A Study on the Initiation of Discontinuities in Hypoplastic Granular Materials for Some Simple Motion Fields in Classical Continua
Publication: Journal of Engineering Mechanics
Volume 149, Issue 1
Abstract
Some theoretical criteria are set forth to study the onset of a strong and/or a weak discontinuity in hypoplastic granular materials under some simple motion fields. The theoretical criteria were based on direct analysis, considering both kinematical and dynamical conditions necessary to be satisfied in order to make a discontinuity of either type possible. We mean by simple motion fields those motion fields that are typically observed in standard laboratory tests, including homogeneous motion fields. A series of comparisons with available experimental data have been made for a simple hypoplastic constitutive equation.
Practical Applications
In geomechanics and other fields related to granular or porous materials, it is of particular importance to see whether the material is stable while deforming under applied loads. The phrase stability means, in a general sense, an ability to sustain the applied loads or remain in a particular form, without further deformation, following total loss of strength. Examples are the stability of underground tunnels or deep excavations prior to the construction of, say, a high-rise building. In both cases, deformation occurs while tunnel boring or ground excavation takes place, resulting in the alteration of the stress state followed by possible instabilities. A good example of instability is the catastrophic failure of tunnels in rock that takes place by sliding and falling of heavy blocks of rock along cracks and joints, in general, along planes of discontinuity. A plane of discontinuity often indicates the onset of instability in most materials. The results of this paper are expected to be useful in performing stability analysis in terms of assessing the possibility of the formation of such planes of discontinuity in a particular class of materials called hypoplastic materials.
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Data Availability Statement
No data, model or code were generated or used during the study.
Acknowledgments
The authors would like to draw their appreciation to Dr. Arsalan Ghahramani (Professor Emeritus in Geomechanics) and Dr. Mojtaba Mahzoon (Professor in Applied Mechanics and Mathematics), Shiraz University, for their substantial scientific support of this work.
References
Arthur, J. R. F., T. Dunstan, Q. A. J. L. Al-Ani, and A. Assadi. 1977. “Plastic deformation and failure in granular media.” Géotechnique 27 (1): 53–74. https://doi.org/10.1680/geot.1977.27.1.53.
Bardet, J. P. 1990. “A comprehensive review of strain localization in elastoplastic soils.” Comput. Geotech. 10 (3): 163–188. https://doi.org/10.1016/0266-352X(90)90034-S.
Bauer, E. 1996. “Calibration of a comprehensive hypoplastic model for granular materials.” Soils Found. 36 (1): 13–26. https://doi.org/10.3208/sandf.36.13.
Bauer, E. 1999. “Analysis of shear band bifurcation with a hypoplastic model for a pressure and density sensitive granular material.” Mech. Mater. 31 (9): 597–609. https://doi.org/10.1016/S0167-6636(99)00017-4.
Belytschko, T., and T. Black. 1999. “Elastic crack growth in finite elements with minimal remeshing.” Int. J. Numer. Methods Eng. 45 (5): 601–620. https://doi.org/10.1002/(SICI)1097-0207(19990620)45:5%3C601::AID-NME598%3E3.0.CO;2-S.
Belytschko, T., R. Gracie, and G. Ventura. 2009. “A review of extended/generalized finite element methods for materials modeling.” Modell. Simul. Mater. Sci. Eng. 17 (4): 043001. https://doi.org/10.1088/0965-0393/17/4/043001.
Fu, P., and Y. F. Dafalias. 2012. “Quantification of large and localized deformation in granular materials.” Int. J. Solids Struct. 49 (13): 1741–1752. https://doi.org/10.1016/j.ijsolstr.2012.03.006.
Ghahramani, A., and S. P. Clemence. 1980. “Zero extension line theory of dynamic passive pressure.” J. Geotech. Eng. Div. 106 (6): 631–644. https://doi.org/10.1061/AJGEB6.0000976.
Green, A. E. 1956. “Hypo-elasticity and plasticity.” Proc. R. Soc. London, Ser. A 234 (6): 46–59. https://doi.org/10.1098/rspa.1956.0014.
Gudehus, G., and D. Mašín. 2009. “Graphical representation of constitutive equations.” Géotechnique 59 (2): 147–151. https://doi.org/10.1680/geot.2007.00155.
Guo, N., and J. Zhao. 2016. “3D multiscale modeling of strain localization in granular media.” Comput. Geotech. 80 (Jan): 360–372. https://doi.org/10.1016/j.compgeo.2016.01.020.
Gutierrez, M. 2017. “Comparison of the Rudnicki-Rice and Vermeer bifurcation criteria.” J. Eng. Mech. 143 (6): 04017027. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001221.
Hadamard, J. 1903. Leçon sur la propagation des ondes et les equations de I’hydrodynamique, Librarie scientifique. Paris, France: Hermann.
