Journal of Hydrology, 36 (1978) 383--391
383
© Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands
[4]
THE I N F I L T R A T I O N CYLINDER: SOME COMMENTS ON ITS USE
ALAN S. TR I C KER
Department of Geography, University of Dundee, Dundee DD1 4HN (Great Britain)
(Received May 24, 1977; accepted for publication September 26, 1977)
ABSTRACT
Tricker, A.S., 1978. The infiltration cylinder: some comments on its use. J. Hydrol., 36:
383--391.
Values of infiltration capacity obtained from cylinder infiltrometers are always distorted because of the lateral seepage of water. Recommendations are made as to the best
size of cylinder to achieve reasonable accuracy with a small demand for water supply.
Laboratory experiments are described also, from which an equation to correct measured
infiltration capacities for lateral seepage is derived and tested.
INTRODUCTION
Despite the problems associated with the use of cylinder infiltrometers
(see Hills, 1970, pp. 10, 11) they have proved a popular method of infiltration determination because they are cheap to manufacture and easily operated by the individual research worker. The aim of the instrument is to measure
the maximum rate of entry of water into the soil, or the "infiltration capacity"
as defined by Horton (1940). No attempt is made to simulate the beating of
raindrops, and so it must be accepted that it is the measurement of water penetration rather than rainfall infiltration.
In many studies of infiltration using cylinders a high degree of data variability is experienced within the samples selected (Burgy and Luthin, 1956). In
part this is due to disturbance of the soil during installation of the cylinder,
b u t largely it is due to the uncontrolled lateral movement of water beneath
the boundary plate. In any infiltration determination using a cylinder infiltrometer, the measured infiltration capacity has t w o components:
fm -- fc + q
(1)
where f m = measured infiltration capacity; fc = true (vertical) infiltration capacity; and q = exaggeration of infiltration capacity due to lateral seepage
(provided that all other measurement errors are reduced to a minimum).
384
This limitation led Horton (1940) to suggest that cylinder infiltrometers
may not be of use even to assess the relative differences in infiltration capacities. He maintained that if it is assumed that the ratio of true infiltration
capacities is [c~ If%, because of " b o u n d a r y effects" the ratio of measured infiltration capacities will be fc, +q~/f%+q2"However, q~ and q2 may be markedly different depending on the expertise of the operator, occurrence of stones,
and other factors so that the new ratio may bear no relation to fc,/f%.
Attempts have been made to eliminate " b o u n d a r y effects" so that measurements taken more closely resemble the ture vertical infiltration rate. Methods
of improvement have included the use of large cylinders and double cylinder
systems (Parr and Bertrand, 1960). However, the former makes the whole
instrument somewhat cumbersome, and although the latter system has proved
effective under laboratory conditions (Swartzendruber and Olsen, 1961),
under field conditions the validity of the technique is questionable because of
irregularities in the wetted shapes produced under both the central cylinder
and " b u f f e r zone" by soil horizons of differing permeabilities.
The simplest technique for measuring infiltration is the small single cylinder
Any alteration to this system destroys the simplicity and reduces the number
of replications that can be quickly made. Consequently, the aim of this brief
study was firstly to determine the size of cylinder that could be expected to
achieve a level of accuracy comparable to more elaborate measurement
systems and secondly to produce a simple procedure for correcting these
cylinder measurements for the exaggerating lateral flow component.
CYLINDER SIZE
Several writers have indicated the relationship between the size of the
cylinder and the amount of error in infiltration measurement produced by
" b o u n d a r y effects" (Johnson, 1963). Data presented by Aronovici (1955) are
analysed here to assess the smallest diameter cylinder that can be expected to
give reasonable results under field conditions.
