Skip to main content
SpringerLink
Log in

Nonlinear Problems During Consolidation Process

  • Chapter
Advanced Numerical Applications and Plasticity in Geomechanics

Part of the book series: International Centre for Mechanical Sciences ((CISM,volume 426))

  • 275 Accesses

Abstract

The geometrical nonlinear problems oriented at geotechnical problems are presented herein. Lagrangian, Eulerian and updated Lagrangian procedures are discussed. The description of a two phase medium i.e. soil skeleton and water is formulated. Both geometrical and material nonlinearites for the fully coupled problem are considered. The updated Lagrange description is applied to model geometrically non-linear effects during consolidation process. The interaction problems between structure and soil foundation are studied. The description of the contact phenomenon which take place at interface soil-structure for a two-phase medium, i.e. skeleton and water, is formulated. Galerkin’s and variational methods are used to derive the equations for the interface element in consolidation problems. The finite element equations for consolidation problems in large strains are formulated. The changes of the permeability in relation to the current porosity are discussed. The numerical tests for elastic and elasto-plastic skeleton models are shown and discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Atkinson, J. H., and Salfors, G. (1991). Experimental determination of stress-strain-time characteristics in laboratory and in situ tests, General report, Proceedings 10 h ECSMFE, Firence, Vol. 3, 915–956.

    Google Scholar 

  • Asaoka, A., Noda, T., and Fernando, G. S.K. (1997). Effects of changes in geometry on the linear elastic consolidation deformation, Soils and Foundations, Japanese Society of Soil Mechanics and Foundation Engineering, Vol. 37, No. 1. 29–39.

    Google Scholar 

  • Asaoka, A., Nakano, M., and Noda, T. (1997). Soil-water coupled behaviour of heavily overconsolidated clay near/at critical state, Soils and Foundations, Japanese Society of Soil Mechanics and Foundation Engineering, Vol. 37, No. 1., 13–28.

    Google Scholar 

  • Asaoka, A., Noda, T., Fernando, G. S.K., and Yamada, E. (1998). Creep-like delayed failure of clayey ground after the end of embankment construction, Proceedings of the 4th European Conference on Numerical Methods in Geotechnical Engineering, Udine, Italy, 243–252.

    Google Scholar 

  • Bakker, K. J., and Vermeer P. A. (1986). Finite element analysis of sheetpile walls, Proceedings of the 2nd International Symposium on Numerical Models in Geomechanics, Ghent, Belgium, 409–416.

    Google Scholar 

  • Bakker, K. J., and Brinkgreve R. B. J. (1990). The use of hybrid beam elements to model sheetpile behaviour in two dimensional deformation analysis. Proceedings 2“ d European Specialty Conference on Numerical Methods in Geotechnical Engineering, Santander, Spain, 559–571.

    Google Scholar 

  • Bathe, K. J. (1982). Finite element procedures in engineering analysis. Prentice-Hall, Inc. New Jersey.

    Google Scholar 

  • Biot, M. A. (1941). General theory of three-dimensional consolidation. Journal of Applied Physics, Vol. 12, 155–164.

    Article  MATH  Google Scholar 

  • Biot, M. A. (1956). General solution of the equations of elasticity and consolidation for porous materials. Journal ofApplied Mechanics, Vol. 23, 91–96.

    MathSciNet  MATH  Google Scholar 

  • Booker, J. R., Small, J. S. (1975). An investigation of the stability of numerical solutions of Biot’s equations of consolidation. International Journal Solids and Structures, Vol. 11, 907–917.

    Article  MATH  Google Scholar 

  • Burland, J. B. (1967). Deformation of soft clay. Ph.D. Thesis, University Cambridge.

    Google Scholar 

  • Chacinski, Z., Dluzewski, J. M. (1995). Badanie charakterystyk przeplywu w procesie konsolidacji gruntôw organicznych. II Seminarium Instytutu Zaopatrzenia w Wodç i Budownictwa Wodnego, Warszawa. (Study of the permeability relation for soft organic soils, Proceedings of 2nd Seminar Institute of Water Supply and Hydrotechnical Structures, Warsaw, Poland ), 69–74.

    Google Scholar 

  • Cormeau, C. (1975). Numerical stability in quasi static elasto-visco-plasticity. International Journal of the Numerical Methods Engineering, Vol. 9, 109–127.

    Article  MathSciNet  MATH  Google Scholar 

  • Cormeau, C. (1976). Viscoplasticity and plasticity in the finite element methods. Ph.D. Thesis, Swansea.

    Google Scholar 

  • Crisfield, M. A. (1996). Non-linear Finite Element Analysis of Solids and Structures. Vol. 1, John Wiley & Sons, New York.

