Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30135
Probabilistic Simulation of Triaxial Undrained Cyclic Behavior of Soils

Authors: Arezoo Sadrinezhad, Kallol Sett, S. I. Hariharan

Abstract:

In this paper, a probabilistic framework based on Fokker-Planck-Kolmogorov (FPK) approach has been applied to simulate triaxial cyclic constitutive behavior of uncertain soils. The framework builds upon previous work of the writers, and it has been extended for cyclic probabilistic simulation of triaxial undrained behavior of soils. von Mises elastic-perfectly plastic material model is considered. It is shown that by using probabilistic framework, some of the most important aspects of soil behavior under cyclic loading can be captured even with a simple elastic-perfectly plastic constitutive model.

Keywords: Elasto-plasticity, uncertainty, soils, Fokker-Planck equation, Fourier Spectral method, Finite Difference method.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1123979

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1205

References:


[1] A. N. Schofield and P. Wroth, Critical state soil mechanics. McGraw-Hill, 1968, (Reissued by Dover Publications, 2003).
[2] Y. F. Dafalias and M. T. Manzari, “Simple plasticity sand model accounting for fabric change effects,” ASCE Journal of Engineering Mechanics, vol. 130, no. 6, pp. 622–634, June 2004.
[3] A. Vytiniotis, “Contributions to the analysis and mitigation of liquefaction in loose sand slopes,” Doctoral Dissertation, Massachusetts Institute of Technology, Boston, MA, September 2011.
[4] R. W. Boulanger and K. Ziotopoulou, “Formulation of a sand plasticity plane-strain model for earthquake engineering applications,” Soil Dynamics and Earthquake Engineering, vol. 53, pp. 254–267, 2013.
[5] G. A. Fenton, “Estimation of stochastic soil models,” Journal of Geotechnical and Geoenvironmental Engineering, ASCE, vol. 125, no. 6, pp. 470–485, June 1999.
[6] D. J. DeGroot and G. B. Baecher, “Estimating autocovariance of in-situ soil properties,” Journal of Geotechnical Engineering, vol. 119, no. 1, pp. 147–166, January 1993.
[7] G. M. Hammitt, “Statistical analysis of data from a comparative laboratory test program sponsored by ACITL,” U.S. Army Waterways Experiment Station, Vicksburg, MS, 1966.
[8] K.-K. Phoon and F. H. Kulhawy, “Characterization of geotechnical variability,” Canadian Geotechnical Journal, vol. 36, no. 4, pp. 612–624, 1999.
[9] K. T. Marosi and D. R. Hiltunen, “Characterization of spectral analysis of surface waves shear wave velocity measurement uncertainty,” Journal of Geotechnical and Geoenvironmental Engineering, ASCE, vol. 130, no. 10, pp. 1034–1041, October 2004.
[10] S. Lacasse and F. Nadim, “Uncertainties in characterizing soil properties,” in Uncertainty in Geologic Environment: From Theory to Practice, Proceedings of Uncertainty ’96, July 31-August 3, 1996, Madison, Wisconsin, ser. Geotechnical Special Publication No. 58, C. D. Shackelford and P. P. Nelson, Eds., vol. 1. ASCE, New York, 1996, pp. 49–75.
[11] K.-K. Phoon and F. H. Kulhawy, “Evaluation of geotechnical property variability,” Canadian Geotechnical Journal, vol. 36, no. 4, pp. 625–639, 1999.
[12] G. M. Paice, D. V. Griffiths, and G. A. Fenton, “Finite element modeling of settlement on spatially random soil,” Journal of Geotechnical Engineering, vol. 122, no. 9, pp. 777–779, 1996.
[13] R. Popescu, J. H. Prevost, and G. Deodatis, “Effects of spatial variability on soil liquefaction: Some design recommendations,” Geotechnique, vol. 47, no. 5, pp. 1019–1036, 1997.
[14] B. S. L. P. De Lima, E. C. Teixeira, and N. F. F. Ebecken, “Probabilistic and possibilistic methods for the elastoplastic analysis of soils,” Advances in Engineering Software, vol. 132, pp. 569–585, 2001.
[15] S. Koutsourelakis, J. H. Prevost, and G. Deodatis, “Risk assesment of an interacting structure-soil system due to liquefaction,” Earthquake Engineering and Structural Dynamics, vol. 31, pp. 851–879, 2002.
[16] D. V. Griffiths, G. A. Fenton, and N. Manoharan, “Bearing capacity of rough rigid strip footing on cohesive soil: Probabilistic study,” Journal of Geotechnical and Geoenvironmental Engineering, ASCE, vol. 128, no. 9, pp. 743–755, 2002.
[17] M. Kleiber and T. D. Hien, The Stochastic Finite Element Method: Basic Perturbation Technique and Computer Implementation. Baffins Lane, Chichester, West Sussex PO19 1UD , England: John Wiley & Sons, 1992.
[18] B. Sudret and A. Der Kiureghian, “Stochastic finite element methods and reliability: A state of the art report,” University of California, Berkeley, Technical Report UCB/SEMM-2000/08, 2000.
[19] K. Sett and B. Jeremi´c, “Probabilistic yielding and cyclic behavior of geomaterials,” International Journal for Numerical and Analytical Methods in Geomechanics, vol. 34, no. 15, pp. 1541–1559, 2010.
[20] K. Sett, B. Unutmaz, K. O. C¸ etin, S. Koprivica, and B. Jeremi´c, “Soil uncertainty and its influence on simulated G/Gmax and damping behavior,” Journal of Geotechnical and Geoenvironmental Engineering, vol. 137, no. 3, pp. 197–204, March 2011.
[21] M. L. Kavvas, “Applied Stochastic Methods in Engineering (ECI 266) classnotes,” Lecture Notes, University of California, Davis, 1993.
[22] B. Jeremi´c, K. Sett, and M. L. Kavvas, “Probabilistic elasto-plasticity: Formulation in 1–D,” Acta Geotechnica, vol. 2, no. 3, pp. 197–210, September 2007.
[23] K. Sett, B. Jeremi´c, and M. L. Kavvas, “Probabilistic elasto-plasticity: Solution and verification in 1–D,” Acta Geotechnica, vol. 2, no. 3, pp. 211–220, September 2007.
[24] K. Sett, B. Jeremi´c, and M. L. Kavvas, “The role of nonlinear hardening/softening in probabilistic elasto–plasticity,” International Journal for Numerical and Analytical Methods in Geomechanics, vol. 31, no. 7, pp. 953–975, June 2007.
[25] B. Jeremi´c and K. Sett, “On probabilistic yielding of materials,” Communications in Numerical Methods in Engineering, vol. 25, no. 3, pp. 291–300, 2009.
[26] W. F. Chen and D. J. Han, Plasticity for Structural Engineers. Springer-Verlag, 1988.
[27] B. M. Das, Soil Mechanics Laboratory Manual, 8th ed. New York, NY: Oxford University Press, 2013.
[28] D. C. Montgomery and G. C. Runger, Applied Statistics and Probability for Engineers, 3rd ed. 605 Third Avenue, New York, NY 10158: John Wiley & Sons, 2003.
[29] Z. Hashin, “Analysis of composite materials,” Journal of Applied Mechanics, vol. 50, pp. 481–501, 1983.