There is no reason for the creep of 250 000 000 m3 of rock masses to have been continuous in time and space over a period of three and a half years. As it is not possible to explain the Vajont slide with the dynamics of a continuous progressive flow of masses, an attempt will be made to develop a theory of discontinuous flow of rock masses.
14.7.1 The progressive failure of the rock masses; the formation of a thick sliding zone
It has been amply explained in previous chapters that progressive small displacements of crystals and grains during shear tests cause a drop of the shear strength in most sedimentary rocks. It is acceptable to compare this test result obtained on rock material to rock masses.
Borings have clearly established that there was no real 'gliding surface', but a 'gliding zone probably several metres thick' (Miiller, 1968). The friction factor within such a zone must have been very low. Such an assump- tion is physically acceptable. It is also required for mathematical reasons. If it is accepted that the tan (cf>0 + A<£0) was less than 0-176 (<£0 + A<£0 < 10°) as average value during the slide, the tan^Oa must have been locally and temporarily even well below this very low value.
A dynamical explanation 415 It is very tempting to think that percolating water penetrating in the rock fissures has been instrumental in lowering the friction factor. It can hardly be so, because as will be seen, the first rupture to occur - on the steeper region of the slopes - was located well above the water level in the reservoir. Further- more, the correlations between water-level variations and rock slides were so immediate that slow percolation of interstitial water cannot be an explana- tion. Finally, it has been proved (Muller, 1964) that there was no correlation between rainfalls and rock displacements.
14.7.2 Deep-reaching weakening of the rock masses; seismic wave measurements
General worsening of rock conditions was proved by seismic wave measure- ments by Professor Caloi (1966). According to him, over a short period, the longitudinal wave velocity in the rock masses had decreased from about 5000 or 6000 m/s to only 2500 or 3000 m/s. Caloi reported that already between 1959 and 1960 the fracturing process had penetrated into deeper- lying rock levels owing to increasing pressure and yielding of the rock. The depth of broken rock layers at the surface, which in 1959 was about 10 mto 20 m, was as thick as 50 m to 70 m or even 150 m in 1960.
These facts are clues and proof of the far-reaching deterioration of rock masses years before the catastrophe.
14.7.3 Measured creep velocities
This deterioration and physical weakening of the rock was not uniform.
There is one diagram published by Muller (1964) which is most informative.
It has been reproduced in fig. 14.9. Rock displacements were measured in boreholes at different depths. On the boreholes located in the upper range of the creeping rock mass, the diagram shows that the rock displacements are parallel and all identical whereas on the borehole located near the lower end of the creeping mass of rock the velocities are highest at the top and nil at the bottom. In fluid mechanics, and in rheology, parallel uniform velocities represent a flow where there is no internal viscosity or turbulence and with low wall friction. On the other hand, the unequal velocity distribution, as measured in the borehole at the downstream end of the creeping rock masses, represents a flow where some energy is being destroyed. There is no doubt that these most general theories of rheology are also valid for the creeping displacement or flow of large rock masses (C. Jaeger, 1956).
Figure 14.10 represents Muller's impression of the disruption of rock masses at the lower edge of the rock-creeping movement. Rocks were continuously falling in the gorge by 'extreme rotation'. This confirms the previous figure.
14.7.4 The discontinuous flow or creep of rock masses
The theory of 'progressive failure' should be developed a step further by introducing the idea of 'discontinuous flow'. Discontinuous flow is well
indicate the velocity distribution. (Y) outline of rock layers; (/) La Pozza; (M) zone of predominant driving forces; (AO zone of predominant resisting forces;
(C) zone of progressive failure; (D) probable slide surface; (P) compression zone;
(Q) tension zone; (R) distribution of velocities; (5n) exploratory boreholes; (Z) exploration tunnel (after Miiller, 1964).
Fig. 14.10 Vertical section through the north front of the rock slide at the 'Pinnacolo'. Above, side view; below, scheme of movement; Q, tension; S, external rotation; T, relative movements (after Miiller, 1964).
A dynamical explanation 417 known in fluid mechanics (C. Jaeger, 1956). An extremely interesting example of a continuous flow becoming progressively discontinuous can be observed on rivers carrying floating ice (Jaeger, 1968tf, b).
A river like the Saint Lawrence, Canada, has been observed over a very long period; ice and water levels and ice thickness being measured at regular intervals. The whole thawing process can be reproduced on a model. Such a model - 500 ft long - has been built in the Lasalle Research Laboratory, Montreal, the horizontal scale being 1:600, the vertical scale 1:150. Water levels and velocities can be correctly reproduced on this model and checked in nature at the equivalent locations. This same model has been used to represent the breaking-up of ice in the Spring. The floating ice was represented by pieces of plastic material, about the correct density and average size of floating blocks of ice. The plastic material was chosen because it has no surface tension when floating on water. At the upstream end of the model the discharge of water and of plastic material is maintained constant over a certain period of time. A varying regime is rapidly established downstream with floating pieces of plastic accumulating in those water channels where ice would normally build up. Some areas of the river where the flow is slow and where the water is covered with a thin sheet of ice, are reproduced on the model by a thin layer of plastic over the water. The depth of the floating plastic cover on the model can be checked against the real depth of ice. The accumulation of floating material at narrow passages causes the water level to rise in the upstream area. Potential energy is being accumulated, and the level rises until the shear strength along the river bed is exceeded. The barrier breaks down and a wave of water and ice progresses rapidly downstream on the model as in nature. This unsteady discontinuous flow is typical of the accumulation of potential energy and momentum behind an obstacle and the explosive character of the flow when the forces are relieved.
Figures 14.9 and 14.10 clearly show that a similar explanation is acceptable for the first phase of the slow sliding masses along the slopes of Mount Toe.
Sometime in 1960 an M-shaped perimetral crack occurred high up along the slopes of Mount Toe (up to elevation 1400 m); the slow-sliding masses in the steep upper reaches, where the angle a of the slopes was probably steeper than the tan <f>Oi of the friction factor (tan a > tan </>Ol) started moving along a 'sliding zone' which acted as a lubricated smooth surface. According to fig.
14.9 (zone /) high pressures were being developed by the upper zone of the slide on the lower zone, pressures which also explain the rotation of the masses nearest to the gorge. Geologists observing the movements at the surface of the slide could not have recognized what had happened deeper inside the mass.
14.7.5 The two-phase slide
It was suggested in 1965 (Jaeger) that the sliding movement consisted of two phases: a first phase was similar to a 'visco-plastic discontinuous rock
creep, or flow' which was the one observed by the geologists from 1960 up to the night of 9 October 1963. The second phase was a short-lasting brittle fracture in the lower part of the slide; along the less inclined branch of the chair-like sliding surface. This type of flow was suggested by fig. 14.9 but also later confirmed by some geological diagrams published by Broili (1967) and Miiller (1968). On these diagrams it can clearly be seen that the slide, which in the upper reaches occurred parallel to the strata, cut right through the strata, suggesting a brittle fracture in the lower part rather than a sliding movement.
This short-lasting brittle fracture is now confirmed by Caloi, who com- mented in a private report about seismic wave recordings that a brittle fracture occurred first, which lasted 60 to 70 seconds, immediately followed by the slide which for the whole slide area lasted 20 seconds.
The basic assumption concerning the two phases (Jaeger, 1965a, 19686, 19696), one visco-plastic during which forces and momentum were concen- trated, the second, a nearly instantaneous brittle fracture, is now positively confirmed by Caloi's remark.