    Google Scholar 

  • Crisfield, M. A. (1997). Non-linear Finite Element Analysis of Solids and Structures. Vol. 2, Advanced Topics, John Wiley & Sons, New York.

    Google Scholar 

  • Day, R. A., and Poots, D. M. (1994). Zero thickness interface elements–numerical stability and application. International Journal for Numerical and Analytical Methods in Geomechanics, Vol 18, 689–708.

    Article  Google Scholar 

  • Dafalias, Y. F., and Herrmann, L. R. (1980). A bounding surface soil plasticity model. Proceedings of International Symposium Soils under Cyclic Trans. Load., Swansea, 335–345.

    Google Scholar 

  • Derski, W., Izbicki, R., Kisiel, I., and Mroz Z. (1988). Rock and Soil Mechanics. PWN-Elsevier, Warszawa-Amsterdam.

    Google Scholar 

  • Desai, C. S., and Zhang, D. (1987). Viscoplastic model for geologic materials with generalized flow rule. International Journal for Numerical and Analytical Methods In Geomechanics, Vol. 11, 38–45.

    Article  Google Scholar 

  • Desai, C. S., Zaman, M. M., Lightner, J. G., Siriwardane, H. J. (1984). Thin-layer element for interfaces and joints. International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 8, 19–43.

    Article  Google Scholar 

  • Dienes, J. K. (1979). On the analysis of rotation and stress rate in deforming bodies. Acta Mechanica, Vol. 32, 217–232.

    Article  MathSciNet  MATH  Google Scholar 

  • Dluzewski, J. M. (1988). Total formulation for large strains in soils. International Journal Computers and Geotechnics, Vol. 5, No. 3, 197–211.

    Article  Google Scholar 

  • Dluzewski, J. M., Termaat, R. J. (1990). Consolidation by finite element method in engineering problems. Proceedings 2“ d European Speciality Conference on Numerical Methods in Geotechnical Engineering, Santander, Spain, 213–222.

    Google Scholar 

  • Dluewski, J. M. (1991). Soil structure interactions in consolidation problems. Proceedings 7th Conference of International Associations for Computer Methods and Advances in Geomechanics, Carinas, Australia, May, 1141–1146.

    Google Scholar 

  • Dluewski, J. M. (1993). Numerical modelling of soil structure interactions in consolidation problems. Warsaw University of Technology Publications, Civil Engineering, Vol. 123

    Google Scholar 

  • Dluzewski, P., and Antunez, H. (1994). Finite element simulation of dislocation field movement. Computer. Assist. Mechanics Engineering. Science. 2, 141–145.

    Google Scholar 

  • Dluzewski, J. M. (1997). HYDRO-GEO Program elementbw skonczonych dla geotechniki, hydrotechniki i inzynierii srodowiska. Oficyna Wydawnicza Politechniki Warszawskiej, Warszawa. (HYDRO-GEO — finite element program for hydrotechnics, geotechnics and environmental engineering. Warsaw University of Technology Publications)

    Google Scholar 

  • Dluewski, J. M. (1997). Nonlinear consolidation in finite element modelling. Proceedings of the IX International Conference on Computer Methods and Advances in Geomechanics, Wuhan, China, 1089–1094.

    Google Scholar 

  • Dluewski, J. M. (1998). Large strain consolidation for elasto-plastic materials. Proceedings of the 4th European Conference on Numerical Methods in Geotechnical Engineering, Udine, Italy, 473–482.

    Google Scholar 

  • Dluzewski, J.M., Popielski, P., Sternik, K., and Gryczmanski, M. (1999). Consolidation of soft soils in terms of finite element modelling. Proceedings of the Seventh International Conference on Numerical Models in Geomechanics (NUMOG VII) Graz, Austria, September, 569–572.

    Google Scholar 

  • Eringen, A. C. (1974). Basic Principles in “Continuum Physics”. Vol. 2, Academic Press, NY. Fung, Y. C. (1965). Foundations of solid mechanics. Prentice Hall.

    Google Scholar 

  • Ghaboussi, J., Wilson E. L., and Isenberg, J. (1973). Finite element for rock joints and interfaces. Journal of the Soil Mechanics and Foundations Division, ASCE, 99, SM10, October, 833–848.

    Google Scholar 

  • Gibson, R. E., Schiffman, R. L., and Pu S. L. (1970). Plane strain and axially symmetric consolidation of a clay layer on a smooth impervious base. Quart. Journal Mechanics and Applied Mathematics., Vol. XXIII, Pt. 4, 505–520.

