J. Hydrol. Hydromech., 66, 2, 153–160
DOI: 10.1515/johh-2017-0059

Operational validation of HYDRUS (2D/3D) for capillary barriers using
data of a 10-m tipping troughKlaus Berger
University of Hamburg, Institute of Soil Science, Allende-Platz 2, 20146 Hamburg, Germany.
Tel.: +49 40 42838 2006. Fax: +49 40 42838 2024. E-mail: klaus.berger@uni-hamburg.de

Abstract: Capillary barriers are an interesting alternative component for cover systems of landfills and contaminatedsites. Provided they are sufficiently validated, soil hydrological models could be fast and powerful tools for the dimensioning of capillary barriers. Outflow rates measured in a 10 m long tipping trough for one material combination and two
slopes from stationary periods were compared to simulation results of HYDRUS (2D/3D), Version 2.05. The measured
outflow rates show a typical pattern with slope-dependent threshold values indicating the efficiency of the capillary barrier. This flow pattern could not be reproduced with HYDRUS (2D/3D) that for different input setups produced smooth
patterns without thresholds. The input setup was varied for different soil hydraulic models (van Genuchten-Mualem vs.
Brooks-Corey), homogeneous and heterogeneous transport domains (no scaling vs. stochastically distributed scaling factors considering the Miller-Miller similitude), different HYDRUS versions (standard vs. alternative; i.e., with material
properties assigned either to finite element nodes or finite elements, respectively), and different lower boundary conditions (seepage face vs. free drainage). Differences between measured and simulated outflow patterns could be caused by
the measurements, the application of the model, or by the model itself. The van Genuchten-Mualem model may not besuitable to describe the soil hydrological relationships of these particular materials. The reason for the mismatch, however, could not be identified yet.
Keywords: Capillary barriers; Funneled flow; Landfills; Cover systems; Operational validation; HYDRUS (2D/3D).
INTRODUCTION
Capillary barriers are two-layer systems consisting of an upper layer made of a relatively fine-grained and fine-porous
material (e.g., sand), the so-called ‘capillary layer’, underlain
by a lower layer made of a relatively coarse-grained and coarseporous material (e.g., gravel), the so-called ‘capillary block’.
There is a sharp interface between the two layers that is sloped.
Water percolating through a capillary layer under unsaturated
conditions is held at the interface due to capillary forces (acapillary barrier effect). When inflow into the capillary layer isrelatively small, nearly no water breaks through the interface
into the capillary block. Instead, water moves laterally in thecapillary layer along the interface (a wick[ing] effect or acapillary diversion) (see, e.g., Oldenburg and Pruess, 1993; Yehet al., 1994). This type of flow is called ‘funneled flow’ (Kung1990; illustrated using the dye tracer experiment depicted in
Figure 1). However, when inflow into the capillary layer becomes higher, water begins to break through the interface. As
inflow decreases, breakthrough decreases as well and the capillary barrier ‘recovers’.
Capillary barriers are not only a curious soil hydrologicalphenomenon, but they also represent an interesting component
in cover systems for landfills and contaminated sites. Coversystems are multi-layer systems consisting of layers that perform specific tasks. Especially on steep slopes, capillary barriers can be used as a stand-alone barrier or as a component of aliner that is overlain by a compacted cohesive layer or ageomembrane for limiting inflow into the capillary layer.
For the use in cover systems, capillary barriers have to bedimensioned. This means that suitable material combinations of
the capillary layer and capillary block, and a suitable maximum
distance to a drain that removes water from the system have tobe determined depending on site-specific conditions. The following parameters are relevant:Fig. 1. A front view of the filled 10-m tipping trough (dark brownmaterial = capillary block, light-colored material = capillary layer,
and collection sump in the left-most segment). A dye tracer
experiment with a red tracer is depicted on the left side. The
irrigation system is inside the black box on the top of the tipping
trough. Photo: Institute of Soil Science, University of Hamburg.

