Pressure-Level Dependency and Densification Behavior of Sand Through Generalized Plasticity Model
Publication: Journal of Engineering Mechanics
Volume 129, Issue 8
Abstract
Natural soil deposits and man-made earth structures exhibit complicated engineering behavior that is influenced by factors such as the stress level and drainage conditions. The stress conditions within a soil structure vary greatly, ranging from very low to very high values, due to the dead weight, loading and boundary conditions. Saturated sand deposits that exhibit drained conditions under static loading become undrained when subject to earthquake excitations. The Pastor–Zienkiewicz–Chan model has demonstrated considerable success in describing the inelastic behavior of soils under isotropic monotonic and cyclic loadings, including liquefaction and cyclic mobility. This study proposed modifications to the Pastor–Zienkiewicz–Chan model so that effects of stress level and densification behavior are simulated. The proposed model suggested that the angle of internal friction, elastic and plastic moduli are dependent on the pressure levels. Relevant modifications were made to incorporate a power term of mean effective stress on the loading plastic modulus so that a stress-level dependent volume change is obtained in combination with the stress-dilatancy relationship. To better simulate cyclic loading with reference to densification behavior, an exponential term of plastic volumetric strain is included for the unloading and reloading plastic moduli. A total of 11 parameters are needed for monotonic loading, whereas 15 parameters are needed in describing the cyclic behavior. The model simulations were compared with undrained and drained triaxial test results of several kinds of sand under dense and loose states. The predictive capability for monotonic and cyclic loading conditions was also demonstrated.
Get full access to this article
View all available purchase options and get full access to this article.
References
Bahda, F., Pastor, M., and Saitta, A. (1997). “A double hardening model based on generalized plasticity and state parameters for cyclic loading of sands.” Numerical models in Geomechanics, Pietruszczak and Pande, eds., Balkema, Rotterdam, The Netherlands, 33–38.
Banks, D. C., and Maclver, B. N. (1969). “Variation in angle of internal friction with confining pressure.” Rep. to U.S. Army Engineer Nuclear Cratering Group.
Bardet, J. P.(1986). “Bounding surface plasticity model for sands.” J. Eng. Mech., 112(11), 1198–1217.
Been, K., and Jefferies, M. G.(1985). “A state parameter for sands.” Geotechnique, 35(2), 99–112.
Bolton, M. D.(1986). “The strength and dilatancy of sands.” Geotechnique, 36(1), 65–78.
Bouckovalas, G., Marr, W. A., and Christian, J. T.(1986). “Analyzing permanent drift due to cyclic loads.” J. Geotech. Eng., 112(6), 579–593.
Boyce, H. R. (1980). “A nonlinear model for the elastic behavior of granular materials under repeated loading.” Proc., Int. Symp. on Soils under Cyclic and Transient Loading, Swansea, U.K., 285–294.
Crouch, R. S., Wolf, J. P., and Dafalias, Y. F.(1994). “Unified critical-state bounding-surface plasticity model for soil.” J. Eng. Mech., 120(11), 2251–2270.
Crouch, R. S., and Wolf, J. P.(1994). “Unified 3D critical state bounding-surface plasticity model for soils incorporating continuous plastic loading under cyclic paths. Part I: Constitutive relations.” Int. J. Numer. Analyt. Meth. Geomech., 18, 735–758.
Cuellar, V., Bazant, Z. P., Krizek, R. J., and Silver, M. L.(1977). “Densification and hysteresis of sand under cyclic shear.” J. Geotech. Eng. Div., Am. Soc. Civ. Eng., 103(5), 399–416.
Dafalias, Y. F.(1986). “Bounding surface plasticity, I: Mathematical foundation and hypoplasticity.” J. Eng. Mech., 112(9), 966–987.
Dobry, R., and Petrakis, E.(1990). “Micromechanics model to predict sand densification by cyclic straining.” J. Eng. Mech., 116(2), 288–308.
