New Viscoplastic Bounding Surface Subloading Model for Time-Dependent Behavior of Sands
Publication: International Journal of Geomechanics
Volume 21, Issue 4
Abstract
This research focuses on experimental and constitutive time-dependent modeling of sands considering rate dependency, fabric, and stepwise sudden frequency changes during loadings. Several cyclic triaxial undrained tests were performed on Toyoura sand having various void ratios, while the deviatoric stress was applied by changing the frequency in a successive number of cycles. In order to predict the viscoplastic behavior of sands, a bounding surface model accounting for fabric changes that could predict sands cyclic behavior was employed as a reference model. A subloading surface model accounting for time-dependent behavior was incorporated into the bounding surface model to develop a new viscoplastic model. A linear integration method combined with the explicit method integrates the elastoplastic part and viscoplastic part of the model. Performance of the model was verified with the experimental data obtained from triaxial undrained tests in which a good agreement was observed.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The authors would like to thank Prof. Junichi Koseki and his colleagues at Geotechnical Lab, The University of Tokyo, who provided us with experimental facilities and supervised the junior author when conducting the undrained triaxial tests that are presented in this paper.
References
Abrantes, A. E., and J. A. Yamamuro. 2003. “Effect of strain rates in cohesionless soil.” In Constitutive modeling of geomaterials, 188–194. Cleveland, OH: CRC Press.
Bardet, J. P., and J. Proubet. 1991. “A numerical investigation of the structure of persistent shear bands in granular media.” Géotechnique 41 (4): 599–613. https://doi.org/10.1680/geot.1991.41.4.599.
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.
Bjerrum, L. 1973. “Geotechnical problems involved in foundations of structures in the North Sea.” Géotechnique 23 (3): 319–358. https://doi.org/10.1680/geot.1973.23.3.319.
Bopp, P. A., and P. V. Lade. 1997. “Effects of initial density on soil instability at high pressures.” J. Geotech. Geoenviron. Eng. 123 (7): 671–677. https://doi.org/10.1061/(ASCE)1090-0241(1997)123:7(671).
Casagrande, A., and W. Shannon. 1948. “Panama canal - The sea-level project: A symposium.” In Strength of soils under dynamic loads, 591–608. Reston, VA: ASCE.
Dafalias, Y. F. 1986. “Bounding surface plasticity. I: Mathematical foundation and hypoplasticity.” J. Eng. Mech. 112 (9): 966–987. https://doi.org/10.1061/(ASCE)0733-9399(1986)112:9(966).
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).
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).
Dafalias, Y. F., and E. P. Popov. 1975. “A model of nonlinearly hardening materials for complex loading.” Acta Mech. 21 (3): 173–192. https://doi.org/10.1007/BF01181053.
Di Benedetto, H., F. Tatsuoka, and M. Ishihara. 2002. “Time-dependent shear deformation characteristics of sand and their constitutive modelling.” Soils Found. 42 (2): 1–22. https://doi.org/10.3208/sandf.42.2_1.
Hashiguchi, K., and Z.-P. Chen. 1998. “Elastoplastic constitutive equation of soils with the subloading surface and the rotational hardening.” Int. J. Numer. Anal. Methods Geomech. 22: 197–227.https://doi.org/10.1002/(SICI)1096-9853(199803)22:3%3C197::AID-NAG914%3E3.0.CO;2-T.
Higgins, W., T. Chakraborty, and D. Basu. 2013. “A high strain-rate constitutive model for sand and its application in finite-element analysis of tunnels subjected to blast.” Int. J. Numer. Anal. Methods Geomech. 37 (15): 2590–2610. https://doi.org/10.1002/nag.2153.
Ishihara, K., F. Tatsuoka, and S. Yasuda. 1975. “Undrained deformation and liquefaction of sand under cyclic stresses.” Soils Found. 15 (1): 29–44. https://doi.org/10.3208/sandf1972.15.29.
Kaliakin, N. 1991. “Application of the elastoplastic-viscoplastic bounding surface model to cyclic loading.” In Proc., Int. Conf. on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics. Rolla, MO: Missouri Univ. of Science and Technology.
Kiyota, T., F. Tatsuoka, and J. Yamamuro. 2005. “Drained and undrained creep characteristics of loose saturated sand.” In Site Characterization and Modeling, Geotechnical Special Publication 138, edited by P. W. Mayne, E. Rathje, J. DeJong, A. Rechenmacher, J. Yamamuro, S. Sharma, and C. Willson, 1–10. Reston, VA: ASCE.
Ko, D. H., H. Itou, F. Tatsuoka, and T. Nishi. 2003. “Significance of viscous effects in the development of residual strain in cyclic triaxial tests on sand.” In Proc. 3rd Int. Symp. on Deformation Characteristics of Geomaterials, 559–568. Rotterdam, Netherlands: A. A. Balkema.
