Dynamic Analysis of Porous Media using Generalized Plasticity Model and Non-Darcy Flow Rule
Authors
Abstract
Biot equations that consider fluid and soil interaction at the same time are the most applicable relationships in the soil dynamic analysis. However, in dynamic analysis, due to the sudden increase in the excess pore pressure caused by seismic excitation and the occurrence of high hydraulic gradients, the assumption of the Darcy flow used in these equations is questionable. In the present study, in the u-p form of Biot equations, non-Darcy flow is considered. Also, the nonlinear behavior of soil is modeled by the Pastor-Zienkiewicz -Chan model. For validation, the VELACS No.1 experiment is modeled and the effect of the nonlinear fluid flow assumption on the results is examined. The results indicate that in the low permeability coefficients, the obtained results of the non-Darcy and Darcy flow are in agreement; however, in high permeability coefficients, these two methods differ by time and depth.
Keywords
1. Taiebat, M., and Pak, A., “A Fully Coupled Dynamic Analysis of Velacs Experiment No. 1, Using A Critical State Two-Surface Plasticity Model For Sands”, 13th World Conference on Earthquake Engineering Vancouver, B.C., Canada. August 1-6, Paper No. 2239, 2004.
2. Shahir, H., Pak, A., Taiebat, M., and Jeremic, B., “Evaluation of Variation of Permeability in Liquefiable Soil under Earthquake Loading”, Computers and Geotechnics, Vol. 40, pp. 74-88, 2012.
3. Rahmani, A., Ghasemi Fare, O., and Pak, A., “Investigation of the Influence of Permeability Coefficient on the Numerical Modeling of the Liquefaction Phenomenon”, Scientia Iranica A, Vol. 19, No. 2, pp. 179-187, 2012.
4. Khoei, A. R., Azami, A. R., and Haeri, S. M, “Implementation of Plasticity Based Models in Dynamic Analysis of Earth and Rockfill Dams: A Comparison of Pastor-Zienkiewicz and Cap Models”, Computers and Geotechnics, Vol. 31, pp. 385-410, 2004.
5. Pastor, M., Zienkiewicz, O. C., and Chan, A. H. C., “Generalized Plasticity and the Modeling of Soil Behavior”, International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 14, pp. 151-190, 1990.
6. Iraji, A., Farzaneh, O., and Seyedi Hosseininia, E., “A Modification to Dense Sand Dynamic Simulation Capability of Pastor-Zienkiewicz-Chan Model”, Acta Geotechnica, Vol. 9, pp. 343-353, 2014.
7. Tamayo, L., Palomino, J., and Awruch, A. M., “On the Validation of a Numerical Model for the Analysis of Soil-Structure Interaction Problems”, Latin American Journal of Solids and Structures, Vol. 13, pp. 1545-1575, 2016.
8. Taslimian, R., Noorzad, A., Maleki Javan, M. R., “Numerical Simulation of Liquefaction in Porous Media using Nonlinear Fluid Flow Law”, International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 39, pp. 229-250, 2014, DOI: 10.1002/nag.2297.
9. Andrianopoulos, K., Papadimitriou, A., and Bouckovalas, G., “Use of a New Bounding Surface Model for the Analysis of Earthquake-Induced Liquefaction Phenomena”, 4th International Conference on Earthquake Geotechnical Engineering, No. 1443, 2007.
10. Sadeghian, S., and Latifi, N. M., “Using State Parameter to Improve Numerical Prediction of a Generalized Plasticity Constitutive Model”, Computers & Geosciences, Vol. 51, pp. 255-268, 2013.
11. Tasiopoulou, P., Taiebat, M., and Tafazzoli, N. “On Validation of Fully Coupled Behavior of Porous Media using Centrifuge Test Results”, Coupled Systems Mechanics, Vol. 4, pp. 37-65, 2015a.
12. Arulmoli, K., Muraleetharan, K. K., Hossain, M. M., and Fruth, L. S., VELACS: Verification of Liquefaction Analyses by Centrifuge StudiesLaboratory Testing Program, Soil Data Report, Earth Technology Corporation, 1992.
13. Zienkiewicz, O. C., Chan, A. H. C., Pastor, M., Paul, D. K., and Shiomi, T., “Static and Dynamic Behavior of Soils; a Rational Approach to Quantitative Solution. I. Fully Saturated Problems”, Proceedings of the Royal Society of London A, Vol. 429, pp. 285-309, 1990.
14. Ergun S., “Fluid Flow Through Packed Columns”, Journal of Chemical Engineering and Science, Vol. 48, pp. 89-94, 1952.
15. Zienkiewicz, O. C., and Taylor, R. L., The Finite Element Method, Vol. 2, London: McGrawHill,1991.
16. Mroz, Z., and Zienkiewicz, O. C., Uniform Formulation of Constitutive Equations for Clays and Sand In: Desai, C. S., and Gallagher, R. H., (Eds.), Chapter 22, Mechanics of engineering materials, John Wiley & Sons, pp. 415-459, 1984.
17. Taslimian, R., “Numerical Simulation of Liquefaction using Nonlinear Flow with Irregular Embedded Topographic Porous Layers”, A Thesis Submitted to the Graduate Studies Office in Partial Fulfillment of the Requirements for the Degree of M.Sc. in Civil Engineering- Earthquake Engineering, Tehran University, Iran, 2012.
18. Hosseini, S. M., and Sonei, E., “Seepage Analysis Through Rockfill Dams by Finite Element Method in a Fixed Gird”, Journal of Computational Methods In Engineering, Vol. 22, pp. 91-108, 2003.
19. Chan, A. H. C., “A Unified Finite Element Solution to Static and Dynamic Geomechanics Problems”, Ph.D. Thesis, University College Swansea, 1988.
20. Chan, A. H. C., User Manual for DIANA SWANDYNE-II School of Civil Engineering, University of Birmingham, 1995.
21. Taboada, V. M., and Dobry, R., “Experimental Results and Numerical Predictions of Model No 1”, In: Arulanandan, K., and Scott, R. F., (Eds.), Proceedings of the International Conference on the Verification of Numerical Procedures for the Analysis of Soil Liquefaction Problems, California, United States, 1993.
22. Arulanandan, K., and Scott, R. F., (Eds.), Verification of Numerical Procedures for the Analysis of Soil Liquefaction Problems, Volume 1, Experimental Results and Numerical Predictions (Class A & B), Published by Taylor & Francis, A.A. Balkema,1993.
2. Shahir, H., Pak, A., Taiebat, M., and Jeremic, B., “Evaluation of Variation of Permeability in Liquefiable Soil under Earthquake Loading”, Computers and Geotechnics, Vol. 40, pp. 74-88, 2012.
3. Rahmani, A., Ghasemi Fare, O., and Pak, A., “Investigation of the Influence of Permeability Coefficient on the Numerical Modeling of the Liquefaction Phenomenon”, Scientia Iranica A, Vol. 19, No. 2, pp. 179-187, 2012.
4. Khoei, A. R., Azami, A. R., and Haeri, S. M, “Implementation of Plasticity Based Models in Dynamic Analysis of Earth and Rockfill Dams: A Comparison of Pastor-Zienkiewicz and Cap Models”, Computers and Geotechnics, Vol. 31, pp. 385-410, 2004.
5. Pastor, M., Zienkiewicz, O. C., and Chan, A. H. C., “Generalized Plasticity and the Modeling of Soil Behavior”, International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 14, pp. 151-190, 1990.
6. Iraji, A., Farzaneh, O., and Seyedi Hosseininia, E., “A Modification to Dense Sand Dynamic Simulation Capability of Pastor-Zienkiewicz-Chan Model”, Acta Geotechnica, Vol. 9, pp. 343-353, 2014.
