Summary
In this paper a bifurcation analysis of the triaxial compression test on rock specimens is presented. Rock behavior is modelled by a deformation theory of elasto-plasticity for a pressure sensitive, cohesive-frictional, dilatant material with microstructure. In particular a Cosserat continuum model for a granular rock is developed. Shape and size effects are discussed on the basis of an analysis of diffuse bifurcation of triaxial tests on a particular sandstone [25].
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Rudnicki, J. N., Rice, J. R.: Conditions for the localization of the deformation in pressure sensitive dilatant material. J. Mech. Phys. Solids23, 371–394 (1975).
Cheng, S. Y., Ariaratnam, S. T., Dubey, R. N.: Axisymmetric bifurcation in a elastic plastic cylinder under axial load and lateral hydrostatic pressure. Quart. Appl. Mathematics29, 41–51 (1971).
Hutchinson, J. N., Miles, J. P.: Bifurcation analysis of the onset of necking in an elastic/plastic cylinder under uniaxial tension. J. Mech. Phys. Solids22, 61–71 (1974).
Vardoulakis, I.: Bifurcation analysis of the triaxial test on sand samples. Acta Mechanica32, 35–54 (1979).
Vardoulakis, I.: Constitutive properties of dry sand, observable in the triaxial test. Acta Mechanica38, 219–239 (1981).
Vardoulakis, I.: Rigid granular plasticity model and bifurcation in the triaxial test. Acta Mechanica49, 57–59 (1983).
Bazant, Z. P.: L'instabilité d'un milieu continu et la résistance en compression. Bulletin Rilem35, 99–112 (1967).
Vardoulakis, I.: Rock bursting as a surface instability phenomenon. Int. J. Rock. Mech. & Min. Sci. and Geomech. Abstr.21, 137–144 (1984).
Vardoulakis, I., Mühlhaus, H. B.: Local rock surface instabilities. Int. J. Rock. Mech. & Min. Sci. and Geomech. Abstr.23, 379–383 (1986).
Mühlhaus, H. B., Vardoulakis, I.: Buckling of laminated half space with bending stiffness. Mechanics of Materials5, 109–120 (1986).
Mühlhaus, H. B.: Delamination phenomena in prestressed rock. Proc. 2nd Int. Symp. on Rock-bursts and Seismicity in Mines, University of Minnesota, in print, (1988).
Vardoulakis, I., Papamichos, E.: Surface instabilities in elastic anisotropic media with surface parallel Griffith cracks. Int. J. Rock Mech. & Min. Sci. and Geomech. Abst., accepted for publication (1989).
Papamichos, E., Vardoulakis, I.: The coupling effect of surface instabilities and surface parallel Griffith cracks. Proc. Int. Symp. Rock Mech. and Rock Phys. at Great Depth, Pau, France, Balkema, in print (1989).
Batdorf, S. B., Budiansky, B.: A mathematical theory of plasticity based on the concept of slip. NACA Tech. Note 1871 (1949).
Schaeffer, D. G.: Instability and ill-posedness in the deformation of granular materials, Int. J. Num. Anal. Meth. Geomech., in print (1989).
Mühlhaus, H. B.: Scherfugenanalyse bei granularem Material im Rahmen der Cosserat Theorie. Ingenieur Archiv56, 389–399 (1986).
Mühlhaus, H. B., Vardoulakis, I.: The thickness of shear bands in granular materials. Géotechnique37, 271–283 (1987).
Papanastasiou, P., Vardoulakis, I.: Bifurcation analysis of deep boreholes: II Scale effect. Int. J. Num. Anal. Meth. Geomech.13, 183–198 (1989).
Sulem, J., Vardoulakis, I.: Simplified bifurcation analysis of deep boreholes in rocks with microstructure. Proc. Int. Symp. Rock at Great Depth, Pau, France, Balkema, in print (1989).
Mindlin, R. D.: Microstructure in linear elasticity. Arch. Rat. Mech. Anal.16, 51–67 (1964).
Schaefer, H.: Das Cosserat Kontinuum. Z. Angew. Math. Mech.47, 485–498 (1967).
Vardoulakis, I., Sulem, J., Guenot, A.: Borehole instabilities as bifurcation phenomena. Int. J. Rock Mech. & Min. Sci. and Geomech. Abstr.25, 159–170 (1988).
Sulem, J., Vardoulakis, I.: A new approach to borehole stability based on bifurcation theory. Proc. 6th Int. Conf. Num. Meth. in Geomechanics3, Innsbruck, pp. 1929–1935, Balkema 1988.
Kachanov, L. M.: Fundamentals of the theory of plasticity. Moscow: Mir 1974.
Santarelli, F. J.: Theoretical and experimental investigation of the stability of the axisymmetric wellbore. PhD thesis. Imperial College, London (1987).
Vukuturi, V. S., Lama, R. D., Saluja, S. S.: Handbook of mechanical properties of rocks. Trans. Tech. Publ.1 (1974).
Mogi, K.: Some precise measurements of fracture strength of rocks under uniform compressive stress. Rock Mech. Eng. Geol.4, 41–47 (1966).
Brace, W. F.: The effect of size on mechanical properties of rock. Geophy. Res. Lett.8, 651–652 (1981).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Sulem, J., Vardoulakis, I. Bifurcation analysis of the triaxial test on rock specimens. A theoretical model for shape and size effect. Acta Mechanica 83, 195–212 (1990). https://doi.org/10.1007/BF01172981
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01172981