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Agricultural Water Management 68 (2004) 151–175
Field research on the performance of variousdrainage materials in Lithuania
A. Rimidis a, W. Dierickx b,∗
a Water Management Institute of the Lithuanian University of Agriculture, Parko 6,
LT-5048 Vilainiai, K edainiai, Lithuaniab Department of Mechanisation, Labour, Buildings, Animal Welfare and Environmental Protection, Agricultural
Research Centre, B. Van Gansberghelaan 115, B-9820 Merelbeke, Belgium
Accepted 10 March 2004
Abstract
Field evaluation of the performance of a drainage system or of various drainage materials is a
long-lasting research, very often with disappointing results. These disappointing results stem either
from a too wide a spread of the field data, or one or more necessary parameters which were notmeasured, or an insufficient knowledge of the flow occurrence in the vicinity of the drain resulting
in a wrong interpretation and evaluation of the research findings. Yet, a correct evaluation of the
performance of a drainage system is of primary importance to ascertain the real value of a drainage
system or to compare various drainage materials. As a result of the wide spread of field data within a
measuring season, a large amount of data from several seasons is required to obtain reliable results.
From discharge and total head loss measurements a second-degree polynomial results which only
permits a determination of whether the design criteria are met. The similarity with Hooghoudt’s
equation allows the determination of soil hydraulic conductivity and the equivalent depth of the
impervious layer. With this data the drain spacing can be checked. Too wide a spacing can be the cause
of malfunctioning of a drainage system, but the drainage materials can also affect its performance.
To evaluate or compare drainage materials it is necessary to measure the so-called approach-flowhead loss in the vicinity of the drain. The relationship between discharge and approach-flow head
loss should theoretically be linear and the regression coefficient gives the approach-flow resistance.
However, the relationship depends to a large extent on the approach-flow occurrence in the vicinity of
the drain. For non-linear relationships, the approach-flow resistance can be estimated from the slope
of the tangent line, which tends to a constant value at greater discharges for flow patterns covering
the whole drain circumference. The approach-flow resistance depends on the hydraulic conductivity
of the soil and does not permit a direct comparison of various drainage materials. Therefore, the
approach-flow constant or the dimensionless approach-flow resistance is calculated. This parameter
∗ Corresponding author. Tel.:+32-9-272-27-63; fax: +32-9-272-28-01.
E-mail addresses: [email protected], [email protected], [email protected]
(W. Dierickx).
0378-3774/$ – see front matter © 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.agwat.2004.03.004
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152 A. Rimidis, W. Dierickx / Agricultural Water Management 68 (2004) 151–175
is related to the material itself and to the installation conditions reflected in the hydraulic conductivity
of the trench backfill. Consequently the comparison of the various drainage materials includes the
trench backfill. The approach-flow head loss fraction is that part of the total head loss which is
dissipated by the approach-flow. The relationship between approach-flow head loss and total headloss should theoretically be and is, indeed, linear so that the slope of the regression line gives the
approach-flow head loss fraction. This parameter combines the influence of drainage material and
flow pattern so that real flow situations in the vicinity of the drain, which are not necessarily the same
for all materials, can be compared.
© 2004 Elsevier B.V. All rights reserved.
Keywords: Drainage performance; Drainage materials; Drain discharge; Total head loss; Approach-flow head
loss; Approach-flow resistance; Approach-flow head loss fraction
1. Introduction
Subsurface drainage is one of the most important measures to maintain or enhance the
productivity of agricultural lands. In some areas of the temperate zone, drainage systems
continue to be an essential tool of groundwater control. To achieve that aim, drainage
systems should be properly designed and adequately installed using appropriate materials
(Stuyt et al., 2000). In Lithuania, about 3.4 million of the total agricultural area of 3.9 million
ha required some kind of drainage to improve agricultural productivity and, therefore, quite
a large area of agricultural land was already drained. To remove the excess water 62,722 km
of open ditches were excavated while the total length of subsurface drainage measures1590×103 km composed of 267×103 km of collectors and 1320×103 km of laterals. The
laterals have a diameter of 50 (clay drain tiles) and 63 mm (corrugated polyethylene pipes),
and the collector diameter ranges from 7.5 up to 160 cm. The larger-diameter-pipes are in fact
collectors which replace open ditches. The size of subsurface drainage systems varies from
a few up to more than 100 ha. Currently, the total area of drained lands covers 2980×103 ha,
2580×103 ha of which are provided with a subsurface drainage system. (Anonymous, 2002).
InLithuania,drainageworksstartedasearlyas1910,butthemainpartwasdoneduringthe
period 1956–1990. From 1991 to date, the construction of new drainage systems decreased
significantly. As the financial support of the state is limited (about 45 million Lithuanian
Litas or 13.08 million Euro), the available financial means go to ditch maintenance, repairand reconstruction of subsurface drainage systems (Mork unas, 2002; Smilgevicius, 2003).
Therefore, it is, more than ever before, important to know how to evaluate the real situation
of drained land and to follow a new course to monitor and maintain drainage systems.
