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The Malpasset Dam failure
Engineering Geology, 24 (1987) 331--338
331
Elsevier Science Publishers B.V., Amsterdam -- Printed in The Netherlands
THE MALPASSET DAM F A I L U R E
P. HABIB
Laboratoire de MSchanique des Solides, Ecole Polytechnique, ENSM Paris, ENPC (France) (Accepted for publication December, 1986)
After the failure of Malpasset Dam a large number of studies, analyses and tests were undertaken, among which was a detailed study of the abutment rock by the Solids Mechanics Laboratory of the Ecole Polytechnique, b y order of consulting engineers of Bureau d'Etudes A. Coyne et J. Bellier. We were left to conduct all and any tests we felt appropriate, and we in fact examined practically all the classical mechanical properties of the rock (density, elasticity modulus, Poisson ratio, shear strength, sound wave transmission speed, creep, etc.) and the correlations between them. The rock in the left abutment did not appear unusual: samples revealed an elasticity modulus of around 45,000 MPa and standard 36 mm diameter (10 cm 2 cross-sectional area) core samples revealed an entirely acceptable compressive strength (uniaxial compression test) of between 25 MPa and 50 MPa. It soon appeared, however, that the natural fissuring of the rock was a fundamental element in its behaviour. Only later was it realized that the behaviour of the rock was exceptional. I am n o t at all certain that the natural fissuring of such a rock would be examined t o d a y in the same manner as it was then, b u t the studies carried o u t were full of revelations. We first observed a scale effect and a scattering o f uniaxial compression test results. Table I shows the average value m of compressive strength and the standard deviation s for core samples of different diameters (d) taken from the same location (test series on the least resistant samples taken on the site). A systematic series of tests on different rock types from dispersed sources (from different locations in the abutments and foundation at Malpasset, from totally different regions and from the foundations of other French dams) allowed us to prove the existence of correlations between the degree of fissuration of rocks and the following three phenomena: (1) scale effect in uniaxial compression tests; (2) scatter of results; and (3) the significant effect of effective stress on permeability. This last p h e n o m e n o n proved to be extremely useful for the study of rock fissuration. Before describing our findings, I shall first briefly outline the general technique we developed to identify the effect on permeability: radial permeability tests were carried out using long hollow cylindrical samples (Fig.l). The test equipment allows the direction of seepage to be reversed, 0013-7952/87/$03.50
© 1987 Elsevier Science Publishers B.V.
332 TABLE I Gneiss from Malpasset left abutment (sample MIII 2 A) d=10mm
Rc= {sm=52'TMPa19.0MPa
d=36mm
Rc= {m=25"OMPa10.0MPa
d=60mm
Rc= {sm=18'0MPa6.0MPa
See text for explanation of symbols.
'jj
IIlll P
till
p
I
V V
CROSS SECTION
Fig.1. Standard sample for radial seepage test. Flow net.
w
333
although the formula used to determine the permeability coefficient k is the same for b o t h directions, i.e.: k -
Q
2•DWp
log R
where Wp = differential pressure between inner radius r and outer radius R, Q = rate of infiltration, D = length of sample. This formula does not take account of the disturbance to edges and supposes seepage to strictly follow the radial plane, which is an acceptable approximation in view of the length of the samples (see Fig.2). Contrary to what one should obtain with a porous, permeable material, the values measured on this equipment are different for flow in different directions, the permeability ratio being greater for flow from the inside to the outside. This can be explained quite simply: when the seepage is convergent, i.e. towards the inner radius, the stresses applied to the rock tend to close the fissures, whereas divergent flow causes tensile stresses which open them. It must be understood that Darcy's law is in no way contradicted b y this and that its validity has in fact been confirmed b y direct measurement.
Fig.2. Standard sample for radial seepage test.
334 What these very simple tests did prove though, is the variation of the permeability coefficient with effective stress, and this also has been proven by different and more sophisticated tests. Fig.3 shows the overall results of radial permeability tests, i.e., the variation of k with respect to the difference between internal and external pressures. The results are practically reversible for convergent radial permeability tests, i.e., for effective compressive stress. During divergent flow tests the samples break up due to strain if the pressure differential reaches a critical point. This yield point depends on the degree of fissuring and the tensile strength of the rock, but was never less than 0.1 MPa for the samples in question. The "sensitivity" of permeability was therefore expressed by the following formula:
K cm/s ill
Convergent radial seepage I
Diver}~ent radlal
: 0 P /"
seepage
l
10.7
flI" ~ . 8
%-
10.9
L r~
P bar I~
10-lo 2~
10
0
10
20
30
40
50
Fig.3. Radial seepage. Sample: Malpasset M I I I 2.
