleases always forced run-up far too high on the northslope of the valley. Moreover, the sequence of releasehas to be largely east to west. This ordering forces lotsof water toward the dam while depositing an elevatedbarrier at the eastern side of the landslide. Without thebarrier, much of the water initially pushed westwardwill run back off the slide to the lower elevations of theeastern reservoir rather than over the dam. Our slide ini-tiates in a section about 3/4 of the distance from thedam to its east end. From there, release propagates botheast and west over about 60s.

Fig. 3 snaps three shots of the landslide simulation atT=0:00, 0:31 and 2:03. The three left hand panels contourlandslide thickness. The right hand panels show western,central and eastern cross sections. (All of the simulationspresented in this article are accompanied by Quicktimemovie animations. See Appendix B. View the movie offig. 3 at http://es.ucsc.edu/~ward/vaiont-slide.mov). Theinformation in the yellow box in the left panels includesthe mean speed of the moving slide, the number of mov-ing slide bits, the total number of slide bits (60,000), theirkinetic energy and lost potential energy. In any accept-able landslide model, the former must be less than thelatter in absolute value.

Each landslide cross section contains about 60 s ofaction.

⇒T: 0-30s after release (fig. 3, Rows 1 and 2): Fromits original elevation between 100 m and 400 m above thereservoir, each slide section accelerates to about 15 m/s asit slams down.

⇒T: 30-45s after release: Each slide section traversesthe 1 km width of the reservoir and more or less stopsagainst the north slope.

⇒T: 45-90s after release (fig. 3, Row 3): The last in-section slide bits falling from the highest elevations reachthe base and final re-equalizations of the surface occur.

Including the 60 s delay in sequencing, 90% of theslide comes to a halt within two minutes. Total potentialenergy lost in the landslide is 7.5×1014J. Its peak kineticenergy is 7.5×1013J. The ratio of kinetic energy to potentialenergy lost tops out at 66%, seven seconds into sliding.

Fig. 4 summarizes landslide kinematics embodied asmean acceleration, mean velocity and mean displacementof the slump. Recall, we zeroed out-of-section (eastward)accelerations to mimic slump like characteristics, so fig. 4shows only north and vertical components. The primarynorth-south acceleration pulse (fig. 4, upper left) spannedabout 50s, consistent with the duration of the slideinferred from seismic records and eyewitnesses. Becausethe slump released sequentially, some parts of the slideare moving while others were finished or had yet to start.Sequenced release kept low the velocities in the mean.Although individual slide bits reached 15-20 m/s, mean


Fig. 4 - Summary of landslide kinematics. The panels show theNorth and Up components of mean acceleration, mean velocity andmean displacement for the slump mass. Maximum and minimumlimits for the plots are ±5%g, ±10m/s, and ±500m.


velocity barely exceeded 8 m/s (fig. 4, upper center). Meanhorizontal and vertical displacements for the slumpequaled 480 m and 160 m respectively.

1963 FLOOD SIMULATION

For the flood simulation, 10 million tsunami ballsfilled the reconstructed pre-slide topography to the reser-voirs’ 712 m elevation – 134×106 m3 of water in all. Weextracted the wave-driving changes in the elevationwithin the landslide excavation and deposition zones at1s intervals from the calculation of fig. 3. Following theequations in WARD & DAY (2010), we updated thetsunami ball acceleration, position and velocity everyDt=0.05 s and generated a movie frame at 2 or 4 s inter-

vals. Unlike the landslide bits, fluid tsunami balls have nobasal friction lest they get stuck on a slope. The balls dosuffer dynamic drag (velocity squared resistance) how-ever, with Cd=2×10-4/m for balls within the original reser-voir and Cd=9×10-4/m for those balls ejected from thereservoir. The thinking here is that water flowing over-land in thin sheets meets more resistance than watermovements in the deep reservoir. We see below that Cd

limits the velocity of overland flow.Fig. 5 shows the Vaiont flood in 2D map view at

T=00:20, 00:52. 02:00 and 4:00. (Movie at http://es.ucsc.edu/~ward/viaont-wave2d.mov). The circled numbersmeasure flow depths (on previously dry land) or waveheights above still water (in the reservoir) in meters. Thenumber in the thin yellow box lists the volume of waterover the dam up to that time.

