General definitions and present status of the landscape ecology basic concepts of landscape ecology different approaches to landscape classifications spatial patterns in natural and cultural landscapes principles of landscape dynamics descriptive and quantitative methods in landscape ecology - analysis and synthesis planning, management, conservation and restoration of cultural landscapes in practice synthesis - practical examples of landscape studies from spatial quantitative analysis to holistic problem-solving procedures.

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Principles and Methods in Landscape Ecology

Porous Materials Water in Porous Materials Flow in Porous Materials Unsaturated Flows Unsaturated Flow in Building Physics Composite Materials Evaporation and Drying Topics in Water Transport Appendices Symbols Used Properties of Water Minerals, Salts and Solutions Other Liquids Other Data

Water Transport in Brick, Stone and Concrete

Received 4 November 2005; revised 15 December 2005; accepted 20 December 2005; published 31 January 2006. [1] The relationship between permeability and porosity is reviewed and investigated. The classical Kozeny-Carman approach and a fractal pore-space geometry assumption are used to derive a new permeability-porosity equation. The equation contains only two fitting parameters: a Kozeny coefficient and a fractal exponent. The strongest features of the model are related to its simplicity and its capability to describe measured permeability values of different non-granular porous media better than other models. Citation: Costa, A. (2006), Permeability-porosity relationship: A reexamination of the Kozeny-Carman equation based on a fractal pore-space geometry assumption, Geophys. Res. Lett., 33, L02318, doi:10.1029/2005GL025134. [2] Estimation of permeability is of pivotal importance for the description of different physical processes, such as hydrocarbon recovery, fluid circulation in geothermal systems and degassing from vesiculating magmas. Mainly due to the intricate geometry of the connected pore space and to the complexity of porous media, it has been very difficult to formulate satisfactory theoretical models for permeability. One of the most largely used methods remains the KozenyCarman approach. [3] In this study we briefly review the Kozeny-Carman model. Then, using the hypothesis of a fractal pore-space geometry and the empirically based Archie law, we reformulate that model without introducing the concept of hydraulic radius and obtain a new simple permeabilityporosity equation. As an application, we used the obtained equation to predict permeability of fiber mat systems and of vesicular rocks.

https://agupubs.onlinelibrary.wiley.com/doi/epdf/10.1029/2005GL025134

Permeability-porosity relationship: a reexamination of the Kozeny-Carman equation based on a fractal pore-space geometry assumption

The flow in porous media has received a great deal of attention due to its importance and many unresolved problems in science and engineering such as geophysics, soil science, underground water resources, petroleum engineering, fibrous composite manufacturing, biophysics (tissues and organs), etc. It has been shown that natural and some synthetic porous media are fractals, and these media may be called fractal porous media. The flow and transport properties such as flow resistance and permeability for fractal porous media have steadily attracted much attention in the past decades. This review article intends to summarize the theories, methods, mathematical models, achievements, and open questions in the area of flow in fractal porous media by applying the fractal geometry theory and technique. The emphases are placed on the theoretical analysis based on the fractal geometry applied to fractal porous media. This review article shows that fractal geometry and technique have the potentials in analysis of flow and transport properties in fractal porous media. A few remarks are made with respect to the theoretical studies that should further be made in this area in the future. This article contains 220 references.

Analysis of Flow in Fractal Porous Media

Influencing factors of geometrical structure of surface shrinkage cracks in clayey soils

https://horizon.documentation.ird.fr/exl-doc/pleins_textes/pleins_textes_7/b_fdi_53-54/010020216.pdf

Generalizing the fractal model of soil structure : the pore-solid fractal approach