    Google Scholar 

  • Goodman, R. E., Taylor R. L., and Brakke T. L. (1968). A model for the mechanics of jointed rock. Journal of the Mechanics Division, ASCE, 94, SM3, 637–659.

    Google Scholar 

  • Goodman, R. E., and Dubois J. (1972). Duplication of dilatancy in analysis of jointed rocks. Journal of the Soil Mechanics and Foundations Division, ASCE, 98, SM4, April, 399–422.

    Google Scholar 

  • Gryczmariski, M. (1994). Analytical and numerical subsoil models for soil-foundation interaction problems. Studia Geotechnika et Mechanica, Vol. XVI, No. 3–4, 29–72.

    Google Scholar 

  • Gryczmariski, M. (1995). Pr6ba klasyfikacji modeli konstytutywnych grunt6w. Zeszyty Naukowe Politechniki Slqskiej, Budownictwo, 81. (Trial of the constitutive soil models classification. Scientific Note, Silesian University of Technology, Civil Engineering, 81, 433–446.

    Google Scholar 

  • Gryczmariski, M. (1995). Wprowadzenie do opisu sprOysto plastycznych modeli gruntôw. Studia z zakresu inzynierii, 40, KILiW, IPPT PAN, Warszawa. (Introduction to elastoplastic soil models. Civil Engineering Study No. 40, Polish Academy of Science, Institute of Fundamental Technical Research, Warsaw ).

    Google Scholar 

  • Hashiguchi, K. (1986). A mathematical description of elastic-plastic deformation in normal-yield and sub-yield states. Proceedings of the International Symposium on Numerical Models in Geomechanics „NUMOG 2“, Ghent, 17–24.

    Google Scholar 

  • Hibbit, H. D., Marcal, P. V., and Rice, J. R. (1970). A finite element formulation for problems of large strain and large displacement. International Journal of Solids and Structures, Vol. 6, 1069–186.

    Article  Google Scholar 

  • Hill, R. (1968). On constitutive inequalities for simple materials. I, II, Journal Mechanics Physics. Solids, Vol. 16, 229–242.

    Google Scholar 

  • Hill, R. (1978). Aspects of invariance in solid mechanics. Advances in Applied Mechanics, Vol. 18, Academic Press, 1–75.

    Google Scholar 

  • Hohberg, J. M. (1990). A note on spurious oscillations in FEM joint elements. Earthq. Engineering Struct. Dynamic, Vol. 19

    Google Scholar 

  • Huyakorn, P. S., and Pinder, G. F. (1983). Computational Methods in Subsurface Flow. Academic Press, NY.

    MATH  Google Scholar 

  • Kanchi, M. B., Zienkiewicz, O. C., and Owen, P.R.J. (1978). The visco-plastic approach to problems of plasticity and creep involving geometric nonlinear effects. International Journal for the Numerical Methods in Engineering Vol. 12, 169–181.

    Article  MATH  Google Scholar 

  • Kleiber, M. (1975). Lagrangian and Eulerian finite element formulation for large strain elastoplasticity. Bull. Acad. Polon. Sci. Ser. Techn. 23, 117–1. 26.

    Google Scholar 

  • Koiter, W. T. (1960). General theorem for elastic-plastic solids. Progress in Solid Mechanics, Vol.1 (eds. I.N. Sneddon and R.Hill), North-Holland Publishing Co., Amsterdam. 165–221

    Google Scholar 

  • Kuklik, P., Sejnoha, M., and Mares, J. (1998). Dimensional reduction applied to specific problems of consolidation. Proceedings of the IV European Conference on Numerical Methods in Geotechnical Engineering–NUMGE98, Udine, Italy, 337–346.

    Google Scholar 

  • Kuklik, P., and Zalesky, J. (1995). Analysis of some experiments carried on the Cam-clay model. WORKSHOP 95, Prague, 357–358.

    Google Scholar 

  • Kuklik, P. (1998). Veryfication of Cam-clay model in description of consolidation. SS CC98, Durban, South Africa, 281–285.

    Google Scholar 

  • Lee, E. H. (1969). Elasto-plastic deformation at finite strain. Journal of Applied Mechanics 36, 1–6.

    Article  MATH  Google Scholar 

  • Lee, E. H., and McMeeking, R. M. (1980). Concerning elastic and plastic components of deformations. International Journal Solids and Structures, Vol. 18, 715–721.

    Article  MathSciNet  Google Scholar 

  • Lewis, R. W., and Schrefler, B. A. (1998). The finite element method in the static and dynamic deformation and consolidation of porous media. John Wiley, Second edition, New York.

