Geology Reference
In-Depth Information
above the gully head (m
2
)
, S
is the slope (%) of
approach channel above the gully head;
P
is the
summation of rainfall from 24-hour rains equal to
or larger than 12.7 mm for the time period of
interest (mm), and
E
is the clay content (%) of the
eroding soil profile.
Seginer (1966) studied the advancement of
gully headcuts in southern Israel and proposed
the following equation:
A
p
is an antecedent moisture index (mm); and
I
is
a piping index.
These relationships, established in the same
study area during the same period, show that gul-
lies retreat at very different rates, reacting at
minimal perturbation (e.g. piped gully headcut -
Stocking (1981) commented that piping strongly
increases the rate of retreat) or only during intense
storms because the causative factors can be quite
different. Several studies of this type produced
equations similar to those produced by Stocking
(1981). These equations are all of local values
because the role of soil and soil characteristics is
not parameterized. For example, the exponents of
Equation (19.12) vary between 1.02 and 1.88 for
P
, 0.38 and 1.00 for
A
c
, and 0.42 and 1.27 for
H
.
The two gully headcut retreat equations devel-
oped by Stocking (1981) indicate that when soil
dispersion occurs, seepage and piping can signifi-
cantly modify the type of processes and erosion
rates and can even change the dominant factors
involved. At present, for gully development in
dispersive soils no mathematical model is availa-
ble but a series of observations allows one to
understand better gully generation and expansion.
Dispersivity characteristics are well known to
affect dramatically the erodibility of the material
(Fitzpatrick
et al
., 1992). When dispersivity is
coupled with seepage, then subsurface erosion,
pipes and gullies are certain to occur. Faulkner
et al
. (2004) observed that variations in sodium
absorption ratio (
SAR
) in the Mocatán catchment
(Almeria, Spain) follow hydraulic gradients, with
peaks corresponding to the most incised part of the
studied gully, locally increasing the soil erodibil-
ity. They also observed that
SAR
increases with
clay content. When clay swells, rain infiltration is
reduced and even completely impeded, forcing
water to move laterally instead of vertically in the
soil profile, hence enhancing the development of
pipes running subparallel to the soil surface. This
process can also prevent pipes from deepening and
widening. In some cases pipes are confined under
a crust rich in calcium, which replaces sodium
during leaching. Most of the rills develop from
these pipes after pipe roof collapse. The depth-to-
width ratio of linear incisions in dispersive
0.50
RaA
=
(19.10)
where
R
is the mean medium-term (15 years)
annual gully head retreat rate (m y
−1
)
, A
is the area
of the drainage basin (km
2
), and
a
is the coeffi-
cient ranging between 2.1 and 6.0, depending on
the studied catchment.
The US Soil Conservation Service (1966) ana-
lysed headward advancement for 210 gullies in
six widely scattered land resource areas east of
the Rocky Mountains, and proposed the follow-
ing relationship:
0.46
0.20
R
=
0.36
A
P
(19.11)
where
R
is the mean annual gully head advance
(m y
−1
)
, A
is the drainage area above gully
head (ha); and
P
is the annual precipitation
(mm) on days with precipitation in excess of
12.7 mm day.
Stocking (1980, 1981) examined the gully
headcut retreat rate of 66 valley-bottom gullies in
central Zimbabwe in an area of sodium-rich, fine,
sandy soils over different time spans, producing a
series of multiple-factor regression models. Here
two equations are reported, the first describing
waterfall-head gullies and the second piped-head
gullies:
R
=
0.00687
P
1.34
A H
0.52
(19.12)
c
0.57
1.72
R
=
0.00793
A
I
(19.13)
p
p
where
R
and
R
p
are the soil volume (m
3
) loss at
headcut per rain event
, P
is the event rain depth
(mm)
, A
c
is the catchment area at headcut (km
2
)
,
H
is the headcut height (m) of the waterfall head
,
