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| Titel |
Fractal analysis of the hydraulic conductivity on a sandy porous media reproduced in a laboratory facility. |
| VerfasserIn |
S. De Bartolo, C. Fallico, S. Straface, S. Troisi, M. Veltri |
| Konferenz |
EGU General Assembly 2009
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 11 (2009) |
| Datensatznummer |
250025925
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| Zusammenfassung |
| The complexity characterization of the porous media structure, in terms of the “pore” phase
and the “solid” phase, can be carried out by means of the fractal geometry which is
able to put in relationship the soil structural properties and the water content. It is
particularly complicated to describe analytically the hydraulic conductivity for
the irregularity of the porous media structure. However these can be described by
many fractal models considering the soil structure as the distribution of particles
dimensions, the distribution of the solid aggregates, the surface of the pore-solid
interface and the fractal mass of the “pore” and “solid” phases. In this paper the fractal
model of Yu and Cheng (2002) and Yu and Liu (2004), for a saturated bidispersed
porous media, was considered. This model, using the Sierpinsky-type gasket scheme,
doesn’t contain empiric constants and furnishes a well accord with the experimental
data.
For this study an unconfined aquifer was reproduced by means of a tank with a volume of
10 Ã 7 Ã 3 m3, filled with a homogeneous sand (95% of SiO2), with a high percentage
(86.4%) of grains between 0.063mm and 0.125mm and a medium-high permeability.
From the hydraulic point of view, 17 boreholes, a pumping well and a drainage ring
around its edge were placed. The permeability was measured utilizing three different
methods, consisting respectively in pumping test, slug test and laboratory analysis of
an undisturbed soil cores, each of that involving in the measurement a different
support volume. The temporal series of the drawdown obtained by the pumping test
were analyzed by the Neuman-type Curve method (1972), because the saturated
part above the bottom of the facility represents an unconfined aquifer. The data
analysis of the slug test were performed by the Bouwer & Rice (1976) method and the
laboratory analysis were performed on undisturbed saturated soil samples utilizing a
falling head permeameter. The obtained values either of the fractal dimension of the
area of the pores (Df) or of the fractal dimension of capillary tortuosity (DT),
very similar to those reported in literature (Yu and Cheng, 2002; Yu and Liu, 2004;
Yu, 2005) and falling in the range of definition (1 < Df < 2), resulted very
close to those carried out in a previous study performed on the same apparatus
but with a limited number of values (De Bartolo et al., in review). In fact in the
present study the laboratory analysis were performed on other 10 undisturbed soil
samples and moreover three new values of slug test and 12 new of pumping test were
considered.
Moreover the trend of DT growing with the scale length (L) was confirmed,
as well as the invariability of, due to the homogeneity of the considered porous
media.
The linear scaling law of the permeability (k) close to scale length was investigated
furnishing more reliable results. However for a better definition of a law of scale for Df, DT
and k several number of scale length are need and a greater number of experimental data
should be carried out. For this purpose the considered experimental apparatus is limited from
its restricted dimensions and geometric bounds; therefore further investigations in
experimental field are desirable.
Bibliografy
Bouwer, H. & Rice, R. C. 1976. A Slug Test for Hydraulic Conductivity of Unconfined
Aquifers With Completely or Partially Penetrating Wells, Water Resources Research,
12(3).
De Bartolo, S., Fallico, C., Straface, S., Troisi, S. & Veltri M. (in review). Scaling of the
hydraulic conductivity measurements by a fractal analysis on an unconfined
aquifer reproduced in a laboratory facility, Geoderma Special Issue 2008.
Neuman, S.P. 1972. Theory of flow in unconfined aquifers considering delayed response
of the water table, Water Resources Research, 8(4), 1031-1045.
Yu, B.M. 2005. Fractal Character for Tortuous Streamtubes in Porous Media, Chin. Phis.
Lett., 22(1), 158.
Yu, B.M. & Cheng, P. 2002. A Fractal Permeability Model for Bi-Dispersed Porous
Media, Int. J. Heat Mass Transfer 45(14), 2983.
Yu, B.M. & Liu W. 2004. Fractal Analysis of Permeabilities for Porous Media, American
Institute of Chemical Engineers 50(1), 46-57. |
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