At present, nobody can predict the functionality of drainage systems and their technical
state, even for the most widespread loamy soils. During the Soviet period the lifetime of
land reclamation structures was not evaluated. There was only episodic data with different
evaluation criteria. In the future, when land reform is over and drainage systems are passed
to the landowners, the problem of the functionality of the drainage systems will inevitably
be raised. Therefore, a unified way to evaluate drainage performance is necessary. In West
Europe where ownership is rather a long tradition, the monitoring of drainage performanceis put into practice immediately after installation (Dieleman and Trafford, 1984; Cavelaars
et al., 1994).
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A. Rimidis, W. Dierickx / Agricultural Water Management 68 (2004) 151–175 153
Rimidis and Dierickx (2003) carried out some research work on the evaluation of the
performance of drainage systems at an experimental site in the central part of Lithuania
during the period 1994–1998. This site consisted of seven plots with various combinations of
drainage materials. To evaluate drainage performances, discharges and water heads on top of and midway between drains were measured. These observations allowed the determination
of whether design criteria were met or not, but they were largely inadequate to detect
the cause of drain malfunctioning and to compare the performance of the various drainage
materials. To solve these problems information on the approach-flow head loss in the vicinity
of drains is required. Therefore, a new experimental set-up was planned and installed, and
measurements were carried out during the period 1999–2003. On the basis of these results, a
monitoring programme on the performance of drainage systems can be drawn up to inform
future landowners on the real value of their drainage systems and on the measures to take
for maintaining or improving their functionality.
2. Experimental site
With a view to land reclamation, Lithuania is subdivided into three zones (Fig. 1): the west
(A), the centre (B) and the east (C). The experimental site is located in the central part (B) of
the country, at Pikeliai, a village in the Kedainiai district. This zone has a more continental
climate than the western zone (A) with an average annual rainfall of 568 mm ( Klimienie
and Buitkuviene, 1991) and an average annual temperature of 6.1 ◦C (Aloseviciene, 1992).
Fig. 1. Map of Lithuania with the three reclamation zones: the west (A), the centre (B) and the east (C).
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154 A. Rimidis, W. Dierickx / Agricultural Water Management 68 (2004) 151–175
Table 1
Rainfall (mm) and temperature (◦C) recorded at Dotnuva in the vicinity of the experimental site with field obser-
vations lasting the whole month (dark shading) and a fortnight only (light shading)
The monthly and yearly rainfall and temperature during the years of measurement as well
as the 50-year average monthly and yearly rainfall and temperature, measured at Dotnuvain the immediate vicinity of the Pikeliai village, are given in Table 1 which also indicates
the periods of measurement. The observations show that rainfall is somewhat higher during
the summer than during the winter months.
The relief of the central zone is a slight to moderate rolling plain, diversified by river and
stream valleys, where soggy gley soils of light to medium moraine sandy loam predominate
(Zelionka, 1967). These are the better soils of Lithuania which result in the largest increase
in productivity after being drained.
The site was first drained in 1959–1960. In 1994 the northern part of the site was re-
constructed because, in the early nineties, it was noticed that groundwater table response
was very slow and that the high groundwater table caused crop damage. With a view tothe construction of an experimental site, the old drainage system was rendered inoperative.
Instead of one large drainage system, covering the whole area of 9.07 ha, the total area was
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A. Rimidis, W. Dierickx / Agricultural Water Management 68 (2004) 151–175 155
Fig. 2. Lay-out of the experimental plots 2–6 and 10.
subdivided into smaller experimental systems which discharge through collector drains into
the open drainage ditch. The new drain lines were installed with a multibucket excavator.
Organic as well as synthetic envelopes were used to protect the drain pipes against sil-tation. In the southern part of the experimental site, an old drainage system with a total
area of 5.5 ha was still operating without any repair or reconstruction work. Plots 2–6 of
the northern part and plot 10 of the southern part (Fig. 2) were involved in this research.
The incorporation of plot 10 offered the possibility to compare the performance of an old
drainage system with the performance of various, more modern materials used at plots 2–6.
In these plots laterals consisted of both 33 cm long clay drain pipes with an inner diameter
of 50 mm and corrugated polyethylene pipes with an outside diameter of 63 mm protected
against soil particle invasion by various envelope materials. The laterals of plot 10 were
installed with a ditch plough and consisted of clay drain pipes with an inner diameter of
40 mm. Collector drains of all plots were clay drain pipes with diameters ranging from
75 to 200 mm depending on their length. Drains were installed at a depth of 0.90–1.10 m
and their spacing, which was based on the physical properties of the soil profile according
to Janert (1961) and slightly adapted to the Lithuanian circumstances (Ceicys, 1965), was
22 m at plots 2–6 while it was 20 m at plot 10. According to the classification system of
FAO (1990), the soil of the experimental site mainly consists of sandy to sandy clay loam
as can be seen in Table 2 which gives the soil texture from surface to drain depth for each
plot. The following material combinations were investigated:
• Clay drain pipes covered with a layer of 7–10 cm loose corn straw on top and along both
sides but without protecting the pipes from underneath (plot 2).• Corrugated polyethylene pipes pre-wrapped with corn straw with a thickness of 2–3 cm
and an average density of 0.1–0.2 g/cm3 (Rimidis and Kozhushko, 1995) (plot 3).
