Samuele De Bartolo

Usage of infinitesimals in the Menger’s Sponge model of porosity

Abstract The 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.

An indirect assessment on the impact of connectivity of conductivity classes upon longitudinal asymptotic macrodispersivity

Solute transport takes place in heterogeneous porous formations, with the log conductivity, Y = ln K, modeled as a stationary random space function of given univariate normal probability density fu ...

Scaling Effect of the Hydraulic Conductivity in a Confined Aquifer

Abstract 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.

A Note on the Fractal Behavior of Hydraulic Conductivity and Effective Porosity for Experimental Values in a Confined Aquifer

Hydraulic 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.

Spatial dependence of the hydraulic conductivity in a well-type configuration at the mesoscale

Correspondence Gerardo Severino, Division of Water Resources Management and Biosystems Engineering, Universitá 100, I80055-Portici (Naples), Italy. Email: severino@unina.it Abstract The spatial distribution of the hydraulic conductivityκ is modelled by a power law, and we present a methodological approach to quantify the exponent (crowding index) of such a law as detected within a well-type flow configuration. Based upon the outcome of several pumping tests conducted into a caisson (mesoscale), we identify the crowding index as function of the volumetric flow rate. Hence, we develop a simple (although approximated) procedure to assess whether the spatial distribution of κ can be characterized by a power law. We demonstrate that, even at the mesoscale, the conductivity κ can not be regarded as a formations property (nonlocality), in agreement with the recent developments on the theory of flows into radial configurations.

A fractal analysis of the water retention curve: A fractal analysis of the water retention curve

Correspondence Gerardo Severino, Department of Agricultural Sciences, University of Naples Federico II, Italy. Email: gerardo.severino@unina.it Abstract The dependence of the soil water content θ upon the matric potentialψ 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 ofψ . 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).

Relation between grid, channel, and Peano networks in high‐resolution digital elevation models

The topological interconnection between grid, channel, and Peano networks is investigated by extracting grid and channel networks from high-resolution digital elevation models of real drainage basins, and by using a perturbed form of the equation describing how the average junction degree varies with Horton-Strahler order in Peano networks. The perturbed equation is used to fit the data observed over the Hortonian substructures of real networks. The perturbation parameter, denoted as “uniformity factor,” is shown to indicate the degree of topological similarity between Hortonian and Peano networks. The sensitivities of computed uniformity factors and drainage densities to grid cell size and selected threshold for channel initiation are evaluated. While the topological relation between real and Peano networks may not vary significantly with grid cell size, these networks are found to exhibit the same drainage density only for specific grid cell sizes, which may depend on the selected threshold for channel initiation.

A direct scaling analysis for the sea level rise

The estimation of long-term sea level variability is of primary importance for a climate change assessment. Despite the value of the subject, no scientific consensus has yet been reached on the existing acceleration in observed values. The existence of this acceleration is crucial for coastal protection planning purposes. The absence of the acceleration would enhance the debate on the general validity of current future projections. Methodologically, the evaluation of the acceleration is a controversial and still open discussion, reported in a number of review articles, which illustrate the state-of-art in the field of sea level research. In the present paper, the well-proven direct scaling analysis approach is proposed in order to describe the long-term sea level variability at 12 worldwide-selected tide gauge stations. For each of the stations, it has been shown that the long-term sea level variability exhibits a trimodal scaling behaviour, which can be modelled by a power law with three different pairs of shape and scale parameters. Compared to alternative methods in literature, which take into account multiple correlated factors, this simple method allows to reduce the uncertainties on the sea level rise parameters estimation.