50
70
80
go
100
335
s=
k(--0.1 MPa) k(5 MPa)
This is an easy measurement to make, and is uncomplicated, precise and consistent. We have used it systematically since its development, on the request of Electricit6 de France, when testing the rock at the sites of numerous projected or existing dams. The sensitivity s defines a degree of fissuring which enables determination of the extent to which the fissures and porosity are individually responsible for permeability: for a sintered metal, s = 1; for sound and slightly fissured rock, s is between 3 and 10; a value between 10 and 20 identifies rock of average quality; and a value above 20 indicates an extremely fissured rock. The gneiss at Malpasset is the most fissured material we have encountered on this scale with an average value of s = 100 (with some measurements well over 1000). Beyond the simple quantitative evaluation of the degree of fissuring of rock (confirmed by other experiments), this test revealed the existence of a p h e n o m e n o n that we had not imagined, and that is the enormous variation of rock permeability ratios as a function of effective stress. The rock from the Malpasset abutments provides an exceptional example of this. The full originality of these findings must be stressed: it is true that, in soil mechanics, clays exhibit a variable value k for a varying void ratio (permeability test carried out in conjunction with consolidation tests), but this variation is slight in comparison with the natural distribution of the permeability quality of different rocks and with their anisotropy, so slight in fact that such experimental results have never been used in calculations. In the case o f Malpasset rock, on the other hand, the permeability variations are such that the calculation of seepage and underpressure in homogeneous rock appears not only unsuitable and therefore useless, but dangerous: correlative calculation of s and k (which was unheard of at the time) would appear to be the very least that should have been done, but in fact the magnitude of permeability coefficient variation does mean that good approximations are quite sufficient. For example, the force applied obliquely downstream to the rock by the dam foundation can first be estimated and then the stress analysis made: for static loads this provides the effective stress. If the permeability ratio variation with respect to effective stress is greater than 10, the rock mass can be regarded as impermeable and the corresponding underpressure can be determined. Of course an iterative calculation would be better, but a general appreciation of the foundation stability can be obtained in this way. The observations made on Malpasset rock then led us to investigate all the transfer qualities of the rock and their correlation with fissures and stress. These investigations covered the permeability tensor in relation to the effective stress tensor, the speed at which ultrasonic waves are transmitted and damped (both longitudinally and transversally), heat transfer, electrical conductivity, etc. These studies lead to the development of a model of the fissured rock and brought about considerable advances in rock mechanics.
336
All of this has taken me well beyond the confines of the intended field, i.e., the problems posed by the Malpasset disaster, but it is certain that the variation of a rock's permeability ratio as a function of the applied stress was an u n k n o w n p h e n o m e n o n before the elaborate and systematic analysis undertaken as a result of the accident was made. The existence of fissures in rock masses was however known by a large number of researchers and engineers, but it entered into their work almost exclusively in connection with mechanical stability; when dealing with seepage everybody drew flow nets in accordance with the classical Laplace outlines o f flow potential. It is true too that the permeability of a rock mass is not the same as that of a sample and t h a t here too account must be taken of the effect of the scale of the bodies examined. The permeability of a rock mass is much greater, for it involves other fissure networks than those in the rock matrix -- joints, diaclases, fault systems, etc. -- which cannot be appreciated when blocks are chosen for laboratory analysis since they compose the very discontinuities delimiting the blocks themselves, that is unless a very special procedure is undertaken to remove samples. There is also every reason to believe that there is a very close relationship between the fissuring of a rock sample and t h a t of the rock mass generally. I, for example, have observed there to be a correspondence between the direction of fissures in the quartz crystals and the diaclases of certain granites to be found in France. The same correspondence was evident in the anisotropy of sound wave propagation. Quite independently of any correspondence of course, the same causes have the same effects: the stress applied by a dam in its abutments will close the fissures running roughly normal to the direction of stress and thus reduce the permeability of the rock in the surrounding area; if water flows in the fissures according to Darcy's law, there are pressure losses whose effect is widespread (which y e t again modifies the distribution of stress) and this equivalent force must be borne in mind when assessing the general equilibrium of the foundation. It is obviously in the least permeable areas that the pressure losses will be highest, and if the reduction in permeability is great these areas will behave as a cutoff. If the rock is only slightly fissured in relation to the porosity, the stress pattern beneath an a b u t m e n t may barely be modified. If the reverse is the case, the stress pattern can be fundamentally disturbed, which was what happened at Malpasset. ANSWERS TO QUESTIONS