Nous presentons une extension de l'approche fractale qui consiste a modeliser la courbe de retention d'eau des sols en se basant sur un modele recent de structure des sols, le Pore-Solid Fractal. Ce modele de structure, dans sa forme la plus generale, met en oeuvre une vision symetrique des phases solide et vide qui contraste avec l'asymetrie des modeles fractals de masses. Il en resulte que l'expression generale modelisant la courbe de retention d'eau dans un Pore-Solid Fractal fait apparaitre un parametre de structure, sous forme d'un exposant d'une loi de puissance, parametre lie-non-seulement a la distribution de taille des pores, mais aussi a la distribution de taille des solides. Le modele fournit donc un cadre theorique pour la prediction de la courbe de retention d'eau a partir de la mesure de la distribution de particules solides. Trois cas particuliers sont consideres. Deux se reduisent aux expressions connues dans le cas de fractals de masses. Le troisieme permet de retrouver les expressions en loi de puissance etablies empiriquement, fieux exemples d'application sont traites afin de tester les possibilites de la nouvelle approche en ce qui concerne la prediction d'une courbe de retention d'eau a partir de la granulometrie des solides. Le modele en loi de puissance de la distribution de taille des particules est ajuste aux donnees. Bien que la qualite des ajustements effectues reste discutable, une dimension fractale en est deduite, puis utilisee pour prevoir la courbe de retention d'eau. Les resultats sont encourageants et montrent la necessite de poursuivre les recherches theoriques et experimentales a la lumiere de la nouvelle theorie presentee.

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The water retention function for a model of soil structure with pore and solid fractal distributions

The relationship between water content and water potential for a soil is termed its water retention curve. This basic hydraulic property is closely related to the soil pore size distribution, for which it serves as a conventional method of measurement. In this paper a general model of the water retention curve is derived for soils whose pore size distribution is fractal in the sense of the Mandelbrot number-size distribution. This model, which contains two adjustable parameters (the fractal dimension and the upper limiting value of the fractal porosity) is shown to include other fractal approaches to the water retention curve as special cases. Application of the general model to a number of published data sets covering a broad range of soil texture indicated that unique, independent values of the two adjustable parameters may be difficult to obtain by statistical analysis of water retention data for a given soil. Discrimination among different fractal approaches thus will require water retention data of high density and precision.

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Models of the water retention curve for soils with a fractal pore size distribution

To study relationships between soil hydraulic properties and soil structural properties, a computer micro model of soil is constructed. We present first a general method of building a two-dimensional porous structure, including both pores and particles, with different levels of aggregation resulting from a fragmentation process. A fractal structure is obtained when self similarity is imposed over the successive scales of fragmentation. Emphasis is put upon the modeling of the retention curve. A classical capillary model and methods taken from percolation theory enable us to simulate qualitatively the primaiy and secondary loops of this hysteretic curve. In the fractal case, theoretical analytical expressions proposed for adjusting retention data are tested. The unsaturated hydraulic conductivity is also calculated on the same simulated soil by analogy with an electrical network. The soil structures are deformable and simulation proves to be a useful tool to investigate the behavior of swelling soils. , I- .

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Computer construction of fractal soil structures: Simulation of their hydraulic and shrinkage properties

We wish to point out a significant conceptual error in the derivation of a fractal model water retention curve by Perfect et al. [1996]. Their derivation is based on the properties of the Menger sponge (see, e.g., Figure l b in the work by Rieu and Sposito [1991a]), a well-known fractal model for porous media that exhibit length-scaling invariance [Mandelbrot, 1983, p. 1341. A crucial step in the derivation presented by Perfect et al. [1996, equation (6a)l is their decision to equate the volumetric water content ( with the subunit porosity ( @ i . l , j ) at one hierarchical level below level i, after the same number of iterations j of the generator. Their postulate is thus:

/pdf/comment-on-an-improved-fractal-equation-for-the-soil-water-4jgwxgyj78.pdf

Michel Rieu

Papers

Generalizing the fractal model of soil structure : the pore-solid fractal approach

The water retention function for a model of soil structure with pore and solid fractal distributions

Models of the water retention curve for soils with a fractal pore size distribution

Computer construction of fractal soil structures: Simulation of their hydraulic and shrinkage properties

Comment on “An improved fractal equation for the soil water retention curve” by E. Perfect et al.