Browse > Article

http://dx.doi.org/10.12989/csm.2013.2.4.375
###

Use of infinite elements in simulating liquefaction phenomenon using coupled approach |

Kumari, Sunita
(Department of Civil Engineering, Indian Institute of Technology Roorkee)
Sawant, V.A. (Department of Civil Engineering, Indian Institute of Technology Roorkee) |

Publication Information

Abstract

Soils consist of an assemblage of particles with different sizes and shapes which form a skeleton whose voids are filled with water and air. Hence, soil behaviour must be analyzed by incorporating the effects of the transient flow of the pore-fluid through the voids, and therefore requires a two-phase continuum formulation for saturated porous media. The present paper presents briefly the Biot's basic theory of dynamics of saturated porous media with u-P formulation to determine the responses of pore fluid and soil skeleton during cyclic loading. Kelvin elements are attached to transmitting boundary. The Pastor-Zienkiewicz-Chan model has been used to describe the inelastic behavior of soils under isotropic cyclic loadings. Newmark-Beta method is employed to discretize the time domain. The response of fluid-saturated porous media which are subjected to time dependent loads has been simulated numerically to predict the liquefaction potential of a semi-infinite saturated sandy layer using finite-infinite elements. A settlement of 17.1 cm is observed at top surface. It is also noticed that liquefaction occurs at shallow depth. The mathematical advantage of the coupled finite element analysis is that the excess pore pressure and displacement can be evaluated simultaneously without using any empirical relationship.

Keywords

2-D isoparametric continuum element; kelvin element; transmitting boundary; 2-D infinite elements; liquefaction; pastor-zienkiewicz-chan model;

Citations & Related Records

- Reference

1 | Nova, R. and Wood, D.M. (1982), A Constitutive Model for Soil Under Monotonic and Cyclic Loading, Soil Mechanics-Transient and Cyclic Loads (Edited by G.N. Pande and O.C. Zienkiewicz), John Wiley & Sons Ltd., New York, USA. |

2 | Kramer, S.L. and Seed, B.H. (1988), "Initiation of static liquefaction under static loading conditions", J. Geotech. Eng. Div. ASCE, 114(4), 412-430. DOI |

3 | Ladhane, K.B. and Sawant, V.A. (2012), "Dynamic response of 2 piles in series and parallel arrangement", J. Eng., 16(4), 63-72. DOI |

4 | Liyanapathirana, D.S. and Poulos, H.G. (2002), "Numerical simulation of soil liquefaction due to earthquake loading", Soil Dyn. Earthq. Eng., 22(7), 511-523. DOI ScienceOn |

5 | Mesgouez, A., Lefeuve-Mesgouez, G. and Chambarel, A. (2005), "Transient mechanical wave propagation in semi-infinite porous media using a finite element approach", Soil Dyn. Earthq. Eng., 25(6), 421-430. DOI ScienceOn |

6 | Finn, W.D.L., Lee, K.W. and Martin, G.R. (1977), "An effective stress model for liquefaction", J. Geotech. Eng. Div. ASCE, 103(GT6), 513-533. |

7 | Katona, M.G. and Zienkiewicz, O.C. (1985), "A unified set of single step algorithms Part 3: the Beta-m method, a generalization of the Newmark scheme", Int. J. Numer. Meth. Eng., 21(7), 1345-1359. DOI ScienceOn |

8 | Prevost, J.H. (1985), "A simple plasticity theory for frictional cohesionless soils", Soil. Dyn. Earthq. Eng., 4(1), 9-17. |

9 | Prevost, J.H. (1989), DYNA1D, A Computer Program for Nonlinear Seismic Site Response Analysis: Technical Documentation, Technical Report NCEER-89-0025, National Center for Earthquake Engineering Research, State University of New York at Buffalo, NY, USA. |

10 | Sadeghian, S. and Manouchehr, L.N. (2012), "Using state parameter to improve numerical prediction of a generalized plasticity constitutive model", J. Comp. Geosci., 51, 255-268. |

11 | Seed, H.B. and Idriss, I.M. (1971), "Simplified procedure for evaluating soil liquefaction potential", J. Soil Mech. Found. Div. ASCE, 92(SM6), 1249-1273. |

12 | Seed, H.B. and Lee, K.L. (1966), "Liquefaction of saturated sands during cyclic loading", J. Geotech. Eng. ASCE, 92(SM6), 105-134. |

13 | Taiebat, M., Shahir, H. and Pak, A. (2007), "Study of pore pressure variation during liquefaction using two constitutive models for sand", Soil. Dyn. Earthq. Eng., 27(1), 60-72. DOI ScienceOn |

14 | Seed, H.B., Tokimatsu, K., Harder, L.F. and Chung, R. (1985), "Influence of SPT procedures in soil liquefaction resistance evaluations", J. Geotech. Eng., ASCE, 111(12), 1425-1445. DOI ScienceOn |

15 | Patil, V.A., Sawant, V.A. and Deb, K. (2013b), "3-D finite element dynamic analysis of rigid pavement using infinite elements", Int. J. Geomech. ASCE, 13(5), 533-544. DOI |

16 | Nemat-Nasser, S. and Shokooh, A. (1979), "A unified approach to densification and liquefaction of cohesionless sand in cyclic shearing", Can. Geotech. J., 16(4), 659-678. DOI ScienceOn |

17 | Oka, F., Yashima, A., Shibata, T., Kato, M. and Uzuoka, R. (1994), "FEM-FDM coupled liquefaction analysis of a porous soil using an elasto-plastic model", Appl. Sci., 52(3), 209-245. DOI ScienceOn |

18 | 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. DOI |

19 | Biot, M.A. and Willis, D.G. (1957), "The elastic coefficients of a theory of consolidation", J. Appl. Mech. T. ASME, 29, 594-601. |

20 | Biot, M.A. (1955), "Theory of elasticity and consolidation for a porous anisotropic solid", J. Appl. Phys., 26(2), 182-185. DOI |

21 | Biot, M.A. (1956), "Theory of propagation of elastic waves in a fluid-saturated porous solid", J. Acou. Soc. Am., 28(2), 168-178. DOI |

22 | Patil, V.A., Sawant, V.A. and Deb, K. (2013a), "2-D finite element analysis of rigid pavement considering dynamic vehicle pavement interaction effects", Appl. Math. Model., 37(3), 1282-1294. DOI ScienceOn |

23 | Elgamal, A., Yang, Z., Parra, E. and Ragheb, A. (2003), "Modeling of cyclic mobility in saturated cohesionless soils", Int. J. Plasticity, 19(6), 883-905. DOI ScienceOn |

24 | Seed, H.B. (1979), "Soil liquefaction and cyclic mobility evaluation for level ground during earthquakes", J. Geotech. Eng. Div. ASCE, 105(GT2), 201-255. |

25 | Simon, B.R., Wu. J.S.S., Zienkiewicz, O.C. and Paul, D.K. (1986), "Evaluation of u-w and u- finite element methods for the dynamic response of saturated porous media using one-dimensional models", SIAM. J. Numer. Anal., 10(5), 461-482. |

26 | Zienkiewicz, O.C. and Mroz, Z. (1984), Generalized Plasticity Formulation and Applications to Geomechanics, Mech. Eng. Mater., (Edited by C.S. Desai and R.H. Gallagher), Wiley, New York, USA. |

27 | Zienkiewicz, O.C. and Shiomi, T. (1984), "Dynamic behaviour of saturated porous media; The generalized biot formulation and its numerical solution", Numer. Meth., 8(1), 71-96. |