TECHNICAL PAPERS
Jun 1, 1987

True Triaxial Yielding and Hardening of Rock

Publication: Journal of Geotechnical Engineering
Volume 113, Issue 6

Abstract

Analysis of test results for intact and granulated marbles (cemented and noncemented granular materials) adds to the indications that strain softening does not express a real material behavior; it highlights similarities in stressstrain relations and confirms equality of a stress and a plastic strain invariant. The physical meaning of the parameters of a yield equation, which express energy dissipating in frictional and nonfrictional processes and define the deviation from the normality condition, is shown. A hardening rule that takes into account friction and dilatancy is formulated from yield relations and from an experimentally proved consistency condition. Variation of constitutive parameters and evolution of various yield states is considered together with application of the hardening rule. Variation of the normality condition deviation angle along yield states obtained under low and very high confinement is constitutively modeled. Meridian and deviatoric sections of yield surfaces, obtained by low and high pressure experiments and substantiated by results compiled from the literature, are considered. A polyaxial yield equation and hardening rule are proposed and experimentally verified.

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References

1.
Atkinson, R. H., and Ko Hon‐Yim, “A Fluid Cushion, Multiaxial Cell for Testing Cubical Rock Specimens,” International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts, Vol. 10, 1973, pp. 351–361.
2.
Brook, N., “Estimating the Triaxial Strength of Rocks,” International Journal of Rock Mechanics Mining Sciences and Geomechanics Abstracts, Vol. 16, 1979, pp. 261–264.
3.
Byerlee, J. D., “Frictional Characteristics of Granite under high confining pressure,” Journal of Geophysical Research, Vol. 72, No. 14, 1967, pp. 3639–3648.
4.
Byerlee, J. D., “Brittle‐Ductile Transition in Rocks,” Journal of Geophysical Research, Vol. 73, No. 14, 1968, pp. 4741–4750.
5.
Byerlee, J. D., “The Fracture Strength and Frictional Strength of Weber Sandstone,” International Journal of Rock Mechanics Mining Sciences and Geomechanical Abstracts, Vol. 12, 1975, pp. 1–4.
6.
Dafalias, Y. F., and Herrmann, L. R., “Bounding Surface Formulation of Soil Plasticity,” Soil Mechanics‐Transient and Cyclic Loads, G. N. Pande and O. C. Zienkiewicz, Eds., John Wiley and Sons, New York, N.Y., 1982, pp. 253–282.
7.
Desai, C. S., Janardahanam, R., and Sture, S., “High Capacity Multiaxial Testing Device,” Geotechnical Testing Journal, Vol. 5, No. 1, 1982, pp. 26–33.
8.
Elliot, G. T., “An investigation of a Yield Criterion for Porous Rock,” thesis presented to the University of London, at London, U.K., in 1982, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
9.
Farmer, I. W., “Rock Strength and Yield,” Engineering Behaviour of Rocks, Chapman and Hall, England, 1983, pp. 81–118.
10.
Franklin, J. A., “Triaxial Strength of Rock Materials,” Rock Mechanics, Vol. 3, 1971, pp. 86–98.
11.
Gerogiannopoulos, N., and Brown, E. T., “The Critical State Concept applied to Rock,” International Journal of Rock Mechanics Mining Sciences and Geomechanics Abstracts, Vol. 15, No. 1, 1978, pp. 1–10.
12.
Gudehus, G., “Elastoplastische Stoffleichungen fur trockenen Sand,” Ingenieur‐Archiv., Vol. 42, 1973.
13.
Hettler, A., and Vardoulakis, I., “Behaviour of Dry Sand Tested in a Large Triaxial Apparatus,” Geotechnique, Vol. 34, No. 2, 1984, pp. 183–198.
14.
Hudson, J. A., Brown, E. T., and Fairhurst, C., “Shape of the Complete Stress‐Strain Curve for Rock,” Proceedings, 13th U.S. Symposium on Rock Mechanics, University of Illinois, Urbana, Ill., 1971.
15.
International Society for Rock Mechanics, Commission on Standardization of Laboratory and Field Tests, “Suggested Methods for Determining the Strength of Rock Materials in Triaxial Compression,” International Journal of Rock Mechanics Mining Sciences and Geomechanics Abstracts, Vol. 15, 1978, pp. 47–51.
16.
Jaeger, J. C., “Rock Mechanics—Theory and Practice,” Proceedings, 11th U.S. Symposium on Rock Mechanics, University of California, Berkeley, Calif., 1969.
17.
Jumikis, A. R., “Deformation of Rock,” Rock Mechanics, Trans Tech Publications, Clausthal‐Zellerfeld, F.R.G., 1983, pp. 169–224.
18.