1. Is the state o f the art in rock mechanics sufficient to estimate the deformability o f rock masses in the foundations and abutments o f arch dams? In my opinion the state of the art is quite up to providing an acceptable estimation of the deformability of a rock mass, even if nothing is ever really entirely sufficient! It is certain that the effective prognostication of deformation from in-situ mechanical tests such as jack tests is not good and often gives underestimated moduli since the reliability of their results depends on
337 the amount of fracturing caused b y the preparation of the test, and, particularly in tunnels, by the use of explosives: in the case of Malpasset, measurements taken in tunnels gave values of between 800 and 1600 MPa, which are significantly lower than the values obtained at precise locations on samples with electrical resistance extensometers. Borehole dilatometer testing usually overestimates the elasticity modulus because the stresses applied in tests are greater than those existing in nature. But the general scope of short- and long
There are n o t many programs for analyzing stress due to external influences and the weight of the dam itself which include the effects of seepage, despite the fact that that would pose no major mathematical problems, nor require excessive computer time, at least if one remained within the field of linear elastic behaviour. If we go b e y o n d that into the fields of plasticity and viscoelasticity, we are obviously delving into the realms of research at the moment: the cost of such analysis would be exorbitant for routine design analysis. That said, however, it is nonetheless true that experimental evaluation of the relation between the stress tensor and the permeability tensor b y in-situ tests has not to my knowledge been attempted and would certainly run up against enormous difficulties. On the other hand, as I mentioned previously, if reductions of more than 10 on the permeability ratio appear in a given area, these areas are practically equivalent to impermeable rock and the pressure losses are concentrated there: it then becomes almost pointless to conduct exhaustive analysis of correlated pore pressures. It should be remembered t o o that stress analysis of a fissured rock is itself very complicated. The analysis put forward b y Maury (1970) for stratified rock, using photoelastic models, and models using photoelastic material divided into blocks which allow fissures in two directions, demonstrate that the distribution of stresses is n o t an easy thing to appreciate: the assumption
338
of linear elastic analysis is a very rough approximation which can give results bearing very little relation to the real situation. REFERENCES Bernaix, J., 1967. Etude g4oteehnique de la roche de Malpasset. Doctoral thesis for University of Paris, Dunod, Paris. Maury, V., 1970. M~canique des milieux stratifies. Doctoral thesis for University of Paris, Dunod, Paris.
331
Elsevier Science Publishers B.V., Amsterdam -- Printed in The Netherlands
THE MALPASSET DAM F A I L U R E
P. HABIB
Laboratoire de MSchanique des Solides, Ecole Polytechnique, ENSM Paris, ENPC (France) (Accepted for publication December, 1986)
After the failure of Malpasset Dam a large number of studies, analyses and tests were undertaken, among which was a detailed study of the abutment rock by the Solids Mechanics Laboratory of the Ecole Polytechnique, b y order of consulting engineers of Bureau d'Etudes A. Coyne et J. Bellier. We were left to conduct all and any tests we felt appropriate, and we in fact examined practically all the classical mechanical properties of the rock (density, elasticity modulus, Poisson ratio, shear strength, sound wave transmission speed, creep, etc.) and the correlations between them. The rock in the left abutment did not appear unusual: samples revealed an elasticity modulus of around 45,000 MPa and standard 36 mm diameter (10 cm 2 cross-sectional area) core samples revealed an entirely acceptable compressive strength (uniaxial compression test) of between 25 MPa and 50 MPa. It soon appeared, however, that the natural fissuring of the rock was a fundamental element in its behaviour. Only later was it realized that the behaviour of the rock was exceptional. I am n o t at all certain that the natural fissuring of such a rock would be examined t o d a y in the same manner as it was then, b u t the studies carried o u t were full of revelations. We first observed a scale effect and a scattering o f uniaxial compression test results. Table I shows the average value m of compressive strength and the standard deviation s for core samples of different diameters (d) taken from the same location (test series on the least resistant samples taken on the site). A systematic series of tests on different rock types from dispersed sources (from different locations in the abutments and foundation at Malpasset, from totally different regions and from the foundations of other French dams) allowed us to prove the existence of correlations between the degree of fissuration of rocks and the following three phenomena: (1) scale effect in uniaxial compression tests; (2) scatter of results; and (3) the significant effect of effective stress on permeability. This last p h e n o m e n o n proved to be extremely useful for the study of rock fissuration. Before describing our findings, I shall first briefly outline the general technique we developed to identify the effect on permeability: radial permeability tests were carried out using long hollow cylindrical samples (Fig.l). The test equipment allows the direction of seepage to be reversed, 0013-7952/87/$03.50
© 1987 Elsevier Science Publishers B.V.
