Novel Undrained Servomechanism in Discrete-Element Modeling and Its Application in Multidirectional Cyclic Shearing Simulations
Publication: Journal of Engineering Mechanics
Volume 147, Issue 3
Abstract
Multidirectional shearing of granular soils involves shearing more than one shear stress component, and thus may result in more-complex soil responses than unidirectional shearing. This study developed an advanced numerical procedure that can impose an arbitrary loading path on a granular assembly in three-dimensional space as a basis for discrete-element simulations to investigate the behavior of granular assemblies under undrained cyclic multidirectional shearing conditions. The tests included varying stress trajectories on the deviatoric stress plane, including straight-line, circular, figure-8, and teardrop shapes. The numerical results indicated that the liquefaction resistance of a sample for a given cyclic shear stress ratio (CSR) depends on the stress orbits, and that of the teardrop shape was the highest and that of the figure-8 shape was the lowest. The microstructure of the granular assembly was quantified by the contact-normal-based fabric tensor, and its evolution trend correlation with stress–strain responses was explored. The evolution of fabric and stress–strain relationships from discrete-element modeling under multidirectional shearing conditions can provide useful insights into the behavior of granular soils.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
The codes for implementing the undrained servomechanism and data of discrete-element simulations in this study are available upon reasonable request.
Acknowledgments
This research was funded by the Natural Science Foundation of China under Grant Nos. 51825803 and 52020105003, the Fundamental Research Funds for the Central Universities under Grant Nos. 2020QNA4028 and 52020105003, and the Science and Technology Project of Communication of Zhejiang Province under Grant No. 2019058.
References
Asadzadeh, M., and A. Soroush. 2017. “Macro-and micromechanical evaluation of cyclic simple shear test by discrete-element method.” Particuology 31 (Apr): 129–139. https://doi.org/10.1016/j.partic.2016.05.015.
Bagi, K. 1999. “Microstructural stress tensor of granular assemblies with volume forces.” J. Appl. Mech. 66 (4): 934–936. https://doi.org/10.1115/1.2791800.
Boulanger, R. W., C. K. Chan, H. B. Seed, R. B. Seed, and J. Sousa. 1993. “A low-compliance bi-directional cyclic simple shear apparatus.” Geotech. Test. J. 16 (1): 36–45. https://doi.org/10.1520/GTJ10265J.
Chang, C. S., and Z.-Y. Yin. 2010. “Micromechanical modeling for inherent anisotropy in granular materials.” J. Eng. Mech. 136 (7): 830–839. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000125.
Chiaro, G. 2010. “Deformation properties of sand with initial static shear in undrained cyclic torsional shear tests and their modeling.” Ph.D. dissertation, Dept. of Civil Engineering, Univ. of Tokyo.
Chiaro, G., J. Koseki, and T. Sato. 2012. “Effects of initial static shear on liquefaction and large deformation properties of loose saturated Toyoura sand in undrained cyclic torsional shear tests.” Soils Found. 52 (3): 498–510. https://doi.org/10.1016/j.sandf.2012.05.008.
Christoffersen, J., M. M. Mehrabadi, and S. Nematnasser. 1981. “A micromechanical description of granular material behavior.” J. Appl. Mech. 48 (2): 339. https://doi.org/10.1115/1.3157619.
Cundall, P. A., and O. D. L. Strack. 1979. “A discrete numerical model for granular assemblies.” Géotechnique 29 (1): 47–65. https://doi.org/10.1680/geot.1979.29.1.47.
Duku, P. M., J. P. Stewart, D. H. Whang, and R. Venugopal. 2007. “Digitally controlled simple shear apparatus for dynamic soil testing.” Geotech. Test. J. 30 (5): 368–377. https://doi.org/10.1520/GTJ100518.
Durán, O., N. P. Kruyt, and S. Luding. 2010. “Analysis of three dimensional micro-mechanical strain formulations for granular materials: Evaluation of accuracy.” Int. J. Solids Struct. 47 (2): 251–260. https://doi.org/10.1016/j.ijsolstr.2009.09.035.