Kim, M. K., and Lade, P. V., “Modelling Rock Strength in Three Dimensions,” International Journal of Rock Mechanics Mining Sciences and Geomechanics Abstracts, Vol. 21, No. 1, 1984, pp. 21–33.
19.
Kovari, K., and Tisa, A., “Multiple Failure State and Strain Controlled Triaxial Tests,” Rock Mechanics, Vol. 7, 1975, pp. 17–33.
20.
Ladanyi, B., and Don, N., “Study of Strains in Rock Associated with Brittle Failure,” Proceedings, 6th Canadian Rock Mechanics Symposium, Montreal, Canada, 1970, pp. 49–64.
21.
Michelis, P. N., “Work‐Softening and Hardening Behavior of Granular Rocks,” Journal of Rock Mechanics, Vol. 14, 1981, pp. 187–200.
22.
Michelis, P. N., “A True Triaxial Cell for Low and High Pressure Experiments,” technical note, International Journal of Rock Mechanics Mining Sciences and Geomechanics Abstracts, Vol. 22, No. 3, 1985, pp. 183–188.
23.
Michelis, P. N., “Polyaxial Yielding of Granular Rock,” Journal of Engineering Mechanics, ASCE, Vol. 111, No. 8, Aug., 1985, pp. 1049–1066.
24.
Michelis, P. N., and Brown, E. T., “A Yield Equation for Rock,” Canadian Geotechnical Journal, Vol. 23, No. 1, 1986, pp. 9–17.
25.
Mills, L. L., and Zimmerman, R. M., “Compressive Strength of Plain Concrete under Multiaxial Loading Conditions,” Proceedings of ACI Journal, Vol. 67, Oct., 1970, pp. 802–807.
26.
Mogi, K., “Deformation and Fracture of Rocks under Confining Pressure. Elasticity and Plasticity of Some Rocks,” Bulletin of Earthquake Research Institute, Tokyo Univ., Tokyo, Japan, 1965, pp. 349–379.
27.
Mogi, K., “Effect of the Intermediate Principal Stress on Rock Failure,” Journal of Geophysical Research, Vol. 72, No. 20, 1967, pp. 5117–5131.
28.
Mogi, K., “Flow and Fracture of Rock under General Triaxial Compression,” Proceedings, 4th Congress of ISRM, Vol. 3, Montreaux, Switzerland, 1979, pp. 123–130.
29.
Mroz, Z., “On the Description of Anisotropic Work Hardening,” Journal of Mechanics and Physics of Solids, Vol. 15, 1967, pp. 163–175.
30.
Ochiai, H., and Lade, P. V., “Three‐Dimensional Behavior of Sand with Anisotropic Fabric,” Journal of Geotechnical Engineering, ASCE, Vol. 109, No. 10, Oct., 1983, pp. 1313–1328.
31.
Ramez, M. R. H., “Fracture and the Strength of a Sandstone under Triaxial Compression,” International Journal of Rock Mechanics Mining Sciences and Geomechanics Abstracts, Vol. 4, 1967, pp. 257–268.
32.
Read, H. E., and Hegemier, G. A., “Strain Softening of Rock, Soil and Concrete—A Review Article,” Mechanics of Material, Vol. 3, 1984, pp. 271–294.
33.
Reches, Z., and Dieterich, J. H., “Faulting of Rocks in Three‐dimensional Strain Fields. 1: Failure of Rocks in Polyaxial, Servo‐controlled Experiments,” Tectonophysics, Vol. 95, 1983, pp. 111–132.
34.
Rosengren, K. J., and Jaeger, J. C., “The Mechanical Properties of an Interlocked Low‐porosity Aggregate,” Géotechnique, Vol. 18, 1968, pp. 317–326.
35.
Sangha, C. M., and Dhir, R. K., “Strength and Deformation of Rock Subject to Multiaxial Compressive Stresses,” International Journal of Rock Mechanics Mining Sciences and Geomechanics Abstracts, Vol. 12, 1975, pp. 277–282.
36.
Swanson, S. R., and Brown, W. S., “An Observation of Loading Path Dependence of Fracture in Rock,” International Journal of Rock Mechanics Mining Sciences and Geomechanics Abstracts, Vol. 8, 1971, pp. 277–281.
37.
Valanis, K. C., “A Theory of Viscoplasticity without a Yield Surface, Part I: General Theory, Part II: Application to Mechanical Behavior of Metals,” Archives of Mechanics, Vol. 23, 1971, pp. 517–551.
38.
Vardoulakis, J., “Bifurcation Analysis of the Triaxial Test on Sand Samples,” Acta Mechanica, Vol. 32, 1979, pp. 35–54.
39.
Vermeer, P. A., and Borst, R., “Nonassociated Plasticity for Soils, Concrete and Rock,” Heron, Vol. 29, No. 3, 1984, pp. 1–64.
40.
Wawersik, W. R., “Detailed Analysis of Rock Failure in Laboratory Compression Tests,” thesis presented to the University of Minnesota at Duluth, Minn., in 1968, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.

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Go to Journal of Geotechnical Engineering
Journal of Geotechnical Engineering
Volume 113Issue 6June 1987
Pages: 616 - 635

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Published online: Jun 1, 1987
Published in print: Jun 1987

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Paul Michelis, A. M. ASCE
Researcher, Dept. of Civ. Engrg., National Tech. Univ. of Athens, 106 82 Athens, Greece

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