Characterization of plastic limit surface and bifurcation domain of geomaterials
Prunier, Florent1; Duriez, Jérôme2; Sibille, Luc3; Darve, Félix3
1 Université de Lyon, INSA de Lyon, laboratoire GEOMAS, France
2 INRAE, Aix Marseille Univ, RECOVER, Aix-en-Provence, France
3 Université Grenoble Alpes, laboratoire 3S-r, France
Open Geomechanics, Volume 6 (2025), article no. 1, 19 p.

Instabilities and failure in ductile non associated materials have been widely investigated during last decades especially in the case of geomaterials. It has been shown experimentally that collapse of some specimens can occur strictly within the ultimate plasticity limit, which is experimentally characterized by the maximum shear stress in a drained triaxial test. From a theoretical point of view such instability problems are well described using the so called second order work criterion derived from the Hill’s stability analysis. Hence a question arises as to the experimental characterization of the ultimate plasticity limit with respect to the choice of stress paths. After a few reminders on Hill’s theory, we prove in a general framework that the drained triaxial paths allow to determine with certainty this ultimate plasticity limit without any risk of preliminary bifurcation whatever the elasto-plastic material considered. We conclude that the plasticity limit is only slightly sensitive to variation of the internal state of the material, which can be described by different micromechanical quantities such as the void ratio and the fabric tensor. Furthermore, we define the limit of the bifurcation domain as the surface drawn in the 6-dimensional stress space that delimits the unconditionally stable space from the one where instabilities and failures can occur within the plasticity limit. However, we show that this latter limit is itself very sensitive to the evolution of the internal state of the soil sample.

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DOI: 10.5802/ogeo.22
Keywords: geomaterials, stability, plasticity limit characterization, bifurcation
Prunier, Florent 1; Duriez, Jérôme 2; Sibille, Luc 3; Darve, Félix 3

1 Université de Lyon, INSA de Lyon, laboratoire GEOMAS, France
2 INRAE, Aix Marseille Univ, RECOVER, Aix-en-Provence, France
3 Université Grenoble Alpes, laboratoire 3S-r, France
License: CC-BY-NC-SA 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Prunier, Florent; Duriez, Jérôme; Sibille, Luc; Darve, Félix. Characterization of plastic limit surface and bifurcation domain of geomaterials. Open Geomechanics, Volume 6 (2025), article  no. 1, 19 p. doi : 10.5802/ogeo.22. https://opengeomechanics.centre-mersenne.org/articles/10.5802/ogeo.22/

[1] Barnichon, J. D. Finite element modelling in structural and petroleum geology, Ph. D. Thesis, Université de Liège, Belgique (1998)

[2] Cheng, Zhao; Detournay, Christine Formulation, validation and application of a practice-oriented two-surface plasticity sand model, Computers and Geotechnics, Volume 132 (2021), 103984 https://www.sciencedirect.com/science/article/pii/s0266352x20305474 | DOI

[3] Cui, Junhe; Karapiperis, Konstantinos; Torgersrud, Øyvind; Andò, Edward; Viggiani, Gioacchino; Andrade, Jose Deciphering necking in granular materials: Micromechanical insights into sand behavior during cycles of triaxial compression and extension, Journal of the Mechanics and Physics of Solids, Volume 196 (2025), 106022 https://www.sciencedirect.com/science/article/pii/s0022509624004885 | DOI

[4] Darve, F.; Chau, B. Constitutive instabilities in incrementally non-linear modelling, Constitutive laws for Engineering Materials, C. S. Desai (1987), pp. 301-310

[5] Doanh, T.; Dubujet, P.; Protière, X. On the undrained strain-induced anisotropy of loose sand, Acta geotecnica, Volume 8 (2013), pp. 293-309 | DOI

[6] Darve, F.; Flavigny, E.; Meghachou, M. Yield surfaces and principle of superposition revisited by incrementally non-linear constitutive relations, International Journal of Plasticity, Volume 11(8) (1995), pp. 927-948 | DOI | Zbl

[7] Darve, F.; Flavigny, E.; Rojas, E. A class of incrementally non-linear constitutive relations and applications to clays, Computers and Geotechnics, Volume 2 (1986) no. 1, pp. 43-66 https://www.sciencedirect.com/science/article/pii/0266352x86900157 | DOI

[8] Darve, F.; Labanieh, S. Incremental constitutive law for sands and clays: Simulations of monotonic and cyclic tests, International Journal for Numerical and Analytical Methods in Geomechanics, Volume 6 (1982) no. 2, pp. 243-275 | arXiv | DOI | Zbl

[9] Dafalias, Yannis F.; Manzari, Majid T. Simple Plasticity Sand Model Accounting for Fabric Change Effects, Journal of Engineering Mechanics, Volume 130 (2004) no. 6, pp. 622-634 | DOI

[10] Darve, F.; Servant, G.; Laouafa, F.; Khoa, H. D. V. Failure in geomaterials : continuous and discrete analyses, Computer Methods in Applied Mechanics and Engineering, Volume 193 (2004), pp. 3057-3085 | DOI | Zbl

[11] Degradations and instabilities in geomaterials (Darve, F.; Vardoulakis, I., eds.), CISM courses, 461, SPRINGER, 2004 | DOI

[12] Farahnak, Mojtaba; Wan, Richard; Pouragha, Mehdi; Nicot, François A multiscale bifurcation analysis using micromechanical-based constitutive tensor for granular material, International Journal of Solids and Structures, Volume 298 (2024), p. 112866 https://www.sciencedirect.com/science/article/pii/s0020768324002257 | DOI