Duncan, J. M., Byrne, P., Wong, K. S., and Mabry, P. (1980). “Strength, stress-strain and bulk modulus parameters for finite element analyses of stresses and movements in soil masses.” Geotechnical Engineering Research Rep. No. UCB/GT/80-01, Dept. of Civil Engineering, Univ. of California, Berkeley.
Fukushima, S., and Tatsuoka, F.(1984). “Strength and deformation characteristics of saturated sand at extremely low pressures.” Soils Found., 24(4), 30–48.
Hardin, B. O., and Richart, F. E.(1963). “Elastic wave velocity in granular soils.” J. Soil Mech. Found. Div., Am. Soc. Civ. Eng., 89(1), 33–65.
Houlsby, G. T.(1985). “The use of a variable shear modulus in elastic-plastic models for clays.” Comput. Geotech., 1, 3–13.
Hueckel, T., Tutumluer, E., and Pellegrini, R.(1992). “A note on nonlinear elasticity of isotropic overconsolidated clays.” Int. J. Numer. Analyt. Meth. Geomech., 16, 603–618.
Ibsen, L. B. (1999). “The mechanism controlling static liquefaction and cyclic strength of sand.” Physics and mechanics of soil liquefaction, P. V. Lade, and J. A. Yamamuro, eds., Balkema, Rotterdam, The Netherlands, 29–39.
Ishihara, K. (1996). Soil behavior in earthquake engineering, Oxford.
Jefferies, M. G.(1993). “Nor-Sand: A simple critical state model for sand.” Geotechnique, 43(1), 91–103.
Lade, P. V., and Kim, M. K.(1988). “Single hardening constitutive model for frictional materials. II yield criterion and plastic work contours.” Comput. Geotech., 6(1), 13–30.
Lade, P. V., and Yamamuro, J. A.(1996). “Undrained sand behavior in axisymmetric tests at high pressures.” J. Geotech. Eng., 122(2), 120–129.
Lee, K. L., and Seed, H. B.(1967). “Drained strength characteristics of sands.” J. Soil Mech. Found. Div., Am. Soc. Civ. Eng., 93(6), 117–141.
Li, X. S., Dafalias, Y. F., and Wang, Z. L.(1999). “State-dependent dilatancy in critical-state constitutive modelling of sand.” Can. Geotech. J., 36(4), 599–611.
Luong, M. P. (1980). “Stress-strain aspects of cohesionless soils under cyclic and transient loading.” Proc., Int. Symp. Soils under Cyclic and Transient Loading, Swansea, UK, 315–324.
Maeda, K., and Miura, K.(1999). “Confining stress dependency of mechanical properties of sands.” Soils Found., 39(1), 53–67.
Manzari, M. T., and Dafalias, Y. F.(1997). “A critical state two-surface plasticity model for sands.” Geotechnique, 47(2), 255–272.
Miura, N., Murata, H., and Yasufuku, N.(1984). “Stress-strain characteristics of sand in a particle-crushing region.” Soils Found., 24(1), 77–89.
Mroz, Z., and Zienkiewicz, O. C. (1984). “Uniform formulation of constitutive equations for clay and sand.” Mechanics of engineering materials, C. S. Desai and R. H. Gallangher, eds., Wiley, New York, 415–450.
Nova, R., and Wood, D. M.(1979). “A constitutive model for sand in triaxial compression.” Int. J. Numer. Analyt. Meth. Geomech., 3, 255–278.
Pastor, M., Zienkiewicz, O. C., and Leung, K. H.(1985). “Simple model for transient soil loading in earthquake analysis. II: Non-associative models for sands.” Int. J. Numer. Analyt. Meth. Geomech., 9(5), 477–498.
Pastor, M., and Zienkiewicz, O. C. (1986). “A generalized plasticity, hierarchial model for sand under monotonic and cyclic loading.” Numerical methods in geomechanics, G. N. Pande, and van W. F. Impe, eds., Jackson, London, 131–150.