⇒T: 0-20s (fig. 5: Frame a): The initial high speedimpact of the slide squeezes reservoir water into a 50 mhigh pile at the east end of the slide zone where the slumpfirst released.

⇒T: 20-50s (fig. 5: Frame b): Water runs up 200 m onthe North slope brushing the Casso Village Site. 40-50 mwaves run to the east and west. The landslide deposit damhas largely formed by now, effectively cutting the reser-voir in two.

⇒T: 1-2min (fig. 5: Frame c): Water overtops the dam atabout T=45 s, tumbles down the canyon, and runs 2000 macross the Piave Valley in about a minute. The leadingelements of the flood race ahead at ~40 m/s. By two min-utes, 12 million cubic meters have passed over the dam.For comparison, the pace of the initial torrent tumblinginto Vaiont Gorge equaled 80 times the rate at which waterpours over Niagara Falls at high flow (See fig. 6, top). Thetowns of Longarone and Pirago at the foot of the falls,


Fig. 5 - Two-dimensional snapshots of the flood simulation at T= 0:20,0:52, 2:00 and 4:00. The orange inundation zone well-matches theobserved trimline (red) on the north slope. The letters (L, P, C, etc.)abbreviate the village names listed in fig. 1. Orange numbers aremeasured at elevations higher than the original reservoir level.

Fig. 6 - (top) Time history of water flow past Vaiont Dam. Red linesshow 30 and 90 times the rate that water runs over Niagara Falls athigh flow, [0.168×106 m3/min]. (bottom) Time history of depth offlooding at 475 m elevation in Longarone.


received the full force of fury. Flood water depth at Lon-garone’s eastern edge (elevation 475 m) jumps from zero to14 m in less than 60 s (fig. 5, bottom). For all the times thatthe phrase «wall of water» has been employed in tsunamiliterature, in this instance the description holds true.

⇒T: 2-4min (fig. 5: Frame d): Water striking the westbank of Piave Valley ponds and divides into north andsouth flows. The northern flow moves up-stream on aslight slope to approach Roggia and Codissago. Waterreaches its peak depth of nearly 20 m in the flatlands infront of Longarone/Pirago at T~3:00 (fig. 6, bottom).Within four minutes, 22 million m3 of water has escaped(fig. 6, top). Much of the remaining 20 million m3 trappedin the western section of the divided reservoir slowlydrains out over the next 20 minutes.

Fig. 7 maps the flood at t=19:08 and shows flood his-tories at Longarone (top yellow box) and five other pointsdown stream. Compared to their onset, flood watersleisurely vacate Longarone – dropping to 4 m depth atT=10:00 and 1 m depth at T=18:00. Locations furtherwest in the town at higher elevations certainly sufferedless inundation and faster draining. Although the theflood’s vanguards spewed out of Vaiont Gorge at ~40 m/s,dynamic friction slows the flow as it washes south downPiave Valley. From fig. 7 we measure flow velocities of13 m/s, two km south of Vaiont Gorge, and 7.5 m/s six kmfurther south. Lacking basal friction, overland flowspeeds of tsunami balls are limited by dynamic drag toVlimit=(g sinQ/Cd)1/2, where g is the acceleration of gravity,Q is the slope and Cd is the dynamic drag coefficient.Toward the south of the Piave Valley, sinQ~10/1600 which,with Cd=0.0009/m, gives Vlimit=8.5 m/s – completely com-patible with the flow speed measured in the simulation.

