Hypoplastic Modeling of Anisotropic Sand Behavior Accounting for Rotation of Principal Stress Direction
Publication: Journal of Engineering Mechanics
Volume 148, Issue 10
Abstract
The rotation of the principal stress direction has a significant influence on the stress–strain relation and deformation characteristics of sand. This study proposes a hypoplastic model to simulate the noncoaxial response of anisotropic sand subjected to the rotation of the principal stress direction. The densification effect of sand is considered through a properly defined function, enabling the model to simulate a gradually stabilized strain accumulation upon rotational shearing. A fabric tensor is used to describe the anisotropic microstructure of sand, and worked in conjunction with the stress in the form of a joint invariant–based state variable to simulate the impact of fabric anisotropy on the behavior of sand. The fabric tensor is integrated with the hypoplastic flow direction, making the model capable of generating a noncoaxial response. The model response was compared with the experimental data for rotational shear tests under various conditions.
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Data Availability Statement
The codes for implementing the hypoplastic model in this study are available from the corresponding author upon reasonable request.
Acknowledgments
The support from the Natural Science Foundation of China (Nos. 51825803 and 52020105003) is gratefully acknowledged.
References
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.
Chen, Z., and M. Huang. 2020. “Non-coaxial behavior modeling of sands subjected to principal stress rotation.” Acta Geotech. 15 (3): 655–669. https://doi.org/10.1007/s11440-018-0760-4.
Dafalias, Y. F., A. G. Papadimitriou, and X. S. Li. 2004. “Sand plasticity model accounting for inherent fabric anisotropy.” J. Eng. Mech. 130 (11): 1319–1333. https://doi.org/10.1061/(ASCE)0733-9399(2004)130:11(1319).
Fuentes, W., D. Mašín, and J. Duque. 2021. “Constitutive model for monotonic and cyclic loading on anisotropic clays.” Géotechnique 71 (8): 657–673. https://doi.org/10.1680/jgeot.18.P.176.
Gao, Z., and J. Zhao. 2015. “Constitutive modeling of anisotropic sand behavior in monotonic and cyclic loading.” J. Eng. Mech. 141 (8): 04015017. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000907.
Gao, Z., and J. Zhao. 2017. “A non-coaxial critical-state model for sand accounting for fabric anisotropy and fabric evolution.” Int. J. Solids Struct. 106–107 (Feb): 200–212. https://doi.org/10.1016/j.ijsolstr.2016.11.019.
Gudehus, G. 1996. “A comprehensive constitutive equation for granular materials.” Soils Found. 36 (1): 1–12. https://doi.org/10.3208/sandf.36.1.
Gutierrez, M., K. Ishihara, and I. Towhata. 1993. “Model for the deformation of sand during rotation of principal stress directions.” Soils Found. 33 (3): 105–117. https://doi.org/10.3208/sandf1972.33.3_105.
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.
Huang, M., Z. Chen, and X. Lu. 2018. “Bifurcation prediction of shear banding in sand with non-coaxial critical state model considering inherent anisotropy.” Soils Found. 58 (3): 641–653. https://doi.org/10.1016/j.sandf.2018.03.002.
Ishihara, K., and I. Towhata. 1983. “Sand response to cyclic rotation of principal stress directions as induced by wave loads.” Soils Found. 23 (4): 11–26. https://doi.org/10.3208/sandf1972.23.4_11.
Ken-Ichi, K. 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.
Lashkari, A., and M. Latifi. 2008. “A non-coaxial constitutive model for sand deformation under rotation of principal stress axes.” Int. J. Numer. Anal. Methods Geomech. 32 (9): 1051–1086. https://doi.org/10.1002/nag.659.
Li, X., and H.-S. Yu. 2010. “Numerical investigation of granular material behaviour under rotational shear.” Géotechnique 60 (5): 381–394. https://doi.org/10.1680/geot.2010.60.5.381.
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. 2004. “A constitutive framework for anisotropic sand including non-proportional loading.” Géotechnique 54 (1): 41–55. https://doi.org/10.1680/geot.2004.54.1.41.
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.
Liao, D., and Z. Yang. 2021a. “Non-coaxial hypoplastic model for sand with evolving fabric anisotropy including non-proportional loading.” Int. J. Numer. Anal. Methods Geomech. 45 (16): 2433–2463. https://doi.org/10.1002/nag.3272.
Liao, D., and Z. X. Yang. 2021b. “Hypoplastic modeling of anisotropic sand behavior accounting for fabric evolution under monotonic and cyclic loading.” Acta Geotech. 16 (7): 2003–2029. https://doi.org/10.1007/s11440-020-01127-z.
Liao, D., and Z. X. Yang. 2022. “Hypoplastic model for sand under multidirectional shearing conditions considering fabric change effect.” Soil Dyn. Earthquake Eng. 155 (Apr): 107168. https://doi.org/10.1016/j.soildyn.2022.107168.
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.
