The entry says that the number 700 came from a model, and that the model answered the question it was asked. This piece is about the model itself, as its author described it: the report that Augusto Ghetti, director of the Institute of Hydraulics of the University of Padua, signed on 3 July 1962 for SADE, Esame su modello degli effetti di un’eventuale frana nel lago-serbatoio del Vajont, “Examination on a model of the effects of a possible landslide in the Vajont reservoir”. It is twelve typed pages with two tables and fourteen photographs, and it was, the parliamentary commission’s minority wrote, kept “jealously guarded” in Ghetti’s offices on SADE’s behalf. The quotations are in my translation.

What it was for

The report opens with the commission. “The Hydraulic Construction Service of SADE proposed in the first months of 1961 to carry out, at the ‘E. Scimemi’ Hydraulic Models Centre at Nove, a research on a hydraulic model, to examine the effects of a possible feared landslide in the Vajont reservoir, as regards the flooding of the banks and the overflow at the crest of the dam from the consequent phenomena of unsteady motion in the water of the basin.” The landslide “is located on the left bank, a short distance from the dam, and consists in the movement of a conspicuous mass of loose ground with rocky debris, for some time already in a state of precarious equilibrium, which has probably been disturbed by the filling of the reservoir, carried out up to about level 650, after the completion of the dam (August 1960)”. The moving bank had two parts, upstream and downstream of the Massalezza torrent, on fronts of 1,000 and 800 metres; the mass ran from about 600 metres to 1,200, “with a maximum depth on the sliding plane estimated at about 200 m”; and it was “geologically well distinct from the rock on which the dam is founded”, 75 metres from its downstream limit, so that no disturbance of the dam itself was to be expected. What was to be feared was the wave, “whose size will be commensurate with the volume of ground that will slide into the lake, and with the law in time according to which such a collapse will occur”.

So the whole lake was built. Its surface ran some five kilometres from the dam, with the side valleys of the tributary streams. The scale was 1:200, “which was the maximum conveniently possible”, and it was chosen because at that scale the waves could be trusted: by the similarity of Froude, which governs the motion of water under gravity, “without appreciable disturbing intervention, at least in the first phases of the phenomenon, of the factors of viscosity or surface tension”. A length of 200 metres in nature was a metre in the model; a time of fourteen seconds in nature, the square root of 200, was a second. The model was built in the open in the summer of 1961 at the institute’s model centre at SADE’s power station at Nove: 29 metres long, up to 12 wide, its rim 1.80 metres above the ground, “realised in masonry structure, with an internal surface reproducing the real topographical configuration, making use of contour lines and profiles”, and the dam “reproduced in its particulars”.

The gravel

The problem was the landslide. “The problem of reproducing in the model the natural landslide event, in the most faithful way possible so as to draw reliable deductions from it, could be solved according to two different approaches, which were both followed.”

The first approach was to try to make the slide happen in the model as it would in nature, “by the action of gravity and provoked, as it may be held could occur in nature, by the yielding of the steep slope that overhangs the water surface in the landslide zone”. But the real slope was rock on clay, and “it would have been exceedingly difficult to reproduce a sliding of visco-plastic character proper to clayey ground, and so the simplest hypothesis was made, under certain aspects also geologically plausible, that it was a matter of incoherent material (ground of slope debris)”. In its place “rounded gravelly material (diameter 8 to 10 mm) was used in the model, with the aim of reducing internal friction as far as possible”. Ghetti was explicit that this changed the physics: “Although, as regards similarity, the intervention of this factor certainly modifies, and in a way that cannot be evaluated, the gravitational aspect of the phenomenon, it may be held that the latter still turns out to be prevalent, and so the velocities and times of descent can be determined in the ratio of one to the square root of 200 between model and original.”

To make the gravel slide it was laid on “a prepared plane, consisting of a boarded surface clad in sheet metal”, which could be set at different angles; in the tests, 30 and 42 degrees. The gravel was shaped on top “according to the irregularities of the slope”. At the foot it was held by “flexible metal nets, tied with ropes in tension that could be rapidly slackened, thus setting the landslide in movement with a velocity depending on the action of gravity and of friction”. That was the first series.

The second approach “is based on the concept of not being able to obtain in the model a reliable similarity of the landslide phenomenon, and so of relying on the forecasts that the geological study can give in that sense, trying to make the event occur in the model in a manner corresponding to those forecasts”. The geologists expected the slope to move on a curved, “concoid” surface, and gravel will not slide on a curve. So the gravel was laid on a carefully reproduced copy of that surface, and the slide was “made to occur artificially by towing the mass”. The towing gear was “rigid sectors immersed in the gravel, moved by means of ropes by a tractor with an interposed block for the regulation of the velocity”. In that way “the effects of the landslide could be examined, transferring the data from the model to the original in the ratio of one to the square root of 200, for different velocities of descent, and the result could be measured against the value held reasonably most probable”. Because “the possible landslide may involve only one of the two zones, or in one it may occur with some delay with respect to the other”, the gear was built to move either half on its own. In the second series too the foot was held by nets, slackened as the towing began, and the tow was stopped “when the foot of the landslide reached the opposite bank within the lake”.

