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A general model for the mechanics of saturated-unsaturated porous materials

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Abstract

A general predictive model for the mechanical analysis of isothermal and non-isothermal saturated-unsaturated porous materials is presented. The model is developed along the lines of Biot's theory and applies both for high water content and for low to medium water content in the pore space. Due to the similarity of the matrices in both situations, even if the transfer mechanisms are different, a single computer program can handle all of them. Examples belonging to both domains in the isothermal case as well as to heat and mass transfer in deforming porous media are shown.

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Abbreviations

b :

Body force vector

c :

Coefficient of consolidation

c :

Stress-independent vector definding the creep strain rate

C α :

Specific heat of the α-phase

D T :

Tangential stiffness matrix

g :

Gravity acceleration

h :

Elevation above some datum

k :

Absolute permeability matrix

k rα :

Relative permeability of the α-phase

R sα :

Solution ratio of the α-phase

C s :

Specific moisture content

κ:

Coefficient of thermal diffusivity

K α :

Bulk modulus of the α-phase

L :

Differential operator which relates displacements to strains

m :

(111000)T

m T :

Transpose ofm

p :

Pore pressure

q e :

Volumetric outflow of the fluid per unit volume of the solid

q h :

Outflow of heat per unit volume of solid

t :

Time variable

\(\hat t\) :

Dimensionless time parameter

T :

Temperature increase over an equilibrium state

\(\hat t\) :

Boundary traction vector

u :

Displacement vector

V a :

Apparent velocity of the fluid

βα :

Thermal expansion coefficient of the α-phase

ε:

Total strain vector of the soil skeleton

ε0 :

Represents all other strain not directly associated with stress change

εc :

Creep strain

λ:

Thermal conductivity matrix of the soil

μ:

Dynamic viscosity

ρα :

Density of the α-phase

ϕ:

Porosity

g:

Gaseous phase

w:

Water

s:

Solid phase

m:

Moisture

v:

Steam

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Authors and Affiliations

  1. Istituto di Scienza e Tecnica delle Costruzioni, Università di Padova, Padova, Italy

    B. A. Schrefler, L. Simoni & C. E. Majorana

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  1. B. A. Schrefler
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  2. L. Simoni
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  3. C. E. Majorana
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Schrefler, B.A., Simoni, L. & Majorana, C.E. A general model for the mechanics of saturated-unsaturated porous materials. Materials and Structures 22, 323–334 (1989). https://doi.org/10.1007/BF02472501

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