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156 A. Rimidis, W. Dierickx / Agricultural Water Management 68 (2004) 151–175
Table 2
Soil texture of the experimental plots at various depths
Experimental
plot
Depth (cm) Clay fraction
(< 2m)
Silt fraction
(2–50m)
Sand fraction
(50–2000m)
Textural class
2 0–30 24.2 24.4 51.4 Sandy clay loam
30–50 18.3 25.4 56.3 Sandy loam
50–85 25.5 15.1 59.4 Sandy clay loam
85–110 13.9 16.1 70.0 Sandy loam
3 0–30 12.7 20.0 67.3 Sandy loam
30–50 24.4 31.8 43.8 Loam
50–70 12.9 15.7 71.5 Sandy loam
70–100 12.4 15.1 72.5 Sandy loam
4 0–30 13.9 23.5 62.6 Sandy loam
30–60 26.4 23.8 49.8 Sandy clay loam60–80 8.9 19.7 71.4 Sandy loam
80–130 10.2 17.8 72.0 Sandy loam
5 0–30 13.2 24.6 62.2 Sandy loam
30–50 28.1 15.8 56.1 Sandy clay loam
50–60 9.7 17.3 73.0 Sandy loam
100–135 11.7 17.2 71.1 Sandy loam
6 0–30 13.6 17.8 68.6 Sandy loam
30–70 15.9 18.0 66.1 Sandy loam
70–90 19.2 13.3 67.5 Sandy loam
90–130 15.2 16.6 68.2 Sandy loam
10 0–30 13.5 26.9 59.6 Sandy loam
30–50 13.2 23.7 63.1 Sandy loam
50–70 9.2 22.3 68.5 Sandy loam
100–120 3.9 10.4 85.7 Loamy sand
• Corrugated polyethylene pipes pre-wrapped with a sheet of locally made non-woven
synthetic fibre material, called Melita (plot 4).
• Clay drain pipes covered with a layer of 7–10 cm loose bulky flax boon on top and along
both sides but without protecting the pipes from underneath (plot 5).
• Clay drain pipes provided with a glass fibre sheet underneath and on top during installationof the pipes (plot 6).
• Clay drain pipes with an inner diameter of 40 mm and without any envelope material,
installed in 1960 (plot 10).
3. Experimental set-up
Measurements of drain discharge and hydraulic head or groundwater table midway be-
tween drains suffice to evaluate the performance of a drainage system. However, these
measurements are not sufficient to detect the cause in case of malfunctioning or to find dif-ferences between various materials (Rimidis and Dierickx, 2003). More information on the
possible cause of malfunctioning, or on differences between various materials, requires hy-
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A. Rimidis, W. Dierickx / Agricultural Water Management 68 (2004) 151–175 157
L/2 L/2 L/2 L/2
1 2 3 4 5 6 7
0.40 m 0.40 m
Fig. 3. Scheme of the row of piezometers consisting of two piezometers on top of the drains, two piezometers at
a distance of 0.40 m from the drains and three piezometers midway between drains.
draulic head measurements close to the drains, just outside the trench backfill. Furthermore,
hydraulic head measurements on top of the drain provide information on water standing
above the drain. Additional measurements of the hydraulic head in the drain are required to
find out whether standing water above the drain is dueto backpressure in the drain or entrance
resistance. In many cases, the hydraulic head in the drain is not measured and the drain is
considered as an equipotential with the head equal to the top of the drain. This assumption is
justified as long as the hydraulic head above the drain is zero or negligibly small which was
the case for the observations at the experimental site. Therefore, to evaluate the performancesof various material combinations, measurements were made of hydraulic heads midway
between drains, at a distance of 0.40 m from the drain and above the drain in addition to dis-
charge measurements. To measure these hydraulic heads, seven piezometers were installed
in one row in each of the experimental plots (Fig. 3). The piezometers were made of 1.50 m
long smooth polyethylene pipes with a diameter of 50 mm. The bottom part of the pipe
was perforated over a length of 30 cm with 5 mm holes. This perforated part was wrapped
with two layers of the locally made non-woven fabric “Melita” to prevent soil invasion. The
piezometer tubes were inserted in auger holes. At the surface, the soil around the piezometer
tubes was compacted to a depth of 0.40 m to avoid direct inflow of surface water along the
pipe wall. Water levels in the piezometer tubes were measured with an electric gauge.Each collector of the various plots discharged in a manhole where volumetric discharge
measurements with a graduated receptacle and stopwatch were carried out. Since the dis-
charge of the individual experimental drains was not measured separately, the average
discharge per unit surface area, or the average drainage coefficient of each plot, was calcu-
lated for each discharge measurement. The total discharge of the experimental drain results
from the average drainage coefficient, drain spacing and total drain length.
4. Data collection and processing
From 1999 to 2003 measurements of discharge and hydraulic heads were carried out
every 3–4 days, depending on rainfall amounts, in the autumn, during snowless winter
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158 A. Rimidis, W. Dierickx / Agricultural Water Management 68 (2004) 151–175
periods and in the spring. Table 1 gives the months in which measurements were done.
They were done during either the whole month or a fortnight (first fortnight in December
2001 and 2002; second fortnight in March 2003).
For each experimental plot and every measurement, the collected data at similar locationswas averaged so that only one value of head midway between drains, one value of head
at a distance of 0.40 m from the drain and one value of head on the drain corresponded
with one discharge measurement. As no piezometers were installed to measure water heads
inside the drain pipes, it could not be stated whether the drains were flowing under pressure
or not. However, the water heads in the piezometers on top of the drain, which may result
from either backpressure in the drain or entrance resistance, were zero to negligibly small
and, therefore, it may readily be accepted that the drains were not flowing under pressure.