Nakata, Y., M. Hyodo, H. Murata, and N. Yasufuku. 1998. “Flow deformation of sands subjected to principal stress rotation.” Soils Found. 38 (2): 115–128. https://doi.org/10.3208/sandf.38.2_115.
Oda, M. 1972. “Initial fabrics and their relations to mechanical properties of granular material.” Soils Found. 12 (1): 17–36. https://doi.org/10.3208/sandf1960.12.17.
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.
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.
Poblete, M., W. Fuentes, and T. Triantafyllidis. 2016. “On the simulation of multidimensional cyclic loading with intergranular strain.” Acta Geotech. 11 (6): 1263–1285. https://doi.org/10.1007/s11440-016-0492-2.
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.
Tian, Y., and Y.-P. Yao. 2018. “Constitutive modeling of principal stress rotation by considering inherent and induced anisotropy of soils.” Acta Geotech. 13 (6): 1299–1311. https://doi.org/10.1007/s11440-018-0680-3.
Tobita, Y., and E. Yanagisawa. 1988. “Contact tensor in constitutive model for granular materials.” Stud. Appl. Mech. 20: 263–270.
Tong, Z.-X., J.-M. Zhang, Y.-L. Yu, and G. Zhang. 2010. “Drained deformation behavior of anisotropic sands during cyclic rotation of principal stress axes.” J. Geotech. Geoenviron. Eng. 136 (11): 1509–1518. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000378.
Towhata, I., and K. Ishihara. 1985. “Undrained strength of sand undergoing cyclic rotation of principal stress axes.” Soils Found. 25 (2): 135–147. https://doi.org/10.3208/sandf1972.25.2_135.
Wang, Z., Y. Yang, and H.-S. Yu. 2017. “Effects of principal stress rotation on the wave–seabed interactions.” Acta Geotech. 12 (1): 97–106. https://doi.org/10.1007/s11440-016-0450-z.
Wu, Q. X., Z. X. Yang, and X. Li. 2019. “Numerical simulations of granular material behavior under rotation of principal stresses: Micromechanical observation and energy consideration.” Meccanica 54 (4–5): 723–740. https://doi.org/10.1007/s11012-018-00939-4.
Wu, W., and E. Bauer. 1994. “A simple hypoplastic constitutive model for sand.” Int. J. Numer. Anal. Methods Geomech. 18 (12): 833–862. https://doi.org/10.1002/nag.1610181203.
Wu, W., and D. Kolymbas. 1990. “Numerical testing of the stability criterion for hypoplastic constitutive equations.” Mech. Mater. 9 (3): 245–253. https://doi.org/10.1016/0167-6636(90)90006-2.
Wu, W., and A. Niemunis. 1996. “Failure criterion, flow rule and dissipation function derived from hypoplasticity.” Mech. Cohesive-Frict. Mater. 1 (2): 145–163. https://doi.org/10.1002/(SICI)1099-1484(199604)1:2%3C145::AID-CFM8%3E3.0.CO;2-9.
Xue, L., J.-K. Yu, J.-H. Pan, R. Wang, and J.-M. Zhang. 2021. “Three-dimensional anisotropic plasticity model for sand subjected to principal stress value change and axes rotation.” Int. J. Numer. Anal. Methods Geomech. 45 (3): 353–381. https://doi.org/10.1002/nag.3159.
Yang, L. T. 2013. “Experimental study of soil Anisotropy using hollow cylinder testing.” Ph.D. dissertation, Dept. of Civil and Environmental Engineering, Univ. of Nottingham.
Yang, Y., and H. S. Yu. 2006. “A non-coaxial critical state soil model and its application to simple shear simulations.” Int. J. Numer. Anal. Methods Geomech. 30 (13): 1369–1390. https://doi.org/10.1002/nag.531.
Yang, Z., D. Liao, and T. Xu. 2020. “A hypoplastic model for granular soils incorporating anisotropic critical state theory.” Int. J. Numer. Anal. Methods Geomech. 44 (6): 723–748. https://doi.org/10.1002/nag.3025.
Yang, Z. X., X. S. Li, and J. Yang. 2007. “Undrained anisotropy and rotational shear in granular soil.” Géotechnique 58 (4): 237–248. https://doi.org/10.1680/geot.2007.57.4.371.
Yang, Z. X., X. S. Li, and J. Yang. 2008. “Quantifying and modelling fabric anisotropy of granular soils.” Géotechnique 57 (4): 371–384. https://doi.org/10.1680/geot.2008.58.4.237.
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.
Zhao, J., and Z. Gao. 2016. “Unified anisotropic elastoplastic model for sand.” J. Eng. Mech. 142 (1): 04015056. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000962.
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Published In
Journal of Engineering Mechanics
Volume 148 • Issue 10 • October 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Dec 19, 2021
Accepted: May 19, 2022
Published online: Jul 29, 2022
Published in print: Oct 1, 2022
Discussion open until: Dec 29, 2022
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