Fang, H., Y. Shen, and Y. Zhao. 2019. “Multishear bounding surface modelling of anisotropic sands accounting for fabric and its evolution.” Comput. Geotech. 110 (Jun): 57–70. https://doi.org/10.1016/j.compgeo.2019.02.015.
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.
Gao, Z. W., and J. D. 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.
Hosono, Y., and M. Yoshimine. 2004. “Liquefaction of sand in simple shear condition.” In Vol. 31 of Proc., Int. Conf. on Cyclic Behaviour of Soils and Liquefaction Phenomena, 129–136. Rotterdam, Netherlands: A.A. Balkema.
Hosono, Y., and M. Yoshimine. 2008. “Effects of anisotropic consolidation 568 and initial shear load on liquefaction resistance of sand in simple shear condition.” In Geotechnical engineering for disaster mitigation and rehabilitation, 352–358. Berlin: Springer.
Ishihara, K., and F. Yamazaki. 1980. “Cyclic simple shear tests on saturated sand in multidirectional loading.” Soils Found. 20 (1): 45–59. https://doi.org/10.3208/sandf1972.20.45.
Jiang, M., T. Li, and Z. Shen. 2016. “Fabric rates of elliptical particle assembly in monotonic and cyclic simple shear tests: a numerical study.” Granular Matter 18 (3): 54. https://doi.org/10.1007/s10035-016-0641-1.
Kammerer, A. M. 2002. “Undrained response of Monterey 0/30 sand under multidirectional cyclic simple shear loading conditions.” Ph.D. dissertation, Dept. of Civil and Environmental Engineering, Univ. of California, Berkeley.
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.
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. 2006. “Micro-scale investigation on the quasi-static behavior of granular material.” Ph.D. dissertation, Dept. of Civil Engineering, Hong Kong Univ. of Science and Technology.
Li, X., D. S. Yang, and H.-S. Yu. 2016. “Macro deformation and micro-structure of 3D granular assemblies subjected to rotation of principal stress axes.” Granular Matter 18 (3): 53. https://doi.org/10.1007/s10035-016-0632-2.
Li, X., and H.-S. Yu. 2009. “Influence of loading direction on the behavior of anisotropic granular materials.” Int. J. Eng. Sci. 47 (11–12): 1284–1296. https://doi.org/10.1016/j.ijengsci.2009.03.001.
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., H.-S. Yu, and X.-S. Li. 2013. “A virtual experiment technique on the elementary behaviour of granular materials with discrete element method.” Int. J. Numer. Anal. Methods Geomech. 37 (1): 75–96. https://doi.org/10.1002/nag.1086.
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.
Martin, G. R., W. D. L. Finn, and H. B. Seed. 1975. “Fundamentals of liquefaction under cyclic loading.” J. Geotech. Eng. Div. 101 (5): 423–438.
Matsuda, H., H. Shinozaki, N. Okada, K. Takamiya, and K. Shinyama. 2004. “Effects of multi-directional cyclic shear on the post-earthquake settlement of ground.” In Proc., 13th World Conf. on Earthquake Engineering. Tokyo: International Association for Earthquake Engineering.
Miura, K. I., 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., and H. Nakayama. 1988. “Introduction of inherent anisotropy of soils in the yield function.” Stud. Appl. Mech. 20 (Jan): 81–90. https://doi.org/10.1016/B978-0-444-70523-5.50017-5.
O’Sullivan, C. 2011. Particulate discrete element modelling: A geomechanics perspective. Boca Raton, FL: CRC Press.
Pan, K., and Z. X. Yang. 2018. “Effects of initial static shear on cyclic resistance and pore pressure generation of saturated sand.” Acta Geotech. 13 (2): 473–487. https://doi.org/10.1007/s11440-017-0614-5.
Pyke, R. M., H. B. Seed, and C. K. Chan. 1974. “Settlement of sands under multidirectional shaking.” J. Geotech. Eng. 101 (4): 379–398.
