Discrepancy in the Critical State Void Ratio of Poorly Graded Sand due to Shear Strain Localization
Publication: Journal of Geotechnical and Geoenvironmental Engineering
Volume 146, Issue 8
Abstract
The critical state (CS) concept is a theoretical framework that models the constitutive behavior of soils, including sand and other granular materials. It supports the notion of a unique postfailure state, where the soil ultimately experiences continuous shearing with no change in the plastic volumetric strain. However, the published literature has frequently noted the nonconvergence of sand specimens with different initial densities to a unique CS in the compression plane due to many factors such as specimen fabric, particle morphology, breakage, and grain size distribution. This paper examines the CS for poorly graded (uniform) glass beads and 3 different types of silica sands using 50 conventional triaxial compression (CTC) experiments, 12 oedometer tests, and in situ synchrotron microcomputed tomography (SMT) scans for 10 CTC experiments. The results of the 50 CTC experiments revealed a diffused CS zone in the compression plane, which was further examined using the in situ SMT scans. A thorough three-dimensional image analysis of the SMT scans accurately quantified the evolution of the local void ratio () versus axial compression within zones of intensive shearing toward the center of the specimen. The evolution of the void ratio was also measured using the entire volume of the specimen (). At the CS, the ratio was assessed to be when a single shear band developed within the scanned specimens and for specimens that failed via external bulging that was internally manifested by the development of multiple shear bands. This finding suggests that the CS zone in the compression plane can be attributed to the common wrong consideration of evolution in lieu of within the developing shear bands. Furthermore, the lack of shear band development in uniaxial compression has made the results of the oedometer test reliable in quantifying the CS parameters in the compression plane.
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Acknowledgments
This material was partially funded by the US National Science Foundation (NSF) under Grant CMMI-1266230. Any opinions, findings, conclusions, and recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the NSF. The SMT scans presented in this paper were collected using the X-Ray Operations and Research Beamline Station 13-BMD of the Advanced Photon Source (APS), a US Department of Energy (DOE) Office of Science User Facility operated by the Argonne National Laboratory (ANL) under Contract DE-AC02-06CH11357. We acknowledge the support of GeoSoilEnviroCARS (Sector 13), which is funded by the NSF Earth Sciences (EAR-1128799), and the DOE Geosciences (DE-FG02-94ER14466). We thank Dr. Mark Rivers for his guidance at APS.
References
Alshibli, K., S. Batiste, and S. Sture. 2003. “Strain localization in sand: Plane strain versus triaxial compression.” J. Geotech. Geoenviron. Eng. 129 (6): 483–494. https://doi.org/10.1061/(ASCE)1090-0241(2003)129:6(483).
Alshibli, K., and M. Cil. 2018. “Influence of particle morphology on the friction and dilatancy of sand.” J. Geotech. Geoenviron. Eng. 144 (3): 04017118. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001841.
Alshibli, K., A. Druckrey, R. Al-Raoush, T. Weiskittel, and N. Lavrik. 2014. “Quantifying morphology of sands using 3D imaging.” J. Mater. Civ. Eng. 27 (10): 04014275. https://doi.org/10.1061/(ASCE)MT.1943-5533.0001246.
Alshibli, K., and A. Hasan. 2008. “Spatial variation of void ratio and shear band thickness in sand using X-ray computed tomography.” Géotechnique 58 (4): 249–257. https://doi.org/10.1680/geot.2008.58.4.249.
Alshibli, K., M. Jarrar, A. Druckrey, and R. Al-Raoush. 2016. “Influence of particle morphology on 3D kinematic behavior and strain localization of sheared sand.” J. Geotech. Geoenviron. Eng. 143 (2): 04016097. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001601.
Alshibli, K., and L. Roussel. 2006. “Experimental investigation of slip-stick behaviour in granular materials.” Int. J. Numer. Anal. Methods Geomech. 30 (14): 1391–1407. https://doi.org/10.1002/nag.517.
Altuhafi, F., B. A. Baudet, and P. Sammonds. 2010. “The mechanics of subglacial sediment: An example of new ‘transitional’ behaviour.” Can. Geotech. J. 47 (7): 775–790. https://doi.org/10.1139/T09-136.
Altuhafi, F., and M. R. Coop. 2011. “Changes to particle characteristics associated with the compression of sands.” Géotechnique 61 (6): 459–471. https://doi.org/10.1680/geot.9.P.114.
Amirrahmat, S., A. Druckrey, K. Alshibli, and R. Al-Raoush. 2018. “Micro shear bands: Precursor for strain localization in sheared granular materials.” J. Geotech. Geoenviron. Eng. 145 (2): 04018104. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001989.
