Modelling Unsaturated Moisture Transport in Heterogeneous Limestone

In this paper we investigate the influence of microheterogeneity on the phenomenological macroscopic material properties. The material analysed is Savonnières: a French layered oolitic limestone. Due to the complex microstructure of the material the moisture permeability cannot uniquely be determined based on indirect measurement data. To overcome this problem we present an upscaling technique based on the modelling of transport phenomena on the mesoscale. The technique allows to determine an equivalent macroscopic permeability based on the geometric configuration and the permeability of the composing constituents.

[1]  Filip Descamps,et al.  A Multiscale Network Model for Simulating Moisture Transfer Properties of Porous Media , 1999 .

[2]  Jan Carmeliet,et al.  Characterisation of pore structure by combining mercury porosimetry and micrography , 2001 .

[3]  C.A.J. Appelo,et al.  FLOW AND TRANSPORT , 2004 .

[4]  W. R. Gardner.  SOME STEADY‐STATE SOLUTIONS OF THE UNSATURATED MOISTURE FLOW EQUATION WITH APPLICATION TO EVAPORATION FROM A WATER TABLE , 1958 .

[5]  A.H.J.M. Vervuurt,et al.  Interface Fracture in Concrete , 1997 .

[6]  Allan L. Gutjahr,et al.  Stochastic Analysis of Unsaturated Flow in Heterogeneous Soils: 1. Statistically Isotropic Media , 1985 .

[7]  Leo L Pel,et al.  MOISTURE TRANSPORT IN POROUS BUILDING MATERIALS , 1996 .

[8]  Jan Carmeliet,et al.  Determination of the Isothermal Moisture Transport Properties of Porous Building Materials , 2001 .

[9]  Hamid Sadouki,et al.  Simulation and analysis of composite structures , 1985 .

[10]  Y. Mualem,et al.  Hysteretical models for prediction of the hydraulic conductivity of unsaturated porous media , 1976 .

[11]  Allan L. Gutjahr,et al.  Cross‐correlated random field generation with the direct Fourier Transform Method , 1993 .

[12]  J. W. Biggar,et al.  Stochastic analysis of unsaturated flow: One‐dimensional Monte Carlo simulations and comparisons with spectral perturbation analysis and field observations , 1990 .

[13]  John Crank,et al.  The Mathematics Of Diffusion , 1956 .

[14]  Jan Carmeliet,et al.  Microscopic analysis of imbibition processes in oolitic limestone , 2000 .

[15]  G. Matheron.  Éléments pour une théorie des milieux poreux , 1967 .

[16]  M. Sahimi.  Flow phenomena in rocks : from continuum models to fractals, percolation, cellular automata, and simulated annealing , 1993 .

[17]  Aristotelis Mantoglou,et al.  Stochastic modeling of large‐scale transient unsaturated flow systems , 1987 .

[18]  Ke Xu,et al.  Multiscale Structures to Describe Porous Media Part I: Theoretical Background and Invasion by Fluids , 1997 .

[19]  R. H. Brooks,et al.  Properties of Porous Media Affecting Fluid Flow , 1966 .

[20]  P. Witherspoon,et al.  Porous media equivalents for networks of discontinuous fractures , 1982 .

[21]  S. Whitaker.  Simultaneous Heat, Mass, and Momentum Transfer in Porous Media: A Theory of Drying , 1977 .

[22]  G. Dagan.  Flow and transport in porous formations , 1989 .

[23]  Jacob Bear,et al.  Effective and relative permeabilities of anisotropie porous media , 1987 .

[24]  F. Dullien,et al.  Simulation of capillary pressure curves using bond correlated site percolation on a simple cubic network , 1987 .

[25]  P. E. Roelfstra,et al.  Le béton numérique , 1985 .

[26]  P. Renard,et al.  Calculating equivalent permeability: a review , 1997 .

[27]  L. Durlofsky.  Numerical calculation of equivalent grid block permeability tensors for heterogeneous porous media , 1991 .

[28]  I. Fatt.  The Network Model of Porous Media , 1956 .

[29]  H.E.J.G. Schlangen,et al.  Experimental and numerical analysis of fracture processes in concrete : proefschrift , 1993 .

[30]  Jan Carmeliet,et al.  Mesh adaptive finite element formulation for moisture transfer in materials with a critical moisture content , 1999 .