Qian, J.-G., Z.-B. Du, and Z.-Y. Yin. 2018. “Cyclic degradation and non-coaxiality of soft clay subjected to pure rotation of principal stress directions.” Acta Geotech. 13 (4): 943–959. https://doi.org/10.1007/s11440-017-0567-8.
Qian, J.-G., Y.-G. Wang, Z.-Y. Yin, and M.-S. Huang. 2016. “Experimental identification of plastic shakedown behavior of saturated clay subjected to traffic loading with principal stress rotation.” Eng. Geol. 214 (Nov): 29–42. https://doi.org/10.1016/j.enggeo.2016.09.012.
Reyes, A., J. Adinata, and M. Taiebat. 2019. “Impact of bidirectional seismic shearing on the volumetric response of sand deposits.” Soil Dyn. Earthquake Eng. 125 (Oct): 105665. https://doi.org/10.1016/j.soildyn.2019.05.004.
Rutherford, C. J., and G. Biscontin. 2013. “Development of a multidirectional simple shear testing device.” Geotech. Test. J. 36 (6): 20120173. https://doi.org/10.1520/GTJ20120173.
Seed, H. B., I. M. Idriss, F. I. Makdisi, and N. G. Banerjee. 1975a. Representation of irregular stress time histories by equivalent uniform stress series in liquefaction analysis. Earthquake Engineering Research Center, Univ. of California, Berkeley.
Seed, H. B., K. L. Lee, I. M. Idriss, and F. I. Makdisi. 1975b. “The slides in the San Fernando dams during the Earthquake of February 9, 1971.” J. Geotech. Eng. Div. 101 (7): 889–911.
Seed, H. B., R. M. Pyke, and G. R. Martin. 1978. “Effect of multidirectional 612 shaking on pore pressure development in sands.” J. Geotech. Geoenviron. Eng. 104 (1): 27–44.
Silver, M. L., F. Tatsuoka, A. Phukunhaphan, and A. S. Avramidis. 1980. “Cyclic undrained strength of sand by triaxial test and simple shear test.” In Proc., 7th World Conf. on Earthquake Engineering, 281–288. Tokyo: International Association for Earthquake Engineering.
Sivathayalan, S., and D. Ha. 2011. “Effect of static shear stress on the cyclic resistance of sands in simple shear loading.” Can. Geotech. J. 48 (10): 1471–1484. https://doi.org/10.1139/t11-056.
Sun, M., and G. Biscontin. 2018. “Development of pore pressure and shear strain in clean Hostun sands under multi-directional loading paths.” In GeoShanghai Int. Conf., 112–118. New York: Springer.
Symes, M. J., A. Gens, and D. W. Hight. 1988. “Drained principal stress rotation in saturated sand.” Géotechnique 38 (1): 59–81. https://doi.org/10.1680/geot.1988.38.1.59.
Theocharis, A. I., E. Vairaktaris, Y. F. Dafalias, and A. G. Papadimitriou. 2019. “Necessary and sufficient conditions for reaching and maintaining critical state.” Int. J. Numer. Anal. Methods Geomech. 43 (12): 2041–2055. https://doi.org/10.1002/nag.2943.
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.
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.
Vaid, Y. P., and S. Sivathayalan. 1996. “Static and cyclic liquefaction potential of Fraser Delta sand in simple shear and triaxial tests.” Can. Geotech. J. 33 (2): 281–289. https://doi.org/10.1139/t96-007.
Wan, R. G., and P. J. Guo. 2004. “Stress dilatancy and fabric dependencies on sand behavior.” J. Eng. Mech. 130 (6): 635–645. https://doi.org/10.1061/(ASCE)0733-9399(2004)130:6(635).
Wei, J., D. Huang, and G. Wang. 2020. “Fabric evolution of granular soils under multidirectional cyclic loading.” Acta Geotech. 15 (9): 2529–2543. https://doi.org/10.1007/s11440-020-00942-8.
