Keywords: moisture transfer, deforming porous medium, soil, pore pressures.

In this paper, a numerical model of coupled hydro-mechanical behaviour of soils is presented. The micro-mechanics-based model which covers the theory of deformation of soils (soil skeleton) and other porous materials is based on the concept of effective stresses. The final set of equations is simplified and derived for water flow in porous media and the finite element method is used for the spatial discretization. The model was implemented in the SIFEL software package [1] and two numerical examples are presented.

Significant improvement in numerical modelling of coupled heat and moisture transport in porous materials has been attained. There are many material models in the literature that allow for the description of coupled heat and moisture transport. For example, there are phenomenological models based on diffusion [2,3,4]. These models are suitable for numerical simulations and modelling of building structures under common climatic conditions. On the other hand, complex micro-mechanical based models, e.g. Tenchev's approach [6] and Lewis and Schrefler's approach [5], using averaging techniques are applied namely to modelling of concrete structures suject to high temperature conditions and the modelling of soil behaviour. The latter approach was used in the authors' finite element code and extended by the dependence of the moisture permeability on void ratio. According to this approach, soils generally consist of three components - grains (skeleton), liquid (water) and gas (water vapour and air). Total stress in the soil can be decomposed into effective stress between grains, pore water pressure and pore gas pressure. Transport of water and heat together with deformation of solid represent the non-linear coupled transport problems which can be described using three types of equations. There are constitutive equations (retention curves, material properties), transport equations (Fick's law and Darcy's law) and continuity equations. After discretization of driving equations using the finite element method, a system of non-symmetric and non-linear algebraic equations is obtained generally, even if the deformation of the solid is linear elastic. On the other hand, the moisture transfer is a very slow process and therefore, in the case of linear consolidation, no iteration is necessary within time steps. From experiments, it is evident that such a description of consolidation by the linear elastic model for a porous medium along with the constant permeability could not be realistic. At least the permeability is mostly subject of variation reflecting the dependence of the permeability on void ratio. The Cam-Clay model with the bilinear form of the normal consolidation line is then adopted as a suitable model which describes the effect of over-consolidation and structure strength on time dependent processes in soils.

1

J. Kruis, T. Koudelka, T. Krejcí, "Multi-physics Analyses of Selected Civil Engineering Concrete Structures", Commun. Comput. Phys., 12, 885-918, 2012. doi:10.4208/cicp.031110.080711s

2

H.M. Künzel, K. Kiessl, "Calculation of heat and moisture transfer in exposed building components", Int. J. Heat Mass Transfer, 40, 159-167, 1977.

3

D. Gawin, C.E. Majorana, B.A. Schrefler, "Numerical analysis of hygro-thermic behaviour and damage of concrete at high temperature", Mech. Cohes-Frict. Mat, 4, 37-74, 1999.

4

J. Kocí, V. Kocí, J. Madera, P. Rovnaníková, R. Cerný, "Computational analysis of hygrothermal performance of renovation renders", Advanced Computational Methods and Experiments in Heat Transfer, XI, 267-277, 2010. doi:10.2495/HT100231

5

R.W. Lewis, B.A. Schrefler, "The finite element method in static and dynamic deformation and consolidation of porous media", John Wiley & Sons, Chiester-Toronto, 1971.

6

R.T. Tenchev, L.Y. Li, J.A. Purkiss, "Finite Element Analysis of Coupled Heat and Moisture Transfer in Concrete Subjected to Fire", Numerical Heat Transfer, 39, 685-710, 2001. doi:10.1080/10407780152032839

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