Fig. 8 pictures the flood in a three dimensional stylelooking eastward into the gorge mouth. (Movie athttp://es.ucsc.edu/ ~ward/vaiont-wave3d(EW).mov). Tohelp visualize the sequence, the topography and waveshave been given considerable vertical exaggeration. Land-

slip on the south slope (T=0.28, Frame A) begins to domereservoir water and directs a surge northward. By T=1:48(Frame B) peak runup everywhere on the northern slopeopposite the slide has already receded. «Backslosh» nowfloods newly deposited landslide material on the southslope. By T=4:28 (Frame C) Longarone has seen the worstand the inundation in north Piave Valley nears its maxi-mum extent. Large seiche waves bounce back and forth


Fig. 7 - Map of the flood extent at t=19:08 and flood histories atLongarone (top box) and five marked locations down stream. Fromthis information, the speed of the overland flow can be determined.

Fig. 8 - 3D view of the flood looking east into the mouth of Vaiont Gorge at T= 0:28, 1:48, 4:28 and 18:20. Numbers in the big yellow box quotethe current kinetic and potential energies. For example, at T=18:20, the landslide and water had lost 7.5×1014J and 6.9×1013J of gravitationalpotential energy respectively. Total kinetic energy of the water is 7.4×1012J. The ability to monitor these quantitative aspects of the landslideand flood provides a reality check on the output and separates physics-based simulations from simple artist conceptions.


along the length of the eastern reservoir. By T=18:20(Frame D) most of the water has slipped from the westernbasin, clearly separated from the surviving eastern por-tion of the reservoir by the landslide dam.

Fig. 9 captures the flood in a three dimensional, per-spective «fly-by» style. (Movie at http://es.ucsc.edu/~ward/Vaiont-FlyBy.mov). Frame A (T=0:36) catches peak northslope inundation at the eastern end of the landslide andthe 40 m wave approaching the dam. Frame B (T=2:30)snaps conditions near peak flood stage at Longarone. Youcan clearly see the 20 m high bulge of water in front ofthe town site. Note too, the large volume of water skirtingthe north and south ends of the dam. At this point, Vaiontgorge has a «Niagara Falls» look but with eighty timesNiagara’s flow rate. The lands on either side of the damstripped to bare rock testify to the torrent (photograph infig. 2B). Frame C (T=5:00) conveys the full impression ofthe Piave Valley flood – 1000 m wide now. Note the eeriesimilarity of this view with the actual photograph in fig. 2C.Frame D (T=12:30) flies us down Piave Valley several kmto the leading edge of the flood. Note the variations in thewater depth as the flow interacts with the sidewalls andriver bottom topography.

ASSESSMENT OF THE FLOOD SIMULATION

How does the flood simulation compare with obser-vations?

Reservoir shore and slope opposite the landslide. Themodel successfully reproduces the inundation between

900 and 950 meters elevation north of the landslide. Thisis no surprise of course, seeing that landslide parameterswere adjusted generally to make this so. We do note thatthe simulation slightly overestimates the inundation nearCasso. The cause of this can be found from the movie ver-sion of fig. 5. Having more than entertainment value,these animations allow the action to be dissected. Forinstance, a close examination of the movie shows that theexcess inundation near Casso resulted from a short lived(1:12 to 1:32) jet of water expelled northward from thechaotic pile of water trapped in front of the dam. Ran-dom events like this are difficult to predict or control,both in simulations and in real life.

Reservoir shores to the east. SEMENZA (1965) mapsinundation to 800 to 750 m elevation along the northshore of the reservoir east of the slide. Model inundation(fig. 5D) successfully tracks the 800 m contour eastwardnearly to Erto where highest run up drops to 750 m. At800 m elevation, Erto escaped the flood, consistent withthe prediction. The initial eastward travelling wave in thesimulation quickly covers the lower ends of the lateralvalleys on the south side of the reservoir, east of the slideand matches the observed trimline there (fig. 2B). Theclosed eastern reservoir sees considerable sloshing afterthe initial wave passes and at any given location, peakinundation may occur much later. Some survivors onsouth shore of the reservoir recount that maximum inun-dation at their homestead happened 2 to 3 minutes afterthe start of the landslide.

