Abstract:We study the scale dependence of the saturated hydraulic conductivity K s through the effective porosity n e by means of a newly developed power-law model (PLM) which allows to use simultaneously measurements at different scales. The model is expressed as product between a single PLM (capturing the impact of the dominating scale) and a characteristic function κ ⋆ accounting for the correction because of the other scale(s). The simple (closed form) expression of the κ ⋆ -function enables one to easily identify the scales which are relevant for K s . The proposed model is then applied to a set of real data taken at the experimental site of Montalto Uffugo (Italy), and we show that in this case two (i.e. laboratory and field) scales appear to be the main ones. The implications toward an important application (solute transport) in Hydrology are finally discussed.

To describe flow or transport phenomena in porous media, relations between aquifer hydraulic conductivity and effective porosity can prove useful, avoiding the need to perform expensive and time consuming measurements. The practical applications generally require the determination of this parameter at field scale, while most of the empirical and semiempirical formulas, based on grain size analysis and allowing determination of the hydraulic conductivity from the porosity, are related to the laboratory scale and thus are not representative of the aquifer volumes to which one refers. Therefore, following the grain size distribution methodology, a new experimental relation between hydraulic conductivity and effective porosity, representative of aquifer volumes at field scale, is given for a confined aquifer. The experimental values used to determine this law were obtained for both parameters using only field measurements methods. The experimental results found, also if in the strict sense valid only for the investigated aquifer, can give useful suggestions for other alluvial aquifers with analogous characteristics of grain-size distribution. Limited to the investigated range, a useful comparison with the best known empirical formulas based on grain size analysis was carried out. The experimental data allowed also investigation of the existence of a scaling behaviour for both parameters considered.

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Previous studies showed that the values of the representative parameters of an aquifer, such as the hydraulic conductivity (k), increase with the scale, that is, with the aquifer volume involved in the measurement. The main cause of this behavior is commonly ascribed to the heterogeneity of the porous media. Heterogeneity influences the scaling behavior differently for laboratory or field measurement, but the scale dependence of hydraulic conductivity is not dependent on the specific measurement method. In the present study, the scaling law of this parameter was determined on a real confined aquifer, using measurements obtained, both in the laboratory (flow cells) and the field (slug tests and aquifer tests). The corresponding data were statistically analyzed. A scaling law was proposed for both the laboratory and field scale, using the data obtained from flow cells, slug tests, and aquifer tests. Afterward, the scaling law was estimated at just the field scale, first using the slug tests and aquifer tests and then using only the aquifer test data.The scale dependence of the storativity was also investigated for all field measurements and then using only the aquifer test data. In conclusion, for both hydraulic conductivity and storativity, the trend to reach an upper bound increasing the scale parameter was investigated in the scale ranges of 67 and 99 m, respectively, examining only the data set relative to aquifer test measurements.

Scaling analysis of water retention curves for unsaturated sandy loam soils by using fractal geometryC . F a l l i c o a , A . M . T a r q u i s b,c , S . D e B a r t o l o a & M . V e l t r i a SummaryFractal geometry was deployed to analyse water retention curves (WRC). The three models used to estimate the curves were the general pore-solid fractal (PSF) model and two specific cases of the PSF model: the Tyler & Wheatcraft (TW) and the Rieu & Sposito (RS) models. The study was conducted on 30 undisturbed, sandy loam soil samples taken from a field and subjected to laboratory analysis. The fractal dimension, a non-variable scale factor characterizing each water retention model proposed, was estimated by direct scaling. The method for determining the fractal dimension proposed here entails limiting the analysis to the interval between an upper and lower pressure head cut-off on a log-log plot, and defining the dimension itself as the straight regression line that interpolates the points in the interval with the largest coefficient of determination, R 2 . The scale relative to the cut-off interval used to determine the fractal behaviour in each model used is presented. Furthermore, a second range of pressure head values was analysed to approximate the fractal dimension of the pore surface. The PSF model exhibited greater spatial variation than the TW or RS models for the parameter values typical of a sandy loam soil. An indication of the variability of the fractal dimension across the entire area studied is also provided.