Each full run moved “about 15 cubic metres” of gravel. The surge was recorded by cameras, by three float gauges and by readings of the highest excursion at nine other points along the banks, and a basin below the dam caught and measured whatever went over; the report calls the lines joining the highest marks the limits of the “foreseeable flooding”.

The runs

Table A lists the first series: five runs, all from the lake full at 722.50 metres, “that is with the reservoir full”. Two were on the plane at 30 degrees. The upstream part of the mountain, let down first, took a time “related to the original of 184 seconds”; the downstream part, let down afterwards into a lake already partly filled by the first, took 156. Two more were at 42 degrees, with times of 84 and 90 seconds. On the steeper plane the volume of gravel that came to rest below the lake’s surface was about the same, ten million cubic metres in nature’s terms for the first half and seven and a half for the second, but the peak overflow doubled, to 26,450 cubic metres a second, “and this in relation to the greater velocity of descent”. A fifth run let down the downstream part alone, in 85 seconds, “with a very conspicuous effect as regards the overflowing discharge, which reached 30,480 cubic metres a second with a surge over the crest of more than 22 metres”; 2.7 million cubic metres of water went over in 178 seconds. Table B lists the second series, seventeen runs, numbered 6 to 22, “all made with continuous movement of descent of the landslide mass, artificially obtained as said above; only in runs 8 and 9 was a jerky movement provoked, meaning by it to represent a discontinuous fall in successive phases”. From the full lake the two halves towed in succession, in 210 and 127 seconds, gave “limited effects, much lower than those of the corresponding runs 4 and 5 of natural descent”; the jerky runs gave a little more. The downstream half alone, towed in 113 seconds into an empty lake, gave 9,270 cubic metres a second. The worst of the second series came when the upstream half was towed first and the downstream half after an interval timed so that it fell “at the most unfavourable moment, that is when in the landslide zone the new rise of level showed itself, after the lowering consequent on the initial surge”: 20,280 cubic metres a second, a surge of 15.9 metres at the dam and 22 at the point opposite, 27.5 metres at a point 430 metres from the dam, and ten million cubic metres of water over the crest in 990 seconds, “an average discharge of 10,000 cubic metres a second”.

Then the lake was lowered. “Passing now to the runs carried out from an initial level in the reservoir below the maximum, one has that with the filling level of 700 metres the variations of level in the reservoir for the runs of partial descent of the landslide (downstream part) do not reach the overflow of the dam, not even considering the very reduced time of 63 seconds (run 18). In this case, which is the most severe, a surge of 20.6 to 20.7 metres is reached at the dam position and at position 2.” With the two halves in the most unfavourable succession, “the greatest effect of surge is at position 1 with 31.4 metres, while at the dam there is a surge of 27 metres which determines a limited overflow (maximum discharge 2,280 cubic metres a second)”. From 670 metres, the downstream half alone in 61 seconds gave a surge of 21 metres at position 2 and nothing over the dam.

The conclusion

The summary that follows is the part of the report that was read. It begins by saying that the dam itself is not in question: the slide’s downstream limit lay more than 75 metres from the abutment, in rock “compact and consistent and well distinct, also geologically, from the said mass”, so that “absolutely no disturbance of a static order to the dam is to be feared from the occurrence of the landslide, and so only the effects of the wave surge in the lake and of the overflow at the crest of the dam in consequence of the fall are to be considered”. Then it says what the model had to assume. “The forecasts of the manner of the landslide event are as uncertain as could be from the geological point of view.” The mass was “constituted of incoherent material and slope debris for the most part”; its slope was steepest in the lower part above the lake, “and a yielding of this part would probably be followed by the collapse of the upper mass”; and it was unlikely to come down along its whole front at once, “the better-founded hypothesis being that one or the other of the two zones upstream or downstream of the Massalezza torrent will come down first, and that this collapse will be followed, after a shorter or longer interval, by that of the remaining zone”.

“Such being the evaluations and the uncertainties in the forecast of the natural phenomenon, an attempt was made in the model to explore a numerous variety of cases”, with the mass as wholly incoherent gravel falling under gravity on planes of different inclination, and as partly cohesive material towed at different speeds on the geologists’ surface. From the full lake, in the first series, “the descent of the two landslide zones was made to occur with a natural fall in times of the order of 3 minutes and 1.5 minutes (related to the original). The most relevant effects are seen for the fall of the downstream zone; it is in any case a matter of velocities of descent somewhat high with respect to the possible forecasts.” The slower gave an overflow of about 12,000 cubic metres a second and a surge of 11.5 metres at the dam; the faster, over 30,000 and more than 22 metres. In the second series, with fall times of one to three and a half minutes and intervals of two and a half to ten and a half, the fastest gave over 20,000 cubic metres a second, 16 metres at the dam and 27.5 at 430 metres from it; at two minutes, under 14,000 and 12.6 metres; the downstream half alone in two minutes, a little over 9,000 and about 10 metres. “These data seem sufficiently indicative of the magnitude that the wave phenomenon can present even in the most unfavourable forecasts of the fall of the landslide mass.”