Herle, I., and G. Gudehus. 1999. “Determination of parameters of a hypoplastic constitutive model from properties of grain assemblies.” Mech. Cohesive-Frict. Mater. 4 (5): 461–486. https://doi.org/10.1002/(SICI)1099-1484(199909)4:5%3C461::AID-CFM71%3E3.0.CO;2-P.
Hill, R. 1962. “Acceleration waves in solids.” J. Mech. Phys. Solids 10 (1): 1–16. https://doi.org/10.1016/0022-5096(62)90024-8.
Khoei, A. R. 2015. Extended finite element method, theory and applications. New York: Wiley.
Khoei, A. R., and K. Karimi. 2008. “An enriched-FEM model for simulation of localization phenomenon in Cosserat continuum theory.” Comput. Mater. Sci. 44 (2): 733–749. https://doi.org/10.1016/j.commatsci.2008.05.019.
Khoei, A. R., S. Yadegari, and S. O. R. Biabanaki. 2010. “3D finite element modeling of shear band localization via the micro-polar Cosserat continuum theory.” Comput. Mater. Sci. 49 (4): 720–733. https://doi.org/10.1016/j.commatsci.2010.06.015.
Kolymbas, D. 1991. “An outline of hypoplasticity.” Arch. App. Mech. 61 (5): 143–151. https://doi.org/10.1007/BF00788048.
Kolymbas, D. 2000. Introduction to hypoplasticity. Rotterdam, Netherlands: A. A. Balkema.
Lade, P. V., and M. K. Kim. 1995. “Single hardening constitutive model for soil, rock and concrete.” Int. J. Solids Struct. 32 (14): 1963–1978. https://doi.org/10.1016/0020-7683(94)00247-T.
Mašín, D. 2012a. “Clay hypoplasticity with explicitly defined asymptotic states.” Acta Geotech. 8 (5): 481–496. https://doi.org/10.1007/s11440-012-0199-y.
Mašín, D. 2012b. “Hypoplastic Cam-clay model.” Géotechnique 62 (6): 549–553. https://doi.org/10.1680/geot.11.T.019.
Mašín, D. 2014. “Clay hypoplasticity model including stiffness anisotropy.” Géotechnique 64 (3): 232–238. https://doi.org/10.1680/geot.13.P.065.
Mir Tamizdoust, M., M. Veiskarami, and H. Mohammadi. 2017. “A note on the effect of intermediate principal stress on the onset of strain localization in granular soils.” Iran. J. Sci. Technol. Trans. Civ. Eng. 41 (4): 429–432. https://doi.org/10.1007/s40996-017-0078-8.
Moës, N., J. Dolbow, and T. Belytschko. 1999. “A finite element method for crack growth without remeshing.” Int. J. Numer. Methods Eng. 46 (1): 131–150. https://doi.org/10.1002/(SICI)1097-0207(19990910)46:1%3C131::AID-NME726%3E3.0.CO;2-J.
Molaei, H., M. Veiskarami, and S. Pietruszczak. 2021. “Localization of deformation in anisotropic granular materials utilizing the microstructure tensor.” Int. J. Geomech. 21 (7): 04021106. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002015.
Noll, W. 1955. “On the continuity of the solid and fluid states.” J. Ration. Mech. Anal. 4 (Jan): 3–81.
Phuong, N. T. V., A. Rohe, R. B. J. Brinkgreve, and A. F. van Tol. 2018. “Hypoplastic model for crushable sand.” Soils Found. 58 (3): 615–626. https://doi.org/10.1016/j.sandf.2018.02.022.
Regueiro, R. A., and R. I. Borja. 2001. “Plane strain finite element analysis of pressure-sensitive plasticity with strong discontinuity.” Int. J. Solids Struct. 38 (21): 3647–3672. https://doi.org/10.1016/S0020-7683(00)00250-X.
Rice, J. R. 1976. “The localization of plastic deformation.” In Vol. 1 Proc., 4th Int. Congress on Theoretical and Applied Mechanics, edited by W. T. Koiter, 207–220. Delft, Netherlands: North-Holland Publishing Co.
Rice, J. R., and J. W. Rudnicki. 1980. “A note on some features of the theory of localization of deformation.” Int. J. Solids Struct. 16 (7): 597–605. https://doi.org/10.1016/0020-7683(80)90019-0.
Roscoe, K. H. 1970. “The influence of strains in soil mechanics.” Géotechnique 20 (2): 129–170. https://doi.org/10.1680/geot.1970.20.2.129.
Rudnicki, J. W., and J. R. Rice. 1975. “Conditions for the localization of deformation in pressure-sensitive dilatant materials.” J. Mech. Phys. Solids 23 (6): 371–394. https://doi.org/10.1016/0022-5096(75)90001-0.