Considering drain midpoint as reference level and assuming the drain just flowing full
without backpressure, the drain circumference can be considered as an equipotential with
the head equal to the radius of the drain pipe. Consequently, the total head loss ht (m) of
flow towards a drain is given by
ht = hm − ro (1)
with hm (m) the head in the piezometer midway between drains, or the height of the ground-
water table midway between drains above the reference level and r o (m) the outside drain
radius.
The approach-flow head loss, hap (m), or the head loss in the vicinity of the drainage
system due to drain pipe, envelope material and surrounding soil results from:
hap = hv − ro (2)
with hv (m) the head in the piezometer 0.40 m from drain midpoint. From the approach-flow
head loss, the approach-flow resistance, W ap (day per m), and the approach-flow constant,
αap, can be calculated:
W ap =hap
qL=
hap
q1(3)
and
αap = W apK (4)
with q (m per day) the specific discharge, q1 (m2 per day) the discharge per unit drain
length, L (m) the drain spacing, and K (m per day) the hydraulic conductivity of the soil.
Theoretically, αap only depends on the materials used if the soil and trench backfill have the
same hydraulic conductivity. If not, αap also includes the positive or negative effect of the
trench backfill. The approach-flow head loss as a fraction of the total head loss is given by
F ap =hap
ht(5)
with F ap the approach-flow head loss fraction.With this data the performance of a drainage system can be evaluated, the functioning of
various envelopes compared, and in case of drainage malfunctioning the cause ascertained.
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From the relationship between ht and q the performance of a drainage system can be
evaluated. To draft this relationship the same procedure used by Rimidis and Dierickx
(2003) was followed. A second-degree polynomial of the form
q = Ah2t + Bht (6)
gave the best fitted curve through the data points and is, moreover, similar to the well-known
equation of Hooghoudt (1940):
q =4Kah2
t
L2+
8Kbdht
L2(7)
with K a and K b (m per day) the hydraulic conductivity, respectively above and below drain
level, and d (m) Hooghoudt’s equivalent depth.
The best fitted curve was drawn through the set of points and forced through the origin
because it may readily be assumed that the discharge equals zero for a head equal to zero.
A small positive or negative intercept at ht = 0 could imply a small calibration error of the
piezometer midway between drains to the reference level and/or inaccuracies inherent to the
experimental work. Observation points beyond the 95% confidence limits of the individual
values were considered as erratic and a new regression line was calculated without these
observations.
The approach-flow resistance as a result of the head loss of drain pipe, envelope, trench
backfill and surrounding soil determines the functioning of the drainage material in the
immediate surrounding of the drain pipe. The approach-flow resistance, W ap, can be derivedfrom
hap = W apq1 + b (8)
which gives the relationship between the approach-flow head loss, hap, and the discharge
per unit drain length q1. A small positive or negative value of the intercept b may be
attributed to small calibration errors of the piezometers to the reference level and/or to
inaccuracies typical of measurements. In principle W ap is constant but many factors affect
it such as: (a) the flow pattern around the drain which may not be fully radial; (b) the water
entry through a section of the drain circumference only; and (c) the hydraulic conductivity
of the surrounding soil among others (Dierickx, 1980; Stuyt et al., 2000). Plotting the
approach-flow resistance against the total head loss shows indeed a linear decrease in the
approach-flow resistance with increasing total head loss and confirms that the approach-flow
resistance is a parameter which depends on the flow pattern and eventual variations in soil
properties. In spite of the small coefficient of determination, a reliability test proves the
existence of a linear relationship with 95% confidence.
The approach-flow head loss fraction, F ap, is given by the regression coefficient of the
linear relationship between ht and hap according to
hap = F apht + c (9)
As for the other observations, small positive or negative values of the intercept c are typical
of experimental work.
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160 A. Rimidis, W. Dierickx / Agricultural Water Management 68 (2004) 151–175
5. Research results
5.1. Performance of the drainage system
The q–ht relationship determines the performance of a drainage system. Rimidis and
Dierickx (2003) already determined this relationship for a number of plots, including plots
2–6, during the seasons 1994/1995 to 1997/1998. As total head loss and discharge measure-
ments were continued from 1999/2000 to 2002/2003 for plots 2–6, the q–ht relationships
of the latter measurement period could be compared with the available relationships of
the former period. The results of plots 2–6 for each of the four seasons of the measuring
period 1994/1995 to 1997/1998 are shown in Fig. 4, and the coefficients A and B of the q–ht
second degree polynomials and their respective coefficient of determination r 2 are given in
Table 3. The table also contains these parameters for the same plots 2–6 and plot 10 for the
measuring period 1999/2000 to 2002/2003 while Fig. 5 depicts the results.
