Theory of Water Flow through Unsaturated Soils - Unsaturated Soil Mechanics in Engineering Practice - page 328

of flow law, however, does not provide a fundamental basis
for describing water flow since water can also flow from a
region of low water content to a region of high water content
when there are variations in the soils involved, hysteretic
effects, or stress history variations. Consequently, the water
content gradient should not be used as a fundamental driving
potential for the flow of water (Fredlund, 1981b).
A matric suction gradient has sometimes been used as
the driving potential for water flow in an unsaturated soil.
However, the flow of water does not fundamentally and
exclusively depend upon a gradient in matric suction (i.e.,
u a −

1.0E-01

1.0E-02

1.0E-03

1.0E-04

u w , where u a is pore-air pressure and u w is pore-water
pressure). Figure 7.3 demonstrates three hypothetical cases
where the air and water pressure gradients are controlled
across an unsaturated soil element at a constant elevation.
In all cases, the air and water pressures on the left-hand side
are greater than the pressures on the right-hand side.
The matric suction on the left-hand side may be smaller
than on the right-hand side (case 1), equal to the right-hand
side (case 2), or larger than on the right-hand side (case 3).
However, air and water will flow from left to right in
response to the (pressure) head gradient in the individual
phases, regardless of the matric suction gradient. Even in
case 2, where the matric suction gradient is zero, air and
water will still flow as two independent phases. It can be
concluded that water cannot always be assumed to flow

1.0E-05

Drying

Wetting

1.0E-06

0.1 1 10 100

Soil suction (kPa)

Figure 7.1 Shape of drying and wetting permeability functions
for glass beads (after Mualem, 1976b).

100

80

Case 1

60

Air pressure
u a (kPa)

− 25 − 50

Unsaturated
soil

40

Water pressure
u w (kPa)

50 − 100

−

50

25

Matric suction
( u a − u w ) (kPa)

20

Drying
Wetting

Case 2

0 − 50

0 u a

0.1 1 10 100

Unsaturated
soil

Soil suction (kPa)

− 150 − 200

u w

Figure 7.2 SWCCs for glass beads showing drying and wetting
hysteresis (after Mualem, 1976b).

150 150

( u a − u w )

Case 3

200 0

u a

an unsaturated soil provided hydraulic head is shown to be
an acceptable and fundamental description of flow.
Let us first consider some alternatives to using a hydraulic
head gradient to define water flow through an unsaturated
soil. A gradient of (volumetric) water content has sometimes
been used to describe the flow of water through unsaturated
soils. It is assumed that water flows from a point of high
water content to a point of lower water content. This form

Unsaturated
soil

− 100 − 200

u w
( u a − u w ) 300 200

Figure 7.3 Air pressures, water pressures, and matric suction gra-
dients across unsaturated soil specimen.