332 TABLE I Gneiss from Malpasset left abutment (sample MIII 2 A) d=10mm
Rc= {sm=52'TMPa19.0MPa
d=36mm
Rc= {m=25"OMPa10.0MPa
d=60mm
Rc= {sm=18'0MPa6.0MPa
See text for explanation of symbols.
'jj
IIlll P
till
p
I
V V
CROSS SECTION
Fig.1. Standard sample for radial seepage test. Flow net.
w
333
although the formula used to determine the permeability coefficient k is the same for b o t h directions, i.e.: k -
Q
2•DWp
log R
where Wp = differential pressure between inner radius r and outer radius R, Q = rate of infiltration, D = length of sample. This formula does not take account of the disturbance to edges and supposes seepage to strictly follow the radial plane, which is an acceptable approximation in view of the length of the samples (see Fig.2). Contrary to what one should obtain with a porous, permeable material, the values measured on this equipment are different for flow in different directions, the permeability ratio being greater for flow from the inside to the outside. This can be explained quite simply: when the seepage is convergent, i.e. towards the inner radius, the stresses applied to the rock tend to close the fissures, whereas divergent flow causes tensile stresses which open them. It must be understood that Darcy's law is in no way contradicted b y this and that its validity has in fact been confirmed b y direct measurement.
Fig.2. Standard sample for radial seepage test.
334 What these very simple tests did prove though, is the variation of the permeability coefficient with effective stress, and this also has been proven by different and more sophisticated tests. Fig.3 shows the overall results of radial permeability tests, i.e., the variation of k with respect to the difference between internal and external pressures. The results are practically reversible for convergent radial permeability tests, i.e., for effective compressive stress. During divergent flow tests the samples break up due to strain if the pressure differential reaches a critical point. This yield point depends on the degree of fissuring and the tensile strength of the rock, but was never less than 0.1 MPa for the samples in question. The "sensitivity" of permeability was therefore expressed by the following formula:
K cm/s ill
Convergent radial seepage I
Diver}~ent radlal
: 0 P /"
seepage
l
10.7
flI" ~ . 8
%-
10.9
L r~
P bar I~
10-lo 2~
10
0
10
20
30
40
50
Fig.3. Radial seepage. Sample: Malpasset M I I I 2.
50
70
80
go
100
335
s=
k(--0.1 MPa) k(5 MPa)
This is an easy measurement to make, and is uncomplicated, precise and consistent. We have used it systematically since its development, on the request of Electricit6 de France, when testing the rock at the sites of numerous projected or existing dams. The sensitivity s defines a degree of fissuring which enables determination of the extent to which the fissures and porosity are individually responsible for permeability: for a sintered metal, s = 1; for sound and slightly fissured rock, s is between 3 and 10; a value between 10 and 20 identifies rock of average quality; and a value above 20 indicates an extremely fissured rock. The gneiss at Malpasset is the most fissured material we have encountered on this scale with an average value of s = 100 (with some measurements well over 1000). Beyond the simple quantitative evaluation of the degree of fissuring of rock (confirmed by other experiments), this test revealed the existence of a p h e n o m e n o n that we had not imagined, and that is the enormous variation of rock permeability ratios as a function of effective stress. The rock from the Malpasset abutments provides an exceptional example of this. The full originality of these findings must be stressed: it is true that, in soil mechanics, clays exhibit a variable value k for a varying void ratio (permeability test carried out in conjunction with consolidation tests), but this variation is slight in comparison with the natural distribution of the permeability quality of different rocks and with their anisotropy, so slight in fact that such experimental results have never been used in calculations. In the case o f Malpasset rock, on the other hand, the permeability variations are such that the calculation of seepage and underpressure in homogeneous rock appears not only unsuitable and therefore useless, but dangerous: correlative calculation of s and k (which was unheard of at the time) would appear to be the very least that should have been done, but in fact the magnitude of permeability coefficient variation does mean that good approximations are quite sufficient. For example, the force applied obliquely downstream to the rock by the dam foundation can first be estimated and then the stress analysis made: for static loads this provides the effective stress. If the permeability ratio variation with respect to effective stress is greater than 10, the rock mass can be regarded as impermeable and the corresponding underpressure can be determined. Of course an iterative calculation would be better, but a general appreciation of the foundation stability can be obtained in this way. The observations made on Malpasset rock then led us to investigate all the transfer qualities of the rock and their correlation with fissures and stress. These investigations covered the permeability tensor in relation to the effective stress tensor, the speed at which ultrasonic waves are transmitted and damped (both longitudinally and transversally), heat transfer, electrical conductivity, etc. These studies lead to the development of a model of the fissured rock and brought about considerable advances in rock mechanics.