Pastor, M., Zienkiewicz, O. C., and Chan, A. H. C.(1990). “Generalized plasticity and the modeling of soil behavior.” Int. J. Numer. Analyt. Meth. Geomech., 14(3), 151–190.
Pastor, M., Zienkiewicz, O. C., Xu, G. D., and Peraire, J. (1993). “Modeling of sand behavior: Cyclic loading, anisotropy and localization.” Modern approaches to plasticity, D. Kolymbas, ed., Elsevier, New York, 469–492.
Pestana, J. M., and Whittle, A. J.(1999). “Formulation of a unified constitutive model for clays and sands.” Int. J. Numer. Analyt. Meth. Geomech., 23, 1215–1243.
Ponce, V. M., and Bell, J. M.(1971). “Shear strength of sand at extremely low pressures.” J. Soil Mech. Found. Div., Am. Soc. Civ. Eng., 97(4), 625–638.
Pradhan, T. B. S. (1989). “The behavior of sand subjected to monotonic and cyclic loadings.” PhD thesis, Kyoto Univ., Japan.
Prevost, J. H.(1978). “Plasticity theory for soil stress-strain behavior.” J. Eng. Mech., 104(5), 1177–1194.
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, 500–527.
Sassa, S., and Sekiguchi, H.(2001). “Analysis of waved-induced liquefaction of sand beds.” Geotechnique, 51(2), 115–126.
Silver, M. L., and Seed, H. B.(1971). “Deformation characteristics of sands under cyclic loading.” J. Soil Mech. Found. Div., Am. Soc. Civ. Eng., 97(8), 1081–1098.
Tatsuoka, F. (1972). “A fundamental study of the behavior of sand by triaxial testing.” PhD thesis, Univ. of Tokyo, Tokyo.
Tatsuoka, F., Sakamoto, M., Kawamura, T., and Fukushima, S.(1986). “Strength and deformation characteristics of sand in plane strain compression at extremely low pressures.” Soils Found., 26(1), 65–84.
Tatsuoka, F., Siddiquee, M. S. A., Park, C. S., Sakamoto, M., and Abe, F.(1993). “Modelling stress-strain relations of sand.” Soils Found., 33(2), 60–81.
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, 44, 413–433.
Vesic, A. S., and Clough, G. B.(1968). “Behavior of granular materials under high stresses.” J. Soil Mech. Found. Div., Am. Soc. Civ. Eng., 94(3), 661–668.
Wan, R. G., and Guo, P. J.(1998). “A simple constitutive model for granular soils: Modified stress-dilatancy approach.” Comput. Geotech., 22(2), 109–133.
Wang, Z.-L., Dafalias, Y. F., and Shen, C.-K.(1990). “Bounding surface hypoplasticity model for sand.” J. Eng. Mech., 116(5), 983–1001.
Yamamuro, J. A., andLade, P. V.(1996). “Drained sand behavior in axisymmetric tests at high pressures.” J. Geotech. Eng., 122(2), 109–119.
Zienkiewicz, O. C., Leung, K. H., and Pastor, M.(1985). “Simple model for transient soil loading in earthquake analysis. I: Basic model and its application.” Int. J. Numer. Analyt. Meth. Geomech., 9(5), 453–476.
Zienkiewicz, O. C., and Mroz, Z. (1984). “Generalized plasticity formulation and applications to geomechanics.” Mechanics of engineering materials, C. S. Desai, and R. H. Gallagher, eds., Wiley, New York, 655–679.
Zytynski, M., Randolph, M. F., Nova, R., and Wroth, C. P.(1978). “On modeling the unloading-reloading behavior of soils.” Int. J. Numer. Analyt. Meth. Geomech., 2, 87–94.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 129 • Issue 8 • August 2003
Pages: 851 - 860
Copyright
Copyright © 2003 American Society of Civil Engineers.
History
Received: Feb 22, 2002
Accepted: Dec 4, 2002
Published online: Jul 15, 2003
Published in print: Aug 2003
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.