13.3 The Malpasset dam disaster
13.3.2 Comments and discussions by other experts
A close analysis of the official French report shows that the experts emphasize two phases in the collapse: one of slow progressive deformations of the rock foundations and straining of the dam shell, the second of spectacular, nearly instantaneous failure of dam and foundations. The report does not say why the disaster occurred and does not point to any cause which makes the site and rock of Malpasset different from that of any other.
Shortly after the disaster, several well-known experts delved into the problem and they came up with several physical explanations. All these tentative explanations have to be examined carefully from two angles: do they explain the failure of the rock and of the dam? do they explain why no failures similar to Malpasset have occurred anywhere else?
(1) K. Terzaghi (1962a) commented as follows:
The left abutment of this dam appears to have failed by sliding along a continuous seam of weak material covering a large area. A conventional site exploration, including careful examination of the rock outcrops and the recovery of cores from 2 in boreholes by a competent driller, would show - and very likely has shown - that the rock contained numerous joints, some of which are open or filled with clay.
From this data an experienced geologist could have drawn the conclusion that the site is a potentially dangerous one, but he could not have made any positive state- ment concerning the location of the surface of least resistance against sliding along such a surface.... All foundation failures that have occurred, in spite of competent subsurface exploration and strict adherence to the specifications during construc- tion, have one feature in common. The seat of the failure was located in thin weak layers, or in 'weak spots' with very limited dimensions.
None of the methods of exploration, including those used by mining and petro- leum engineers, provides adequate information concerning such minor geological details.
Figure 13.6 clearly shows how the rock foundation was ruptured along two inclined faults, one upstream the other downstream of the dam, nearly
at right angles to each other. Furthermore, the rock on the left-hand bank of the river at the level where the rupture occurred is densely fissured. A detailed study of the rock made after the failure indicated a treble system of microfissures, microfractures and macrofractures. This confirms Terzaghi's opinion to some extent. But on closer analysis the facts are not in agreement.
The left-hand, V-shaped concrete abutment of the dam was extremely strong. It failed at the very last moment when the dam shell had already suffered severe strains, and when the thrust on it had already altered its direction and increased far more than normally expected.
The two upstream and downstream faults and the clayish material filling them has been carefully analysed in the Research Laboratory of the ficole Polytechnique in Paris. The friction factor of this material was found to be not larger than tan"1 <£max = 60° and not lower than tan"1 ^u l t = 45° which is too high to justify Terzaghi's hypothesis of rock sliding along a weak fault.
Even when this material is in a wet state, its friction factor remains too high for possible rupture by shearing along the faults. It is likely that cohesion of the material was very low; the rupture of the dam was not caused by this particular type of rock weakness. The left bank finally ruptured, as described, after something else - still to be discovered - had occurred.
(2) Laginha Serafim at the Thirteenth International Meeting of the Austrian Society of Rock Mechanics in Salzburg (5 October 1962) gave the results of model tests he had made to find local rock weakness. In fig. 13.8 a local rock
fissure
Fig. 13.8 Assumed dam failure by weak rock and tensile fissure of the shell (Serafim).
mass with low modulus of elasticity is shown along the dam foundation.
According to Serafim, under such circumstances high tensile stresses may develop in a direction parallel to the foundation, near the area of rock weakness.
The French examined the problem of rock elasticity and rock plasticity with great care. Electricite de France carried out tests inside two galleries near the dam site on the left abutment. The most characteristic data are reproduced in table 13.1.
These figures are exceedingly low for gneiss and the ratios of highest to lowest values about 3 to 1 or 2-5 to 1. The French concluded that the ratio
The Malpasset dam disaster 393 Table 13.1. Malpasset gneiss, left bank, Modulus of elasticity Er and
modulus of total deformation Et in kg/cm2.
1st gallery 2nd gallery
E
1st cycle 3200 to 17 000 5000 to 18 000
r
3rd cycle 4000 to 18 000 6000 to 25 000
Et total 3rd cycle 2300 to 7300 1200 to 8000
n = EcjEr was larger than 6*5 and probably less than 25. The Commission accepted a value Er = 10 000 kg/cm2 as probable but did not exclude a value Er = 5000 kg/cm2. A trial-load calculation has shown the dam to be safe even for this low value Er = 10 000 kg/cm2.
The conclusions of the Commission are indirectly confirmed by many model tests and other mathematical dam analysis which have proved that thin and very thin arch dams, designed to rule, built in sound concrete and anchored in homogeneous rock (even rock with a low modulus of elasticity), have a great reserve of strength and a high safety factor for normal hydro- static loads. Rupture of such dam models occurred only when they were heavily overloaded (Semenza, Oberti, Rocha, Serafim et al.). The most striking example of how tough these dam shells are is the disaster of the Vajont Gorge rock slide. This very thin arch dam, designed by Semenza, withstood a tremendous overload; it suffered only very minor damage even when overtopped by a deep wave.
