Fluidgesättigte Böden

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Application of the TPM to Soil-Modelling

Description of Cohesive and Non-Cohesive Soils


Motivation 

  • Goal:description of the material behaviour of fluid saturated porous solids by a multi-phase model
  • Example:consolidation of soil

konsolidierung

Basis:Theory of Porous Media (TPM)

  • Description of the coupled solid-fluid problem on the micro scale; condition: exact knowledge of the inner pore geometry (normally not known)
  • Assumption of superimposed continua as a result of a homogenization process -> mixture theory
  • Perception of the fractions of the constituents by scalar structur variables: volume fractions -> Theory of Porous Media

 

Homogenization

Phenomenological approach: assumption of homogenized structures, neglect of the micro structure 
 
supkont
   geom. model                       homogenized model
-> superimposed continua

Modelling of the constituents

  • saturated two phase model of solid and pore-fluid
  • no mass exchange between solid and pore-fluid
  • incompressibility of both constituents
  • isothermal conditions


Material properties

  • elasto-plastic solid
  • viscous pore-fluid


Balance equations

  • mass balance equation of the solid and the pore-fluid, reduction to a volume balance equation because of the material incompressibility of both constituents
  • linear momentum balance for the solid and the pore-fluid (quasi-static)
  • saturation constraint (i.e. no material-free voids)


Determination of the variables

  • solid displacement
  • seepage velocity, i.e. relative velocity between fluid and solid
  • pore-fluid pressure
  • volume fractions


Elasto-plastic material model for the solid

Graphical representation of the yield function in the principal stress space[Ehlers, 1993]
fliessfl

     

     

     

     

     

     

     

    Stress states 
     

    • inside the yield surface: elastic deformation
    • on the yield surface: plastic deformation


Example: strip footing on water saturated soil

    Boundary value problem

                                                          rwp

     

     

     

     

     

     

     

    • Soil-model:
         
      • elasto-plastic formulation for the solid skeleton

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    • Numerical simulation:
         
      • linear increase of the load to qmax = 500 kN/sqm
      • beginning of consolidation at t = 0

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    Decrease of the pore-pressure coupled with settlements(scaled plot)

    druckvert

     

     

     

     

     

     

     

     

     

    Load-settlement- and time-settlement-curves

     

    setz

     

     

     

     

     

     

     

     

     

Publications

  • W. Ehlers, P. Blome, H. Müllerschön:Baugrund-Modellierung auf der Basis der Theorie Poröser Medien. In R. Katzenbach und U. Arslan (Hrsg.): Vorträge zum Workshop Baugrund-Tragwerk-Interaktion am 21. November 1997, Mitteilungen des Institutes und der Versuchsanstalt für Geotechnik der Technischen Universität Darmstadt, Heft 38, Darmstadt 1997, pp. 65-90.
  • W. Ehlers, P. Blome:Ein Mehrphasen-Stoffmodell für Böden mit Übergang auf Interface-Gesetze. Zwischenbericht zum Teilprojekt 1 im Rahmen der DFG-Forschergruppe "Baugrund-Tragwerk-Interaktion" an der Technischen Universität Darmstadt, Berichte aus dem Institut für Mechanik (Bauwesen), Nr. 98-II-14, Universität Stuttgart 1998.
  • W. Ehlers, P. Ellsiepen, P. Blome, D. Mahnkopf, B. Markert:Theoretische und numerische Studien zur Lösung von Rand- und Anfangswertproblemen in der Theorie Poröser Medien. Abschlußbericht zum DFG-Forschungsvorhaben Eh 107/6-2, Berichte aus dem Institut für Mechanik (Bauwesen), Nr. 99-II-1, Universität Stuttgart 1999.

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Contact

Dipl.-Ing. Peter Blome
University of Stuttgart
Institute of Applied Mechanics (Civil Engineering)
Chair II
Pfaffenwaldring 7
D-70569 Stuttgart, GERMANY 
Telefon: +49 (0) 711 / 685 - 66340
Telefax: +49 (0) 711 / 685 - 66347
E-mail: blome @ mechbau.uni-stuttgart.de

 

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