Andò, E., E. Salvatore, J. Desrues, P. Charrier, J.-B. Toni, G. Modoni, and G. Viggiani. 2017. “Strain localisation in sand in cycles of triaxial compression and extension: Continuum and grain-scale analysis.” In Proc., Int. Workshop on Bifurcation and Degradation in Geomaterials, 489–497. New York: Springer.
Been, K., and M. G. Jefferies. 1985. “A state parameter for sands.” Géotechnique 35 (2): 99–112. https://doi.org/10.1680/geot.1985.35.2.99.
Coop, M. 1990. “The mechanics of uncemented carbonate sands.” Géotechnique 40 (4): 607–626. https://doi.org/10.1680/geot.1990.40.4.607.
Coop, M. 2015. “Limitations of a Critical State framework applied to the behaviour of natural and ‘transitional’ soils.” In Proc., 6th Int. Symp. on Deformation Characteristics of Geomaterials, IS-Buenos Aires, 115–155. Amsterdam, Netherlands: IOS Press. https://doi.org/10.3233/978-1-61499-601-9-115.
Coop, M., and I. Lee. 1993. “The behaviour of granular soils at elevated stresses.” In Predictive Soil Mechanics: Proc., Wroth Memorial Symp. Held at St Catherine's College, 186–198. London: Thomas Telford Publishing.
Dafalias, Y. F., and M. T. Manzari. 2004. “Simple plasticity sand model accounting for fabric change effects.” J. Eng. Mech. 130 (6): 622–634. https://doi.org/10.1061/(ASCE)0733-9399(2004)130:6(622).
Desrues, J., and G. Viggiani. 2004. “Strain localization in sand: An overview of the experimental results obtained in Grenoble using stereophotogrammetry.” Int. J. Numer. Anal. Methods Geomech. 28 (4): 279–321. https://doi.org/10.1002/nag.338.
Druckrey, A., K. Alshibli, and R. Al-Raoush. 2016. “3D characterization of sand particle-to-particle contact and morphology.” Comput. Geotech. 74 (Apr): 26–35. https://doi.org/10.1016/j.compgeo.2015.12.014.
Druckrey, A., K. Alshibli, and R. Al-Raoush. 2018. “Discrete particle translation gradient concept to expose strain localisation in sheared granular materials using 3D experimental kinematic measurements.” Géotechnique 68 (2): 162–170. https://doi.org/10.1680/jgeot.16.P.148.
Evans, T. M., and J. D. Frost. 2010. “Multiscale investigation of shear bands in sand: Physical and numerical experiments.” Int. J. Numer. Anal. Methods Geomech. 34 (15): 1634–1650. https://doi.org/10.1002/nag.877.
Ferreira, P., and A. Bica. 2006. “Problems in identifying the effects of structure and critical state in a soil with a transitional behaviour.” Géotechnique 56 (7): 445–454. https://doi.org/10.1680/geot.2006.56.7.445.
Finno, R. J., and A. L. Rechenmacher. 2003. “Effects of consolidation history on critical state of sand.” J. Geotech. Geoenviron. Eng. 129 (4): 350–360. https://doi.org/10.1061/(ASCE)1090-0241(2003)129:4(350).
Frost, J. D., and D.-J. Jang. 2000. “Evolution of sand microstructure during shear.” J. Geotech. Geoenviron. Eng. 126 (2): 116–130. https://doi.org/10.1061/(ASCE)1090-0241(2000)126:2(116).
Fu, P., and Y. F. Dafalias. 2011. “Fabric evolution within shear bands of granular materials and its relation to critical state theory.” Int. J. Numer. Anal. Methods Geomech. 35 (18): 1918–1948. https://doi.org/10.1002/nag.988.
Gao, Z., J. Zhao, X. S. Li, and Y. F. Dafalias. 2014. “A critical state sand plasticity model accounting for fabric evolution.” Int. J. Numer. Anal. Methods Geomech. 38 (4): 370–390. https://doi.org/10.1002/nag.2211.
Garga, V. K., and H. Zhang. 1997. “Volume changes in undrained triaxial tests on sands.” Can. Geotech. J. 34 (5): 762–772. https://doi.org/10.1139/t97-038.
Gu, X., M. Huang, and J. Qian. 2014. “Discrete element modeling of shear band in granular materials.” Theor. Appl. Fract. Mech. 72 (Aug): 37–49. https://doi.org/10.1016/j.tafmec.2014.06.008.
Harris, W. W., G. Viggiani, M. A. Mooney, and R. J. Finno. 1995. “Use of stereophotogrammetry to analyze the development of shear bands in sand.” Geotech. Test. J. 18 (4): 405–420. https://doi.org/10.1520/GTJ11016J.
Hasan, A., and K. Alshibli. 2012. “Three dimensional fabric evolution of sheared sand.” Granular Matter 14 (4): 469–482. https://doi.org/10.1007/s10035-012-0353-0.
