Abstract
A combined fabric evolution (CFE) model is used to predict real-world fabric evolution of a strongly anisometric granular material under triaxial loading, connecting advances in theoretical developments and experimental measurement technology for fabric evolution. X-ray tomography is used to quantify particle orientation and contact normal fabric evolution in five triaxial compression experiments on lentil specimens of different initial bedding plane angles. The CFE model coupling contact normal fabric evolution with particle orientation fabric is calibrated based on two of the experiments and used to predict the fabric evolution in the others. Good overall agreement between theoretical prediction and experimental measurement is achieved for the evolution of both types of fabric tensors. The comparison between prediction and measurement highlights an optimistic future for the development of constitutive relations incorporating fabric features based on actual experimental micromechanical observations. Nonetheless, the special case of 90° deposition is relatively poorly predicted due to the strongly heterogeneous local dilation caused by the extreme particle shape and alignment. This suggests that there is still more to be considered in the continuum description of the fabric evolution of granular materials, especially with respect to local information.
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Data Availability Statement
All data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
Thought-provoking discussions with Takashi Matsushima and Stéphane Roux are acknowledged. Special thanks go to Jacques Desrues, who designed the experimental apparatus in the first place, and also inspired the experimental campaign. Rui Wang would like to thank the National Natural Science Foundation of China (No. 52022046) and the State Key Laboratory of Hydroscience and Hydraulic Engineering (No. 2021-KY-04) for funding this study. This project has received funding from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant Agreement No. 812638 (CALIPER). Laboratoire 3SR is part of the LabEx Tec 21 (Investissements d’Avenir—Grant Agreement No. ANR-11-LABX-0030).
References
Andò, E. 2013. “Experimental investigation of microstructural changes in deforming granular media using x-ray tomography.” Ph.D. thesis, Matériaux, Mécanique, Génie Civil, Electrochimie, Univ. Grenoble Alpes.
Andò, E., J. Dijkstra, E. Roubin, C. Dano, and E. Boller. 2019. “A peek into the origin of creep in sand.” Granular Matter 21 (1): 11. https://doi.org/10.1007/s10035-018-0863-5.
Andò, E., and G. Viggiani. 2018. “On the ease of experimental access to deformation entities in granular assemblies.” Ital. Geotech. J. 52 (2): 44–51.
Arthur, J. R. F., and B. Menzies. 1972. “Inherent anisotropy in a sand.” Géotechnique 22 (1): 115–128. https://doi.org/10.1680/geot.1972.22.1.115.
Bagi, K. 1996. “Stress and strain in granular assemblies.” Mech. Mater. 22 (3): 165–177. https://doi.org/10.1016/0167-6636(95)00044-5.
Casagrande, A., and N. Carillo. 1944. “Shear failure of anisotropic materials.” J. Boston Soc. Civ. Eng. 31 (4): 74–87.
Fisher, N. I., T. Lewis, and B. J. Embleton. 1993. Statistical analysis of spherical data. Cambridge, UK: Cambridge University Press.
Fu, P., and Y. F. Dafalias. 2011a. “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.
Fu, P., and Y. F. Dafalias. 2011b. “Study of anisotropic shear strength of granular materials using dem simulation.” Int. J. Numer. Anal. Methods Geomech. 35 (10): 1098–1126. https://doi.org/10.1002/nag.945.
Guo, N., and J. Zhao. 2013. “The signature of shear-induced anisotropy in granular media.” Comput. Geotech. 47 (Jan): 1–15. https://doi.org/10.1016/j.compgeo.2012.07.002.
Gutierrez, M., K. Ishihara, and I. Towhata. 1991. “Flow theory for sand during rotation of principal stress direction.” Soils Found. 31 (4): 121–132. https://doi.org/10.3208/sandf1972.31.4_121.
Hall, S. A., M. Bornert, J. Desrues, Y. Pannier, N. Lenoir, G. Viggiani, and P. Bésuelle. 2010. “Discrete and continuum analysis of localised deformation in sand using X-ray CT and volumetric digital image correlation.” Géotechnique 60 (5): 315–322. https://doi.org/10.1680/geot.2010.60.5.315.