336
All of this has taken me well beyond the confines of the intended field, i.e., the problems posed by the Malpasset disaster, but it is certain that the variation of a rock's permeability ratio as a function of the applied stress was an u n k n o w n p h e n o m e n o n before the elaborate and systematic analysis undertaken as a result of the accident was made. The existence of fissures in rock masses was however known by a large number of researchers and engineers, but it entered into their work almost exclusively in connection with mechanical stability; when dealing with seepage everybody drew flow nets in accordance with the classical Laplace outlines o f flow potential. It is true too that the permeability of a rock mass is not the same as that of a sample and t h a t here too account must be taken of the effect of the scale of the bodies examined. The permeability of a rock mass is much greater, for it involves other fissure networks than those in the rock matrix -- joints, diaclases, fault systems, etc. -- which cannot be appreciated when blocks are chosen for laboratory analysis since they compose the very discontinuities delimiting the blocks themselves, that is unless a very special procedure is undertaken to remove samples. There is also every reason to believe that there is a very close relationship between the fissuring of a rock sample and t h a t of the rock mass generally. I, for example, have observed there to be a correspondence between the direction of fissures in the quartz crystals and the diaclases of certain granites to be found in France. The same correspondence was evident in the anisotropy of sound wave propagation. Quite independently of any correspondence of course, the same causes have the same effects: the stress applied by a dam in its abutments will close the fissures running roughly normal to the direction of stress and thus reduce the permeability of the rock in the surrounding area; if water flows in the fissures according to Darcy's law, there are pressure losses whose effect is widespread (which y e t again modifies the distribution of stress) and this equivalent force must be borne in mind when assessing the general equilibrium of the foundation. It is obviously in the least permeable areas that the pressure losses will be highest, and if the reduction in permeability is great these areas will behave as a cutoff. If the rock is only slightly fissured in relation to the porosity, the stress pattern beneath an a b u t m e n t may barely be modified. If the reverse is the case, the stress pattern can be fundamentally disturbed, which was what happened at Malpasset. ANSWERS TO QUESTIONS
1. Is the state o f the art in rock mechanics sufficient to estimate the deformability o f rock masses in the foundations and abutments o f arch dams? In my opinion the state of the art is quite up to providing an acceptable estimation of the deformability of a rock mass, even if nothing is ever really entirely sufficient! It is certain that the effective prognostication of deformation from in-situ mechanical tests such as jack tests is not good and often gives underestimated moduli since the reliability of their results depends on
337 the amount of fracturing caused b y the preparation of the test, and, particularly in tunnels, by the use of explosives: in the case of Malpasset, measurements taken in tunnels gave values of between 800 and 1600 MPa, which are significantly lower than the values obtained at precise locations on samples with electrical resistance extensometers. Borehole dilatometer testing usually overestimates the elasticity modulus because the stresses applied in tests are greater than those existing in nature. But the general scope of short- and long
There are n o t many programs for analyzing stress due to external influences and the weight of the dam itself which include the effects of seepage, despite the fact that that would pose no major mathematical problems, nor require excessive computer time, at least if one remained within the field of linear elastic behaviour. If we go b e y o n d that into the fields of plasticity and viscoelasticity, we are obviously delving into the realms of research at the moment: the cost of such analysis would be exorbitant for routine design analysis. That said, however, it is nonetheless true that experimental evaluation of the relation between the stress tensor and the permeability tensor b y in-situ tests has not to my knowledge been attempted and would certainly run up against enormous difficulties. On the other hand, as I mentioned previously, if reductions of more than 10 on the permeability ratio appear in a given area, these areas are practically equivalent to impermeable rock and the pressure losses are concentrated there: it then becomes almost pointless to conduct exhaustive analysis of correlated pore pressures. It should be remembered t o o that stress analysis of a fissured rock is itself very complicated. The analysis put forward b y Maury (1970) for stratified rock, using photoelastic models, and models using photoelastic material divided into blocks which allow fissures in two directions, demonstrate that the distribution of stresses is n o t an easy thing to appreciate: the assumption
338
of linear elastic analysis is a very rough approximation which can give results bearing very little relation to the real situation. REFERENCES Bernaix, J., 1967. Etude g4oteehnique de la roche de Malpasset. Doctoral thesis for University of Paris, Dunod, Paris. Maury, V., 1970. M~canique des milieux stratifies. Doctoral thesis for University of Paris, Dunod, Paris.