From 700 metres, “the most unfavourable event, that is the fall of the downstream zone in one minute following a previous fall of the upstream zone, causes barely, with a surge of 27 metres near the dam (and a maximum of 31 metres at 430 metres from it), an overflow a little over 2,000 cubic metres a second. Starting from the level of 670 metres, even with the fastest landslide the surge is very limited and well below the crest.” And so: “It therefore seems possible to conclude that, starting from the reservoir at maximum filling, the descent of the foreseen landslide mass only in catastrophic conditions, that is occurring in the exceptionally reduced time of 1 to 1.5 minutes, could come to produce a peak overflow of the order of 30,000 cubic metres a second and a wave surge of 27.5 metres; merely by doubling this time the phenomenon attenuates to below 14,000 cubic metres a second of overflow and 14 metres of surge. Lowering the level of the initial filling, these effects of surge and overflow reduce rapidly, and already the level of 700 metres above the sea may be considered of absolute safety in respect even of the most catastrophic foreseeable landslide event.”

The last paragraph asks for more. “It will in any case be opportune, in the foreseen continuation of the research, to examine on the model suitably extended the effects, in the bed of the Vajont and at the confluence with the Piave, of the passage of flood waves of a size equal to that indicated above for the possible overflows at the dam. In that way surer indications will be had of the possibility of permitting even higher fillings in the reservoir, without danger of damage below the dam in the event of a landslide.” The research was not continued. The minority of the parliamentary commission found that the directing committee of the Nove centre had decided on 30 April 1962, before the report was signed, that “at least for the moment” no research was to be made on the propagation of a flood wave below the dam, and recorded that SADE had nonetheless wanted “to know the distribution of a wave coming from the Vajont at the town of Longarone”.

What was taken from it

Three things in the report stand beside what happened.

The first is the time. Ghetti’s natural runs fell in 84 to 184 seconds of nature’s time, and he called even these “somewhat high velocities of descent with respect to the possible forecasts”; his towed runs ran from 61 seconds to three and a half minutes, and the one-minute fall of the lower half was his catastrophic case. On 9 October 1963 the whole mass, both halves together, crossed the valley in less than a minute, at 20 to 30 metres a second by the Corps of Engineers’ estimate. The model’s fastest run, 61 seconds for half the mountain from 670 metres, lay at the edge of what the tractor could do; the mountain lay beyond it.

The second is the shape of the fall. The report’s worst cases were two halves falling one after the other; its safety at 700 metres was computed for the lower half falling a minute after the upper. “It is to be considered,” the commission’s minority wrote, “that this catastrophic event was foreseen by Professor Ghetti always starting from the hypothesis that it was a matter of two distinct landslides.” The mass that fell was one, 1.7 kilometres across, and the ministerial experts wrote that it kept “a formidable unity”.

The third is the sentence that travelled. The commission found that the report was known to the Ministry’s men though never formally sent, and it found, in the government assistant’s report of 8 October 1963, the model reduced to one line: “from tests carried out on a model it has resulted that with the maximum filling and with the instantaneous collapse of the landslide the consequent wave would reach a height of 25 metres”. Nothing in Ghetti’s tables says 25 metres; the nearest figures are 22.1 and 27.5. The majority recorded “a reason for perplexity” that the model had given 700 as the safe limit and the lake had been authorised to 715. The courts indicted Ghetti in 1968 with the engineers and the officials, and the appeal court in 1970 acquitted him “for not having committed the act”.

Sources

• Augusto Ghetti, Esame su modello degli effetti di un’eventuale frana nel lago-serbatoio del Vajont. Relazione e fotografie, Istituto di Idraulica e Costruzioni Idrauliche dell’Università di Padova, Centro modelli idraulici “E. Scimemi”, research N/10 for SADE, Padua, 3 July 1962, twelve pages with two tables and fourteen photographs. Read in full in the scan posted by ProgettoDighe; the quotations are in my translation. progettodighe.it
• Commissione parlamentare d’inchiesta sul disastro del Vajont, Relazione finale, Senato della Repubblica, IV Legislatura, Documento n. 76-bis, 15 July 1965: the majority on the model, the visits and the “perplexity”; the minority on the directing committee’s decision of 30 April 1962, the two-landslide hypothesis, the Rizzato affair and Longarone; Bertolissi’s report of 8 October 1963. certifico.com
• A. J. Hendron Jr. and F. D. Patton, The Vaiont Slide, Technical Report GL-85-5, US Army Corps of Engineers, 1985, Volume II, Appendix G: Edoardo Semenza’s account of the model, the gravel and the bricks. archive.org
• Wikipedia (Italian), “Disastro del Vajont,” for the appeal court’s acquittal of Ghetti on 3 October 1970. it.wikipedia.org