Imseeh, W. H., A. M. Druckrey, and K. A. Alshibli. 2017. “3D experimental quantification of fabric and fabric evolution of sheared granular materials using synchrotron micro-computed tomography.” Granular Matter 20 (2): 24. https://doi.org/10.1007/s10035-018-0798-x.
Iwashita, K., and M. Oda. 1998. “Rolling resistance at contacts in simulation of shear band development by DEM.” J. Eng. Mech. 124 (3): 285–292. https://doi.org/10.1061/(ASCE)0733-9399(1998)124:3(285).
Iwashita, K., and M. Oda. 2000. “Micro-deformation mechanism of shear banding process based on modified distinct element method.” Powder Technol. 109 (1–3): 192–205. https://doi.org/10.1016/S0032-5910(99)00236-3.
Jefferies, M., and K. Been. 2000. “Implications for critical state theory from isotropic compression of sand.” Géotechnique 50 (4): 419–429. https://doi.org/10.1680/geot.2000.50.4.419.
Jiang, M., H. Yan, H. Zhu, and S. Utili. 2011. “Modeling shear behavior and strain localization in cemented sands by two-dimensional distinct element method analyses.” Comput. Geotech. 38 (1): 14–29. https://doi.org/10.1016/j.compgeo.2010.09.001.
Kandasami, R. K., and T. G. Murthy. 2017. “Manifestation of particle morphology on the mechanical behaviour of granular ensembles.” Granular Matter 19 (2): 21. https://doi.org/10.1007/s10035-017-0703-z.
Kwa, K., and D. Airey. 2016. “Critical state interpretation of effects of fines in silty sands.” Geotech. Lett. 6 (1): 100–105. https://doi.org/10.1680/jgele.15.00176.
Li, X. S., and Y. Wang. 1998. “Linear representation of steady state line for sand.” J. Geotech. Environ. Eng. 124 (12): 1215–1217. https://doi.org/10.1061/(ASCE)1090-0241(1998)124:12(1215).
Lu, Y., and D. Frost. 2010. “Three-dimensional DEM modeling of triaxial compression of sands.” In Proc., Soil Behavior and Geo-Micromechanics, 220–226. Reston, VA: ASCE. https://doi.org/10.1061/41101(374)33.
Marschi, N. D., C. K. Chan, and H. B. Seed. 1972. “Evaluation of properties of rockfill materials.” J. Soil Mech. Found. Div. 98 (1): 95–114.
Martins, F. B., L. A. Bressani, M. R. Coop, and A. V. D. Bica. 2001. “Some aspects of the compressibility behaviour of a clayey sand.” Can. Geotech. J. 38 (6): 1177–1186. https://doi.org/10.1139/t01-048.
McDowell, G., and M. Bolton. 1998. “On the micromechanics of crushable aggregates.” Géotechnique 48 (5): 667–679. https://doi.org/10.1680/geot.1998.48.5.667.
Mooney, M. A., R. J. Finno, and M. G. Viggiani. 1998. “A unique critical state for sand?” J. Geotech. Geoenviron. Eng. 124 (11): 1100–1108. https://doi.org/10.1061/(ASCE)1090-0241(1998)124:11(1100).
Nocilla, A., M. Coop, and F. Colleselli. 2006. “The mechanics of an Italian silt: An example of ‘transitional’ behaviour.” Géotechnique 56 (4): 261–271. https://doi.org/10.1680/geot.2006.56.4.261.
Pestana, J. M., and A. J. Whittle. 1994. “Model prediction of anisotropic clay behavior due to consolidation stress history.” In Proc., 8th Int. Conf. Computer Methods and Advances in Geomechanics. Rotterdam, Netherlands: A.A. Balkema.
Pestana, J. M., and A. J. Whittle. 1999. “Formulation of a unified constitutive model for clays and sands.” Int. J. Numer. Anal. Methods Geomech. 23 (12): 1215–1243. https://doi.org/10.1002/(SICI)1096-9853(199910)23:12%3C1215::AID-NAG29%3E3.0.CO;2-F.
Petalas, A. L., Y. F. Dafalias, and A. G. Papadimitriou. 2019. “SANISAND-FN: An evolving fabric-based sand model accounting for stress principal axes rotation.” Int. J. Numer. Anal. Methods Geomech. 43 (1): 97–123. https://doi.org/10.1002/nag.2855.
Ponzoni, E., A. Nocilla, and M. Coop. 2017. “The behaviour of a gap graded sand with mixed mineralogy.” Soils Found. 57 (6): 1030–1044. https://doi.org/10.1016/j.sandf.2017.08.029.
Poorooshasb, H., I. Holubec, and A. Sherbourne. 1966. “Yielding and flow of sand in triaxial compression. I.” Can. Geotech. J. 3 (4): 179–190. https://doi.org/10.1139/t66-023.