    Google Scholar 

  • Malvern, L. E., Introduction to the Mechanics of a Continuos Medium,Prentice Hall, Englewood Cliffs NY

    Google Scholar 

  • Mandel, J. (1972). Plasticite classique et viscoplasticite. Lecture Notes International Centre for Mechanical Sciences, Udine, Springer-Verlag, Berlin

    Google Scholar 

  • McMeeking, R. M., and Rice, J. R. (1975). Finite-element formulations for problems of large elasto-plastic deformation. International Journal Solids and Structures, Vol. 11, 601–616.

    Article  MATH  Google Scholar 

  • Meijer, K. L. (1985). Computation of stresses and strains in saturated soil. Delft University of Technology, Ph.D. thesis, The Netherlands.

    Google Scholar 

  • Meroi, E. A., Schrefler, B. A., and Zienkiewicz, O. C. (1995). Large strain static and dynamic semisaturated soil behaviour. International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 19, 81–106.

    Article  MATH  Google Scholar 

  • Mikasa, M. (1965). The consolidation of soft clay–A new consolidation theory and its application. Civil Engineering in Japan, 21–26.

    Google Scholar 

  • Monte, J. L., and Kritzen, R. J. (1976). One-dimensional mathematical model for large-strain consolidation. Geotechnique 26 (3), 495–510.

    Article  Google Scholar 

  • Mrôz, Z. (1985) Non-linear continuum mechanics of solids. Lecture notes, Polish Academy of Science, Institute of Fundamental Technical Research, Warsaw.

    Google Scholar 

  • Norris, V. A., and Lewis, R. W. (1979). A finite element procedure for consolidation with nonlinear constitutive law. International Journal for Numerical and Analytical Methods in Geomechanics Vol. 1.

    Google Scholar 

  • Pande, G. N., and Sharma, K. G. (1979). On joint/interface elements and associated problems of numerical ill-conditioning, International Journal for Numerical and Analytical Methods in Geomechanics, 3, 293–300.

    Article  Google Scholar 

  • Perzyna, P. (1966). Fundamental problems in visco-plasticity. Advances in Applied Mechanics, Vol. 9, Academic Press, New York, 243–377.

    Google Scholar 

  • Reed, M. B. (1993). Incorporation of strain-hardening in the implicit elasto-viscoplasticity algorithm. Communication in Numerical Methods in Engineering, Vol. 9, 331–336.

    Article  MATH  Google Scholar 

  • Rice, J. M. (1971). Inelastic constitutive relations for solids: an interval variable theory and its application to metal plasticity. Journal of Mechanics and Physics of Solids, 19, 433–455.

    Article  MATH  Google Scholar 

  • Russell, D. (1992). An element to model thin, highly permeable materials in two dimensional finite element consolidation analysis. Proceedings of the 2“ d European Speciality Conference on Numerical Methods in Geotechnical Engineering, Santander, Spain, 303–310.

    Google Scholar 

  • Sandhu, R. S. (1968). Fluid flow in saturated porous elastic media. Ph.D. thesis, University of California, Berkeley.

    Google Scholar 

  • Sandhu, R. S., and Wilson, E. L. (1969). Finite element analysis of seepage in elastic media. ASCE Journal Vol. 95, EMS, 641–652.

    Google Scholar 

  • Schofield, A. N., and Wroth,. C. P. (1968). Critical State Soil Mechanics. Mc Graw-Hill, London.

    Google Scholar 

  • Song Er-Xiang. (1990). Elasto-plastic consolidation under steady and cyclic loads. PhD. thesis, Delft University of Technology, The Netherlands.

    Google Scholar 

  • Stolle, D. F. E. (1991). An interpretation of initial stress and strain methods, and numerical stability. International Journal for Numerical and Analytical, Methods in Geomechanics Vol. 15, 399–416.

    MATH  Google Scholar 

  • Swoboda, G., and Lai X.Y. (1994). Simulation of arch dam-foundation interaction with a new friction interface element. International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 17, 601–617.

    Article  Google Scholar 

  • Szefer, G. (1977). Non-linear problems of consolidation theory. Symposium Franco-Polonais Problems non-lineares de mecanique, Krakow, Poland.

    Google Scholar 

  • Szymanski, A. (1991). The factors determining the deformations analysis of organic subsoil under embankment. (in Polish), habilitation thesis, Warsaw Agricultural University Press, Treaties and Monographs.

    Google Scholar 

  • Tan, A. and Scott, R. F. (1988). Finite strain consolidation, A study of convection. Soil and Foundation, Vol. 28, No.3, Sept, 64–75.

    Google Scholar 

  • Teodosiu, C. (1970). A dynamic theory of dislocations and its applications to the theory of the elastic plastic continuum, In Fundamental Aspects of Dislocation Theory ed. A. Simmonols et al., NBSSP, 317, II, 837–876.