As no approach-flow head loss measurements were carried out during the measuring
period 1994/1995 to 1997/1998, Rimidis and Dierickx (2003), for want of anything better,
attempted to explain the performance of the drainage materials by the evolution of the
yearly relationship. However, considering the spread of the measurements of the total head
loss with discharge within 1 year and the difference in drainage performance between the
four measuring seasons of the various plots of both the previous and current measuring
period (Figs. 4 and 5), a single overall q–ht relationship for the measurements of the 4
years of both measuring periods can be calculated. Thus combining the measurements of
a whole period of 4 years, a single and more reliable relationship between total head lossand discharge results for each plot over the whole measuring period. Fig. 6 shows the q–ht
relationship of each plot for the whole measuring periods 1994/1995 to 1997/1998 (Fig. 6a)
and 1999/2000 to 2002/2003 (Fig. 6b) while Table 4 gives the coefficients A and B of the
regression equations and their respective coefficient of determination r 2.
Differences in the q–ht relationships of the various plots between both measuring periods
are rather limited and, therefore, the measurements of both periods were combined to a
single relationship for each plot. The spread of the data points of the various plots (Fig. 7)
clearly illustrates that this way of processing was justified and so did the regression equations
which coefficients A and B and the coefficient of determination r 2 are also given in Table 4.
From Eqs. (6) and (7) it follows that
A =4Ka
L2(10)
and
B =8Kbd
L2(11)
The q–ht relationship will be quadratic for drains on the impervious layer since d = 0 and
consequently B = 0. A linear relationship emerges for deep soils (soils with the impervious
layer at great depth) since the contribution to the flow of the zone above drain level, given by
the first term Ah2t of Eq. (6), becomes insignificant compared to the zone below drain level,represented by the second term Bht. The stronger the curvature of the q–ht relation, the
larger is the contribution of the layer above the drain. From the curvature of the regression
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Table 3Coefficients A and B of the regression equation q = Ah2
t + Bht with the coefficient of determination r 2 of the various plot
measuring seasons of both the measuring period 1994/1995 to 1997/1998 and 1999/2000 to 2002/2003
Measuring period 1994/95–1997/98
Plot 1994/95 1995/96 1996/97
A
(×10−3 m−1
per day)
B
(×10−4 per
day)
r 2 A
(×10−3 m−1
per day)
B
(×10−4 per
day)
r 2 A
(×10−3 m−1
per day)
B
(×10−4 per
day)
2 2.71 1.05 0.872 1.80 3.12 0.878 2.59 0.99
3 3.52 1.64 0.878 3.63 −1.40 0.975 2.51 6.45
4 2.95 11.3 0.947 0.39 20.5 0.701 0.47 26.5
5 1.88 0.701 0.776 2.87 −1.31 0.824 3.07 −2.68
6 1.76 0.982 0.958 0.56 8.08 0.838 1.36 3.81
Measuring period 1999/2000 to 2002/2003
1999/2000 2000/01 2001/02
2 2.86 0.947 0.785 3.09 0.192 0.882 3.51 0.032
3 2.73 −0.788 0.811 3.38 1.16 0.918 2.08 0.989
4 2.48 10.4 0.907 2.24 15.6 0.899 1.72 13.9
5 3.52 −9.12 0.879 1.64 −0.755 0.836 3.01 −5.09
6 1.72 7.85 0.905 1.24 7.49 0.821 2.00 1.64
10 3.07 33.2 0.967 1.97 19.4 0.783 4.01 31.0
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162 A. Rimidis, W. Dierickx / Agricultural Water Management 68 (2004) 151–175
Fig. 4. Relationship between the total head loss ht and the discharge per unit surface area q of the plots 2–6 for
the individual seasons of the measuring period 1994/1995 to 1997/1998 (after Rimidis and Dierickx, 2003).
lines (Fig. 7), it can readily be accepted that the water mainly comes from the soil layer
above drain level, and that the soil layer below drain level contributes little to the discharge
of the drains. Considering the obtained regression equations (Tables 3 and 4), it is obvious
that equations with a negative second term are not in agreement with Hooghoudt’s equation.
They may be the result of a high approach-flow resistance since one solution of these second
degree polynomials gives a positive head for q = 0, while the second solution, ht = 0 forq = 0, is in fact imposed by forcing the regression line through the origin. Another possible
explanation for this anomaly is a small error in reference level. Too deep a piezometer
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Fig. 5. Relationship between the total head loss ht and the discharge per unit surface area q of the plots 2–6 and
plot 10 for the individual seasons of the measuring period 1999/2000 to 2002/2003.
compared to drain midpoint also gives a positive head for q = 0. The main cause, however,
may be the averaging of the data at similar places to reduce the amount of data and the
rather wide spread of the data points. From Tables 3 and 4 it is obvious that the number
of negative second terms decreases when the amount of data by combining seasons and
periods increases and so does the value. This indicates that a large number of observations
is required to obtain reliable relationships between discharge and total head loss.
From the second degree polynomialq–ht relationship and Eqs.(10)and(11), the hydraulic
conductivity K and the equivalent depth d of the impervious layer can be calculated, provided
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164 A. Rimidis, W. Dierickx / Agricultural Water Management 68 (2004) 151–175
Fig. 6. Relationship between the total head loss ht and the discharge per unit surface area q of each plot for the
whole measuring period 1994/1995 to 1997/1998 (a) and 1999/2000 to 2002/2003 (b).
