Hysteretic Endochronic Theory for Sand
Publication: Journal of Engineering Mechanics
Volume 109, Issue 4
Abstract
A new form of endochronic constitutive model is presented to describe the behavior of dry or drained sand, and its parameters are determined by extensive comparisons with published test data. Jump‐kinematic hardening is used to guarantee that the hysteresis loops always close, yield positive energy dissipation, and give an increase in tangent modulus when unloading changes to reloading. Criteria for virgin loading, unloading and reloading are formulated in terms of deviatoric work, and changes of material parameters at loading‐unloading‐reloading transition points are determined. Two endochronic units coupled in parallel are used to describe the measured response over a broad range of strain amplitude. The inelastic volume change is characterized so as to include both densification and dilatancy. Certain material properties are determined as functions of the void ratio. Calculations show that the lateral stress in a simple shear test quickly becomes almost equal to the vertical stress. A three‐dimensional finite element analysis of the simple shear test with endochronic theory reveals significant stress nonuniformity; but this is found to have little effect on the resulting hysteresis loops.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Ansal, A. M., Bažant, Z. P., Krizek, R. J., “Viscoplasticity of Normally Consolidated Clays,” Journal of the Geotechnical Engineering Division, ASCE, Vol. 105, No. GT4, 1979, pp. 519–537.
2.
Ansal, A. M., Krizek, R. J., Bažant, Z. P., “Seismic Analysis of an Earth Dam Band on Endochronic Theory,” R. Dungar, et al., eds., Proceedings, International Symposium on “Numerical Methods in Geomechanics,” Zurich, Switzerland, Sept., 1982, published by A. A. Bulkema, Rotterdam, Holland, pp. 559–576.
3.
Bažant, Z. P., “Endochronic Theory for Inelasticity and Failure of Concrete Structures‐Addendum,” Structural Engineering Report No. 1976‐12/2/59, to Oak Ridge National Laboratory, by the Department of Civil Engineering, Northwestern University, Evanston, Ill. (available from National Technical Information Service, Springfield, Va.), 1976.
4.
Bažant, Z. P., “Endochronic Inelasticity and Incremental Plasticity,” International Journal of Solids and Structures, Vol. 14, 1978, pp. 691–714.
5.
Bažant, Z. P., “Work Inequalities for Plastic‐Fracturing Materials,” International Journal of Solids and Structures, Vol. 16, 1980, pp. 873–901.
6.
Bažant, Z. P., Ansal, A. M., Krizek, R. J., “Viscoplasticity of Transversely Isotropic Clays,” Journal of the Engineering Mechanics Division, ASCE, Vol. 105, No. EM4, 1979, pp. 549–565.
7.
Bažant, Z. P., Ansal, A. M., and Krizek, R. J., “Endochronic Models for Soils,” in Soil Mechanics—Transient and Cyclic Loads, ed. by G. N. Pande and O. C. Zienkiewicz, J. Wiley & Sons, Inc., London, England, 1982, pp. 419–438.
8.
Bažant, Z. P., and Bhat, P. D., “Endochronic Theory of Inelasticity and Failure of Concrete,” Journal of the Engineering Mechanics Division, ASCE, Vol. 102, No. EM4, Aug., 1976, pp. 701–722.
9.
Bažant, Z. P., Bhat, P. D., and Shieh, C. L., “Endochronic Theory for Inelasticity and Failure Analysis of Concrete Structures,” Structural Engineering Report No. 1976‐12/259, to Oak Ridge National Laboratory, by the Department of Civil Engineering, Northwestern University, Evanston, Ill. (available from National Technical Information Service, Springfield, Va.), 1976.
10.
Bažant, Z. P., and Krizek, R. J., “Endochronic Constitutive Law for Liquefaction of Sand,” Journal of the Engineering Mechanics Division, ASCE, Vol. 102, No. EM2, Apr., 1976, pp. 225–238.
11.
Bažant, Z. P., Krizek, R. J., and Shieh, C. L., “Hysteretic Endochronic Theory for Sand,” Geotechnical Engineering Report No. 79‐4/654h, Northwestern University, Evanston, Ill., Apr., 1979.
12.
Bažant, Z. P., and Shieh, C. L., “Endochronic Model for Nonlinear Triaxial Behavior of Concrete,” Nuclear Engineering and Design, Vol. 47, 1978, pp. 305–315.
13.
Blázquez, R. M., Krizek, R. J., Bažant, Z. P., “Site Factors Controlling Liquefaction,” Journal of the Engineering Mechanics Division, ASCE, Vol. 106, No. GT7, July, 1980, pp. 785–801.