Hu, N., P. Z. Zhuang, D. S. Yang, and H. S. Yu. 2021. “On the evolution law of a contact normal-based fabric tensor for granular materials.” Comput. Geotech. 132 (2021): 103857. https://doi.org/10.1016/j.compgeo.2020.103857.
Hurley, R. C., S. A. Hall, and J. P. Wright. 2017. “Multi-scale mechanics of granular solids from grain-resolved X-ray measurements.” Proc. R. Soc. A: Math. Phys. Eng. Sci. 473 (2207): 20170491. https://doi.org/10.1098/rspa.2017.0491.
Imseeh, W. H., A. M. Druckrey, and K. A. Alshibli. 2018. “3d experimental quantification of fabric and fabric evolution of sheared granular materials using synchrotron micro-computed tomography.” Granular Matter 20 (2): 1–28. https://doi.org/10.1007/s10035-018-0798-x.
Kanatani, K.-I. 1984. “Distribution of directional data and fabric tensors.” Int. J. Eng. Sci. 22 (2): 149–164. https://doi.org/10.1016/0020-7225(84)90090-9.
Kruyt, N. P., and L. Rothenburg. 2004. “Kinematic and static assumptions for homogenization in micromechanics of granular materials.” Mech. Mater. 36 (12): 1157–1173. https://doi.org/10.1016/j.mechmat.2002.12.001.
Lade, P. V. 2008. “Failure criterion for cross-anisotropic soils.” J. Geotech. Geoenviron. Eng. 134 (1): 117–124. https://doi.org/10.1061/(ASCE)1090-0241(2008)134:1(117).
Li, X., and X.-S. Li. 2009. “Micro-macro quantification of the internal structure of granular materials.” J. Eng. Mech. 135 (7): 641–656. https://doi.org/10.1061/(ASCE)0733-9399(2009)135:7(641).
Li, X. S., and Y. F. Dafalias. 2002. “Constitutive modeling of inherently anisotropic sand behavior.” J. Geotech. Geoenviron. Eng. 128 (10): 868–880. https://doi.org/10.1061/(ASCE)1090-0241(2002)128:10(868).
Li, X. S., and Y. F. Dafalias. 2012. “Anisotropic critical state theory: Role of fabric.” J. Eng. Mech. 138 (3): 263–275. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000324.
Miura, K., S. Miura, and S. Toki. 1986. “Deformation behavior of anisotropic dense sand under principal stress axes rotation.” Soils Found. 26 (1): 36–52. https://doi.org/10.3208/sandf1972.26.36.
Oda, M., I. Koishikawa, and T. Higuchi. 1978. “Experimental study of anisotropic shear strength of sand by plane strain test.” Soils Found. 18 (1): 25–38. https://doi.org/10.3208/sandf1972.18.25.
Pietruszczak, S., and Z. Mroz. 2000. “Formulation of anisotropic failure criteria incorporating a microstructure tensor.” Comput. Geotech. 26 (2): 105–112. https://doi.org/10.1016/S0266-352X(99)00034-8.
Roscoe, K. H., A. N. Schofield, and C. P. Wroth. 1958. “On the yielding of soils.” Géotechnique 8 (1): 22–53. https://doi.org/10.1680/geot.1958.8.1.22.
Tanabe, A., K. Fukumizu, S. Oba, T. Takenouchi, and S. Ishii. 2007. “Parameter estimation for von Mises–Fisher distributions.” Comput. Stat. 22 (1): 145–157. https://doi.org/10.1007/s00180-007-0030-7.
Tengattini, A., and E. Andò. 2015. “Kalisphera: An analytical tool to reproduce the partial volume effect of spheres imaged in 3d.” Meas. Sci. Technol. 26 (9): 095606. https://doi.org/10.1088/0957-0233/26/9/095606.
Theocharis, A. I., E. Vairaktaris, Y. F. Dafalias, and A. G. Papadimitriou. 2017. “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.
Wan, R. G., and J. Guo. 2004. “Drained cyclic behavior of sand with fabric dependence.” J. Eng. Mech. 127 (11): 635–645. https://doi.org/10.1061/(ASCE)0733-9399(2001)127:11(1106).
