Pore size distribution

Materials and Methods

3.2 Tillage ~nd water content effects on surface-soil properties

3.2.3 Experimental measurements

3.2.3.5 Pore size distribution

'-"LI ... .-.MIC SYRINGE

150mm

o

Pore size distribution was determined from the matric potential-volumetric water content relationship, often referred to as the water characteristic or water retention curve. Matric potential of soil water (111m) is related to equivalent spherical pore radius (r) in Equation 2.8.

Soil macro-porosity is defined as the total volume of pores drained at -10.0 kPa matrlc potential (i.e. pores >30 "m equivalent spherical diameter (e.s.d.)}. Macro-

porosity corresponds to the summation of soil aeration capacity and transmission porosity where transmission porosity is defined as the volume of pores that drain between -1.0 and -10.0 kPa matric potential (300-30 "m e.s.d.). The total volume of pore$ which drain between -10.0 and -1500 kPa matric potential (i.e. pores between 0.2 and 30 "m e.s.d.) are commonly regarded as the pores which, when water-filled, contain water which is readily available to plants. Residual porosity is defined as the volume of pores which drain at less than -1500 kPa matrlc potential, pores less than 0.2 "m e.s.d.

(De Leenheer, 1977).

Tension tables were used to determine the gravimetric soil water content at matric potentials of -1.0, -3.0, -5.0 and -10.0 kPa. Volumetric soil water contents were

calculated by multiplying the gravimetric values by measured bulk density. The tension tables were constructed from 420 by 360 by 40 mm perspex trays tlsing silica flour ('Snowsil', ACI Resources Ltd., Victoria, Australia; mean particle size approx. 70 "m) as the porous bed.

Fo.ur intact soil cores were taken randomly in each sub-plot by pushing a sampling cylinder into moistened soil while trimming ahead of the sharpened cutting edge. Metal sampling cylinders 70 mm deep and 200 mm I.d. were used In those plots subjected to either the 'minimum' or 'intermediate' tillage treatment while a plastic cylinder 50 mm deep and 104 mm i.d. was used in the finer tilth 'excess' tillage plots. In each case the inside of the sampling cylinder was smeared with petroleum jelly to minimise edge effects. The lower surface of each core was trimmed flush and covered with a fine nylon cloth. The cores were treated with formaldehyde (4 %, w/w) to flush out

earthworms and a fungicide ('Kocide', Shell Chemicals NZ Ltd.) before being saturated with de-aerated water and placed on the tension table. After equilibration the cores were weighed before being transferred to the next tension table. Gravimetric water contents were determined at matric potentials of -1.0 and -3.0 kPa on four samples per sub-plot while water contents at potentials of -5.0 and -10.0 kPa were determined for two samples per sub-plot where the larger samples were used and four samples per sub-plot where the smaller samples were used. At completion of the -10.0 kPa measurement a sub-sample was taken by carefully pushing a thin-walled bevelled aluminium ring (15 mm deep by 42 mm i.d.) into the centre of the tension table sample.

After careful removal the sub-sample was trimmed and a fine gauze mesh secured over the bottom of each ring. Gravimetric water contents were then measured at

potentials of -33, -100, -300, -500 and -1500 kPa using pressure plate apparatus (Soil Moisture Equipment Corp., Santa Barbara, California, USA.). Water contents at -33 and -100 kPa were determined on three samples per sub-plot. One sample per sub-plot was used at -300, -500 and -1500 kPa, although -1500 kPa measurements were repeated from two replicates only. Volumetric water content-matric potential data was used to calculate pore size distributions following Ball and Hunter (1980).

3.2.3.6 Unsaturated hydraulic conductivity

One of the more commonly used methods to approximate K(.p) from the relationship between volumetric water content (8v) and .pm (e.g. Higuchi, 1984; Reid and Hutchison, 1986; Lascano and van Bavel, 1986) is that of Jackson (1972). The calculation procedure of Jackson (1972) was used in this study. The Jackson method for predicting K( .pm) is based on a capillary tube model of water flow through soil pores.

The model Is based on the matrlc potential-pore radius relation (Equation 2.7) and on the Hagen-Poiseuille law (Equation 2.9) and the Darcy equation (Equation 2.11). The Jackson method is a fu'rther development of the Childs and Collis-George (1950) model and of the Marshall (1958) model. It is categorised as a 'series-parallel' type model (Brutsaert, 1967), one in which the soil is assumed to behave like a bunch of parallel , tubes with constrictions due to tube connections, a porous body in which the distribution

of pores of various sizes In space is entirely random.

Consider a column of such a porous body, with a unit cross-section, cut in two thereby exposing two surfaces each with a representative pore size distribution (after Childs, 1969). On one surface there is a particular pore group with average size p and range Ilr and hence size range ^{p -}1lr/2 to ^p + 1lr/2. On the other exposed surface a pore group has mean size ^C1 and range Ilr. The area of the exposure taken by a particular pore group is equal to the part of the porosity accounted for by that grou·p which, in turn, equals the product of concentration of pore volume (i.e. pore volume per unit pore size range) about the chosen size, and the width of the range. The

'concentration of pore volume at the given pore size is a distribution function of the pore size. Hence the area of exposure of pores of mean size pis:

. A = J(p) b%

p • •• (3.4)

while on the other surface the area of exposure of pores of mean size u is:

A = J(u) Az

u • .• (3.5)

In the undisturbed column the two exposures are assumed to come together at random and so the area of the junction occupied by pore sequences characterized by mean pore sizes of p on the first side and u on the second side is the product of Ap and Au' denoted Ap~u :

A = J(p)Az J(u)Az

p~u • •• (3. 6)

The next step is to assess the contribution to total hydraulic conductivity made by the pore sequence described and to compute total conductivity by summing the

contributions made by all of the possible sequences covering the whole range of pore sizes in the material. Two assumptions are necessary to do this. First, as pore size decreases, resistance to flow increases so rapidly (following the Hagen-Poiseuille law) that the resistance of the coarser pore in the sequence can be neglected (i.e. flow resistance is calculated on the basis of one pore size, the smaller of the sequence).

