Research Articles

Nonlinear Poro-Elastic Model for Unsaturated Porous Solids

[+] Author and Article Information
Jan Carmeliet

Chair of Building Physics,
ETH Zürich, Swiss Federal Institute of Technology Zürich,
Wolfgang-Pauli-Strasse 15,
8093 Zürich, Switzerland;
Laboratory of Building Science and Technology,
Empa, Swiss Federal Laboratories for Materials Science and Technology,
Überlandstrasse 129, 8600 Dübendorf, Switzerland
e-mail: carmeliet@arch.ethz.ch

Dominique Derome

e-mail: dominique.derome@empa.ch

Martin Dressler

Laboratory of Building Science and Technology,
Empa, Swiss Federal Laboratories for Materials Science and Technology,
Überlandstrasse 129,
8600 Dübendorf, Switzerland

Robert A. Guyer

Los Alamos National Laboratory,
University of Massachusetts,
Amherst, MA 01003
e-mail: guyer@physics.umass.edu

Manuscript received August 12, 2011; final manuscript received April 9, 2012; accepted manuscript posted October 25, 2012; published online February 6, 2013. Assoc. Editor: Younane Abousleiman.

J. Appl. Mech 80(2), 020909 (Feb 06, 2013) (9 pages) Paper No: JAM-11-1279; doi: 10.1115/1.4007921 History: Received August 12, 2011; Revised April 09, 2012

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.

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Terzaghi, K., 1943, Theoretical Soil Mechanics, Wiley, New York.
Biot, M. A., 1941, “General Theory of Three Dimensional Consolidation,” J. Appl. Phys., 12, pp. 155–164. [CrossRef]
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.
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. [CrossRef]
Coussy, O., 1989, “A General Theory of Thermoporoelastoplasticity for Saturated Porous Materials,” Trans. Porous Med., 4, pp. 281–293. [CrossRef]
Coussy, O., 1991, Mécanique des Milieux Poreux, Technip, Paris.
Coussy, O., 2004, Poromechanics, Wiley, Chichester, UK.
Coussy, O., Eymard, R., and Lassabatère, T., 1998, “Constitutive Modelling of Unsaturated Drying Deformable Materials,” J. Eng. Mech., 124, pp. 658–667. [CrossRef]
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. [CrossRef]
Coussy, O., 2011, Mechanics and Physics of Porous Solids, Wiley, Chichester, UK.
Berryman, J. G., 2002, “Extension of Poroelastic Analysis to Double Porosity Materials: New Technique in Microgeomechanics,” J. Eng. Mech., 128, pp. 840–847. [CrossRef]
Meschke, G., and Grasberger, S., 2003, “Numerical Modeling of Coupled Hygromechanical Degradation of Cementitious Materials,” J. Eng. Mech., 129, pp. 383–392. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Durner, W., 1994, “Hydraulic Conductivity Estimations for Soils With Heterogeneous Pore Structure,” Water Resour. Res., 30, pp. 211–223. [CrossRef]
Wilfred, W., 1942, “Barkas Wood Water Relationships—VII. Swelling Pressure and Sorption Hysteresis in Gels,” Trans. Faraday Soc., 38, pp. 194–209. [CrossRef]
Neuhaus, F. H., 1981, “Elastizitätszahlen von Fichtenholz in Abhängigkeit von der Holzfeuchtigkeit,” Ph.D. thesis, Ruhr-Universität Bochum, Bochum, Germany.
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. [CrossRef] [PubMed]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]


Grahic Jump Location
Fig. 1

Swelling test results at different compressive stresses: (a) stiffness as a function of relative humidity, (b) influence of mechanical stress on the sorption curves, (c) close-up of sorption curves at high RH, (d) swelling

Grahic Jump Location
Fig. 2

Compression test results: (a) stress strain curves at different initial moisture contents; (b) influence of mechanical stress on expelled moisture

Grahic Jump Location
Fig. 3

(a) Young's modulus as a function of moisture content, (b) shear modulus as a function of moisture content, (c) Poisson ratio as a function of moisture content, and (d) swelling strain as a function of saturation (dots = experimental data,solid curve  = poroelastic model)L = longitudinal,R = radial,T = tangential)

Grahic Jump Location
Fig. 4

(a) Compressive stress strain curves for Berea sandstone for different moisture contents, (b) compliance versus stress for two moisture contents, (c) compliance versus moisture content for different stress levels (dots = experimental data, solid curve = poroelastic model)



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