    Google Scholar 

  • Terzaghi, K. (1923). Die Berechnung der Durchlassigkeitsziffer des Tones aus dem Verlauf der hydrodynamischen Spannungserscheinungen. Akademie der Wissenschaften in Wien, Sitzungsberichte, Mathematisch-naturwissenschaftiche Klasse, Ha, 132. (3/4), 125–138

    Google Scholar 

  • Terzaghi, K. (1943). Theoretical Soil Mechanics. New York, J. Wiley & Sons.

    Book  Google Scholar 

  • Tezduya, T. E., and Ganjoo, D. K. Petrov-Galerkin formulations with weighting functions dependent upon spatial and temporal discretizations: Applications to transient convection-diffusion problems“, Computers Methods. Applied Mechanics Engineering 59, 49–71.

    Google Scholar 

  • Truesdell, C., and Toupin, R. A. (1960). The classical field theory. Handbuch der Physik, III/1 Springer.

    Google Scholar 

  • Truesdell, C. And Noll, W. (1965). The non-linear field theories of mechanics. Handbuch der Physik, II1/3 Springer.

    Google Scholar 

  • Van Langen, H., (1991). Numerical analysis of soil-structure interaction. Delft University of Technology, Ph.D. thesis.

    Google Scholar 

  • Van Langen, H., Vermeer, P. A. (1991). Interface elements for singular plasticity points. International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 15, 1–15.

    Article  Google Scholar 

  • Vermeer, P., and Verruijt, A. (1981). An accuracy condition for consolidation by finite elements. International Journal for Numerical and Analytical Methods in Geomechanics, Vol 5, 1–14.

    Article  MathSciNet  MATH  Google Scholar 

  • Vermeer, P., Bonnier, P. G., Brand, P. J. W., Brinkgreve, R. B. J., Dluzewski, J. M., and Van Langen, H. (1990). PLAXIS - Finite Element Code for Soil and Rock Plasticity. Balkema.

    Google Scholar 

  • Verruijt, A. (1977). Generation and dissipation of pore–water pressures. Finite Elements in Geomechanics, Chapter 9, ed. G. Gudehus, Wiley, London, 293–317.

    Google Scholar 

  • Zienkiewicz, O.C., and Cormeau, I. C. (1974). Visco-plasticity—plasticity and creep in elastic solids–a unified numerical solution approach. International Journal for Numerical. Methods in Engineering, Vol. 8, 821–845.

    Article  MATH  Google Scholar 

  • Zienkiewicz, O.C. (1982). Basic formulation of static and dynamic behaviour of soil and other porous media. In Numerical Methods in Geomechanics ed. J. B. Martin, 39–57.

    Google Scholar 

  • Zienkiewicz, O.C., and Shiomi, T. (1984). Static and dynamic behaviour of saturated porous media: the generalized Biot formulation and its numerical solution. International Journal for the Numerical and Analytical Methods in Geomechanics, Vol. 8, 71–96.

    Article  MATH  Google Scholar 

  • Zienkiewicz, O.C., Chan, A. H. C., Pastor, M., Paul, D. K., and Shiomi, T. (1990). Static and dynamic behaviour of soils: a rational approach to quantitative solutions. I — Fully saturated problems, Proceedings ofRoyal Society London, A, 429, 285–309.

    Article  MATH  Google Scholar 

  • Zienkiewicz, O.C., Xie, Y. M., Schrefler, B. A., Ledesma, A., and Bicanic, N. (1990). Static and dynamic behaviour of soils: a rational approach to quantitative solutions. II — Semi-saturated problems, Proceedings ofRoyal Society London, A, 429, 311–321.

    Article  MATH  Google Scholar 

  • Zienkiewicz, O. C., and Taylor R. (1991). The finite element method. Vols. 1 and 2. McGraw - Hill, New York.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Environmental Engineering, Warsaw University of Technology, Poland

    Janusz M. Dłużewski

Authors
  1. Janusz M. Dłużewski
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Colorado School of Mines, USA

    Vaughan D. Griffiths

  2. Politecnico di Milano, Italy

    Giancarlo Gioda

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Wien

About this chapter

Cite this chapter

Dłużewski, J.M. (2001). Nonlinear Problems During Consolidation Process. In: Griffiths, V.D., Gioda, G. (eds) Advanced Numerical Applications and Plasticity in Geomechanics. International Centre for Mechanical Sciences, vol 426. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2578-6_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-7091-2578-6_4

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-83337-7

  • Online ISBN: 978-3-7091-2578-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation