Propagation of Localization Instability Under Active and Passive Loading
Publication: Journal of Geotechnical and Geoenvironmental Engineering
Volume 128, Issue 1
Abstract
The mechanical response of a solid continuum changes drastically as the deformation evolves from a diffuse state to a highly localized state. For this reason the subject of strain localization has received much research attention lately. This paper investigates the impact of strain localization in the form of strong discontinuity, or displacement jump, on the limit strengths of retaining walls supporting an elastoplastic backfill. The analysis focuses on the propagation of strong instability in active and passive loading using a recently developed strong discontinuity finite element model where the elements are enhanced to accommodate the presence of displacement jumps. Specifically, the analysis applies to dilative frictional material that is susceptible to shear banding. For the retaining wall problem, strong instability is shown to initiate at the ground surface and propagate downward at an angle that depends on the state of stress at the onset of localization.
Get full access to this article
View all available purchase options and get full access to this article.
References
Adachi, T., Oka, F., and Yashima, A.(1991). “A finite element analysis of strain localization for soft rock using a constitutive equation with strain softening.” Arch. Appl. Mech., 61, 183–191.
Armero, F., and Garikipati, K. (1995). “Recent advances in the analysis and numerical simulation of strain localization in inelastic solids.” Proceedings of Computational Plasticity IV, D. R. J. Owen, E. Oñate, and E. Hinton, eds., International Center for Numerical Methods in Engineering, Barcelona, Spain, 547–561.
Arthur, J. R. F., Dunstan, T., Al-ani, Q. A. L. J., and Assadi, A.(1977). “Plastic deformation and failure in granular media.” Géotechnique, 27, 53–74.
Aydin, A., and Johnson, A. M.(1978). “Development of faults as zones of deformation bands and as slip surfaces in sandstone.” Pure and Applied Geophysics, 116, 931–942.
Bazant, Z. P., and Pijaudier-Cabot, G.(1988). “Nonlocal continuum damage, localization instability and convergence.” J. Appl. Mech., 55, 287–293.
Borja, R. I.(2000). “A finite element model for strain localization analysis of strongly discontinuous fields based on standard Galerkin approximation.” Comput. Methods Appl. Mech. Eng., 190(11–12)), 1529–1549.
Borja, R. I. (2001). “Propagation of strong discontinuity in elastoplastic solids.” Computer methods and advances in geomechanics, Vol. 1, C. S. Desai et al., eds., Balkema, Rotterdam, 491–495.
Borja, R. I. (2002a). “Bifurcation of elastoplastic solids to shear band mode at finite strain.” Comput. Methods Appl. Mech. Eng., in press.
Borja, R. I. (2002b). “Finite element simulation of strain localization with large deformation: Capturing strong discontinuity using a Petrov-Galerkin multiscale formulation.” Comput. Methods Appl. Mech. Eng., in press.
Borja, R. I., and Regueiro, R. A.(2001). “Strain localization in frictional materials exhibiting displacement jumps.” Comput. Methods Appl. Mech. Eng., 190(20–21), 2555–2580.
Borja, R. I., Regueiro, R. A., and Lai, T. Y.(2000). “FE modeling of strain localization in soft rocks.” J. Geotech. Geoenviron. Eng., 126(4), 335–343.
Brace, W. F., Paulding, B. W., and Scholz, C.(1966). “Dilatancy in the fracture of crystalline rocks.” J. Geophys. Res., 71(16), 3939–3953.
Cook, N. G. W.(1970). “An experiment proving that dilatancy is a pervasive volumetric property of brittle rock loaded to failure.” Rock Mech., 2, 181–188.
de Borst, R., and Mühlhaus, H.-B.(1992). “Gradient-dependent plasticity: Formulation and algorithmic aspects.” Int. J. Numer. Methods Eng., 35, 521–539.
de Borst, R., Pamin, J., and Sluys, L. J. (1995). “Computational issues in gradient plasticity.” In: Continuum models for materials with microstructures, H. B. Mühlhaus, ed., Wiley, N.Y., 159–200.
Design Manual DM-7 (1971). Soil mechanics, foundations, and earth structures, Dept. of the Navy, Naval Facilities Engineering Command, Alexandria, VA.
Dieterich, J. H., and Kilgore, B. D. (1994). “Direct observation of frictional contacts: New insights for state-dependent properties.” Pure and Applied Geophysics, 143(1/2/3), 283–302.
Dieterich, J. H., and Linker, M. F.(1992). “Fault stability under conditions of variable normal stress.” Geophys. Res. Lett., 19(16), 1691–1694.
Labuz, J. F., Dai, S. T., and Papamichos, E.(1996). “Plane-strain compression of rocklike materials.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 33, 573–584.
Lai, T. Y. (2001). “FE modeling of post-localization behavior of elasto-plastic solids with strong discontinuity.” PhD thesis, Stanford University, Stanford, Calif.
