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Water retention curve (WRC) is analyzed by means of the fractal geometry approach. Three models accounting for the fractal distribution of either the pore and solid phase of unsaturated porous media have been considered. By using data collected during a field scale internal drainage, we determine the functional relationship between the WRC, and the fractal dimension(s). In particular, it is shown that the fractal scaling of the WRC is feasible provided that a large enough set of measurements at the lowest water contents is available. (C) 2013 The Authors. Published by Elsevier B.V.

We consider the problem of steady pumping of water from a line drain on the surface of a wet ground. Unlike the classical formulation, which regards the conductivity parameter K as uniformly distributed in the domain, the problem here is solved within a stochastic framework in order to account for the irregular (random), and more realistic, spatial vari- ability of K. Due to the linearity of the problem at stake, we focus on the derivation of the mean Green function G. This is computed by means of an asymptotic expansion. The fundamental result is an analytical (closed form) expression of G which general- izes the classical solution. Based on this, we develop an equivalent conductivity Keq which enables one to tackle the problem similarly to the classical one. In particular, it is shown that the equivalent conductivity grows monotonically with the radial distance r from the drain, and it lies within the range Keq (0) ≤ Keq (r) ≤ Keq (∞) < ∞.

Many studies have shown that the characteristic parameters of an aquifer, specifically the hydraulic conductivity, increase with an increase in the portion of the aquifer tested. The main cause of this behavior is the heterogeneity within the aquifer. Sets of measurements performed on an artificial aquifer by different methods are utilized here, because it was verified that the scale dependence of hydraulic conductivity does not depend on the specific method of measurement. The unconfined aquifer in question was created in the laboratory utilizing sandy porous medium with a well-known grain-size distribution. An experimental scaling law of the power type was obtained for the hydraulic conductivity, utilizing values measured at different scales by different methods (on undisturbed soil samples by flux cells, on the artificial aquifer by slug tests and aquifer tests). Similarly, porosity measurements of a direct and indirect type were carried out: the former performed in the laboratory and the latter utilizing a relation between k and Φ based on the particle size analysis of the porous media considered. Successively, a new empirical relationship is proposed here, to derive Φ, since the k values and vice versa, are well-known, the validity of which is limited to the sands with effective grain size between 0.059 mm and 0.82 mm and for volumes of aquifer not higher than those investigated here. © 2010 Elsevier B.V.