14.
Cuellar, V., Bažant, Z. P., Krizek, R. J., and Silver, M. L., “Densification and Hysteresis of Sand Under Cyclic Shear,” Journal of the Geotechnical Engineering Division, ASCE, Vol. 103, No. GT5, May, 1977, pp. 399–416.
15.
Dougill, J. W., “Some Remarks on Path Independence in the Small in Plasticity,” Quarterly Journal of Applied Mathematics, Vol. 32, 1975, pp. 233–243.
16.
Dungar, R., and Nuh, S., “Endochronic‐Critical State Models for Sand,” Journal of the Engineering Mechanics Division, ASCE, Vol. 106, No. EM5, Oct., 1980, pp. 951–968.
17.
Hsieh, B. J., “On the Uniqueness and Stability of Endochronic Theory,” Journal of Applied Mechanics, ASME, Vol. 47, Dec., 1980, pp. 748–754.
18.
Jeter, J. W., “An Evaluation of Endochronic Concrete Theory,” Report, New Mexico Engineering Research Institute, Albuquerque, N.M., 1982.
19.
Lee, K. L., and Seed, H. B., “Drained Strength Characteristics of Sands,” Journal of Soil Mechanics and Foundations Division, ASCE, Vol. 93, No. SM6, Nov., 1967, pp. 117–141.
20.
Pyke, R. M., “Settlement and Liquefaction of Sands Under Multidirectional Loading,” Dissertation presented to the University of California, at Berkeley, Calif., in 1973, in partial fulfillment of the requirements for the Degree of Doctor of Philosophy.
21.
Richart, R. E., Hall, J. R., and Woods, R. D., “Vibrations of Soils and Foundations,” Prentice‐Hall, Inc., Englewood Cliffs, N.J., 1970.
22.
Rivlin, R. S., “Some Comments on the Endochronic Theory of Plasticity,” International Journal of Solids and Structures, Vol. 17, 1981, pp. 321–248.
23.
Sandler, I. S., “On the Uniqueness and Stability of Endochronic Theories of Material Behavior,” Journal of Applied Mechanics, ASME, Series E, Vol. 45, 1978, pp. 263–266.
24.
Schapery, R. A., “On a Thermodynamic Constitutive Theory and Its Application to Various Nonlinear Materials,” B. A. Boley, ed., Proceedings, IUTAM Symposium East Kilbride, Springer, N.Y., June, 1968.
25.
Sener, C., “An Endochronic Nonlinear Inelastic Constitutive Law for Cohesionless Soils Subjected to Dynamic Loading,” Dissertation presented to Northwestern University, at Evanston, Ill., in Aug., 1979, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
26.
Silver, M. L., and Seed, H. B., “Deformation Characteristics of Sand Under Cyclic Loading,” Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 97, No. SM8, Aug., 1971, pp. 1081–1098.
27.
Silver, M. L., and Seed, H. B., “Volume Changes in Sands During Cyclic Loadings,” Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 97, No. SM9, Sept., 1971, pp. 1171–1182.
28.
Trangenstein, J. A., and Read, H. E., “Inelastic Response Characteristics of the New Endochronic Theory with Singular Kernel,” International Journal of Solids and Structures, Vol. 18, No. 11, 1982, pp. 947–956.
29.
Valanis, K. C., “A Theory of Viscoplasticity Without a Yield Surface,” Archiwum Mechaniki Stossowanej, Vol. 23, 1971, pp. 517–551.
30.
Valanis, K. C., “On the Endochronic Foundation of Elastic Perfectly Plastic Solids,” Proceedings, Society of Engineering Science—Fourteenth Annual Meeting, Lehigh University, Bethlehem, Pa., 1977, pp. 761–763.
31.
Valanis, K. C., “Endochronic Theory With Proper Hysteresis Loop Closure Properties,” Topical Report SSR‐4182, Systems Science and Software, LaJolla, Calif., Aug., 1979.
32.
Valanis, K. C., and Read, H. E., “A New Endochronic Plasticity Model for Soils,” Report EPRI NP‐1388 (Project 810‐5), Electric Power Research Institute, Palo Alto, Calif., Apr., 1980.
33.
Zienkiewicz, O. C., “The Finite Element Method,” Third Edition, John Wiley & Sons, London, 1977.
Information & Authors
Information
Published In
Copyright
Copyright © 1983 ASCE.
History
Published online: Aug 1, 1983
Published in print: Aug 1983
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.