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Table 4
Coefficients A and B of the regression equation q = Ah2t + Bht with the coefficient of determination r 2 of each plot for both the
and 1999/2000 to 2002/2003 and for all measurements together (period 1994/1995 to 2002/2003)
Plot Period 1994/1995 to 1997/1998 Period 1999/2000 to 2002/2003 Perio
A (×10−3 m−1
per day)
B (×10−4
per day)
r 2 A (×10−3 m−1
per day)
B (×10−4
per day)
r 2 A (×
per d
2 2.69 −0.422 0.846 3.31 −0.339 0.873 2.75
3 3.39 0.906 0.868 2.47 2.96 0.852 2.82
4 3.49 10.6 0.913 1.66 15.4 0.857 2.28
5 1.78 1.54 0.819 2.94 −5.58 0.878 2.11
6 1.62 2.23 0.920 1.68 5.18 0.824 1.69
10 – – – 4.66 18.3 0.866 4.66
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166 A. Rimidis, W. Dierickx / Agricultural Water Management 68 (2004) 151–175
Fig. 7. Relationship between the total head loss ht and the discharge per unit drain surface area q of each plot for
both measuring periods 1994/1995 to 1997/1998 and 1999/2000 to 2002/2003 together.
that Ka = Kb which may readily be accepted, considering the textural classes at successive
depths (Table 2). When done for each year, the calculations may give strongly differing
results for the same plot (Rimidis and Dierickx, 2003). Therefore, it is better to consider
the q–ht relationship for each measuring period which only gives one specific value of
K and d for each plot for the considered measuring period. The results of both measuring
periods 1994/1995 to 1997/1998 and 1999/2000 to 2002/2003, given in Table 5, are far fromidentical in spite of the fact that each measuring period contained the measurements of four
seasons. Yet, similar trends can be found with regard to the magnitude of the hydraulic
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A. Rimidis, W. Dierickx / Agricultural Water Management 68 (2004) 151–175 167
Table 5
Hydraulic conductivity K (m per day) and equivalent depth d (m) of the impervious layer resulting from the
coefficients A and B of the regression equations for the measuring periods 1994/1995 to 1997/1998 and 1999/2000
to 2002/2003 and for both measuring periods together (period 1994/1995 to 2002/2003)
Plot Period 1994/1995 to
1997/1998
Period 1999/2000 to
2002/2003
Period 1994/1995 to
2002/2003
K (m per day) d (m) K (m per day) d (m) K (m per day) d (m)
2 0.33 −0.01 0.40 −0.01 0.33 0.02
3 0.41 0.01 0.30 0.06 0.34 0.04
4 0.42 0.15 0.20 0.46 0.28 0.32
5 0.22 0.04 0.36 −0.09 0.26 −0.01
6 0.20 0.07 0.20 0.15 0.20 0.10
10 – – 0.47 0.20 0.47 0.20
conductivity and the equivalent depth of the impervious layer. Only one single value of K
and d is obtained for each plot when both measuring periods are combined. These values,
also given in Table 5, are more reliable and more suitable for further analysis. The negative
equivalent depths result from the negative second term of the second degree polynomial
equations for which a small error in reference level or more likely the averaging of data
may be responsible. In every case, they indicate that the impervious layer is at or near to
drain depth.
5.2. Approach-flow resistance, W ap
According to Eq. (8) a linear relationship between discharge q1 and approach-flow head
loss hap should exist, and the slope of the line, or the coefficient of regression, is W ap. This
means that, in principle, W ap should be a constant. The experimental paired data q1–hap of
the whole measuring period 1999/2000 to 2002/2003 for each plot is given in Fig. 8 and
the best fitted relationship was determined, based on the coefficient of determination r 2. A
linear regression was only obtained for plots 4 and 6 while a power function better fits the
experimental data of plots 3 and 10 and a logarithmic function better fits data of plots 2
and 5. The best fitted equation for each plot and its coefficient of determination is given in
Table 6.
Table 6
Equations giving the best fitted relationship q1–hap and ht–hap for each plot and their coefficient of determination
r 2
Plot q1–hap r 2 ht–hap r 2
2 hap = 0.066 ln q1 + 0.416 0.798 hap = 0.272 ht 0.828
3 hap = 2.248q0.6731 0.701 hap = 0.311 ht 0.755
4 hap = 3.079q1 + 0.046 0.651 hap = 0.251 ht 0.780
5 hap = 0.078 ln q1 + 0.558 0.878 hap = 0.355 ht 0.8926 hap = 6.373q1 + 0.105 0.709 hap = 0.460 ht 0.873
10 hap = 1.277q0.5721 0.817 hap = 0.415 ht 0.845
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168 A. Rimidis, W. Dierickx / Agricultural Water Management 68 (2004) 151–175
Fig. 8. Relationship between the discharge per unit drain length q1 and the approach-flow head loss hap over the
whole measuring period 1999/2000 to 2002/2003, for each experimental plot.