[13] Gateaux, R. Sur les fonctionnelles continues et les fonctionnelles analytiques, Comptes Rendus Académie des Sciences, Volume 157 (1913), pp. 325-327 | Zbl

[14] Gudehus, G. A comparison of some constitutive laws for soils under radially loading symmetric loading and unloading, Third International conference on numerical Methods in Geomechanics, Balkema, A. A. (1979), pp. 1309-1323

[15] Hill, R. A general theory of uniqueness and stability in elasto-plastic solids, Journal of the Mechanics and Physics of Solids, Volume 6 (1958), pp. 236-249 | DOI | Zbl

[16] Lade, P. V. Static instability and liquefaction of loose fine sandy slopes, Journal of Geotechnical Engineering, Volume 118(1) (1992), pp. 51-71 | DOI

[17] Lyapunov, A. M. Annales de la faculté des sciences de Toulouse, 9 (1907), pp. 203-274

[18] Lanier, J.; Zitouni, Z.; Saada, A.; Puccini, P.; Bianchini, G. Comportement tridimensionnel des sables: comparaison d’essais véritablement triaxiaux et d’essais sur cylindre creux, Rev. Fr. Geotech., Volume 49 (1989), pp. 67-76 | DOI

[19] Nicot, F.; Darve, F. Diffuse and localized failure modes, two competing mechanisms., Internationnal Journal for Numerical and Analitical Methods in Geomechanics, Volume 35(5) (2011), pp. 586-601 | DOI | Zbl

[20] Nova, R. Controllability of geotechnical testing, Failure, Degradation and Instabilities in Geomaterials. Revue française de génie civil, Volume 8(5-6) (2004), pp. 613-634 | DOI

[21] Nova, R. A note on sand liquefaction and soil stability, 3 r d International Conference on Constitutive Laws for Engineering Materials: Theory and Applications (1991), pp. 153-156

[22] Nova, R. Controllability of the incremental response of soil specimens subjected to arbitrary loading programs, Journal of the Mechanical behavior of Materials, Volume 5(2) (1994), pp. 193-201 | DOI

[23] Ouadfel, H.; Rothenburg, L. ’Stress-force-fabric’ relationship for assemblies of ellipsoids, Mechanics of Materials, Volume 33 (2001) no. 4, pp. 201-221 | DOI

[24] Pinzon, Gustavo; Ando, Edwardo; Desrues, Jacques; Viggiani, Gioacchino Fabric evolution and strain localisation in inherently anisotropic specimens of anisometric particles (lentils) under triaxial compression, IGranular Matter, Volume 298 (2023), p. 112866 | DOI

[25] Prunier, F.; Laouafa, F.; Darve, F. 3D bifurcation analysis in geomaterials, Investigation of the second order work criterion, European Journal of Environmental and Civil Engineering, Volume 13(2) (2009), pp. 135-147 | DOI

[26] Prunier, F.; Laouafa, F.; Lignon, S.; Darve, F. Bifurcation modeling in geomaterials: from the second-order work criterion to spectral analyses, International Journal for Numerical and Analytical Methods in Geomechanics, Volume 33 (2009), pp. 1169-1202 | DOI | Zbl

[27] Prunier, F.; Nicot, F.; Darve, F.; Laouafa, F.; Lignon, S. 3D multi scale bifurcation analysis of granular media, Journal of Engineering Mechanics (ASCE), Volume 135(6) (2009), pp. 493-509 | DOI

[28] Pastor, M.; Zienkiewicz, O. C.; Chan, A. C. Generalized plasticity and the modelling of soil behaviour, International Journal for Numerical and Analytical Methods in Geomechanics, Volume 14 (1990), pp. 151-190 | DOI | Zbl

[29] Rice, J. R. The localization of plastic deformation, 14 t h IUTAM Congress on Theoretical and Applied Mechanics (Koiter, W. T., ed.) (1976), pp. 207-220

[30] Sibille, L.; Nicot, F.; Donzé, F. V.; Darve, F. Material instability in granular assemblies from fundamentally different models, International Journal for Numerical and Analytical Methods Geomechanics, Volume 31(3) (2007), pp. 457-482 | DOI | Zbl

[31] Wan, R.; Nicot, F.; Darve, F. Failure in geomaterials, a contemporary treatise, ISTE-Wiley, 2017

[32] Wang, Tao; Wautier, Antoine; Tang, Chao-Sheng; Nicot, François 3D DEM simulations of cyclic loading-induced densification and critical state convergence in granular soils, Computers and Geotechnics, Volume 173 (2024), 106559 https://www.sciencedirect.com/science/article/pii/s0266352x24004956 | DOI

[33] Zorzi, G.; Kirsh, F.; Gabireli, F.; Rackwitz, F. Long-term cyclic triaxial tests with DEM simulations, V t h International Conference on Particle-based Methods - Fundamentals and Applications, PARTICLES 2017 (Wriggers, P.; Bishoff, M.; Onate, E.; Owen, D. R. J.; Zohdi, T., eds.) (2017)

[34] Zhao, Chaofa; Kruyt, Niels P.; Pouragha, Mehdi; Wan, Richard Fabric response to stress probing in granular materials: Two-dimensional, anisotropic systems, Computers and Geotechnics, Volume 146 (2022), 104695 https://www.sciencedirect.com/science/article/pii/s0266352x22000593 | DOI

[35] Zhu, Huaxiang; Nguyen, Hien N. G.; Nicot, François; Darve, Félix On a common critical state in localized and diffuse failure modes, Journal of the Mechanics and Physics of Solids, Volume 95 (2016), pp. 112-131 https://www.sciencedirect.com/science/article/pii/s0022509615303951 | DOI

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