TECHNICAL PAPERS
Apr 1, 2000

FE Modeling of Strain Localization in Soft Rock

Publication: Journal of Geotechnical and Geoenvironmental Engineering
Volume 126, Issue 4

Abstract

A finite-element (FE) model of localized deformation in soft rock taking a strong discontinuity approach is presented. The model is formulated within the context of rate-independent, nonassociated Drucker-Prager plasticity with nonlinear cohesion hardening/softening. Strain localization is modeled as a jump in the displacement field and simulated within the framework of the FE method using the standard Galerkin approximation. The model is used to simulate the load-displacement behavior of Gosford sandstone deforming in plane strain, focusing on the prediction of the stress levels necessary to initiate strain localization, based on the strong and weak discontinuity criteria (jumps in displacement and strain, respectively), and on the demonstration of mesh-independence of the FE solutions in the bifurcated state. For the sandstone, the onset of weak discontinuity is detected first, before the onset of strong discontinuity, suggesting a possible coupling of the two types of discontinuities in the strain-softening regime.

Get full access to this article

View all available purchase options and get full access to this article.

References

1.
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.
2.
Armero, F., and Garikipati, K. (1995). “Recent advances in the analysis and numerical simulation of strain localization in inelastic solids.” Proc., Computational Plasticity IV, D. R. J. Owen, E. Oñate, and E. Hinton, eds., International Center for Numerical Methods in Engineering (CIMNE), Barcelona, Spain, 547–561.
3.
Arthur, J. R. F., Dunstan, T., Al-ani, Q. A. L. J., and Assadi, A. (1977). “Plastic deformation and failure in granular media.” Géotechnique, London, 27, 53–74.
4.
Ashby, M. F., and Hallam, S. D. (1986). “The failure of brittle solids containing small cracks under compressive stress states.” Acta Metallurgica, 16, 497–510.
5.
Bazant, Z. P., and Pijaudier-Cabot, G. (1988). “Nonlocal continuum damage, localization instability and convergence.” J. Appl. Mech., 55, 287–293.
6.
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. Engrg. (in press).
7.
Borja, R. I., and Regueiro, R. A. (2000). “Strain localization in frictional materials exhibiting displacement jumps.” Comput. Methods Appl. Mech. Engrg. (in press).
8.
Borja, R. I., and Wren, J. R. (1993). “Discrete micromechanics of elastoplastic crystals.” Int. J. Numer. Methods in Engrg., Chickester, England, 36(22), 3815–3840.
9.
Borja, R. I., and Wren, J. R. (1995a). “Micromechanics of continuum models for granular materials.” Engrg. Mech., Proc., 10th Conf., S. Sture, ed., Vol. 1, ASCE, New York, 497–500.
10.
Borja, R. I., and Wren, J. R. (1995b). “Micromechanics of granular media, Part I: Generation of overall constitutive equation for assemblies of circular disks.” Comput. Methods Appl. Mech. Engrg., 127, 13–36.
11.
Borja, R. I., and Wren, J. R. (1992). “On the bifurcation of elasto-plastic crystals during multiple slip.” Engrg. Mech., Proc., 9th Conf., L. D. Lutes and J. M. Niedzwecki, eds., ASCE, New York, 284–287.
12.
Borja, R. I., Wren, J. R., and Regueiro, R. A. ( 1998). “Micromechanical basis of continuum models for granular media.” Localization and bifurcation theory for soils and rocks, T. Adachi, F. Oka, and A. Yashima, eds., Balkema, Rotterdam, The Netherlands, 295–304.
13.
Brace, W. F., Paulding, B. W., and Scholtz, C. (1966). “Dilatancy in the fracture of crystalline rocks.” J. Geophys. Res., 77, 3939.
14.
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.
15.
Haas, C. J. ( 1981). “Chapter 6: Stress-strain relationships.” Phys. properties of rocks and minerals, Vol. II-2, Y. S. Touloukian et al., eds., McGraw-Hill/CINDAS Data Series on Material Properties, New York.
16.
Handin, J. ( 1966). “Strength and ductility.” Handbook of physical constants, S. P. Clark, Jr., ed., Geol. Soc. Am. Memoir, 97, 223–289.
17.
Horii, H., and Nemat-Nasser, S. (1985). “Compression-induced microcrack growth in brittle solids: Axial splitting and shear failure.” J. Geophys. Res., 90, 3105–3215.
18.
Jaeger, J. C., and Cook, N. G. W. (1976). Fundamentals of rock mechanics, 2nd Ed., Chapman and Hall, London.
19.
Labuz, J. F., Dai, S. T., and Papamichos, E. (1996). “Plane-strain compression of rock-like materials.” Int. J. Rock Mech. Mining Sci. and Geomech. Abstracts, Amsterdam, 33, 573–584.
20.