Aronovici presents data derived from tests on cylinders ranging from 2.0
to 30.0 cm in diameter. For each cylinder diameter, infiltration rates were
measured over four hours. Fig.1 shows the relationship between infiltration
capacity and cylinder diameter produced from this data. Infiltration rates decrease rapidly for each centimetre increase in cylinder diameter, up to the 10
cm diameter. For the next 5 cm increase in diameter the rate of decrease is
much less. Between 15 and 30 cm diameter the decrease has declined to
approximately 0.03 cm/h per centimetre increase in cylinder diameter.
A regression equation was calculated to express the straight-line relationship between infiltration capacity and the reciprocal of cylinder diameter.
The resulting equation is:
y = 6.62x + 1.12
(2)
where y = infiltration capacity; and x = reciprocal of cylinder diameter (l/d).
385
C"
~-20
E
v
>,
~
meosured JnfLttration capacity
u
g_
~"true
~o
~'o
infittration capacity
3'o
~'o
~o
Cylinder diameter (cm)
Fig.1. Relationship between infiltration capacity and cylinder diamater.
From this equation it is possible to predict the infiltration capacity when the
cylinder diameter is infinite, i.e. l i d = O. At this point the error in the
measured rate due to lateral seepage is negligible. The data presented in Table
I show a comparison between the measured rates of cylinders of different
sizes and this "true" rate.
TABLE I
Error associated with cylinders of different sizes
Cylinder diameter (cm)
5
Measured infiltration capacity
Error (%)
10
2.40
114.2
1.75
65.2
15
1.50
33.9
20
1.45
29.5
30
1.35
20.5
50
1.30
1.12
16.1
A graph of the relationship between percentage error and cylinder diameter
(Fig.2) demonstrates that the error decreases rapidly until the cylinder is 15
cm in diameter, and beyond this point the rate of decrease is much less. A
cylinder of 15 cm diameter could combine, therefore, the design requirements
of reasonable accuracy with a small demand for water supply: an important
consideration when tests are conducted in remote areas (Tricker, 1975). The
use of cylinders of small diameter would lead to large measurement errors that
would be difficult to correct.
THEPROBLEM OF L A T E R A L S E E P A G E
A generalised picture of the advance of wetting fronts beneath a single
cylinder is shown in Fig.3. The shaded area in the diagram shows a crosssection of the column for which the true infiltration capacity would apply.
386
100
ib
2b
3o
/o
slo
Cylinder diameter (cm)
Fig. 2. Relationship between cylinder diameter and error of infiltration measurement.
V~,TER LEVEL
SO!L SURFACE
t
I
~'7/////////1
,
z ......
d ,,//
..
'
WETTING
F RONTS
/ tI
u
'/ \
[
.~1 \ \
', ~",,
,,
\/l
{ I{X
/'b-[
.... J\
/
/
t\I " / / / / / / / / /
I
I
i
b)/~Y SOIL tt 4 T ' c
//FLOw'
L tN ES
Fig. 3. Water flow beneath a single cylinder.
The total area within the wetting fronts shows the exaggerated value given by
the measured infiltration capacity. The shape of the wetted area beneath a
cylinder of given size, would vary in form depending upon various soil parameters, such as permeability and moisture distribution.
Both field and laboratory techniques have been devised to correct for
lateral seepage (Marshall and Stirk, 1950). Most of the field-based methods
tend to be both arduous and site destructive and are therefore unsuitable for
research programmes where recurrent measurements are made at the same
387
site. A graphical correction procedure for 10 cm diameter cylinders based on
a series of laboratory sand bath experiments by Hills (1971) avoids these
problems, although it is time consuming to operate when large data collection
programmes are in progress. All methods so far derived, therefore, show considerable inadequacies in accounting for this variable error in cylinder infiltration measurements. However, a modification of the laboratory-derived
correction procedure of Hills (1971) would appear to offer the best solution
to the problem.
The apparatus constructed for the laboratory infiltration tests represented
a section, 5 cm thick, taken through a cylinder infiltrometer. It consisted of
a wooden box with a perspex front measuring 60 cm X 40 cm. The open top
of the box was 60 cm X 5 cm. Two pieces of metal extending 10 cm down
from the top of the box represented sections of a cylinder wall. These were
bolted to the back of the box, and gasket sealing compound ensured a watertight seal with the perspex. The perspex front was secured around the edges
with angle alloy strips which could be easily unscrewed for emptying soil.
