A nonlinear poroelastic constitutive model for unsaturated porous materials is formulated based on a higher order formulation of free energy including mechanical and moisture contributions and the coupling between moisture and mechanics. This orthotropic model leads to the explicit formulation of the dependence of the compliance, moisture capacity, and coupling coefficient on stress and liquid pressure. The nonlinear poroelastic material properties can be easily determined from mechanical testing at different moisture content and free swelling/sorption tests. An academic example illustrates the capacity of the proposed model to describe nonlinear moisture dependent elasticity, stress dependent sorption, and swelling, also called mechano-sorption and moisture expel during mechanical loading. Two materials are analyzed in detail: wood and Berea sandstone. The poroelastic model shows a good agreement with measurements. Different moisture dependence of the elastic properties is found, with wood showing a more complex moisture/mechanical interaction. Berea sandstone is found to show an important nonlinear elastic behavior dependent on stress, similar in dry and wet conditions.

References

References
1.
Terzaghi
,
K.
,
1943
,
Theoretical Soil Mechanics
,
Wiley
,
New York
.
2.
Biot
,
M. A.
,
1941
, “
General Theory of Three Dimensional Consolidation
,”
J. Appl. Phys.
,
12
, pp.
155
164
.10.1063/1.1712886
3.
Powers
,
T.
, and
Helmuth
,
R. A.
,
1953
, “
Theory of Volume Changes in Hardened Portland Cement Paste During Freezing
,”
Highw. Res. Board, Proc.
,
32
(
33
), pp.
286
297
.
4.
Biot
,
M. A.
,
1977
, “
Variational Lagrangian-Thermodynamics of Non Isothermal Finite Strain. Mechanics of Porous Solid and Thermomolecular Diffusion
,”
Int. J. Solids Struct.
,
13
, pp.
579
597
.10.1016/0020-7683(77)90031-2
5.
Coussy
,
O.
,
1989
, “
A General Theory of Thermoporoelastoplasticity for Saturated Porous Materials
,”
Trans. Porous Med.
,
4
, pp.
281
293
.10.1007/BF00138040
6.
Coussy
,
O.
,
1991
,
Mécanique des Milieux Poreux
,
Technip
,
Paris
.
7.
Coussy
,
O.
,
2004
,
Poromechanics
,
Wiley
,
Chichester, UK
.
8.
Coussy
,
O.
,
Eymard
,
R.
, and
Lassabatère
,
T.
,
1998
, “
Constitutive Modelling of Unsaturated Drying Deformable Materials
,”
J. Eng. Mech.
,
124
, pp.
658
667
.10.1061/(ASCE)0733-9399(1998)124:6(658)
9.
Coussy
,
O.
,
2007
, “
Revisiting the Constitutive Equations of Unsaturated Porous Solids Using a Lagrangian Saturation Concept
,”
Int. J. Numer. Anal. Meth. Geomech.
,
31
, pp.
1631
1713
.10.1002/nag.613
10.
Coussy
,
O.
,
2011
,
Mechanics and Physics of Porous Solids
,
Wiley
,
Chichester, UK
.
11.
Berryman
,
J. G.
,
2002
, “
Extension of Poroelastic Analysis to Double Porosity Materials: New Technique in Microgeomechanics
,”
J. Eng. Mech.
,
128
, pp.
840
847
.10.1061/(ASCE)0733-9399(2002)128:8(840)
12.
Meschke
,
G.
, and
Grasberger
,
S.
,
2003
, “
Numerical Modeling of Coupled Hygromechanical Degradation of Cementitious Materials
,”
J. Eng. Mech.
,
129
, pp.
383
392
.10.1061/(ASCE)0733-9399(2003)129:4(383)
13.
Carmeliet
,
J.
,
Descamps
,
F.
, and
Houvenaghel
,
G.
,
1999
, “
A Multiscale Network Model for Simulating Moisture Transfer Properties of Porous Media
,”
Transp. Porous Media
,
35
, pp.
67
88
.10.1023/A:1006500716417
14.
Carmeliet
,
J.
, and
Roels
,
S.
,
2001
, “
Determination of the Isothermal Moisture Transport Properties of Porous Building Materials
,”
J. Thermal Envelopes Build. Sci.
,
24
(
3
), pp.
183
210
.10.1106/Y6T2-9LLP-04Y5-AN6T
15.
Durner
,
W.
,
1994
, “
Hydraulic Conductivity Estimations for Soils With Heterogeneous Pore Structure
,”
Water Resour. Res.
,
30
, pp.
211
223
.10.1029/93WR02676
16.
Wilfred
,
W.
,
1942
, “
Barkas Wood Water Relationships—VII. Swelling Pressure and Sorption Hysteresis in Gels
,”
Trans. Faraday Soc.
,
38
, pp.
194
209
.10.1039/tf9423800194
17.
Neuhaus
,
F. H.
,
1981
, “
Elastizitätszahlen von Fichtenholz in Abhängigkeit von der Holzfeuchtigkeit
,” Ph.D. thesis,
Ruhr-Universität Bochum
,
Bochum, Germany
.
18.
Derome
,
D.
,
Griffa
,
M.
,
Koebel
,
M.
, and
Carmeliet
,
J.
,
2011
, “
Hysteretic Swelling of Wood at Cellular Scale Probed by Phase Contrast X-Ray Tomography
,”
J. Struct. Biol.
,
173
, pp.
180
190
.10.1016/j.jsb.2010.08.011
19.
Carmeliet
,
J.
, and
Van Den Abeele
,
K. E. A.
,
2002
, “
Application of the Preisach-Mayergoyz Space Model to Analyze Moisture Effects on the Nonlinear Elastic Response of Rock
,”
Geophys. Res, Lett.
,
29
(
7
), pp.
1144
1148
.10.1029/2001GL014243
20.
Van Den Abeele
,
K. E. A.
,
Carmeliet
,
J.
,
Johnson
,
P. A.
, and
Zinszner
,
B.
,
2002
, “
Influence of Water Saturation on the Nonlinear Elastic Mesoscopic Response in Earth Materials and the Implications to the Mechanism of Nonlinearity
,”
J. Geophys. Res.
, [Solid Earth],
107
(
6
), pp.
2121
2132
.10.1029/2001JB000368
21.
Carmeliet
,
J.
, and
Van Den Abeele
,
K. E. A.
,
2004
, “
Poromechanical Approach Describing the Moisture Influence on the Non-Linear Quasi-Static and Dynamic Behaviour of Porous Building Materials
,”
Mater. Struct.
,
37
, pp.
271
280
.10.1007/BF02480635
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