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 Theory of Porous Media (TPM) 


$\bullet$Goal: Continuum mechanical description of cohesive and non-cohesive soil materials

$\bullet$Macroscopic approach: TPM, i. e. mixture theory extended by the concept of volume fractions 

\epsfig {figure=poren.eps, width=55mm} 

        real geometry                                           homogenized model 

$\bullet$Multiphase model 

  $\triangleright\ $ solid skeleton (soil): porous, elasto-plastic, materially incompressible
  $\triangleright\ $ pore-liquid (water): viscous, materially incompressible
  $\triangleright\ $ pore-gas (air): viscous, materially compressible


Volumetric Composition of the Soil 

\epsfig {figure=vol.eps, width=55mm} 

$\bullet$Saturation constraint 

  $n^S +\, n^L +\, n^G =\, 1 \quad \mbox{with} \quad n^L +\, n^G =\, n^F\ \ \mbox{(porosity)}$
  $S:\, S\/\mbox{olid}\,,\ L:\,L\/\mbox{iquid}\,,\ G:\, G\/\mbox{as}\,,\ F:\,\mbox{overall}\ F\/\mbox{luid}$

$\bullet$Degrees of saturation 

  $s^L =\, {n^L}/{n^F}\,,\quad s^G =\, {n^G}/{n^F} \quad \mbox{with}\quad s^L +\, s^G =\, 1$


Solid-Fluid Interaction 

$\bullet$Multiphase flow 

\epsfig{file=single.eps, width=55mm, angle=0} 


$\triangleright\ $ capillary-pressure-saturation and relative-permeability-saturation relation
  $\triangleright\ $ Darcy's general filter law


Elasto-Plasticity Model for Frictional Materials 

$\bullet$Yield function in the principal stress space 



$\triangleright\ $ single surface yield criterion with isotropic work-hardening  
  $\triangleright\ $ additional plastic potential  
  $\triangleright\ $ non-associated flow rule  


Numerical Examples 

$\bullet$Back analysis of triaxial tests on Berlin sand 

\epsfig{file=triax.eps, width=55mm, angle=0} 

$\bullet$Strip footing on an elasto-plastic half space 

\epsfig{file=netzbunt.eps, width=55mm, angle=0} 

  • W. Ehlers, P. Blome: On porous soil materials saturated with a compressible pore-fluid mixture. ZAMM, Z. angew. Math. Mech., 80 (Suppl. 1), Springer-Verlag, Berlin (2000), S141-S144.
  • W. Ehlers, P. Blome: Ein Mehrphasen-Stoffmodell für Böden mit Übergang auf Interface-Gesetze. 2. Zwischenbericht zum Teilprojekt 1 der Forschergruppe Baugrund-Tragwerk-Interaktion an der Technischen Universität Darmstadt Ka 1153/5-2, Bericht aus dem Institut für Mechanik (Bauwesen), Nr. 00-II-3, Universität Stuttgart (2000).
  • W. Ehlers, P. Blome: A multi-phase soil model including a soil-foundation interface. ZAMM, Z. angew. Math. Mech., 81 (Suppl. 3), Springer-Verlag, Berlin (2001), S523-S524.
  • W. Ehlers, P. Blome: Konsistente Mehrphasen-Stoffmodelle für Böden. To appear in: R. Katzenbach und U. Arslan (eds.): Vorträge zum 2. Workshop Baugrund-Tragwerk-Interaktion, Mitteilungen des Institutes und der Versuchsanstalt für Geotechnik der Technischen Universität Darmstadt, Darmstadt, Nr. 50, Darmstadt 2001.
  • W. Ehlers, P. Blome: Consistent multiphase models for soils. To appear in: R. Katzenbach und U. Arslan (eds.): Darmstadt Geotechnics, No. 6, Darmstadt 2001.
  • W. Ehlers, P. Blome: A triphasic model for unsaturated soil based on the Theory of Porous Media. Mathematical and Computer Modelling, accepted (2001).
  • W. Ehlers, P. Blome: On two-phasic flow problems in elasto-plastic porous materials. To appear in: ZAMM, Z. angew. Math. Mech., Springer-Verlag, Berlin (2002).


Dipl.-Ing. Peter Blome 
University of Stuttgart 
Institute of Applied Mechanics (Civil Engineering) 
Lehrstuhl II 
Pfaffenwaldring 7 
D-70569 Stuttgart  
Telefon: +49 (0) 711 / 685 - 66340 
Telefax: +49 (0) 711 / 685 - 66347 
email:  blome @
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