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A test of the law of effective stress for crystalline rocks of low porosity
Int. J. Rock Mech. Min. Sci. Vol. 7, pp. 123-124. Pergamon Press 1970. Printed in Great Britain
DISCUSSION Discussion of W. F. BRACE and R. J. MARTIN'S Paper A Test of the Law of Effective Stress for Crystalline Rocks of Low Porosity* by B. LADANYI'~
THE validity of the principle of effective stress which is so generally accepted for highly porous materials such as soils, becomes much less obvious when rocks of low porosity are concerned. For the latter, in fact, as shown by SKEMPTON [1] the principle cannot be used in its original form proposed by TERZAGHI [2] but has to be modified to include the effect of solid intergranular contact. The experimental evidence on the pore pressure behavior of solid materials of low porosity is, however, still very scarce, and any addition to it is particularly welcome. In this respect, the experimental results shown in the Paper by Brace and Martin are very interesting and represent a valuable contribution to the rock mechanics literature. They show very clearly that the difference between the applied and induced pore pressure in the rock specimen depends on a number of factors including the length of drainage path, rock permeability, fluid viscosity, and strain rate. In soil mechanics terminology, the tests carried out by the authors at different strain rates covered apparently the whole range, from the completely drained tests, below what the authors call "the critical strain rate", over partially drained tests, in the intermediate range, to essentially undrained tests at higher strain rates. On the other hand, as expected, the results show that the effect of pore pressure practically disappears when, owing to the phenomenon of dilatancy, the stress in the pore liquid becomes tensile and attains the tensile strength of the liquid, causing the well-known phenomenon of cavitation. According to the results shown in the Paper and summarized in Fig. 5, this apparently happened both in constant applied pore pressure tests at relatively high strain rates (upper shelf in the dotted curve in Fig. 5), and in saturated rock samples tested at atmospheric pressure, which after the pore liquid cavitated, behaved as if they were tested dry. In soil mechanics, the cavitation phenomenon has been studied more in detail in relation with the undrained strength of dense sands [3, 4], where its occurrence and effect could reasonably well be predicted. In triaxial tests with saturated rock specimens, on the contrary, the occurrence of cavitation may be much more difficult to predict, since it depends, not only on the applied back-pressure level, drainage conditions, fluid viscosity, and the applied rate of strain, but also on such uncontrollable factors as the velocity of unstable crack propagation, and the size and continuity of the resulting crack pattern. Nevertheless, when looking at the results shown in the Paper from the soil mechanics viewpoint, one is tempted to conclude that the rocks tested by the authors did not show pore pressure behavior much dissimilar from that normally found in some very dense soils. Or, in other words, even if the true pore pressure within the sample was not measured, many * Int. 3". R o c k M e c h . M i n . Sci. 5, 4 1 5 4 2 6
(1968).
t Department of Mining Engineering, University of Montreal, Canada. 123
124
DISCUSSION
aspects of the results indicate that the rocks in the tests behaved quite well in accordance with the principle of effective stress, as it is understood in soil mechanics. It, therefore, comes quite as a surprise to see that, from the same test results, the authors arrive at the conclusion that the law of effective stress is valid only at a very slow strain rate, but ceases to hold as soon as a "critical strain rate" is exceeded. After a second look, however, one finds that this is only a matter of definition. While in the Introduction of the Paper the authors define the effective stress quite correctly as "the difference between the total normal stress active on any plane through the solid and the pressure of fluids in the pores", in the rest of the paper they seem to follow quite a different definition, implying that the effective stress is the difference between the total applied normal stress and the fluid pressure, applied directly at the external surface of the specimen within the jacket, and kept constant during the test. Now, while the results obtained by the authors quite apparently substantiate the validity of the law according to the first definition, which takes into account any strain-induced pore pressure variation within the sample, the law quickly breaks down if the second definition neglecting this variation is adopted and applied to partially drained and undrained tests. The second definition, which is sometimes encountered in geologic literature, does not seem, however, to offer any advantages over the original one proposed by TERZAGHI [2] and mentioned by the authors in the Introduction. In fact, the second definition can only have a limited application when considering very slow deformation processes such as encountered in geology. In engineering rock mechanics problems, on the contrary, adopting the second definition would inevitably lead to confusion. It is a well-known fact that a great part of the development of soil mechanics has been made possible by an early and proper understanding of the principle of effective stress. It is therefore considered of utmost importance that in the field of rock mechanics, as well, a proper and unique definition of the effective stress be adopted and recognized as soon as possible. Moreover, in the pore pressure research of rocks, the large amount of experimental evidence on the pore pressure behavior of soils, accumulated during nearly forty years of soil mechanics research, may prove to be quite a valuable source of information, at least as a starting point for a similar work in rock mechanics. REFERENCES 1. SKEMP'IX)NA. W. Effective Stress in Soils, Concrete and Rocks, Proceedings of the Conference on Pore Pressure and Suction in Soils, pp. 4-16, Butterworths (1960). 2. TERZAOnIK. The Shearing Resistance of Saturated Soils, Proceedings of the First InternationalConference on Soil Mechanics, Vol. I, pp. 54-66 (1936). 3. BISHOPA. W. and ELDING. Undrained triaxial tests on saturated sands and their significance in the general theory of shear strength. G~otechnique 2, (1) 13-22 (1950). 4. SEEDH. B. and LEE K. L. Undrained strength characteristics of eohesionless soils. Proc. Am. Soc. cir. Engrs 93, (SM6) 333-360 (1967).