W ap is constant and minimum for fully radial approach-flow conditions or approach-flow
conditions which cover the whole drain circumference and increases with increasing devi-
ation from that (Dierickx, 1980; Stuyt et al., 2000). The deviating approach-flow decreases
with increasing discharge and W ap tends to the constant minimum value at higher dis-
charges. W ap can be estimated by determining the slope of the tangent line to the curve at
the maximum measured discharge being 0.08 m2 per day for plot 2, 0.07 m2 per day for plot
3, 0.075 m2 per day for plot 5 and 0.055 m2 per day for plot 10. The slope of the tangent
line results from the first derivative dhap /dq1. For the logarithmic equation
hap = a ln q1 + b (12)
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A. Rimidis, W. Dierickx / Agricultural Water Management 68 (2004) 151–175 169
Table 7
Approach-flow resistances W ap (day per m), approach-flow constant αap and approach-flow head loss fraction F ap
for the various drainage materials
Plot W ap (day per m) αap F ap
2 0.83 0.27 0.272
3 3.61 1.23 0.311
4 3.08 0.86 0.251
5 1.04 0.27 0.355
6 6.37 1.27 0.460
10 2.53 1.19 0.415
W ap is given by
W ap =dhap
dq1=
a
q1(13)
and for the power equation
hap = aqb1 (14)
W ap is given by
W ap =dhap
dq1= abqb−1
1 (15)
It is evident that W ap for the linear equation
hap = aq1 + b (16)
is given by
W ap =dhap
dq1= a (17)
W ap obtained according to either Eqs. (13), (15) or (17) is given in Table 7. The dimension-
less approach-flow constant αap, calculated by applying Eq. (4) using the K -values of the
combined measuring period 1994/1995 to 2002/2003, given in Table 5, is also presented inTable 7.
5.3. Approach-flow head loss fraction, F ap
F ap, given by Eq. (9), results from the regression coefficient, or slope of the linear rela-
tionship between ht and hap. From Fig. 9 it can be seen that the relationship between ht and
hap for the whole measuring period is clearly linear for all plots. It may be accepted that
hap = 0 when ht = 0, and consequently the linear relationship can be forced through the
origin. These linear regression equations and their coefficient of determination are part of
Table 6 while F ap for each plot or each combination of drainage materials forms a part of Table 7. For plot 6 with clay drain pipes provided with a glass fibre sheet underneath and
on top and for plot 10 with clay drain pipes of an inner diameter of 40 mm and without any
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170 A. Rimidis, W. Dierickx / Agricultural Water Management 68 (2004) 151–175
Fig. 9. Relationship between the total head loss ht and the approach-flow head loss hap over the whole measuring
period 1999/2000 to 2002/2003, for each experimental plot.
envelope material, more than 40% of the total head is dissipated as approach-flow head loss
within a distance of 0.40 m from the drain centre.
6. Discussion
6.1. Performance of the drainage system
The results clearly illustrate that differences between the yearly q–ht relationship withinboth measuring periods are rather small for the same plot or the same drainage material
(Figs. 4 and 5). These differences should rather be attributed to the large variability of the
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172 A. Rimidis, W. Dierickx / Agricultural Water Management 68 (2004) 151–175
Plots 2 and 5, clay drain pipes respectively with loose bulky corn straw and loose bulky
flax boon both on top and along both sides, represent a logarithmic relationship between
q1 and hap. Such a relationship has a steep slope and consequently a high W ap at small
discharges, and tends to a rather small slope and a small W ap at greater discharges. Thedifference in W ap between smaller and greater discharges has to be attributed to the absence
of envelope material underneath the drains on the one hand, and that some of the organic
material was still present on top of the drain as was observed after excavations.
W ap for the various plots and hence also for the various combinations of drainage ma-
terials, as given in Table 7, can only be compared if K of all plots is the same. As this is
not the case (Table 5), the dimensionless approach-flow constant αap is a better parameter
to compare the combined effect of material and trench backfill (installation conditions) on
the drainage performance. However, it should be kept in mind that the approach-flow con-
stants, given in Table 7, are values valid for flow at which the whole drain circumference
is involved. From these values it is evident that the clay drain pipes with the bulky mate-
rials (plots 2 and 5) give the smallest αap followed by the corrugated polyethylene pipes
pre-wrapped with the locally made non-woven ‘Melita’ envelope (plot 4). The clay drain
pipes of 40 mm inner diameter without any envelope material (plot 10) come next and then
the corrugated polyethylene pipes originally pre-wrapped with corn straw (plot 3). The clay
drain pipes with a glass fibre sheet underneath and on top (plot 6) exhibit the highest αap.
The difference in αap of the last three materials is rather limited. Since drain pipes are of
secondary importance when used in combination with envelope materials (Dierickx, 1980),
the envelope materials, including the effect of the trench backfill, can be divided into three
classes based on αap and taking into account that minor differences are not important:• Class 1 (good, αap ≤ 0.50): The loose bulky corn straw and flax boon materials (plots 2
and 5).
• Class 2 (moderate, 0.50 < αap < 1.00): The locally made synthetic non-woven ‘Melita’
envelope (plot 4).
• Class 3 (poor, αap ≥ 1.00): The pre-wrapped corn straw; the glass fibre sheet and no
envelope material (plots 3, 6 and 10).
If the drainage materials were arranged according to W ap, a wrong classification and
evaluation should result because W ap is not only related to the material used but also to the
hydraulic conductivity of the soil which differs from plot to plot. The above classificationof the envelope materials was based on flow occurrences at which the whole drain circum-
ference is involved. An estimation of the real performance of the materials in their actual
situation taking into account all possible influences is given by the F ap.