Inundation west along the Piave Valley around Lon-garone. The inundation completely devastated lower Lon-


Fig. 9 - Perspective «Fly By» view of the flood at T=0:36, 2:30, 5:00 and 12:30. Number in the yellow box is volume over the dam. Movie athttp://es.ucsc.edu/~ward/Vaiont-FlyBy.mov.


garone. Being scoured out by the flow, even foundationsand terraces of buildings vanished without trace. Theintense erosion around Longarone is consistent with theinitial high speed (~40 m/s) flow across the valley into thetown and incredibly rapid (<60 s) piling-up of water to~20 m depth as it encountered the opposing slope.

Inundation north and south along the Piave Valley.Although the flood ultimately drained south down thePiave Valley, figs. 5, 8 and 9 clearly show how the pilingof water between the mouth of Vaiont Gorge and Lon-garone, deflected and directed some of the later flowupstream. The extent of the northward inundation is sen-sitive to the peak flow rate of the flood and to the tran-sient water depths in the pile. The close match betweenthe observed (fig. 1) and model inundation (orange zonefig. 7) to the north further evidences a successful simulation.

CONCLUSIONS

This article continues the application of tsunami balltheory to simulate water waves and near shore inunda-tion sourced from landslides. Moreover, this work suc-cessfully extends the technique to simulate overland flowsand floods associated with «dam break» situations andseich like oscillations in closed basins.

The 1963 Vaiont landslide and flood was a tragic, butwell studied engineering failure. For the first time, wecapture in three dimensions the full sequence of eventsincluding: the landslide on the south slope, the wave runup on the north slope, the escape of water over andaround the dam, and the flooding of the valley below.Combining both geological and run up information toconstrain landslide dynamics and kinematics, we findthat a slump of dimension and volume generally consis-tent with observations can indeed slip from 100-400 mheight on the south side of reservoir, splash water up to~200 m on the north slope, push 30+ million m3 of waterover the dam and flood the valley below – all as recordedin the happenings of the day.

Being more than just artist’s conceptions, physics-based simulations like these can accept input from a widerange of observational information and they can outputquantitative predictions on many aspects that were not,or could not, be measured. One compelling physicalquantity that emerged from the analysis was the astound-ing rate at which water eloped from Vaiont Reservoir.Effectively for six minutes, the residents of Longarone satat the foot of a violent cascade possessing thirty times theflow of Niagara Falls.

Given the speed, flexibility and modest computationalrequirements of the tsunami ball approach, the methodshould continue to find wide-spread application in land-slide-generated wave, dam break, and flood situations.Perhaps the technique might help to mitigate losses infuture Vaiont style disasters.

APPENDIX A: Tsunami Ball Approach

This article closely follows WARD & DAY (2010) andWARD (2010) who simulated wave runup and inundationfrom the 1958 Lituya Bay Alaska and the 1889 John-stown, Pennsylvania disasters. Simply put, tsunami ballsare pencil-like columns of water gravitationally acceler-ated over a 3-D surface. The volume density of tsunami

balls at any point equals the thickness of the water col-umn there.

Our landslide tsunami simulations involve twostages. The first stage computes a landslide history. Thesecond stage feeds this history into the tsunami ball cal-culation to induce waves and floods. In this partially cou-pled procedure, the landslide affects the water, but notvice versa.