DISCUSSION Discussion of W. F. BRACE and R. J. MARTIN'S Paper A Test of the Law of Effective Stress for Crystalline Rocks of Low Porosity* by B. LADANYI'~
THE validity of the principle of effective stress which is so generally accepted for highly porous materials such as soils, becomes much less obvious when rocks of low porosity are concerned. For the latter, in fact, as shown by SKEMPTON [1] the principle cannot be used in its original form proposed by TERZAGHI [2] but has to be modified to include the effect of solid intergranular contact. The experimental evidence on the pore pressure behavior of solid materials of low porosity is, however, still very scarce, and any addition to it is particularly welcome. In this respect, the experimental results shown in the Paper by Brace and Martin are very interesting and represent a valuable contribution to the rock mechanics literature. They show very clearly that the difference between the applied and induced pore pressure in the rock specimen depends on a number of factors including the length of drainage path, rock permeability, fluid viscosity, and strain rate. In soil mechanics terminology, the tests carried out by the authors at different strain rates covered apparently the whole range, from the completely drained tests, below what the authors call "the critical strain rate", over partially drained tests, in the intermediate range, to essentially undrained tests at higher strain rates. On the other hand, as expected, the results show that the effect of pore pressure practically disappears when, owing to the phenomenon of dilatancy, the stress in the pore liquid becomes tensile and attains the tensile strength of the liquid, causing the well-known phenomenon of cavitation. According to the results shown in the Paper and summarized in Fig. 5, this apparently happened both in constant applied pore pressure tests at relatively high strain rates (upper shelf in the dotted curve in Fig. 5), and in saturated rock samples tested at atmospheric pressure, which after the pore liquid cavitated, behaved as if they were tested dry. In soil mechanics, the cavitation phenomenon has been studied more in detail in relation with the undrained strength of dense sands [3, 4], where its occurrence and effect could reasonably well be predicted. In triaxial tests with saturated rock specimens, on the contrary, the occurrence of cavitation may be much more difficult to predict, since it depends, not only on the applied back-pressure level, drainage conditions, fluid viscosity, and the applied rate of strain, but also on such uncontrollable factors as the velocity of unstable crack propagation, and the size and continuity of the resulting crack pattern. Nevertheless, when looking at the results shown in the Paper from the soil mechanics viewpoint, one is tempted to conclude that the rocks tested by the authors did not show pore pressure behavior much dissimilar from that normally found in some very dense soils. Or, in other words, even if the true pore pressure within the sample was not measured, many * Int. 3". R o c k M e c h . M i n . Sci. 5, 4 1 5 4 2 6
(1968).
t Department of Mining Engineering, University of Montreal, Canada. 123
124
DISCUSSION
aspects of the results indicate that the rocks in the tests behaved quite well in accordance with the principle of effective stress, as it is understood in soil mechanics. It, therefore, comes quite as a surprise to see that, from the same test results, the authors arrive at the conclusion that the law of effective stress is valid only at a very slow strain rate, but ceases to hold as soon as a "critical strain rate" is exceeded. After a second look, however, one finds that this is only a matter of definition. While in the Introduction of the Paper the authors define the effective stress quite correctly as "the difference between the total normal stress active on any plane through the solid and the pressure of fluids in the pores", in the rest of the paper they seem to follow quite a different definition, implying that the effective stress is the difference between the total applied normal stress and the fluid pressure, applied directly at the external surface of the specimen within the jacket, and kept constant during the test. Now, while the results obtained by the authors quite apparently substantiate the validity of the law according to the first definition, which takes into account any strain-induced pore pressure variation within the sample, the law quickly breaks down if the second definition neglecting this variation is adopted and applied to partially drained and undrained tests. The second definition, which is sometimes encountered in geologic literature, does not seem, however, to offer any advantages over the original one proposed by TERZAGHI [2] and mentioned by the authors in the Introduction. In fact, the second definition can only have a limited application when considering very slow deformation processes such as encountered in geology. In engineering rock mechanics problems, on the contrary, adopting the second definition would inevitably lead to confusion. It is a well-known fact that a great part of the development of soil mechanics has been made possible by an early and proper understanding of the principle of effective stress. It is therefore considered of utmost importance that in the field of rock mechanics, as well, a proper and unique definition of the effective stress be adopted and recognized as soon as possible. Moreover, in the pore pressure research of rocks, the large amount of experimental evidence on the pore pressure behavior of soils, accumulated during nearly forty years of soil mechanics research, may prove to be quite a valuable source of information, at least as a starting point for a similar work in rock mechanics. REFERENCES 1. SKEMP'IX)NA. W. Effective Stress in Soils, Concrete and Rocks, Proceedings of the Conference on Pore Pressure and Suction in Soils, pp. 4-16, Butterworths (1960). 2. TERZAOnIK. The Shearing Resistance of Saturated Soils, Proceedings of the First InternationalConference on Soil Mechanics, Vol. I, pp. 54-66 (1936). 3. BISHOPA. W. and ELDING. Undrained triaxial tests on saturated sands and their significance in the general theory of shear strength. G~otechnique 2, (1) 13-22 (1950). 4. SEEDH. B. and LEE K. L. Undrained strength characteristics of eohesionless soils. Proc. Am. Soc. cir. Engrs 93, (SM6) 333-360 (1967).