1,720,978 research outputs found
Simple scaling analysis of active channel patterns in Fiumara environment
No full textA simple scaling analysis was performed on experimental data relative to a riverbed reach of the Allaro Fiumara, a fluvial environment typical of Southern Italy. For this purpose, a simplified geometrical approach was followed to determine the spatial distribution of the number of active channels for the river stretch considered. In particular, the section lines crossing the braided network skeleton with distance ranging from 5 to 200. m were considered. Firstly, a probabilistic analysis of the experimental data was carried out by using a truncated Poisson distribution to characterize the examined river morphologically. Afterward, a scaling analysis was performed to investigate the existence of a possible multimodal behaviour of the number of active channels and to identify the corresponding cutoff values. For this second approach by the so-called standard coarse graining analysis, we defined a power law usable to give the probability distribution of the active channels number with varying spatial partition (distance between consecutive sections). In this way, verifying the existence of a bimodal scaling behaviour was possible. Moreover, the cutoff limits that characterize the bimodal behaviour of the active channels were found for all the partition distances from 5 to 100. m, while the corresponding shape and scale parameters were also determined. A comparison of the results obtained by the statistical approach and the scaling analysis was carried out. The variability of the characteristic parameters of the Poisson and power type laws with scale was also investigated
A note on the fractal behavior of hydraulic conductivity and effective porosity for experimental values in a confined aquifer
Full text linkHydraulic conductivity and effective porosity values for the confined sandy loam aquifer of the Montalto Uffugo (Italy) test field were obtained by laboratory and field measurements; the first ones were carried out on undisturbed soil samples and the others by slug and aquifer tests. A direct simple-scaling analysis was performed for the whole range of measurement and a comparison among the different types of fractal models describing the scale behavior was made. Some indications about the largest pore size to utilize in the fractal models were given. The results obtained for a sandy loam soil show that it is possible to obtain global indications on the behavior of the hydraulic conductivity versus the porosity utilizing a simple scaling relation and a fractal model in coupled manner. © 2013 Samuele De Bartolo et al
Average steady flow toward a drain through a randomly heterogeneous porous formation
Full text linkWe 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 variability 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 generalizes 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(∞) < ∞
A fractal analysis of the water retention curve
No full textThe dependence of the soil water content θ upon the matric potential ψ is studied within a fractal approach that regards the water retention curve as a sequence of well defined fractal regimes. Each of such regimes accounts for a given functional dependence θ≡θ(ψ), which in turn is characterized by a fractal dimension. The difference between the double fractal (observed into sandy soils) and multifractal (observed into clay soils) regime is explained by recalling that, for a sandy soil, the transition from saturated to dry conditions is driven by a steep reduction of ψ. To the contrary, for a clay (where the change from the highest water contents to the smallest ones is characterized by a large range of the matric potential), the multifractal behaviour is observed. These results are also confirmed by the analysis of experimental data. In particular, we show that the intermediate regime, generally accounting for the fractal multimodality, is due to the sandy nature of the soil at stake, practically immaterial. Finally, we demonstrate that our model can be also regarded as the straightforward generalization of that of Millán and González-Posada (2005)
Scaling analysis of water retention curves for unsaturated sandy loam soils by using fractal geometry
No full textFractal 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, R2. 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. © 2010 The Authors. Journal compilation © 2010 British Society of Soil Science
Usage of infinitesimals in the Menger's Sponge model of porosity
No full textThe present work concerns the calculation of the infinitesimal porosity by using the Menger's Sponge model. This computation is based on the grossone theory considering the pore volume estimation for the Menger's Sponge and afterwards the classical definition of the porosity, given by the ratio between the volume of voids and the total volume (voids plus solid phase). The aim is to investigate the different solutions given by the standard characterization of the porosity and the grossone theory without the direct estimation of the fractal dimension. Once the utility of this procedure had been clarified, the focus moves to possible practical applications in which infinitesimal parts can play a fundamental role. The discussion on this matter still remains open. © 2011 Elsevier Inc. All rights reserved
Scaling analysis of hydraulic conductivity and porosity on a sandy medium of an unconfined aquifer reproduced in the laboratory
No full textMany 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
Comparison among variation models of the hydraulic conductivity with the effective porosity in confined aquifer
Full text linkThis paper presents the experimental investigation results from the modalities of
variation of the hydraulic conductivity scaling law for a confined aquifer, varying the porous medium that constitutes it. In four subsequent stages, different confined aquifers were built up, each with a different typological configuration of a porous medium. For each of the aquifers considered, various hydraulic conductivity (K) measurements were performed by slug tests. The effective porosity (ne) was set as a scale parameter, therefore the scaling laws K = K(ne), already etermined and reported in previous studies, were taken into consideration for each of the four
artificial aquifers considered. The same variation law of K vs ne was also determined by means of some of the well-known empirical and semi-empirical relationships. The latter are based on the particle size distribution and are suitable for application to the porous media considered here, which can be classified as coarse sand. The comparison between the different scaling laws mentioned above allowed us to discuss, through graphical analysis, the reliability of the models considered here. This will facilitate researchers and practitioners working in the field, in the methodological choice of the most appropriate model that should be used for this type of porous media
Scaling effect of the hydraulic conductivity in a confined aquifer
No full textPrevious 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. Copyright © 2012 by Lippincott Williams & Wilkins
Correlation Structure of Steady Well-Type Flows Through Heterogeneous Porous Media: Results and Application
Full text linkSteady flow toward a fully penetrating well takes place in a natural porous formation, where the erratic spatial variations, and the raising uncertainty, of the hydraulic conductivity K are modeled within a stochastic framework which regards the log-conductivity, ln K, as a Gaussian, stationary, random field. The study provides second order moments of the flow variables by regarding the variance of the log-conductivity as a perturbation parameter. Unlike similar studies on the topic, moments are expressed in a quite general (valid for any autocorrelation function of ln K) and very simple (from the computational stand point) form. It is shown that the (cross)variances, unlike the case of mean uniform flows, are not anymore stationary due to the dependence of the mean velocity upon the distance from the well. In particular, they vanish at the well because of the condition of given head along the well’s axis, whereas away from it they behave like those pertaining to a uniform flow. Then, theoretical results are applied to a couple (one serving for calibration and the other used for validation purposes) of pumping tests to illustrate how they can be used to determine the hydraulic properties of the aquifers. In particular, the concept of head-factor is shown to be the key-parameter to identify the statistical moments of the random field K
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