A.1. Tsunami Ball flow chart

The tsunami ball method distills to six flow chart steps.(A) Distribute N tsunami balls over initially wet areas

at initial positions rj with regular spacing DxDy.(B) Assign each ball a zero initial velocity and a

volume V jwater = DxDy H (rj) based on the initial water

thickness at the site H (rj).(C) Evaluate the water surface zwater (rg, t) at time t

on a fixed set of grid points rg (fig. A1)

(A1)

In (A1), V jwater is the water volume of the j-th ball, rj (t)

is the ball’s location at time t, h (rg) is topographic eleva-tion and A (rg, rj (t)) is an averaging function with m-2

units such that when integrated over all (x, y) space

(A2)

Operation (A1) smoothes tsunami ball volume at arbi-trary positions rj (t) to grid positions rg.

(D) Accelerate each tsunami ball for a short durationDt using

(A3)

The rg here is the grid point closest to the ball’s posi-tion, h is the horizontal gradient and zwatersmooth (rg, t) is aversion of (A1) smoothed over time and space.

(E) Update the ball position,

(A4)

ball velocity,

(A5)

and time t=t+Dt.(F) Here you might return to Step (D) several times

keeping the surface fixed at its most recent evaluation(inner loop); or, return to Step (C) to compute a fresh sur-face (outer loop). Regardless if the tsunami ball is inwater or has been tossed onto land, steps (C) to (F) hold.Note that acceleration (A3) includes a dynamic drag fric-tion to control balls that might encounter unreasonablysteep surface gradients and run away.

D

ζ water (rg , t) = Vjwater A (rg , rj (t)) + h (rg )

j=1

N

∑= Hwater (rg , t)+ h (rg )

∫ A (r, ′ r )dr'= 1

v j(t)

t= −g∇hζ smooth

water (rg , t)− Cdv j(t) v j(t)∂

∂

rj +Δ = rj + v j Δ t +Δt2

2

vj

t∂

∂(t t) (t) (t)

(t)

v j(t + ∆t)= v j(t) +∆tvj (t)

t

∂∂



What in the flow chart makes the flood? Floods andwaves get stirred if the underlying topography h(r) in (A1)becomes a function of time

(A6)

where ho(r) is the original value in flow chart step (B) andDh(r,t) is the bottom uplift or subsidence due to a land-slide in this case.

The advantages of a tsunami ball approach to wavegeneration and inundation are three:

(1) Because we track water balls of fixed volume, thecontinuity equation is satisfied automatically. In locationswhere the volume density of balls grows, the water col-umn thickness increases. In locations where the volumedensity drops, the thickness of the water column falls.

(2) The tsunami ball procedure is meshless. Meshlessapplications offer a huge simplification over finite differ-ence/finite element methods in that one can download acoastal DEM and start the calculation immediately withouthaving to worry about mesh density, node locations, etc.

(3) Tsunami balls care little if they find themselves inthe reservoir h (r)>0 or if they have run onto land h (r)<0(fig. A1). Such indifference is made-to-order for inunda-tion applications because it obviates the need for special«dry cell» and «wet cell» behaviors.

Tsunami balls have similarities to wave calculationsusing Smoothed Particle Hydrodynamics: both approachesare meshless; both approaches are Lagrangian in that theyfollow particles; and both approaches derive physical quan-tities by summing over particle properties weighted by di -stance smoothing functions. By considering water columnsrather than spherical particles, the tsunami ball approachcan handle real world-scale problems better than SPH, butat the expense of resolving variations with depth.

A.2. Granular Landslide Simulation

In contrast to existing landslide models for tsunamigeneration (JIANG & LEBLOND, 1993; LYNETT & LIU, 2003;SATAKE, 2007), we build landslides following steps surpris-ingly similar to those in the tsunami ball flow chart above.In fact, tsunami runup and inundation is just a speciallandslide case – a «water landslide» if you will. For Steps

(A) and (B) in a landslide flow chart, the slide bits all haveequal volume and distribute over the landslide area with adensity such to reproduce the prescribed spatial thicknessof the slide mass. The top surface of the landslide and itsthickness is computed in Step (C) again by (A1).