Larsson, R., Runesson, K., and Ottosen, N. S.(1993). “Discontinuous displacement approximation for capturing plastic localization.” Int. J. Numer. Methods Eng., 36, 2087–2105.
Oka, F., Yashima, A., Sawada, K., and Aifantis, E. C.(2000). “Instability of gradient-dependent elastoviscoplastic model for clay and strain localization analysis.” Comput. Methods Appl. Mech. Eng., 183, 67–86.
Ortiz, M., Leroy, Y., and Needleman, A.(1987). “A finite element method for localized failure analysis.” Comput. Methods Appl. Mech. Eng., 61, 189–214.
Perić, D., Runesson, K., and Sture, S.(1992). “Evaluation of plastic bifurcation for plane strain versus axisymmetry.” J. Eng. Mech., 118(3), 512–524.
Perić, D., Runesson, K., and Sture, S.(1993). “Prediction of plastic localization using MRS-Lade model.” J. Geotech. Eng., 119(4), 639–661.
Pietruszczak, S. T., and Mróz, Z.(1981). “Finite element analysis of deformation of strain-softening materials.” Int. J. Numer. Methods Eng., 17, 327–334.
Rankine, W. J. M.(1857). “On the stability of loose earth.” Philos. Trans. R. Soc. London, 147(1), 9–27.
Read, H. E., and Hegemier, G. A.(1984). “Strain softening of rock, soil and concrete—A review article.” Mech. Mater., 3, 271–294.
Regueiro, R. A. (1998). “Finite element analysis of strain localization in geomaterials taking a strong discontinuity approach,” PhD thesis, Stanford University, Stanford, Calif.
Regueiro, R. A., and Borja, R. I.(1999). “A finite element model of localized deformation in frictional materials taking a strong discontinuity approach.” Finite Elem. Anal. Design, 33(4), 283–315.
Regueiro, R. A., and Borja, R. I.(2001). “Plane strain finite element analysis of pressure-sensitive plasticity with strong discontinuity.” Int. J. Solids Struct., 38, 3647–3672.
Rice, J. R.(1980). “Elastic wave emission from damage processes.” J. Nondestruct. Eval., 1, 215–224.
Rice, J. R., and Rudnicki, J. W.(1980). “A note on some features of the theory of localization of deformation.” Int. J. Solids Struct., 16, 597–605.
Rudnicki, J. W., and Rice, J. R.(1975). “Conditions for the localization of deformation in pressure-sensitive dilatant materials.” J. Mech. Phys. Solids, 23, 371–394.
Rudnicki, J. W.(1977). “The inception of faulting in a rock mass with a weakened zone.” J. Geophys. Res., 82(5), 844–854.
Ruina, A.(1983). “Slip instability and state variable friction laws.” J. Geophys. Res., 88, 10 359–10 370.
Runesson, K., Perić, D., and Sture, S.(1991). “Discontinuous bifurcations of elastic–plastic solutions at plane stress and plane strain.” Int. J. Plast., 7, 99–121.
Simo, J. C., Oliver, J., and Armero, F.(1993). “An analysis of strong discontinuities induced by strain-softening in rate-independent inelastic solids.” Comput. Mech., 12, 277–296.
Sleep, N. H.(1997). “Application of a unified rate and state friction theory to the mechanics of fault zones with strain localization.” J. Geophys. Res., 102(B2), 2875–2895.
Vardoulakis, I., and Graf, B.(1985). “Calibration of constitutive models for granular materials using data from biaxial experiments.” Géotechnique, 35(3), 299–317.
Vermeer, P. A., and de Borst, R.(1984). “Nonassociated plasticity for soils, concrete, and rock.” Heron, 29(3), 1–64.
Viggiani, G., Finno, R. J., and Harris, W. W. (1994). “Experimental observations of strain localisation in plane strain compression of a stiff clay.” Localization and bifurcation theory for soils and rocks, R. Chambón, J. Desrues, and I. Vardoulakis, eds., Balkema, Rotterdam, The Netherlands, 189–198.
Wan, R. G., Chan, D. H., and Morgenstern, N. R.(1980). “A finite element method for the analysis of shear bands in geomaterials.” Finite Elem. Anal. Design, 7, 129–143.
Zienkiewicz, O. C., Pastor, M., and Huang, M.(1995). “Softening, localisation and adaptive remeshing. Capture of discontinuous solutions.” Comput. Mech., 17, 98–106.
Information & Authors
Information
Published In
Journal of Geotechnical and Geoenvironmental Engineering
Volume 128 • Issue 1 • January 2002
Pages: 64 - 75
Copyright
Copyright © 2002 American Society of Civil Engineers.
History
Received: Sep 6, 2000
Accepted: Mar 23, 2001
Published online: Jan 1, 2002
Published in print: Jan 2002
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.