Modeling Monotonic and Cyclic Behavior of Granular Materials by Exponential Constitutive Function
Publication: Journal of Engineering Mechanics
Volume 144, Issue 4
Abstract
It is still an open problem to develop a model with a uniform theoretical treatment under various loading conditions. This paper aims to formulate such a model for describing both monotonic and cyclic behaviors of granular materials. An exponential function was adopted to reproduce the stress-strain relation. Within the framework of endochronic models, the shear strain component was enriched with an absolute term to account for a reverse loading effect during shearing. The capacity of the basic model with four parameters for reproducing the basic features of granular materials was examined. Three numerical schemes for simulating undrained triaxial tests, drained triaxial tests under constant or under constant confining stress, and under both monotonic and cyclic loadings were established. Then, three modifications were carried out to enhance the model by introducing a nonlinear elasticity, a nonlinear stress dilatancy, and the critical state concept with four additional parameters. The enhanced version of the model showed good performances in simulating triaxial tests on Toyoura sand under various loading conditions: drained, undrained, constant , constant confining stress, and monotonic and cyclic loadings.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This study was substantially supported by the Natural Science Foundation of China (No. 51579179), and the Region Pays de la Loire of France (project RI-ADAPTCLIM).
References
Biarez, J., and Hicher, P.-Y. (1994). Elementary mechanics of soil behaviour: Saturated remoulded soils, A.A. Balkema, Rotterdam, Netherlands.
Chang, C., Yin, Z.-Y., and Hicher, P.-Y. (2010). “Micromechanical analysis for interparticle and assembly instability of sand.” J. Eng. Mech., 155–168.
Chang, C. S., and Hicher, P. Y. (2005). “An elasto-plastic model for granular materials with microstructural consideration.” Int. J. Solids Struct., 42(14), 4258–4277.
Dafalias, Y. F., and Taiebat, M. (2014). “Rotational hardening with and without anisotropic fabric at critical state.” Geotechnique, 64(6), 507–511.
Darve, F. (1990). “Incrementally non-linear constitutive relationships.” Geomaterials constitutive equations and modelling, F. Darve, ed., Elsevier, New York, 213–238.
Darve, F., and Labanieh, S. (1982). “Incremental constitutive law for sands and clays: Simulations of monotonic and cyclic tests.” Int. J. Numer. Anal. Methods Geomech., 6(2), 243–275.
Duncan, J. M., and Chang, C.-Y. (1970). “Nonlinear analysis of stress and strain in soils.” J. Soil Mech. Found. Div., 96(5), 1629–1653.
Gajo, A., and Wood, M. (1999). “Severn-Trent sand: A kinematic-hardening constitutive model: The q-p formulation.” Geotechnique, 49(5), 595–614.
Gao, Z., Zhao, J., Li, X. S., and Dafalias, Y. F. (2014). “A critical state sand plasticity model accounting for fabric evolution.” Int. J. Numer. Anal. Methods Geomech., 38(4), 370–390.
Gudehus, G. (1997). “Attractors, percolation thresholds and phase limits of granular soils.” Proc., Powder and Grains, R. P. Behringer and J. T. Jenkins, eds., A.A. Balkema, Rotterdam, Netherlands, 169–183.
Jefferies, M. (1993). “Nor-Sand: A simple critical state model for sand.” Geotechnique, 43(1), 91–103.
Li, X. S., and Dafalias, Y. F. (2012). “Anisotropic critical state theory: Role of fabric.” J. Eng. Mech., 263–275.
Li, X. S., and Wang, Y. (1998). “Linear representation of steady-state line for sand.” J. Geotech. Geoenviron. Eng., 1215–1217.
Manzari, M. T., and Dafalias, Y. F. (1997). “A critical state two-surface plasticity model for sands.” Geotechnique, 47(2), 255–272.
Mašín, D., and Khalili, N. (2012). “A thermo-mechanical model for variably saturated soils based on hypoplasticity.” Int. J. Numer. Anal. Methods Geomech., 36(12), 1461–1485.
Matsuoka, H., and Nakai, T. (1974). “Stress-deformation and strength characteristics of soil under three different principal stresses.” Proc., JSCE, 232, 59–70.
Miura, N., Murata, H., and Yasufuku, N. (1984). “Stress-strain characteristics of sand in a particle-crushing region.” Soils Found., 24(1), 77–89.
Miura, N., and Yamanouchi, T. (1975). “Effect of water on the behavior of a quartz-rich sand under high stresses.” Soils Found., 15(4), 23–34.
