Geoscience Reference
In-Depth Information
•
K
s
is the saturated hydraulic conductivity;
•
o
is called the “bubbling” potential;
•
is called the “pore size” index.
Note that both
o
and
are best viewed as fitting rather than physical parameters and may
take different numerical values in the Brooks-Corey and van Genuchten equations when both
functions are fitted to the same set of data.
The two functions, calculated with identical values of the five parameters, are plotted in
Figure B5.4.1. The smoothness of the van Genuchten functions in the area close to saturation
is numerically advantageous when used in modelling (and, in most cases, is probably a more
realistic representation of the soil wetting and drying characteristics). A variant on the Brooks-
Corey relationships has been suggested by Clapp and Hornberger (1978), using a parabolic
function to smooth the sharp break at the bubbling potential,
o
, while Mohanty
et al.
(1997)
have suggested piecewise functions that can take account of a rapid increase in hydraulic
conductivity due to preferential flows close to saturation.
B5.4.4 Similar Media Scaling in Representing the Soil Moisture Characteristics Functions
An early attempt to deal with the heterogeneity of soil properties that has proven to be quite
robust is the local scale scaling theory of Miller and Miller (1956). They derived relationships
for the soil characteristic of different soils that were geometrically similar in terms of the shape
and packing of the particles, differing only in terms of a characteristic length scale (Figure
B5.4.2). In this case, the water content of the soil,
, can be related to the capillary potential,
,as
1
˛
=
(B5.4.5)
Figure B5.4.2
Scaling of two similar media with different length scales ˛.
where
is surface tension,
is the specific weight of water,
˛
is the characteristic length and
the function
1
() is the same for all soils scaled in this way.
A similar relationship can be derived for the hydraulic conductivity of similar soils as
˛
2
2
(
)
K
=
(B5.4.6)
where
is the dynamic viscosity of water and
2
is again constant for soils that are geometri-
cally similar.