Wang, R., W. Cao, L. Xue, and J. M. Zhang. 2021. “An anisotropic plasticity model incorporating fabric evolution for monotonic and cyclic behavior of sand.” Acta Geotech. 16: 43–65. https://doi.org/10.1007/s11440-020-00984-y.
Wang, R., W. Cao, and J.-M. Zhang. 2019. “Dependency of dilatancy ratio on fabric anisotropy in granular materials.” J. Eng. Mech. 145 (10): 04019076. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001660.
Wang, R., Y. F. Dafalias, P. Fu, and J. M. Zhang. 2020. “Fabric evolution and dilatancy within anisotropic critical state theory guided and validated by DEM.” Int. J. Solids Struct. 188–189 (Apr): 210–222. https://doi.org/10.1016/j.ijsolstr.2019.10.013.
Wang, R., P. Fu, J.-M. Zhang, and Y. F. Dafalias. 2017. “Evolution of various fabric tensors for granular media towards the critical state.” J. Eng. Mech. 143 (10): 04017117. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001342.
Wiebicke, M., E. Andò, I. Herle, and G. Viggiani. 2017. “On the metrology of interparticle contacts in sand from X-ray tomography images.” Meas. Sci. Technol. 28 (12): 124007. https://doi.org/10.1088/1361-6501/aa8dbf.
Wiebicke, M., E. Andò, G. Viggiani, and I. Herle. 2020. “Measuring the evolution of contact fabric in shear bands with X-ray tomography.” Acta Geotech. 15 (1): 79–93. https://doi.org/10.1007/s11440-019-00869-9.
Yang, Z. X., and Y. Wu. 2018. “Critical state for anisotropic granular materials: A discrete element perspective.” Int. J. Geomech. 17 (2): 04016054. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000720.
Yao, Y., Y. Tian, and Z. Gao. 2017. “Anisotropic uh model for soils based on a simple transformed stress method.” Int. J. Numer. Anal. Methods Geomech. 41 (1): 54–78. https://doi.org/10.1002/nag.2545.
Yoshimine, M., K. Ishihara, and W. Vargas. 1998. “Effects of principal stress direction and intermediate principal stress on undrained shear behavior of sand.” Soils Found. 38 (3): 179–188. https://doi.org/10.3208/sandf.38.3_179.
Yuan, R., H. S. Yu, D. S. Yang, and N. Hu. 2019. “On a fabric evolution law incorporating the effects of b-value.” Comput. Geotech. 105 (Jan): 142–154. https://doi.org/10.1016/j.compgeo.2018.09.019.
Zhang, B., and R. A. Regueiro. 2015. “On large deformation granular strain measures for generating stress–strain relations based upon three-dimensional discrete element simulations.” Int. J. Solids Struct. 66 (Aug): 151–170. https://doi.org/10.1016/j.ijsolstr.2015.04.012.
Zhao, C. F., and N. P. Kruyt. 2020. “An evolution law for fabric anisotropy and its application in micromechanical modelling of granular materials.” Int. J. Solids Struct. 196–197 (Jul): 53–66. https://doi.org/10.1016/j.ijsolstr.2020.04.007.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 148 • Issue 1 • January 2022
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Feb 21, 2021
Accepted: Aug 27, 2021
Published online: Oct 18, 2021
Published in print: Jan 1, 2022
Discussion open until: Mar 18, 2022
ASCE Technical Topics:
- Building materials
- Chemical processes
- Chemistry
- Compression
- Continuum mechanics
- Design (by type)
- Dynamics (solid mechanics)
- Engineering fundamentals
- Engineering materials (by type)
- Engineering mechanics
- Environmental engineering
- Fabrics
- Geomechanics
- Geotechnical engineering
- Granular materials
- Load factors
- Materials engineering
- Methodology (by type)
- Particles
- Radiation
- Radiography
- Soil dynamics
- Soil mechanics
- Solid mechanics
- Structural design
- Structural dynamics
- Triaxial loads
- X rays
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