Sabzevari, A., and A. Ghahramani. 1972. “The limit equilibrium analysis of bearing capacity and earth pressure problems in nonhomogeneous soils.” Soils Found. Jpn. Soc. Soil Mech. Found. Eng. 12 (3): 33–48. https://doi.org/10.3208/sandf1972.12.3_33.
Sabzevari, A., and A. Ghahramani. 1974. “Dynamic passive earth pressure problem.” J. Geotech. Eng. Div. 100 (1): 15–30. https://doi.org/10.1061/AJGEB6.0000002.
Sanborn, S. E., and J. H. Prévost. 2011. “Frictional slip plane growth by localization detection and the extended finite element method (XFEM).” Int. J. Numer. Anal. Methods Geomech. 35 (11): 1278–1298. https://doi.org/10.1002/nag.958.
Sulem, J., and I. Vardoulakis. 1990. “Analysis of the triaxial test on rocks specimens. A theoretical model for shape and size effect.” Acta Mech. 83 (Apr): 195–212. https://doi.org/10.1007/BF01172981.
Teunissen, J. A. 2008. “Shear band analysis in the biaxial test.” Int. J. Geomech. 8 (5): 311–321. https://doi.org/10.1061/(ASCE)1532-3641(2008)8:5(311).
Thomas, T. Y. 1961. Plastic flow and fracture in solids. New York: Elsevier.
Truesdell, C. A. 1955. “Hypo-elasticity.” J. Ration. Mech. Anal. 4 (12): 83–133.
Truesdell, C. A., and R. Toupin. 1960. “The classical field theories.” In Prinzipien der Klassischen Mechanik und Feldtheorie (Principles of classical mechanics and field theory), 226–858. Berlin: Springer.
Vardoulakis, I., and J. Sulem. 2005. Bifurcation analysis in geomechanics. London: Chapman and Hall.
Veiskarami, M., and M. Doostdar. 2017. “Bearing capacity of non-associative coaxial granular materials by upper bound limit analysis and finite elements.” Geomech. Geoeng. 12 (3): 151–168. https://doi.org/10.1080/17486025.2016.1189600.
Veiskarami, M., T. Farsimadan, and M. Mahzoon. 2019. “Study on the shear band thickness in classical continua by a decomposed deformation field for granular materials.” J. Eng. Mech. 145 (11): 04019087. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001664.
Veiskarami, M., and M. Mir Tamizdoust. 2017. “Bifurcation analysis in sands under true triaxial conditions with coaxial and noncoaxialplastic flow rules.” J. Eng. Mech. 143 (10): 04017120. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001344.
Wang, Q., and P. V. Lade. 2001. “Shear banding in true triaxial tests and its effect on failure in sand.” J. Eng. Mech. 127 (8): 754–761. https://doi.org/10.1061/(ASCE)0733-9399(2001)127:8(754).
Wu, W. 2000. “Non-linear analysis of shear band formation in sand.” Int. J. Numer. Anal. Methods Geomech. 24 (3): 245–263. https://doi.org/10.1002/(SICI)1096-9853(200003)24:3%3C245::AID-NAG52%3E3.0.CO;2-C.
Wu, W. 2006. “On high-order hypoplastic models for granular materials.” J. Eng. Mech. 56 (8): 23–34. https://doi.org/10.1007/s10665-006-9040-7.
Wu, W., and E. Bauer. 1994. “A simple hypoplastic constitutive model for sand.” Int. J. Numer. Anal. Methods Geomech. 18 (5): 833–862. https://doi.org/10.1002/nag.1610181203.
Wu, W., E. Bauer, and D. Kolymbas. 1996. “Hypoplastic constitutive model with critical state for granular materials.” Mech. Mater. 23 (1): 45–69. https://doi.org/10.1016/0167-6636(96)00006-3.
Wu, W., and D. Kolymbas. 1990. Numerical testing of the stability criterion for hypoplastic constitutive equations, 245–253. New York: Elsevier.
Wu, W., J. Lin, and X. Wang. 2017. “A basic hypoplastic constitutive model for sand.” Acta Geotech. 12 (4): 1373–1382. https://doi.org/10.1007/s11440-017-0550-4.
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© 2022 American Society of Civil Engineers.
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Received: Apr 2, 2022
Accepted: Aug 14, 2022
Published online: Nov 8, 2022
Published in print: Jan 1, 2023
Discussion open until: Apr 8, 2023
ASCE Technical Topics:
- Analysis (by type)
- Continuum mechanics
- Discontinuities
- Dynamic analysis
- Dynamics (solid mechanics)
- Engineering fundamentals
- Engineering materials (by type)
- Engineering mechanics
- Field tests
- Granular materials
- Homogeneity
- Kinematics
- Kinetics
- Laboratory tests
- Material mechanics
- Material properties
- Materials engineering
- Mathematical functions
- Mathematics
- Motion (dynamics)
- Solid mechanics
- Tests (by type)
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