Lade, P. V., and C.-T. Liu. 1998. “Experimental study of drained creep behavior of sand.” J. Eng. Mech. 124 (8): 912–920. https://doi.org/10.1061/(ASCE)0733-9399(1998)124:8(912).
Le, T. M., B. Fatahi, and H. Khabbaz. 2015. “Numerical optimisation to obtain elastic viscoplastic model parameters for soft clay.” Int. J. Plast. 65: 1–21. https://doi.org/10.1016/j.ijplas.2014.08.008.
Li, X. S., and Y. F. Dafalias. 2000. “Dilatancy for cohesionless soils.” Géotechnique 50 (4): 449–460. https://doi.org/10.1680/geot.2000.50.4.449.
Li, X. S., and Y. Wang. 1998. “Linear representation of steady-state line for sand.” J. Geotech. Geoenviron. Eng. 124 (12): 1215–1217. https://doi.org/10.1061/(ASCE)1090-0241(1998)124:12(1215).
Mac, N., B. Shahbodaghkhan, and N. Khalili. 2014. “A constitutive model for time-dependent behavior of clay.” Int. J. Civ. Environ. Struct. Constr. Archit. Eng. 8(6): 596–601.
Maranha, J. R., C. Pereira, and A. Vieira. 2016. “A viscoplastic subloading soil model for rate-dependent cyclic anisotropic structured behaviour.” Int. J. Numer. Anal. Methods Geomech. 40 (11): 1531–-1555. https://doi.org/10.1002/nag.2494.
Martindale, H., W. Higgins, T. Chakraborty, and D. Basu. 2010. “Two-surface viscoplastic sand model for high rate loading.” In Proc., Int. Conf. on Geotechnical Engineering. Tunisia, North Africa: Geotechnical Engineering Research Team of National Engineering School of Tunis.
Miura, N. 1979. “A consideration on the stress-strain relation of a sand under high pressures.” Proc. Jpn. Soc. Civ. Eng. 1979 (282): 127–130. https://doi.org/10.2208/jscej1969.1979.282_127.
Miura, N., H. Murata, and N. Yasufuku. 1984. “Stress-strain characteristics of sand in a particle-crushing region.” Soils Found. 24 (1): 77–89. https://doi.org/10.3208/sandf1972.24.77.
Nemat-Nasser, S. 1980. “On behavior of granular materials in simple shear.” Soils Found. 20 (3): 59–73. https://doi.org/10.3208/sandf1972.20.3_59.
Nemat-Nasser, S., and Y. Tobita. 1982. “Influence of fabric on liquefaction and densification potential of cohesionless sand.” Mech. Mater. 1 (1): 43–62. https://doi.org/10.1016/0167-6636(82)90023-0.
Newland, P. L., and B. H. Allely. 1957. “Volume changes in drained taixial tests on granular materials.” Géotechnique 7 (1): 17–34. https://doi.org/10.1680/geot.1957.7.1.17.
Perzyna, P. 1966. “Fundamental problems in viscoplasticity.” Adv Appl Mech 9: 244–377.
Richard, F. E., R. E. Woods, and J. R. Hall. 1970. Vibration of soils and foundations. Englewood Cliffs, NJ: Prentice Hall.
Rowe, P. W. 1962. “The stress-dilatancy relation for static equilibrium of an assembly of particles in contact.” Proc. R. Soc. London, Ser. A 269 (1339): 500–527.
Schofield, A., and P. Wroth. 1968. Critical state soil mechanics. London: McGraw-Hill.
Taiebat, M. 2008. Advanced elastic-plastic constitutive and numerical modeling in geomechanics. Berkeley, CA: Univ. of California.
Vieira, A., J. Maranha, J. Bilé Serra, and R. Correia. 2007. “Modelling the undrained creep behaviour of a hard clay in the super-critical region.” In Proc., 9th Int. Conf. on Computational Plasticity, 836–839. Barcelona, Spain: COMPLAS.
Whitman, R. V., and K. A. Healy. 1962. Shearing resistance of sands during rapid loadings. Cambridge, MA: Massachusetts Institute of Technology.
Wood, D. M. 1990. Soil behaviour and critical state soil mechanics. Cambridge, UK: Cambridge University Press.
Yamamuro, J. A., and P. V. Lade. 1993. “Effects of strain rate on instability of granular soils.” Geotech. Test. J. 13: 304–313. https://doi.org/10.1520/GTJ10051J.
Yamamuro, J. A., and P. V. Lade. 1998. “Steady-state concepts and static liquefaction of silty sands.” J. Geotech. Geoenviron. Eng. 124 (9): 868–877. https://doi.org/10.1061/(ASCE)1090-0241(1998)124:9(868).
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 21 • Issue 4 • April 2021
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Jun 4, 2020
Accepted: Nov 18, 2020
Published online: Feb 11, 2021
Published in print: Apr 1, 2021
Discussion open until: Jul 11, 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.