On the dependence of the saturated hydraulic conductivity upon the effective porosity through a power law model at different scales

Fallico, Carmine; Bartolo, Samuele De; Veltri, Massimo; Severino, Gerardo

doi:10.1002/hyp.10798

Cited by 27 publications

(30 citation statements)

References 41 publications

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“…The scale dependence of the conductivity has been highlighted by several studies (Fallico, Chiara Vita, De Bartolo, & Straface, ; Fallico, De Bartolo, Veltri, & Severino, ; Schulze‐Makuch & Cherkauer, ). It is strictly connected to the parameters accounting for the medium's structure and the flowing fluids.…”

Section: Methodsmentioning

confidence: 91%

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

Fallico

Ianchello

Bartolo

et al. 2018

Hydrological Processes

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The spatial distribution of the hydraulic conductivity κ 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 formation's property (nonlocality), in agreement with the recent developments on the theory of flows into radial configurations.

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Section: Methodsmentioning

confidence: 91%

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

Fallico

Ianchello

Bartolo

et al. 2018

Hydrological Processes

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“…which modifies 0 according to the medium's heterogeneities. One of the main advantages related to the representation (11), (12) is that it allows one to easily identify from measurements the spatial structure of the hydraulic properties (see, e.g., Severino, Santini, & Sommella, 2008;Gómez, Severino, Randazzo, Toraldo, & Otero, 2009;Severino, 2011;Fallico, De Bartolo, Veltri, & Severino, 2016). Furthermore, given the mathematical structure of the second of (10), it is seen that the effective hydraulic conductivity has a tensorial nature (even if it is a scalar at laboratory scale).…”

Section: Methodsmentioning

confidence: 99%

A scale‐invariant property of the water retention curve in weakly heterogeneous vadose zones

Severino

Bartolo

2019

Hydrological Processes

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Abrupt changes of hydraulic properties in a vadose zone are modelled within a stochastic framework, which regards the saturated conductivity and parameters related to the distribution of soil pores as stationary, log‐normally distributed, random space functions. As a consequence, flow variables become random fields, and we aim at deriving an effective Richards equation. To obtain the latter, we adopt a perturbation expansion truncated at the first order (weakly heterogeneous media), which leads to the effective hydraulic conductivity and water retention curves. Overall, the effective properties are scale dependent. However, within the proposed framework, we demonstrate that the inflection point of the laboratory scale retention curve is not affected by the heterogeneity of the vadose zone. Finally, to illustrate the quantitative implications of our results, we consider a monitoring experiment at field scale, and we show how our approach leads to an effective water retention curve, which differs significantly from that which would be obtained without accounting for the above scale‐invariance property.

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“…Due to their erratic variations [see, e.g., White and Sully , ; Russo and Bouton , ; Severino et al ., ; Fallico et al ., ; Severino et al ., ], the log‐transformed parameters

ζ = \ln α

and

Y = \ln K_{s}

are modeled as stationary RSFs. As a consequence, their geometric means:

α_{G} = \exp true〈 ζ true〉

and

K_{G} = \exp true〈 Y true〉

are constant with zero‐mean fluctuations, i.e.,

true〈 ζ^{'} true〉 = ζ - 〈 ζ 〉 = 0 and true〈 Y^{'} true〉 = Y - 〈 Y 〉 = 0

.…”

Section: Mathematical Statement Of the Problemmentioning

confidence: 98%

“…[]) of the soil samples (see also discussion in Fallico et al . []). The usefulness of using laboratory K s ‐measurements stems from the fact that these were more numerous than those at field scale (Table ).…”

Section: Calibration Versus Validationmentioning

confidence: 99%

Stochastic analysis of unsaturated steady flows above the water table

Severino

Scarfato

Comegna

2017

Water Resources Research

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Steady flow takes place into a three‐dimensional partially saturated porous medium where, due to their spatial variability, the saturated conductivity Ks, and the relative conductivity Kr are modeled as random space functions (RSF)s. As a consequence, the flow variables (FVs), i.e., pressure‐head and specific flux, are also RSFs. The focus of the present paper consists into quantifying the uncertainty of the FVs above the water table. The simple expressions (most of which in closed form) of the second‐order moments pertaining to the FVs allow one to follow the transitional behavior from the zone close to the water table (where the FVs are nonstationary), till to their far‐field limit (where the FVs become stationary RSFs). In particular, it is shown how the stationary limits (and the distance from the water table at which stationarity is attained) depend upon the statistical structure of the RSFs Ks, Kr, and the infiltrating rate. The mean pressure head true〈normalΨtrue〉 has been also computed, and it is expressed as 〈Ψ〉=Ψ0(1+ψ), being ψ a characteristic heterogeneity function which modifies the zero‐order approximation Ψ0 of the pressure head (valid for a vadose zone of uniform soil properties) to account for the spatial variability of Ks and Kr. Two asymptotic limits, i.e., close (near field) and away (far field) from the water table, are derived into a very general manner, whereas the transitional behavior of ψ between the near/far field can be determined after specifying the shape of the various input soil properties. Besides the theoretical interest, results of the present paper are useful for practical purposes, as well. Indeed, the model is tested against to real data, and in particular it is shown how it is possible for the specific case study to grasp the behavior of the FVs within an environment (i.e., the vadose zone close to the water table) which is generally very difficult to access by direct inspection.

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On the dependence of the saturated hydraulic conductivity upon the effective porosity through a power law model at different scales

Cited by 27 publications

References 41 publications

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

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

A scale‐invariant property of the water retention curve in weakly heterogeneous vadose zones

Stochastic analysis of unsaturated steady flows above the water table

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