1. Soil hydrological properties of the materials of thecapillary layer and the capillary block;
2. Slope;
3. Slope length / maximum distance to the drain;
4. Shape of the slope (convex - concave; convergent divergent);
5. Infiltration rate into the capillary layer. This depends onthe climate of the site and the layers above the capillarybarrier.
There are several principal methods available to dimension
capillary barriers with specific advantages and disadvantages.
Table 1 gives an overview of the most important methods.
Several empirical investigations with large test fields (lysimeters)

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Klaus Berger
Table 1. Important principle methods for dimensioning capillarybarriers and their advantages and disadvantages.
I.
Advantages:

Empirical investigations with large test fields (lysimeters)
Close to reality due to field size

Disadvantages: Limited to very few parameter values and material combinations
Requires experience and accuracy to avoid systematic errors
Time-consuming (many years)
Very expensive
Measurement results depend on the weather as a boundary condition
and are therefore not reproducible
II.
Empirical investigations with tipping troughs (tilt gutters) in pilot
plant scale
Advantages:
Relatively close to the reality in the field
Measurement results are (approximately) reproducible
Disadvantages: Limited to some parameter values and material combinations
Relatively time-consuming (many months)
Expensive
III. Simulations with 2D or 3D models
Advantages:

Allows analyzing many parameter values and material combinations
Fast
Low costs
Simulation results are reproducible
Disadvantages: Requires sufficient validation of the model for a particular type of
application

were performed in Germany, for example, on the landfill
Georgswerder in Hamburg, which had six test fields, each 50 mlong and 10 m wide, one having a capillary barrier below a
compacted cohesive layer (Melchior, 1993; Melchior et al.,2010). Other test fields in Germany with capillary barrier wereoperated on the landfills ‘Am Stempel’ near Marburg and‘Monte Scherbelino’ near Frankfurt am Main (Jelinek, 1997),
and in Karlsruhe (Zischak, 1997). Further test fields were operated but are mostly only documented in German (overviews ofthese test fields can be found in Steinert (1999) and Pfeiffer(2006)).
Tipping troughs on a pilot plant scale of capillary barriers
existed in Germany at the University of Hamburg (length x
depth x height of 10.0 m x 0.5 m x 1.0 m; Steinert, 1999;
Steinert et al., 1997a,b), the Technical University of Darmstadt(2 troughs with L x D x H of 8.0 m x 0.2 m x 1.5 m; Holfelder,2002; Kämpf, 2000; Kämpf et al., 2003; von der Hude, 1999),
the Technical University of Munich (L x D x H of 6.0 m x 0.6
m x 1.0 m; Barth 2003), and the University of Giessen (L x D x
H of 6.0 m x 0.6 m x 1.0 m; Pfeiffer, 2006). However, objectives of the research and materials of the capillary barriers weredifferent in these studies, and thus the results are difficult tocompare. Furthermore, several tipping troughs on a laboratory
scale (approximately 1 m length) were operated in Germany,e.g., at the University of Hamburg. The results of these small
troughs could, however, hardly be transferred to a field scale(Steinert, 1999).
Comparisons of measured and simulated data for tipping
troughs were performed in Germany for SWMS_2D (Berger,
2017; Steinert, 1997a,b), for HYDRUS-2D (Kämpf, 2000;
Kämpf et al., 2003; Pfeiffer, 2006), and for Feflow 5.0 (Barth,2003). The authors assessed the success of output comparisonsvery differently, from ‘failure’ to ‘in principle possible,’ ‘satisfactory’ to ‘good’. However, Barth (2003) and Kämpf et al.
(2003) especially emphasized the importance of the soil hydraulic properties for the simulation results.
Simulations with two- or three-dimensional models such as
HYDRUS (2D/3D) (Radcliffe and Šimůnek, 2010; Šejna et al.,2016; Šimůnek et al., 2016) have major advantages comparedto empirical investigations (see Table 1), but require priorvalidation. This is required for any particular type of
application to assure that the simulation results are close toreality and can be transferred into the field. Validation is acomplex methodology (Knepell and Arangno, 1993; Konikow