6.3. Approach-flow head loss fraction, F ap
The ranking of F ap of the various plots or materials, given in Table 7, differs from that
for αap because of differences in the approach-flow occurrence. F ap is the smallest for the
pre-wrapped locally made synthetic non-woven ‘Melita’ envelope (plot 4) as only 25.1% of
the total head loss dissipates within a distance of 0.40 m from the drain centre. This resultsfrom a rather low αap combined with an impervious layer which lies about 0.30 m below
drain level. Then, the loose bulky corn straw (plot 2) follows with a very low αap, negatively
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A. Rimidis, W. Dierickx / Agricultural Water Management 68 (2004) 151–175 173
affected, however, by the absence of material underneath the drain and the vicinity of the
impervious layer. The originally pre-wrapped corn straw (plot 3) with a rather high αap but
with the drain level slightly above the impervious layer comes next. Then follows the loose
bulky flax boon (plot 5) with a very low αap but without any material underneath the drainand which is, moreover, situated near the impervious layer. The drain without envelope
(plot 10) and with a rather high αap that may be slightly compensated by the depth of the
impervious layer is next. Despite that the impervious layer is 0.10 m below drain level, the
glass fibre sheet (plot 6) with the highest αap shows also the highest F ap which represents
almost half of the total head loss. A classification of the materials based on F ap can also
consist of three classes:
• Class 1 (good, F ap ≤ 0.30): The loose bulky corn straw and the locally made synthetic
non-woven ‘Melita’ envelope (plots 2 and 4).
• Class 2 (moderate, 0.30 < F ap < 0.40): The pre-wrapped corn straw and the loose bulkyflax boon (plots 3 and 5).
• Class 3 (poor, F ap ≥ 0.40): The glass fibre sheet and no envelope material (plots 6 and 10).
This classification is based on both the material and the actual flow situation while the
classification on αap only considers the material.
7. Conclusions
This research shows the simplicity of determining whether a drainage system meets the
design criteria or not, just by measuring discharge and total head loss. Such measurements,however, do not tell more about the cause in case of malfunctioning when design criteria
are based on soil composition and not on hydraulic conductivity and depth of the imper-
vious layer. Such measurements also do not explain differences in performance between
various drainage materials. To know more about the possible cause of malfunctioning or
the differences in performance between various materials, hap needs be measured.
Since the performance of the drainage systems in the various plots was inadequate to vari-
ous degrees, and since each plot consisted of a different drainage material, a further analysis
of the functioning of the various drainage materials could explain the differences in perfor-
mance. Such an analysis permitted a ranking of the investigated materials, to determine the
actual value of the materials and to select the most appropriate material(s) for future use.
This research also shows the complexity to evaluate the performance of drainage materials
because the approach-flow pattern can be completely different from one material to the other.
A correct interpretation requires a good understanding of the approach-flow occurrence and
can only be done for similar flow conditions at the same hydraulic conductivity. Therefore,
the dimensionless αap is an important parameter. F ap includes the actual situation in which
the drainage materials operate and does not always yield the most suitable materials.
This research learns that:
• A large number of measurements is imperative to obtain reliable relationships between
q and ht; between hap and q1; and between hap and ht.• The design criteria are not met as the result of a too wide a drain spacing and the W ap of
the drainage systems.
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174 A. Rimidis, W. Dierickx / Agricultural Water Management 68 (2004) 151–175
• W ap is in principle a constant as long as the approach-flow pattern does not change with
discharge.
• Envelope materials which do not completely surround drain pipes may also affect the
approach-flow pattern and consequently W ap, especially at low discharges.• F ap does not depend on discharge despite the fact that W ap may vary.
• From the comparison of drains with and without envelope it follows that envelope mate-
rials promote fully circumferential flow.
• An envelope material with a small αap may exhibit a relatively high F ap due to the presence
of an impervious layer in the immediate vicinity of the drain and an incomplete envelope
surround.
• No envelope material and glass fibre sheet both exhibit a large αap and a substantial F ap.
• To compare the performance of drainage materials, it is essential that the approach-flow
pattern and the hydraulic conductivity are the same.
• αap is higher for small flow rates as a result of incomplete circumferential flow and
decreases with increasing flow rates till a constant value at full circumferential flow.
• Loose bulky envelope materials are clearly better than all the other investigated materials,
and much better than the thin glass fibre sheet.
• The locally made non-woven ‘Melita’ envelope performs less good than the bulky mate-
rials but it is the best pre-wrapped envelope material.
• The poor performance of organic materials is indicative of a material decay.
From this research a monitoring programme on the performance of drainage systems
can be derived to inform future landowners on the real value of their drainage system. This
monitoring programme should at least include the measuring of drain discharges and totalhead losses. A comparison of the relationship between discharge and total head loss with
the design criteria will reveal the functionality of the drainage system. Furthermore, if the
approach-flow head loss is measured, a further analysis of the approach-flow constant can
be made. Also as a result of the measurement of the approach-flow head loss, the combined
influence of drainage material and flow situation can be derived from the approach-flow
head loss fraction.
Design criteria usuallydo not consider the approach-flow resistance because it is supposed
that the drainage materials together with the loose backfill of the excavated trench do not
exert an additional flow resistance. However, the drain spacing should be reduced by either
40 or 25% if the approach-flow resistance results in an approach-flow head loss fraction of
respectively 50 or 30%.
From the additional information on hydraulic conductivity and depth of the equivalent
impervious layer, it can then be decided whether another drain midway between two drains
or the replacement of the whole drainage system will resolve the problem.
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