Labuz, J. F., and Papamichos, E. ( 1991). “Preliminary results of plane-strain testing of soft rock.” Rock mechanics as a multidisciplinary science, J.-C. Roegiers, ed., Balkema, Rotterdam, The Netherlands, 667–674.
21.
Larsson, R., Runesson, K., and Ottosen, N. S. (1993). “Discontinuous displacement approximation for capturing plastic localization.” Int. J. Numer. Methods in Engrg., Chichester, England, 36, 2087–2105.
22.
Ord, A., Vardoulakis, I., and Kajewski, R. (1991). “Shear band formation in Gosford sandstone.” Int. J. Rock Mining Sci. and Geomech. Abstracts, Amsterdam, 28(5), 397–409.
23.
Ortiz, M., Leroy, Y., and Needleman, A. (1987). “A finite element method for localized failure analysis.” Comput. Methods Appl. Mech. Engrg., 61, 189–214.
24.
Pietruszczak, S. T., and Mróz, Z. (1981). “Finite element analysis of deformation of strain-softening materials.” Int. J. Numer. Methods in Engrg., Chichester, England, 17, 327–334.
25.
Read, H. E., and Hegemier, G. A. (1984). “Strain softening of rock, soil and concrete—A review article.” Mech. Mat., 3, 271–294.
26.
Regueiro, R. A., and Borja, R. I. ( 1999). “A finite element model of localized deformation in frictional materials taking a strong discontinuity approach.” Finite Elements in Anal. and Des., 33(4), 283–315.
27.
Regueiro, R. A., and Borja, R. I. (2000). “Plane strain finite element analysis of pressure-sensitive plasticity with strong discontinuity.” Int. J. Solids Struct. (in press).
28.
Regueiro, R. A., Lai, T. Y., and Borja, R. I. (1998). “Computational modeling of strain localization in soft rock.” Geotechnics of hard soils–soft rocks, A. Evangelista and L. Picarelli, eds., Balkema, Rotterdam, The Netherlands, 789–797.
29.
Rudnicki, J. W. (1977). “The inception of faulting in a rock mass with a weakened zone.” J. Geophys. Res., 82(5), 844–854.
30.
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.
31.
Runesson, K., Peric, D., and Sture, S. (1991). “Discontinuous bifurcations of elastic-plastic solutions at plane stress and plane strain.” Int. J. Plasticity, 7, 99–121.
32.
Santarelli, F. J., and Brown, E. T. (1989). “Failure of three rocks in triaxial and hollow cylinder compression tests.” Int. J. Rock Mech. Mining Sci. and Geomech. Abstracts, Amsterdam, 26, 401–413.
33.
Simo, J. C., Oliver, J., and Armero, F. (1993). “An analysis of strong discontinuities induced by strain-softening in rate-independent inelastic solids.” Computational Mech., 12, 277–296.
34.
Stakgold, I. (1998). Green's functions and boundary value problems, 2nd Ed., Wiley, New York.
35.
Vermeer, P. A., and de Borst, R. (1984). “Nonassociated plasticity for soils, concrete, and rock.” Heron, 29(3), 1–64.
36.
Wan, R. G., Chan, D. H., and Morgenstern, N. R. (1990). “A finite element method for the analysis of shear bands in geomaterials.” Finite Element Anal. Des., 7, 129–143.
37.
Wawersik, W. R., Rudnicki, J. W., Olsson, W. A., Holcomb, D. J., and Chau, K. T. ( 1990). “Localization of deformation in brittle rock: Theoretical and laboratory investigations.” S. P. Shah, S. E. Swartz, and M. L. Wang, eds., Micromechanics of failure of quasi-brittle materials, Elsevier, New York, 115–124.
38.
Wren, J. R., and Borja, R. I. (1997). “Micromechanics of granular media, Part II: Overall tangential moduli and localization model for periodic assemblies of circular disks.” Comput. Methods Appl. Mech. Engrg., 141, 221–246.
39.
Yumlu, M., and Ozbay, M. U. (1995). “A study of the behaviour of brittle rocks under plane strain and triaxial loading conditions.” Int. J. Rock Mech. Min. Sci. and Geomech. Abstracts, Amsterdam, 32, 725–733.
40.
Zienkiewicz, O. C., Pastor, M., and Huang, M. (1995). “Softening, localisation and adaptive remeshing: Capture of discontinuous solutions.” Computational Mech., 17, 98–106.

Information & Authors

Information

Published In

Go to Journal of Geotechnical and Geoenvironmental Engineering
Journal of Geotechnical and Geoenvironmental Engineering
Volume 126Issue 4April 2000
Pages: 335 - 343

History

Received: Jun 1, 1998
Published online: Apr 1, 2000
Published in print: Apr 2000

Permissions

Request permissions for this article.

Authors

Affiliations

Assoc. Prof., Dept. of Civ. and Envir. Engrg., Terman Engrg. Ctr., Stanford Univ., Stanford, CA 94305-4020.
Grad. Student, Dept. of Civ. and Envir. Engrg., Stanford Univ., Stanford, CA.
Grad. Student, Dept. of Civ. and Envir. Engrg., Stanford Univ., Stanford, CA.

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.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share