Wu, Q. X., T. T. Xu, and Z. X. Yang. 2020a. “Diffuse instability of granular material under various drainage conditions: Discrete element simulation and constitutive modeling.” Acta Geotech. 15 (7): 1763–1778. https://doi.org/10.1007/s11440-019-00885-9.
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, Z.-X., C. Dano, P.-Y. Hicher, and Z.-Y. Yin. Forthcoming. “Estimating normal effective stress degradation in sand under undrained simple shear condition.” Eur. J. Environ. Civ. Eng. https://doi.org/10.1080/19648189.2018.1521750.
Wu, Z.-X., Z.-Y. Yin, C. Dano, and P.-Y. Hicher. 2020b. “Cyclic volumetric strain accumulation for sand under drained simple shear condition.” Appl. Ocean Res. 101 (Aug): 102200. https://doi.org/10.1016/j.apor.2020.102200.
Xie, Y. H., Z. X. Yang, D. Barreto, and M. D. Jiang. 2017. “The influence of particle geometry and the intermediate stress ratio on the shear behavior of granular materials.” Granular Matter 19 (2): 35. https://doi.org/10.1007/s10035-017-0723-8.
Yang, D. S. 2014. “Microscopic study of granular material behaviors under general stress paths.” Ph.D. dissertation, Dept. of Civil Engineering, Univ. of Nottingham.
Yang, M., G. Seidalinov, and M. Taiebat. 2019. “Multidirectional cyclic shearing of clays and sands: Evaluation of two bounding surface plasticity models.” Soil Dyn. Earthquake Eng. 124 (Sep): 230–258. https://doi.org/10.1016/j.soildyn.2018.05.012.
Yang, Z. X., X. S. Li, and J. Yang. 2007. “Undrained anisotropy and rotational shear in granular soil.” Géotechnique 57 (4): 371–384. https://doi.org/10.1680/geot.2007.57.4.371.
Yang, Z., D. Liao, and T. 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., and Y. Wu. 2017. “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.
Yang, Z. X., T. T. Xu, and Y. N. Chen. 2018. “Unified modeling of the influence of consolidation conditions on monotonic soil response considering fabric evolution.” J. Eng. Mech. 144 (8): 04018073. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001499.
Yang, Z. X., J. Yang, and L. Z. Wang. 2013. “Micro-scale modeling of anisotropy effects on undrained behavior of granular soils.” Granular Matter 15 (5): 557–572. https://doi.org/10.1007/s10035-013-0429-5.
Yin, Z.-Y., C. S. Chang, and P.-Y. Hicher. 2011. “Micromechanical modelling for effect of inherent anisotropy on cyclic behaviour of sand.” Int. J. Solids Struct. 47 (14–15): 1933–1951. https://doi.org/10.1016/j.ijsolstr.2010.03.028.
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.
Zhang, L., and T. M. Evans. 2018. “Boundary effects in discrete element method modeling of undrained cyclic triaxial and simple shear element tests.” Granular Matter 20 (4): 60. https://doi.org/10.1007/s10035-018-0832-z.
Zhang, M., Y. Yang, H. Zhang, and H. S. Yu. 2019. “DEM and experimental study of bi-directional simple shear.” Granular Matter 21 (2): 24. https://doi.org/10.1007/s10035-019-0870-1.
Zhao, J., and N. Guo. 2013. “Unique critical state characteristics in granular media considering fabric anisotropy.” Géotechnique 63 (8): 695–704. https://doi.org/10.1680/geot.12.P.040.
Zhu, H.-X., Z.-Y. Yin, and Q. Zhang. 2020. “A novel coupled FDM-DEM modelling method for flexible membrane boundary in laboratory tests.” Int. J. Numer. Anal. Methods Geomech. 44 (3): 389–404. https://doi.org/10.1002/nag.3019.
Information & Authors
Information
Published In
Copyright
© 2020 American Society of Civil Engineers.
History
Received: Jun 2, 2020
Accepted: Oct 26, 2020
Published online: Dec 31, 2020
Published in print: Mar 1, 2021
Discussion open until: May 31, 2021
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.