(A7)

In Step (D), the landslide bits accelerate by

(A8)

The first term on the right hand side represents theacceleration of the slide over fixed and smoothed topogra-phy (the basal surface). The second term is the accelera-tion due to the evolving shape of the smoothed slide massitself. We call this the «self-topography force». Self-topog-raphy forces pull apart and flatten landslide masses. Wereplicate the transition between block-like and flow-likebehaviors seen in landslides by easing in the g in the self-topography term over a duration roughly equal to thetime it takes for the mass to move one slide length.Increasing self-topography forces with time correspondsto a decreasing cohesion of the landslide mass as it frag-ments. The only other term in (A8) not present in (A3) isCb, a unitless basal friction.

A.3. Stabilization

Numerical stability is the primary concern in anyapproach that employs granular material, particularlywith respect to evaluating the gradient operators in (A3)and (A8) that drives the balls. Fluid simulations espe-cially, because they have both flow-like and wave-likebehaviors, can run amok rapidly. No single recipe guar-antees stability, but we find that combinations of thethree methods below usually can generate simulationsthat «look right».

(a) Spatial Smoothing. Water and landslide surfaces(A1) and (A7) at grid points rg are the sum of water orlandslide thickness and topographic elevation. Both func-tions need to be spatially smoothed. The fastest means forthis is rectangular smoothing, first applied to all gridrows and then to all grid columns. The q-th smoothedvalue in a grid row or column might be

(A9)

where Gr are raw values in the row or column, W is thehalf width of smoothing and Norm is some normaliza-tion. The q+1-th smoothed value is

(A10)

ζ slide(rg , t) = V slide A (rg , rj (t)) + h(rg )j=1

N

∑

= Hslide(rg , t)+ h(rg )

v j(t)

t= – g∇h ζ smooth

slide (rg , t) – Cd v j(t) v j(t) – gCbv ˆ j (t)

= g∇h hsmooth (rg )– g∇h Hsmoothslide (rg ,t)

– Cd v j(t) v j(t) – gCb j (t)v ˆ

∂

∂

G q =Σq

Norm; Σq = Gr

r= q−w

q+W

∑

h(r) ⇒ h0 (r)+ ∆ h r,t)(

G q+1 =Σq+1

Norm; Σq+1 = Σq + Gq+w +1 − Gq−w


Fig. A1 - Geometry for tsunami ball calculations. Topography h(r)and water or landslide surface z(r,t) are measured positive upwardfrom some arbitrary level.


You can see that each value (A10) derives from theprevious value by only one addition, one subtraction andone division. The number of numerical operations in rec-tangular smoothing is proportional to the number of gridpoints only, and independent of both the number of ballsand the smoothing half width. It takes experimentation toselect an appropriate smoothing width. Smoothing widthfor the topography may not be the same as that for thewater or landslide thickness. The goal is to stabilize thecalculation, not to lose interesting aspects nor add manyartifacts.

(b) Temporal Smoothing. Water Hwater(r, t) and land-slide thickness Hslide(r, t) are also functions of time, sotemporal smoothing helps to damp artifacts. Smoothingany time series F(t) usually means storing many pastvalues of the function and then averaging. If F(t) is alsoa function of space, storage may be overwhelming.One way to smooth in time without storing long-pastvalues evaluates

(A11)

where q is less than one. For t=NDt, it is easy to see that

(A12)

and that the sum of the weights

(A13)

Evaluating (A12) needs all past values of F,whereas (A11) needs just the one current value. Youchoose q in (A11) to give the desired half-life t1/2 to thesmoothing

(A14)

Different q might be used for smoothing the fluidmass than for smoothing the landslide mass. We employboth spatial and temporal smoothing to generate thesmoothed surfaces z smooth for use in (A3) and (A7).

