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Analytical Models for Soil Pore-Size Distribution After Tillage

^a USDA-ARS, George E. Brown Jr. Salinity Lab. and Dep. of Environmental Sciences, Univ. of California, Riverside, CA 92507-4851
^b Dep. of Plants, Soils, and Biometeorology, Utah State Univ., Logan, UT 84322

View larger version (20K): [in a new window]   Fig. 1. Evolution of pore-size distribution over time according to Eq. [13] with no decay, a time-dependent drift term V(t) given by Eq. [14] with a = 0.01 d-1, b = 5 µm, <r0> = 7.5 µm (shown in insert), and a constant dispersivity: (a) = 1 µm and (b) = 0.1 µm. The initial distribution is according to Eq. [5] with s = 0.469, r = 0.191, = 0.253, and r0 = 7.3 µm.

View larger version (21K): [in a new window]   Fig. 2. Evolution of pore-size distribution over time according to Eq. [24] with no decay, a drift term v(r,t) = u(r)w(t) where w(t) is given by Eq. [14], with a = 0.01 d-1, b = 5 µm, <r0> = 7.5 µm (upper insert), and u(r) is given by Eq. [16] with uo = 0.5 (lower insert), and a dispersion term D(r,t) = -(r)v(r,t) where (r) is given by Eq. [16] with: (a) o = 0.25 and (b) o = 0.05. The initial distribution is again given by Eq. [5] with s = 0.469, r = 0.191, = 0.253, and r0 = 7.3 µm.

View larger version (61K): [in a new window]   Fig. 3. Unit cell with cubic packing of spherical aggregates: (a) initial packing with strain = h/a = 0 and (b) packing with = 0.05. Illustration of coalescence at the contact area of two aggregates because of viscous and capillary forces: (c) definition sketch of aggregates with radius, a, and reduction in distance between aggregate centers, 2h.

View larger version (18K): [in a new window]   Fig. 4. Evolution of the interaggregate pore-size distribution of a Millville silt loam according to Eq. [13] with drift and degradation terms given by Eq. [30] and [31], = 0.1, = 0.5 µm and initial distribution with r0 = 48.45 µm and porosity (s - r) equal to 0.2 as well as = 0.2.

View larger version (13K): [in a new window]   Fig. 5. Temporal behavior of parameters for the interaggregate pore-size distribution of a Millville silt loam shown in Fig. 4: (a) strain (), matric potential (), and lower and upper limits on , (b) drift term (V) and degradation term (M) and (c) first-order normalized (M1) and second-order central (µ2) moments.

View larger version (18K): [in a new window]   Fig. 6. Evolution of the interaggregate pore-size distribution of a Millville silt loam according to to Eq. [24] with time-dependent drift and degradation terms given by Eq. [30] and [31], = 0.1, uo = 0.1, o = 0.05 and initial distribution with <r0> = 48.45 µm and porosity (s - r) = 0.2 as well as = 0.2.

View larger version (15K): [in a new window]   Fig. 7. Temporal behavior of the first-order normalized (M1) and second-order central (µ2) moments for the interaggregate pore-size distribution of a Millville silt loam shown in Fig. 5.

View larger version (17K): [in a new window]   Fig. 8. Parameters inferred from the settlement of a Millville silt loam during wetting (0–30 and 60–90 min) and drying (30–60 and 90–120 min) cycles: (a) observed and optimized axial strain and (b) drift coefficient according to the coalescence model.

View larger version (22K): [in a new window]   Fig. 9. Pore-size distribution and retention curves for the Millville silt loam: (a) initial PSD determined from soil water characteristics (SWC) and pore-size distributions (PSDs) predicted at the end of two drying cycles using the coalescence model, and (b) corresponding SWCs and experimental retention data.