13.3 The Malpasset dam disaster
13.3.3 Fundamental research on rock permeability and
(1) Stability of the foundation rock masses. The most decisive attack on this vital problem of the Malpasset failure was made by a team of French engineers who worked consistently over many years to discover what detri- mental effects water percolation has on dam foundations.
Habib (1968) and Bernaix (1966) have systematically investigated the correlations between the Darcy coefficient of permeability k, the rock stresses and the behaviour of different types of rocks. They examined different limestones, sandstones, marls and gneisses and showed that the coefficient k for most sandstones and similar rocks does not vary with the state of stress, k being about the same for compressed rock and rock under tensile stresses.
The same will occur with most rocks where the voids are spherical. On the contrary, in microfissured and specially in microfractured rocks, k values depend on the state of stress. When such rock samples are put under tensile stress, they are far more pervious than when the same sample is compressed.
The k value can vary from 1000 to 1 depending on the stresses.
This is particularly relevant for schists and gneiss. The Malpasset gneiss proved to be the worst of all rocks tested by Bernaix in Paris. A new percola- tion test, introduced by him, is used to classify rocks which would be dangerous types for use as dam foundations (see section 4.12).
Krsmanovic and others have studied the stress distribution in models of rock masses built up by parallelepipedal blocks of rock, which cannot transmit tensile stresses in a direction perpendicular to the block faces.
These have shown that the distribution of compression stresses in such a 'fissured half-space' is very different from that calculated in a continuous half-space (Boussinesq, 1885). There is a high concentration of compression stresses under the thrust load acting on the surface of the half-space formed by parallelepipedal blocks, whereas the classical theories assume a lateral spreading of the compression stresses.
Let us now assume that the foundations of a thin-arch dam are anchored on a highly fissured and fractured gneiss. The gneiss samples may have a relatively high crushing strength. Because of the fissuration of the rock masses, and depending on the direction of the fissures, there will be a high stress concentration under the dam in the direction of the main thrust. If the rock mass is not already fissured, tensile stresses may develop near the dam heel and progressively penetrate deeper and deeper into the rock. This is what must have happened at Malpasset, remembering how the rock on the left bank, where the foundation finally gave way, was markedly worse than the rock on the right bank where a deep fissure, running along the heel of the dam, can still be seen as proof of what happened all along the dam. The concentration of compression stresses compacted the macrofissured gneiss under the dam, which became impervious. Rock under the dam heel and upstream of it, being under tensile stresses or already fissured, became very pervious. Dam designers very often fail to investigate conditions deep within the rock mass. But a new concept is now being developed (Pacher, Jaeger, Londe et al.) whereby the true forces acting on the rock foundations due to water seepage in the rock faults are analysed. When calculating these forces, the real values of the coefficient of water seepage k in the different parts of the rock masses must be introduced.
Fig. 13.11 A typical cross-section through the left abutment of the Malpasset dam: (a) upstream block of rock alone; (b) downstream block of rock alone;
(c) the two blocks combined. (1) Resultant thrust, uplift neglected; (2) triangular uplift on foundations down to point P where pressure is nil; (3) triangular pressure down to P, half pressure at D, nil at N; (4) full hydrostatic pressure down to P9
triangular pressure from P to AT (after Mary, 1968).
Londe and Bernaix (1966, 1967) applied these basic ideas to the stability analysis of the Malpasset dam, assuming first a uniform k value for the rock masses, secondly a k value depending on the stresses in the rock. To determine these stresses the conventional Boussinseq analysis had been abandoned in favour of a stress distribution of the type obtained for fissured rock. The ideas of Bernaix and Londe are backed by Mary in his authoritative book on arch dam failures (1968).
The basic idea of these calculations is shown in fig. 13.11 where two typical stability conditions for 'no uplift' and 'full uplift' are analysed.
Assuming conventional conditions for homogeneous rock, the Malpasset dam would be stable. Applying the new basic concepts to the same dam there is a possibility for the foundation rock under the dam to slide along one of the major rock faults. The rupture of the rock occurred in a way similar to the one described by Terzaghi but for reasons which he did not suspect.
Summarizing many years of effort and research, it can now be said that the geologists who mentioned that the gneiss was microfissured had, without knowing it, pointed to the main weakness of the foundation rock.
(2) The rock fissure along the dam heel. A few experts have pointed to the rock fissure which follows the upstream heel of the dam, on the right bank, and wondered why it was not mentioned in the Commission's report. A series of recent publications and reports to Congresses emphasize the danger of tensile stresses in the rock on the upstream side of concrete dams of all types.
Mary (1968) supplied some interesting information about the displace- ments of the dam foundation, mainly on the right side of the dam centre.