Field conditions could not be reproduced exactly in the laboratory and so
two simplifications were adopted. Firstly, all tests were conducted in soil
moxes of uniform permeability. In the field, horizons of different permeability would influence the wetted shape but numerous permutations of horizons
could not be considered in laboratory tests. Secondly, all soil mixes were airdried prior to use and consequently the influence of antecedent soil mixture
could not be considered. Undoubtedly, some inaccuracies in the data resulted
from these simplifications, but these must be balanced against the inaccuracies
and problems associated with the field techniques.
For each experiment the box was filled with the soil mix to within 5 cm of
the top of the box, so that the cylinder walls penetrated 5 cm into the soil.
Uniform compaction of the soil was achieved by using a square wooden pole,
5 cm X 5 cm in cross-section, to the top of which a sliding weight was attached.
The box was filled in 5 cm depth increments. A wire mesh baffle on the soil
surface within the cylinder prevented disturbance of the soil when water was
poured in. By keeping the water surface level with the top of the box, a 5 cm
head of water could be readily maintained.
The sand, silt and clay used to simulate soils were obtained from quarry
soil heaps and were mixed to give a gradation of nine permeabilities. It was
considered that these nine tests gave a reasonable sample of different permeabilities that might be expected in the field. For each of the tests, a photograph
of the wetted shape was taken after 2, 5, 10, 15, 20, 25, 30, 45, 60, 90,
120 min, or until the wetting front had reached the edges of the box. Photographs were reproduced at the ~Athe size of the original apparatus. The amount
of water added to the cylinder section to maintain the 5 cm head was noted
for each time period.
For each of the photographs the total wetted area and the wetted area beneath the cylinder were measured. These were then integrated into volume
measurements. Making the assumption that the degree of saturation was uni-
388
form t h r o u g h o u t the wetted shape, then the ratio within any wet front
limiting line of volume beneath the cylinder: volume within the wet front
limit is the necessary degree of correction required for each time period in
each experiment. Hence the true infiltration rates were calculated for each
test using the formula:
fc = fm" (Vc/Vt)
(2)
where fc and fm are as in eq.1; Vc wetted volume beneath the cylinder; and
Vt = total wetted volume.
A CORRECTION PROCEDURE
For each time period in each experiment, therefore, it was possible to
calculate the true infiltration rates. For the experiments, pair-wise correlations
were calculated between the true infiltration capacity and both time and the
measured infiltration capacity. These are presented in Table II. (All data were
transformed into log,0 values for the calculations.) These results suggest that
any correction procedure adopted, therefore, must reflect this dual relationship: a procedure based solely on time or measured infiltration capacity would
not be accurate.
TABLE II
Correlations between fc, fm and t
We
fm
t
[c
[m
t
1.00
0.84
1.00
-0.91
-0.62
1.00
A multiple regression analysis was carried out using the available data
taking fc as the dependent variable and fm and t as the independents. The resulting equation is:
Y = 0.46x, - 0.64x2 + 1.08
(3)
where Y = logl0fc (fc in cm/h); x, = logl0fm (fro in cm/h); and x2 = log,ot (t in
h). (Other parameters of the regression are presented in Table III.) Over 95%
of the total variance of the dependent variable is determined by this equation.
All elements of the equation are significant at at least the 0.01 probability
level. This equation may be used to calculate corrected infiltration capacity
values from capacities measured in the field using a 15 cm diameter cylinder.
The procedure could n o t be used for cylinders of any other size.