Second, all contributions to conductivity, except those due to direct sequences, can be ignored (i.e. capillary assumed straight not tortuou~). These two assumptions provide oppOSite errors and, to some degree, mutually compensate (Childs, 1969). If u is smaller than p in the sequence, the number of sequences occupying the area Ap~u is proportional to Ap~J~ and by Poiseuille the rate of flow through each, per unit '"

gradient is proportional to u4, so that the contribution ~K to the total hydraulic conductivity is:

~

^{= Mu2} J(p)Az J(u)Az and total conductivity is:

K=ML

p=R p=O

u J(p)Az J(u)Az 2

. . . (3.7)

... (3.8)

where M is an experimental constant, R is upper pore size limit (after Childs, 1969). For unsaturated soil, R is the largest pore size which remains full of water at the "'m

appropriate to the prevailing 9. The distribution function I(r), is determined from the water characteristic. The soil water characteristic curve is considered analogous to the pore radii distribution function. Using the capillary law (Equation 2.7), capillary tube radius (r) is uniquely related to the matric potential (I/Im) at which the pore is filled and drained. By definition, I(r)~ Is the contribution of the filled pores of radius r .. r+~r to the water content, namely (Mualem, 1986):

~9(r)

=

^l(r)l1r • •• (3. 9)

and thus:

e

^(a)

= ~").!\J:

... (3.10)

Using this model, K can be computed for any given 9 using the measured soil water characteristic curve. Childs and Collis-George (1950) suggested (to transform the 9(l/Im) to a 9(r) curve [ra:1I1/1m]} dividing it into constant r intervals and carrying outthe computation by Equation 3.8.

This tediou~ computational procedure was Improved by Marshall (1958) who suggested using equal water content intervals. Using this approach, the conductivities are actually obtained by dividing the _9(l/Im) relationship into n equale increments, obtaining the I/Im at each increment and calculating the conductivity using the equation (Marshall,1958):

. .. (3.11)

1=1,2,3 ... m

where Ki

=

hydraulic conductivity (cm h-1) at the i th increment, 'Y is the surface tension of water (g s-2), Pw is the density of water (g cm-3), g is the gravitational constant (cm s-2), 71 is the viscosity of water (g cm-1 s-1), 9 is the water filled porosity at lowest '/ tension class (em3 em-3), p the exponent of 9 is a constant whose value depends on

computational method, n is the total number of pore classes, j and i are summation indices, I/I

m

is matric potential (cm) and m is the number of increments for which the

calculation is to be made. Jackson (1972) showed that because p=2 the'pore

interaction term (9/n) is constant for any water content. Jackson re-wrote the Marshall equation thus:

m

1t1 = A

L [

^(2j+1-21)

^{VI;2 ]}

j=i

••. (3.12)

with A = (1800 ,,(2/Pwg1l)(9/n)2, where any 9 and its corresponding n can be used. This calculation method was shown to require a matching factor to adequately represent experimental data. Using the ratio of measured to calculated saturated conductivity Ks/Ki as the matching factor Jackson wrote:

It = It

1 s ... (3.13)

where p = ,. This is the equation that will be evaluated here for calculation of the K(Vlm) relationship. Discrete Vlm(e) data'lS'required and the K predictions that result are only for the range of Vlm(9) data available.

The Jackson method is thus based on the assumption that the soil is isotrop~ic

with the pore space randomly distributed so that there are no continuous channels.

These conditions do not hold in field soils and hence can lead to calculation errors.

Using measured saturated hydrauliC conductivity as a matching factor will not

necessarily overcome the problem because cracks and channels not allowed for in the model might contribute greatly to the actual conductivity at saturation, but not when unsaturated (Marshall and Holmes, 1988).

However, in suitable soils, hydraulic conductivity functions calculated using this type of 'cut and random re-join' pore model have been reported as being close to those determined by physical measurements. This is providing that a matching factor is used and the matching is done at some degree of unsaturation when necessary (Kunze et aI., 1968; Green and Corey, 1971; Jackson, 1972; Alexander and Skaggs, 1986; Rab et al.,

1987). The Jackson (1972) model was tested by Field et al. (1984) who reported it to be successful In predicting unsaturated conductivities within the scatter of in situ values when field measured water characteristic data was used and the mean in situ saturated hydrauliC C9nductivity was used as a matching factor. The apparent necessity of a matching factor indicates that the method does not really predict hydraulic conductivity as a function of water content, but rather, the rate of decrease in conductivity as expressed by the slope of the K(9) curve (Denning et aI., 1974). In this study, near- saturated hydraulic conductivity was used for matching because of the large macro-pore volume expected in the tilled soil. The assumptions Inherent in the Jackson model make a saturated hydraulic conductivity matching factor Inappropriate in a tilled soil.