The displacement of the base of the dam measured between July 1958 and July 1959 had been far greater than calculated (fig. 13.12). The dam had a
Fig. 13.12 Deformations of the Malpasset dam before rupture. Broken line:
measured deformations. Solid line: calculated deformations. See fig. 13.5 for reference points D-L (after Mary, 1968).
The Malpasset dam disaster 399 double movement of rotation; one around its right abutment and another simultaneously around the dam crest on a line slightly above the crest.
This rotation caused an unforeseen displacement of the foundation and it could have been noticed as early as July 1959, but it is even more apparent
100m
80
60-
40- (b)
50 100 cm (a)
Fig. 13.13 Displacements of fix points, (a) Displacements; (b) levels above the sea.
Broken line: average displacements; solid line: joint H(after Mary, 1968).
m 60
JO 40 30
LR = 105 m
|;;:.M
2] y 4
! / 6
1
1
1.
1 1
^R — 1
1 5
6 , 105 m
7~
X
|
j 1 c
• • ' I 1 x
'1
= 105 m
= 105 m
Fig. 13.14 The Malpasset dam: rock fracture along the dam heel, right bank.
(1) Natural rock surface; (2-3) probable depth of excavation; (4) rock surface after failure; (5) blocks of concrete; (6) rock fracture; (7) trench or gallery; (8) borehole;
(a) rock fracture; (b) mud; (c) fissure (after Mary, 1968).
on the concrete plots measured after the disaster (figs. 13.13,14). It is obvious that this displacement must have caused, at an early stage and long before rupture, the opening of a fissure 10 mm to 20 mm wide on the upstream side of the dam under varying hydraulic pressure. The water levels were 87-30 m in 1958 and 94-10 m in 1959, the top level of 98-50 m was reached on the day of the disaster when the displacements shown on figs. 13.5 and 13.13 caused failure.
Such conditions were obviously dangerous, and it can be said that by July 1959 the rock foundations had already been weakened all along the periphery of the dam on the right wing and probably on the left wing too.
This weakening is confirmed by the fact that, during the rupture, the whole right wing rotated around the right abutment, the crown of the dam, in river axis, showing at its base a final displacement of 820 mm. According to Mary, this caused a widening of the upstream fissure in the rock. The downstream lip of the gap is now 10 cm lower than the upstream lip, because of the movement of the dam shell around its crest. It is vital to stress here that this double rotation was geometrically possible only if the left abutment was still in place. The rupture of the left abutment and the final collapse of the dam occurred after the foundation had been badly damaged along the whole periphery of the shell.
Thin-arch dams have an astonishing reserve of strength against rupture:
the case of the Idbar dam has been dealt with in a previous chapter. Two thin-arch dams, the Moyie dam (Idaho) and the Lanier dam (North Carolina) completely lost their left abutments, which were washed away by flood waters, but the dam shells did not collapse. The left abutment of a third dam, the Frayle, was severely damaged but the dam still stands. Comparing this information with what happened at Malpasset it can reasonably be assumed that there must have been some special weakness there. The upstream fracture of the rock had substantially weakened the whole structure and it was probably an important cause of the final rupture.
The Commission of French experts assumed the failure to have occurred in two phases: A slow deformation of the dam during one or two weeks before the final rupture. Then the formation of an active arch within the dam with a concentration of the thrust at its two ends which caused the left V-shaped abutment to slide and the sudden collapse of the dam. Mary largely agrees with this interpretation putting the weight on the Londe- Bernaix hypothesis.
A slightly different description of the dam rupture can now be suggested, which must have occurred in several phases:
(1) A slow build-up of water pressures in the mass of gneiss and fissura- tion of the rock upstream of the dam.
(2) The slow progressive opening of a 10-mm to 20-mm gap along the dam heel, and from July 1958 to July 1959 a progressive displacement of the dam foot and rotation of the dam shell around its crest.
Final comments 401 (3) Dangerous conditions all along the dam foundations; mainly on the left side.
(4) Then in rapid succession: the displacement of the dam foot increased, reaching in plan view 820 mm in river axis (fig. 11.5); at the same time the whole dam shell was rotating round the dam crest and around a point on the extreme right of the shell, this double rotation is proof that at this moment the dam was still a 'shell' and that the left abutment was still there as a fixed point, it seems that only such a double rotation describes the move- ment of the shell correctly. Then an active arch was formed within the shell.
Because the concrete shell was then more or less loose from the solid rock foundation on all its periphery, a tremendous thrust was transferred to the still-standing, left abutment.
(5) A blow-out occurred on the rock mass on the left bank and the left concrete abutment slid causing collapse of the shell. This blow-out occurred in a way similar to the one described by Terzaghi but for reasons and under conditions not suspected by him.