Keywords: concrete and reinforced concrete, moisture and heat transport analysis, creep and shrinkage analysis, practical implementation, engineering software.

Materials research in concrete has shown that a correct prediction of the distribution and history of moisture content is inevitable for realistic determination of shrinkage, creep and thermal dilatation. Furthermore, the pore moisture content directly affects strength, thermal conductivity and the rate of hydration or maturing. Numerical analysis of drying and wetting is also indispensable for derivation of the constitutive law from creep, shrinkage and thermal dilatation tests at variable moisture conditions.

Similarly, the pore pressure distribution is necessary to analyze long-term deformations of soils. The moisture and heat transport in porous materials consequently affects both the upper structure and its subgrade and, therefore, strongly influences interactions between the two subdomains.

This phenomenon is mostly studied under the assumption that both the liquid and gas phases flow through a rigid porous matrix [1]. However, this assumption is implausible, when analyzing consolidation of soils and certain other slow (quasi-static) phenomena. To remedy insufficiency of the aforementioned approaches, the temperature and moisture fields are completed by the displacement field, describing volume changes in a deforming porous material.

Fast development of porous media theories in conjunction with numerical methods has been attracting an increasing number of researchers and design specialists from all branches of engineering. An extensive historical review can be found in [2]. A concise introduction to the development of porous media theories is given, e.g., in [3]. Recall a few basic contributions of the utmost importance. The deformation of saturated soils under the effective stress principle was studied in [4] and Terzaghi's phenomenological (macromechanics-based) approach was generalized and extended to the three-dimensional case in [5]. A micromechanics-based approach, which is commonly used in constitutive modeling of heterogeneous materials, can be taken as counterpart to the phenomenological ones. The principles are formulated in [6]. Micromechanics-based models appear to be very promising in connection with the intense development of numerical methods in mechanics, such as the finite control volume method (FCVM), finite element method (FEM), and the boundary element method (BEM), allowing for the multi-level (micro-macro) modeling and being supported by effective solvers, such as the FETI (the finite element tearing and interconnecting) method and others.

This paper is presented in two parts. Part I discusses theoretical principles and numerical methods for evaluating transient thermal and moisture transfer behavior, and describes numerical models, enabling a prediction of long-term deformation processes in building materials and structures. First, a review of basic notions and fundamentals of the moisture and heat transfer are given. The fundamental theory set forth and described in previous works is revisited and then augmented by taking into account changes in porosity resulting from deformation of the porous skeleton. Then two variants of discretization of the governing equations are addressed. In the first variant, the discretization is carried out by an implicit-explicit finite control volume scheme with variable meshing. In this case the finite element method is supposed to be applied to the equilibrium equations reflecting volume changes in porous media subjected to deformation. The coupling of the discretized equations is provided by an iterative consecutive solution of these equations. In the second variant the finite element technique is applied to the entire set of governing equations.

Part II is devoted to the implementation of creep and shrinkage into the ATHENA FE software.

1

H. R. Thomas, M. R. Sansom, G. Volkaert, P. Jacobs and M. Kumnan, "An experimental and numerical investigation of the hydration of compacted powder boom clay", Num. Meth. in Geomechanical Engineering. Smith (ed.), Balkema, Rotterdam, 135 - 141, 1994.

2

R. de Boer, "Highlights in the historical development of the porous media theory: toward a consistent macroscopic theory", Appl. Mech. Rev., 49, 201 - 262, 1996. doi:10.1115/1.3101926

3

R.W. Lewis and B. A. Schrefler, "The finite element method in static and dynamic deformation and consolidation of porous media", John Wiley & Sons, Chichester-Toronto, (492), 1998.

4

K. von Terzaghi, "Die Berechnung der Durchlässigkeitsziffer des Tones aus dem Verlauf der hydrodynamischen Spannungserscheinungen", Sitzungsber. Akad. Wiss. Math. - Naturwiss., Section IIa, 132(3/4), 125 - 138, 1923

5

M. A. Biot, "General theory of three-dimensional consolindation", J. Appl. Phys., 12, 155 - 164, 1941. doi:10.1063/1.1712886

6

M. Hassanizadeh and W. G. Gray, "General conservation equations for multiphase systems: 1, averaging procedure", Adv. Water Resources, 2, 131 - 144, 1979. doi:10.1016/0309-1708(79)90025-3

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