Roscoe, K. H., and J. Burland. 1968. On the generalized stress-strain behaviour of wet clay. Berlin: ScienceOpen.
Roscoe, K. H., A. Schofield, and C. Wroth. 1958. “On the yielding of soils.” Géotechnique 8 (1): 22–53. https://doi.org/10.1680/geot.1958.8.1.22.
Salvatore, E., G. Modoni, E. Andò, M. Albano, and G. Viggiani. 2017. “Determination of the critical state of granular materials with triaxial tests.” Soils Found. 57 (5): 733–744. https://doi.org/10.1016/j.sandf.2017.08.005.
Santamarina, J., and G.-C. Cho. 2004.“Soil behaviour: The role of particle shape.” In Proc., Advances in Geotechnical Engineering: The Skempton Conf., 604–617. London: Thomas Telford.
Schofield, A., and P. Wroth. 1968. Critical state soil mechanics. New York: McGraw-hill.
Shipton, B., and M. R. Coop. 2012. “On the compression behaviour of reconstituted soils.” Soils Found. 52 (4): 668–681. https://doi.org/10.1016/j.sandf.2012.07.008.
Shipton, B., and M. R. Coop. 2015. “Transitional behaviour in sands with plastic and non-plastic fines.” Soils Found. 55 (1): 1–16. https://doi.org/10.1016/j.sandf.2014.12.001.
Tagliaferri, F., J. Waller, E. Andò, S. A. Hall, G. Viggiani, P. Bésuelle, and J. T. DeJong. 2011. “Observing strain localisation processes in bio-cemented sand using x-ray imaging.” Granular Matter 13 (3): 247–250. https://doi.org/10.1007/s10035-011-0257-4.
Theocharis, A. I., E. Vairaktaris, Y. F. Dafalias, and A. G. Papadimitriou. 2016. “Proof of incompleteness of critical state theory in granular mechanics and its remedy.” J. Eng. Mech. 143 (2): 04016117. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001166.
Todisco, M., M. Coop, and J.-M. Pereira. 2018. “Fabric characterisation in transitional soils.” Granular Matter 20 (2): 20. https://doi.org/10.1007/s10035-018-0786-1.
Vesic, A. S., and G. W. Clough. 1968. “Behavior of granular materials under high stresses.” J. Soil Mech. Found. Div. 94 (3): 661–688.
Wang, R., P. Fu, J.-M. Zhang, and Y. F. Dafalias. 2017. “Evolution of various fabric tensors for granular media toward the critical state.” J. Eng. Mech. 143 (10): 04017117. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001342.
Whittle, A. J., D. J. DeGroot, C. C. Ladd, and T.-H. Seah. 1994. “Model prediction of anisotropic behavior of Boston blue clay.” J. Geotech. Eng. 120 (1): 199–224. https://doi.org/10.1061/(ASCE)0733-9410(1994)120:1(199).
Whittle, A. J., and M. J. Kavvadas. 1994. “Formulation of MIT-E3 constitutive model for overconsolidated clays.” J. Geotech. Eng. 120 (1): 173–198. https://doi.org/10.1061/(ASCE)0733-9410(1994)120:1(173).
Wood, D. M. 1990. Soil behaviour and critical state soil mechanics. New York: Press Syndicate of the Univ. of Cambridge the Pitt Building.
Xiao, Y., M. Coop, H. Liu, H. Liu, and J. Jiang. 2016. “Transitional behaviors in well-graded coarse granular soils.” J. Geotech. Geoenviron. Eng. 142 (12): 06016018. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001551.
Xiao, Y., H. Liu, X. Ding, Y. Chen, J. Jiang, and W. Zhang. 2015. “Influence of particle breakage on critical state line of rockfill material.” Int. J. Geomech. 16 (1): 04015031. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000538.
Xu, L., and M. Coop. 2017. “The mechanics of a saturated silty loess with a transitional mode.” Géotechnique 67 (7): 581–596. https://doi.org/10.1680/jgeot.16.P.128.
Yang, J., and X. Luo. 2015. “Exploring the relationship between critical state and particle shape for granular materials.” J. Mech. Phys. Solids 84 (Nov): 196–213. https://doi.org/10.1016/j.jmps.2015.08.001.
Zuo, L., and B. A. Baudet. 2015. “Determination of the transitional fines content of sand-non plastic fines mixtures.” Soils Found. 55 (1): 213–219. https://doi.org/10.1016/j.sandf.2014.12.017.
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Journal of Geotechnical and Geoenvironmental Engineering
Volume 146 • Issue 8 • August 2020
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Received: Jul 28, 2019
Accepted: Jan 24, 2020
Published online: Jun 10, 2020
Published in print: Aug 1, 2020
Discussion open until: Nov 10, 2020
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