Nicot, F., and Darve, F. (2011). “The H-microdirectional model: Accounting for a mesoscopic scale.” Mech. Mater., 43(12), 918–929.
Niemunis, A., and Herle, I. (1997). “Hypoplastic model for cohesionless soils with elastic strain range.” Mech. Cohesive-frict. Mater., 2(4), 279–299.
Pradhan, T. B. S. (1990). “The behavior of sand subjected to monotonic and cyclic loadings.” Ph.D. thesis, Kyoto Univ., Kyoto, Japan.
Richart, F. E., Hall, J. R., and Woods, R. D. (1970). “Vibrations of soils and foundations.” International series in theoretical and applied mechanics, Prentice-Hall, Englewood Cliffs, NJ.
Roscoe, K. H., Schofield, A. N., and Thurairajah, A. (1963). “Yielding of clays in states wetter than critical.” Geotechnique, 133, 211–240.
Sandler, I. S. (1978). “On the uniqueness and stability of endochronic theories of material behaviour.” J. Appl. Mech., 45, 263–278.
Schanz, T., Vermeer, P. A., and Bonnier, P. G. (1999). “The hardening soil model: Formulation and verification.” Beyond 2000 in computational geotechnics—10 years of PLAXIS, A.A. Balkema, Rotterdam, Netherlands, 281–296.
Taiebat, M., and Dafalias, Y. F. (2008). “SANISAND: Simple anisotropic sand plasticity model.” Int. J. Numer. Anal. Methods Geomech., 32(8), 915–948.
Uchida, K., and Stedman, J. (2001). “Liquefaction behaviour of Toyoura sand under cyclic strain controlled triaxial loading.” Proc., 11th Int. Offshore and Polar Engineering Conf., ISOPE, Cupertino, CA, 17–22.
Verdugo, R., and Ishihara, K. (1996). “The steady state of sandy soils.” Soils Found., 36(2), 81–91.
Vermeer, P. A. (1978). “A double hardening model for sand.” Geotechnique, 28(4), 413–433.
Wan, R., and Pouragha, M. (2015). “Continuum representation of granular fabric and connectivity.” Continuum Mech. Thermodyn., 27(1–2), 243–259.
Wu, W., Bauer, E., and Kolymbas, D. (1996). “Hypoplastic constitutive model with critical state for granular materials.” Mech. Mater., 23(1), 45–69.
Wu, W., and Kolymbas, D. (2000). “Hypoplasticity then and now.” Constitutive modelling of granular materials, D. Kolymbas, ed., Springer, Berlin, 57–105.
Yang, J., and Sze, H. Y. (2011). “Cyclic behaviour and resistance of saturated sand under non-symmetrical loading conditions.” Geotechnique, 61(1), 59–73.
Yao, Y., Sun, D., and Luo, T. (2004). “A critical state model for sands dependent on stress and density.” Int. J. Numer. Anal. Methods Geomech., 28(4), 323–337.
Yao, Y., Sun, D., and Matsuoka, H. (2008). “A unified constitutive model for both clay and sand with hardening parameter independent on stress path.” Comput. Geotech., 35(2), 210–222.
Yin, Z.-Y., and Chang, C. S. (2013). “Stress-dilatancy behavior for sand under loading and unloading conditions.” Int. J. Numer. Anal. Methods Geomech., 37(8), 855–870.
Yin, Z.-Y., Chang, C. S., and Hicher, P.-Y. (2010). “Micromechanical modelling for effect of inherent anisotropy on cyclic behaviour of sand.” Int. J. Solids Struct., 47(14), 1933–1951.
Yin, Z.-Y., Zhao, J., and Hicher, P.-Y. (2014). “A micromechanics-based model for sand-silt mixtures.” Int. J. Solids Struct., 51(6), 1350–1363.
Yoshimine, M., Ishihara, K., and Vargas, W. (1998). “Effects of principal stress direction and intermediate principal stress on undrained shear behavior of sand.” Soils Found., 38(3), 179–188.
Yu, H. (1998). “CASM: A unified state parameter model for clay and sand.” Int. J. Numer. Anal. Methods Geomech., 22(8), 621–653.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 144 • Issue 4 • April 2018
Copyright
©2018 American Society of Civil Engineers.
History
Received: May 16, 2017
Accepted: Oct 16, 2017
Published online: Feb 9, 2018
Published in print: Apr 1, 2018
Discussion open until: Jul 9, 2018
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.