Probabilistic Simulation of Triaxial Undrained Cyclic Behavior of Soils
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.
[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.
[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.
@article{"International Journal of Earth, Energy and Environmental Sciences:72743", author = "Arezoo Sadrinezhad and Kallol Sett and S. I. Hariharan", title = "Probabilistic Simulation of Triaxial Undrained Cyclic Behavior of Soils", 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.", volume = "10", number = "4", pages = "467-7", }