(c) One Way Gravity. «One-way» gravity is yet anothermeans to keeps accelerations (A3) under control. Oneway gravity picks the value of g in these equations ateach location and time based on the current velocity vj (t)of the tsunami ball being accelerated and the gradientof the surface slope z smooth (rg, t) at the nearest gridlocation

(A15a,b)

In words, if acceleration –g hz smooth (rg, t) opposesball velocity vj (t), then gravity acts in full force. If acceler-ation –g hz smooth (rg, t) reinforces velocity vj (t), then frac-tional gravity e×g, acts. If (A15b) is persistently met overseveral time steps, the tsunami ball accelerates to termi-

nal velocity soon enough, whereas reaction to short livedstimulus is less. Herein lies the temporal smoothing.One way gravity applies only to the water bits, not thelandslide bits.

APPENDIX B. Quicktime movie links to the simulationspresented in this article

Landslide:http://es.ucsc.edu/~ward/vaiont-slide.mov

Flood in Map View:http://es.ucsc.edu/~ward/vaiont-wave2d.mov

Flood in 3D View looking East:http://es.ucsc.edu/~ward/vaiont-wave3d(EW).mov

Flood in 3D View looking North:http://es.ucsc.edu/~ward/vaiont-wave3d(NS).mov

Flood in 3D Perspective «Fly By»:http://es.ucsc.edu/~ward/Vaiont-FlyBy.mov

Composite Movie with Texthttp://es.ucsc.edu/~ward/vaiont-pro.mov

ACKNOWLEDGEMENT

We thank Pierfrancesco Burrato of the Istituto Nazionale diGeofisica e Vulcanologia, Rome, for supplying the 10 m DEM of theVaiont Region and two anonymous reviewers.

REFERENCES

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JIANG L. & LEBLOND P.H. (1993) - Numerical modeling of an underwa-ter Bingham plastic mudslide and the waves which it generates.J. Geophys. Res., 98, 10313-10317.

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MULLER L. (1964) - The rock slide in the Vaiont valley. Rock Mechanicsand Engineering Geology, 2, 148-212.

MULLER L. (1968) - New considerations on the Vaiont slide. RockMechanics and Engineering Geology, 6, 1-91.

SATAKE K. (2007) - Volcanic origin of the 1741 Oshima-Oshima tsunamiin the Japan Sea. Earth Planets Space, 59, 381-390.

SEMENZA E. (1965) - Sintesi degli studi geologici sulla frana del Vaiontdal 1959 al 1964. Mem. Mus. Tridentino Sci. Nat., 16, 52 pp.

SEMENZA E. & MELIDORO G. (1992) - Proceedings of Meeting onthe 1963 Vaiont Landslide, Ferrara 1986. University of Ferrara,Ferrara.

SEMENZA E. & GHIROTTI M. (2000) - History of the 1963 Vaiont slide:the importance of geological factors. Bulletin of EngineeringGeology and the Environment, 59, 87-97.

D

D

Fsmooth(t) = qF(t)+ (1− q)Fsmooth(t − ∆t)

Fsmooth(N∆t) = q(1− q)n F([N − n]n= 0

N

∑ ∆t)

q(1− q)n

n= 0

N → ∞

∑ = 1

q = 1− (1/ 2)∆t / t1/2

–∇hζ smooth(rg ,t)• v j(t) < 0; then g = 9.8 m/s

–∇hζ smooth(rg ,t)• v j(t) > 0; then g = ×9.8 m/s e



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Phys., 3, 222-249. http://es.ucsc.edu/~ward/papers/Tsunami_Balls.pdf.

WARD S.N. & DAY S. (2010) - The 1958 Lituya Bay Landslide and Tsu-nami – A tsunami ball Approach. J. Earthquake and Tsunami. Inpress, http://es.ucsc.edu/~ward/papers/lituya-R.pdf

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Manuscript received 15 April 2010; accepted 2 August 2010; editorial responsability and handling by D. Pantosti.



the 1963 landslide and flood at vaiont reservoir italy. a tsunami

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