7. Tamayo, L., Palomino, J., and Awruch, A. M., “On the Validation of a Numerical Model for the Analysis of Soil-Structure Interaction Problems”, Latin American Journal of Solids and Structures, Vol. 13, pp. 1545-1575, 2016.
8. Taslimian, R., Noorzad, A., Maleki Javan, M. R., “Numerical Simulation of Liquefaction in Porous Media using Nonlinear Fluid Flow Law”, International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 39, pp. 229-250, 2014, DOI: 10.1002/nag.2297.
9. Andrianopoulos, K., Papadimitriou, A., and Bouckovalas, G., “Use of a New Bounding Surface Model for the Analysis of Earthquake-Induced Liquefaction Phenomena”, 4th International Conference on Earthquake Geotechnical Engineering, No. 1443, 2007.
10. Sadeghian, S., and Latifi, N. M., “Using State Parameter to Improve Numerical Prediction of a Generalized Plasticity Constitutive Model”, Computers & Geosciences, Vol. 51, pp. 255-268, 2013.
11. Tasiopoulou, P., Taiebat, M., and Tafazzoli, N. “On Validation of Fully Coupled Behavior of Porous Media using Centrifuge Test Results”, Coupled Systems Mechanics, Vol. 4, pp. 37-65, 2015a.
12. Arulmoli, K., Muraleetharan, K. K., Hossain, M. M., and Fruth, L. S., VELACS: Verification of Liquefaction Analyses by Centrifuge StudiesLaboratory Testing Program, Soil Data Report, Earth Technology Corporation, 1992.
13. Zienkiewicz, O. C., Chan, A. H. C., Pastor, M., Paul, D. K., and Shiomi, T., “Static and Dynamic Behavior of Soils; a Rational Approach to Quantitative Solution. I. Fully Saturated Problems”, Proceedings of the Royal Society of London A, Vol. 429, pp. 285-309, 1990.
14. Ergun S., “Fluid Flow Through Packed Columns”, Journal of Chemical Engineering and Science, Vol. 48, pp. 89-94, 1952.
15. Zienkiewicz, O. C., and Taylor, R. L., The Finite Element Method, Vol. 2, London: McGrawHill,1991.
16. Mroz, Z., and Zienkiewicz, O. C., Uniform Formulation of Constitutive Equations for Clays and Sand In: Desai, C. S., and Gallagher, R. H., (Eds.), Chapter 22, Mechanics of engineering materials, John Wiley & Sons, pp. 415-459, 1984.
17. Taslimian, R., “Numerical Simulation of Liquefaction using Nonlinear Flow with Irregular Embedded Topographic Porous Layers”, A Thesis Submitted to the Graduate Studies Office in Partial Fulfillment of the Requirements for the Degree of M.Sc. in Civil Engineering- Earthquake Engineering, Tehran University, Iran, 2012.
18. Hosseini, S. M., and Sonei, E., “Seepage Analysis Through Rockfill Dams by Finite Element Method in a Fixed Gird”, Journal of Computational Methods In Engineering, Vol. 22, pp. 91-108, 2003.
19. Chan, A. H. C., “A Unified Finite Element Solution to Static and Dynamic Geomechanics Problems”, Ph.D. Thesis, University College Swansea, 1988.
20. Chan, A. H. C., User Manual for DIANA SWANDYNE-II School of Civil Engineering, University of Birmingham, 1995.
21. Taboada, V. M., and Dobry, R., “Experimental Results and Numerical Predictions of Model No 1”, In: Arulanandan, K., and Scott, R. F., (Eds.), Proceedings of the International Conference on the Verification of Numerical Procedures for the Analysis of Soil Liquefaction Problems, California, United States, 1993.
22. Arulanandan, K., and Scott, R. F., (Eds.), Verification of Numerical Procedures for the Analysis of Soil Liquefaction Problems, Volume 1, Experimental Results and Numerical Predictions (Class A & B), Published by Taylor & Francis, A.A. Balkema,1993.
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