The tests for the Tang-e-Soleyman dam in Iraq were made in Portugal (Lisbon). A weak layer of rock E on the left abutment was represented on the model. When overloading the model, failure occurred along the left abutment. The lines of failures were as shown in fig. 13.9. The line of rupture
Fig. 13.9 Assumed dam failure by weak rock and shear fracture of the rock.
(a) Fissure caused by bending; (b) shear fracture in weak rock; (c) shear fracture;
id) gliding of the abutment.
'a9 by compression or bending, which in the case of homogeneous rock occurs vertically along the crown of the dam, is now displaced towards the left abutment. There is a clear inclined shear fracture b in the rock, paral- lel to the inclined left-hand abutment and another shear fracture c to
the right, in a nearly horizontal direction (in one of the tests this shear fracture was inclined upwards to the right). There is a marked similarity between the rupture of the Tang-e-Soleyman dam model and the Malpasset failure which definitely confirms the theory that final failure at Malpasset occurred on the left abutment, the inclined shear fracture going not through the concrete but through the rock as the weakest element of the combined system.
But there are still important unexplained points. If the Malpasset design had been examined by experienced dam designers who had had an idea that there was a local weakness in the rock on the left abutment, their reaction would have been to point out the unusual strength of the left- hand V-shaped concrete abutment (which was in fact partly sheared through before the rock finally gave way). A local weakness of the rock, like a low modulus of elasticity suggested by Serafim or a low shear strength of a thin fault as suspected by Terzaghi, would be compensated by the flexibility of the thin shell-shaped dam. Over 500 arch dams and thin-arch dams still stand undamaged, proving the basic soundness of similar designs, even when built on indifferent rock. (Two Italian thin-arch dams withstood earthquakes without damage (Glover, 1957).)
The lines of rupture observed at Malpasset compared to those on the model of the Tang-e-Soleyman dam again confirm the assumption that failure occurred on the left side but do not explain why it happened. As time went on, more experts began to suspect a possible detrimental action of water percolating through the macrofractures of the rock and tried to estimate the danger of uplift forces.
(3) Serafim, Jaeger, Packer and Londe. Pacher (1963) and his Japanese colleagues mathematically analysed water percolation round Kurobe IV dam and checked it on models. Jaeger (19616, 1964a, b) in several papers, mentioned the problems arising from differences in rock permeability due to rock grouting under dams. Londe (1965) developed a new analytical method for calculating the resulting uplift under a dam (first submitted to the Eighth Congress on Large Dams, Edinburgh, 1964, then to the first Congress on Rock Mechanics, Lisbon, 1966).
In a paper published shortly before his death Terzaghi (19626) made a second suggestion regarding a possible cause of failure of the Malpasset dam.
In an introductory remark he writes:
If water leaks out of a reservoir formed by a concrete dam, the greatest cleft water pressure develops in the joints of the rock at the foot of the slope downstream from the toe of the dam. If a slope failure should occur as a result of cleft water pressures it would start at the foot of the slope.
Terzaghi's point could be made clearer if instead of cleft water pressure, he had introduced the idea of a pressure gradient inside the rock foundation (fig. 13.10).
The Malpasset dam disaster 395
Fig. 13.10 Blow-out of rock under dam foundation as suggested by Jaeger, 19616, 1964a; Terzaghi, 19626; Pacher, 1963; and Londe.
After discussing conditions at the toe of a gravity dam, Terzaghi continues:
If the dam is a thin-arch dam, the cleft-water pressures are also greatest in the proximity of the toe of the dam at the foot of the slope. However, they are very much greater than the corresponding pressures near the toe of a concrete gravity dam of equal height, because the base of an arch dam is much narrower. Furthermore the downstream toe of an arch dam rises along the slopes of the valley in a downstream direction and enters the area occupied by a potential slide scar. Finally, also in the proximity of the foot of the slope the effects of the cleft-water pressures combine with those produced by the thrust of the arch which has a component in the down- stream direction and thus tends to push the rock out of the slope.
Terzaghi refers then to the Malpasset failure. He comments on the accom- panying sketch (fig. 13.10) as follows:
It can be seen that a slide initiated by a blow-out at the foot of the slope would deprive the upper portion of the base of the dam of its support. Hence if a blow-out occurs in the rock supporting an arch dam the consequences are likely to be cata- strophic. The failure of Malpasset Dam was probably started by such a blow-out.
Fortunately the development of cleft water pressures within the rock downstream from arch dams can be avoided by adequate drainage.
Jaeger (19616, 19666), analysing similar conditions, warned about the danger of tensile stresses which forcibly occur in the rock at shallow depth under the upstream dam heel. These are too often neglected; only compression and shear stresses along the dam base are calculated by most experts. He mentions that tensile strains have a tendency to spread beyond the area obtained by theoretical analysis of a continuous foundation, making condi- tions worse than foreseen (1966).