## Soil saturated conductivity after field data

Several different methods, both mono-dimensional (eventually with the introduction of scale effects, for example, Wu etal. 1999, Braud etal. 2001) and bi-dimensional with axial symmetry, have been presented and compared in the literature to interpret the infiltration process from a single ring infiltrometer. Here, two mono-dimensional quasi-steady methods and a two-dimensional axial-symmetric method are presented.

The first method we used to estimate the soil vertical saturated conductivity Ks after in situ experiences is the traditional method derived by the application of Darcy's law (1856) to a quasi-steady, uniform, mono-dimensional flow in a saturated porous media with finite volume (further it will be referred to as the Darcy's method). Under the above hypothesis, the momentum equation can be therefore discretised obtaining the following Equation (9.6):

being q = q k' [LT—1] the apparent velocity of the fluid in the porous medium, Az the soil length inside the infiltrometer, say, Lnf = 0.1 m (Figure 9.1), and H [L] the total water head. For a saturated soil H = Hgeo + p/ym [L], where Hgeo is the geodetic head and p/ym the piezometric head, where ym is the unitary weight of the water. As the ground is assumed as reference level, the geodetic head Hgeo is equal to the height z above ground.

By taking the soil core and the volume of fluid inside the infiltrometer as a control volume and n' being the surface unitary vector positive outward, the conservation of mass is given by the Equation (9.7):

30.0 cm

30.0 cm Figure 9.1 Descriptive sketch of the single ring infiltrome-ter method z Figure 9.2 Descriptive sketch of the Green and Ampt (1911) infiltration conceptual model is the cumulated drawdown of the water table and 00 the initial volumetric soil moisture, shall be less than the length D of the infiltrometer in the soil. Let ^ be the matric potential below the interface between the wet front and the soil at initial dry moisture conditions (Chow et al. 1988), then the Green and Ampt's infiltration model can be modified restoring the dependency of the infiltration by a variable head ponding on the soil surface:

In the previous equation, h0 is the initial depth of the water inside the infiltrometer, and h(t) = h0 — I(t) is the current water depth, that is, equal to the hydraulic head on the upper surface of the saturated soil control volume (A in the sketch). Even if such an application of the GA model takes into account the matric potential below the wetting front, the given description of the phenomenon can be seen as dominated by a transport behaviour. Anyway, since the infiltration process is characterised also by the diffusion of the soil moisture, the wetting front (B in the sketch) is often strongly smoothed. So we took into account such a behaviour by estimating the matric potential ^ as the average matric potential over the interval (0sat; 00). Knowing the initial soil moisture 00 and the parameters of the water retention relationships derived after laboratory tests - in this case the Brooks and Corey's form was used - , ^ was estimated with the equation below:

Figure 9.2 Descriptive sketch of the Green and Ampt (1911) infiltration conceptual model in which h is the water level inside the infiltrometer and it is equal to the hydraulic head at point A in Figure 9.1. At the bottom of the control volume (B in the sketch), n' is equal to —k', so by the substitution of Equation (9.6), Equation (9.7) can be integrated between A and B yielding to the cumulative drawdown versus time curve. The soil saturated conductivity Ks can be therefore estimated as it is the only unknown parameter in the cumulative infiltration curve.

The second mono-dimensional method adopted to estimate the soil saturated conductivity from field data is an application of the Green and Ampt (1911) conceptual infiltration model and will be referred to as the GA method. A sharp wetting front (named B, Figure 9.2) is supposed to penetrate to a depth L into the soil. The model applies to the process until it is strictly mono-dimensional. In order to respect this condition, the saturated soil depth L(t) = I(t)/(0sat — 60), where I(t)

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