The remaining consideration was to test the performance of the correction
procedure under field conditions, where the soil possesses horizons of differing
389
T A B L E III
Regression analysis results
Multiple r
C o e f f i c i e n t of d e t e r m i n a t i o n (%)
Regression s u m o f squares
Residual sum of squares
F value
0.98
95.76
11.81
0.52
509.26
(d.f. = 2)
(d.f. = 45)
(significance > 0.01)
Variable:
x~
x:
b coefficient
0.46
-0.64
standard error
0.04
0.04
d.f.= degreesot" freedom.
--
~ --
permeabilities. In order to accomplish this, the same materials were utilised to
simulate the soil as had been used in the original experiments. Consequently,
a simulated soil was constructed in the box consisting of two layers of a medium and fine sand mix 13 cm (top) and 8 cm thick, separated by a I cm thick
layer of silt and clay. The remainder of the base of the profile consisted of
more silt--clay mix to simulate a less permeable B horizon of a soil. The introduction of the less permeable band led to a more flattened shape (Fig.4)
with apparently greater proportions of the applied water contributing to
lateral flow than might have been expected. Fig.5 shows a comparison between the corrected and true infiltration values for the layered and a nonlayered soil. It may be noted that for the layered soil the equation tends to
underestimate for high infiltration capacities at the start of a test and overestimate for the low rates towards the end of a test. For the non-layered soil
prediction is more accurate throughout. Error in estimation would appear to
be rarely more than +- 20%, which compares favourably with other correction
techniques previously devised (Hills, 1971).
medium/fine sand
silIlctay
Fig.4. W e t t e d shapes in (a) layered and (b) n o n - l a y e r e d soil mixes.
390
h"",~...~a)__ [ayert-d soft
I
10
20
30
~2
,
%',
(b) non tayered soft
--
corrected
#
10
20
0
time from start of test (mins)
Fig.5. Corrected, true, and measured infiltration capacities for (a) layered and (b) nonlayered soil mixes.
CONCLUSIONS
Measurements of the infiltration capacities of field soils using cylinder infiltrometers always Lend to exceed the true (vertical) infiltration capacity.
The use of 15 cm diameter cylinders rather than cylinders of a smaller size,
together with the correction procedure indicated here, allows rapid measurement and computation of results. The method described is not claimed to be
more accurate than methods previously advocated but it would appear to be
as accurate, and it is simple to operate.
ACKNOWLEDGEMENT
This work was accomplished while the author held a N.E.R.C. Research
Studentship at the University of Sheffield.
REFERENCES
Aronovici, V.S., 1955. Model study of ring infiltrometer performance under low initial
soil moisture. Proc. Soil Sci. Soc. Am., 19: 1--6.
Burgy, R.H. and Luthin, J.N., 1956. A test of single and double ring infiltrometers. Trans.
Am. Geophys. Union, 37: 189--192.
391
Hills, R.C., 1970. The determination of the infiltration capacity of field soils using the
cylinder infiltrometer. B.G.R.C., Tech. Bull. 3, 24 pp.
Hills, R.C., 1971. Lateral flow under cylinder i n f i l t r o m e t e r s - - a graphical correction
procedure. J. Hydrol., 13: 153--162.
Horton, R.E., 1940. An approach toward the physical interpretation of infiltration capacity. Proc. Soil Sci. Soc. Am., 5: 339--417.
Johnson, A.I., 1963. A field method for the measurement of infiltration. U.S. Geol. Surv.,
Water Supply Pap. 1544-F.
Marshall, T.J. and Stirk, G.B., 1950. The effect of lateral movement of water in soil on
infiltration measurements. Aust. J. Agric. Res., 1: 253--265.
Parr, J.F. and Bertrand, A.R., 1960. Water infiltration into soils. Adv. Agron., 12: 311-363.
Swartzendruber, D. and Olsen, T.C., 1961. Sand model study of buffer effects in the
double ring infiltrometer. Proc. Soil Sci. Soc. Am., 25: 5--8.
Tricker, A.S., 1975. Infiltration characteristics of a small upland catchment. Ph.D. Thesis,
University of Sheffield, Sheffield (unpublished):