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HYDC05 12/5/05 5:35 PM Page 154

154 Chapter Five

capacity and hydraulic conductivity in soils and
unsaturated rocks and sediments are themselves a
function of pressure head. Expressed in mathematical
notation, θ = θ(ψ), C = C(ψ) and K = K(ψ). It also
follows that K = K(θ). As a result, it is recognized that
flow in the unsaturated zone will vary according to
the value of hydraulic conductivity at a given soil
moisture content. In general, and by considering
one-dimensional flow, the quantity of discharge, Q,
across a sectional area, A, is found from Darcy’s law
applied to the unsaturated zone:
Fig. 5.13 Soil characteristic curves showing the variation of
volumetric moisture content, θ, and hydraulic conductivity, K,
with pressure head, ψ. The unequal variation of the drying and Q =− ψ h d
wetting curves is caused by the effects on soil structure of the AK() d x eq. 5.12

drying (soil shrinkage) and wetting (soil swelling) processes. ψ is
a
the air-entry or bubbling pressure.
where h is the fluid potential or soil water potential.
As discussed in Section 2.8, fluid potential is the work
the soil moisture curve, dθ/dψ, is referred to as the done in moving a unit mass of fluid from the standard
specific moisture capacity, C, and is a measure of the state to a point in a flow system. Ignoring osmotic
storage behaviour of the unsaturated zone. potential, the total soil water potential at a given
The process of drying a soil causes the soil grains point comprises the sum of the gravitational (or
to compact and alters the soil structure through elevation) potential, ψ , and pressure potential, ψ , as
g p
shrinkage and air entrapment. On wetting, the soil follows:
swells as water is added. Consequently, the resulting
characteristic curves for the drying and wetting Φ = ψ + ψ eq. 5.13
g p
phases are different and a hysteretic effect is observed
as shown in Fig. 5.13. Further important causes of By applying gravitational acceleration, equation 5.13
hysteresis are the ‘ink-bottle’ effect and the ‘contact is identical to equation 2.22, emphasizing that the
angle’ effect. As explained by Ward and Robinson gradient of potential energy for subsurface water is
(2000), the ‘ink bottle’ effect results from the fact that continuous throughout the full depth of the unsatu-
a larger suction is necessary to enable air to enter rated and saturated zones. In studies of the unsatu-
the narrow pore neck, and hence drain the pore, than rated zone it is common to use the ground surface as
is necessary during wetting. The ‘contact angle’ effect the datum level for soil water potential values. As
results from the fact that the contact angle of fluid shown in Table 5.2, gravitational potential declines
interfaces on the soil particles tends to be greater uniformly with depth below the ground surface and
when the interface is advancing during wetting than is negative when referred to a ground surface value
when it is receding during drying, such that a given of zero.
water content tends to be associated with a greater
suction in drying than in wetting.
At the start of the drying process, the soil is tension- 5.4.2 Calculation of drainage and
saturated, a condition analogous to a capillary fringe evaporation losses
above a water table, until the air-entry or bubbling
pressure is reached, at which point the soil begins From the above explanation of soil water potential, it
to drain. For soils that are only partially dried, then follows that water will move from a point where the
wetted, and vice versa, the soil characteristic curves total potential energy is high to one where it is lower.
follow the scanning curves shown in Fig. 5.13. Hence, by plotting a profile of soil water potential it is
From the above explanation of characteristic curves, possible to identify the direction of water movement
it is clear that moisture content, specific moisture in the unsaturated zone. As shown in Fig. 5.14b, there