154

and Bredehoft, 1992; Oreskes et al., 1994; see also Berger,
1999). An important aspect of it is operational validation, i.e.,comparisons of simulations and measurement results. One suchoutput comparison was performed for HYDRUS (2D/3D),
version 2.05 (2.05.0230) (Šejna et al., 2016; Šimůnek et al.,2016), using outflow data of a capillary barrier constructed in a
10 m long tipping trough (Steinert, 1999). The aim of thesimulation was to reproduce measured outflow patterns that
describe the efficiency of the capillary barrier.
MATERIAL AND METHODS
Experiments with a 10 m long tipping trough
Design, experiments, and measurement results with the tipping trough (a tilt gutter) are described in detail in German in
Steinert et al. (1997a) and Steinert (1999), and with the first
results and more concisely in Steinert et al. (1997b). The following description is focused on information relevant to thesimulations discussed below.
The tipping trough (see Figs. 1, 2, and 3) was 10 m long and
0.5 m deep. The capillary barrier constructed inside had aheight of 1 m (0.3 m capillary block, 0.7 m capillary layer). The
bottom of the trough was divided into 10 segments by steel
panels of 0.15 m height (for an exception, see below). Eachsegment was 1 m long with a separate outflow at the bottom.
The capillary barrier was constructed in the upper 9 segmentswith a central measurement area of 0.3 m depth and two margins at the front and on the back, each with a depth of 0.1 m,
separated by steel panels of 0.15 m height. The final segment
was separated by a 0.3 m high steel panel and filled with thematerial of the capillary layer. It served as a collection sump forthe capillary layer and had a bottom 0.13 m below the bottomof the other 9 segments.
The slope of the trough was continuously adjustable up to
1:3 (33%) by a scissors jack operated by a crank handle. The
entire trough stood on weighing cells with a resolution of 1 kg.
The empty trough weighed about 4 t; the trough filled withmaterials weighed around 13 t, depending on the mass of waterin the trough. Outflows were measured with a maximum resolution of 0.1 l. An irrigation system on the top of the trough allowed for a uniform irrigation of the entire surface of the capillary layer with a continuously adjustable irrigation rate between
0.1 and 30 mm/d. A second independent irrigation system wasat the end wall.

Fig. 2. A schematic side view of the tipping trough at an
inclination of 1:5 (1: capillary layer; 2: capillary block; 3: cover of
the top irrigation system; 4: end wall irrigation system; 5: soilhydrological measurement field; 6: collection bin of the capillary
layer; 7: collection bins of the capillary block; 8: overflow of the
top irrigation system; 9: weighing cells; 10: scissors jack withcrank handle) (from Steinert (1999), translated into English).
(Note: This Figure is side-inverted to Figs. 1 and 3.)

Operational validation of HYDRUS (2D/3D) for capillary barriers using data of a 10-m tipping troughTable 2. FE mesh parameters (above) and FE mesh statistics (below) used in the numerical simulations. The number of FE nodes
and elements generated by HYDRUS with the same FE meshparameters differ slightly for the two slopes.
Targeted FE-size: 5 cm
Refinements:
1. Upper boundary (irrigation)
2. Lower boundaries (outflows)
3. Interface of the capillary layer
and capillary block

Fig. 3. A schematic top view of the bottom of the tipping trough (1:outflow of the capillary layer/collection sump; 2: outflow of theback margin; 3: central outflow of the 9th capillary block segment;
4: steel bar; 5: central outflow of the 1st capillary block segment; 6:
steel panel; 7: end wall) (from Steinert (1999), translated into
English).

The capillary layer was constructed from medium sand. This
material originates from the dredged material from the river
Elbe that has been treated in a mechanical treatment plant for
harbor sediments (called ‘METHA’), which is operated by theHamburg Port Authority. The capillary block consisted of gravel with grain diameters ranging mainly from 1 to 3 mm. Bothmaterials have a narrow particle size distribution.
Experiments with a material combination of the capillary
layer and capillary block took several months without interruption. The evaluation was focused on outflow rates from thecapillary layer and the capillary block at different inflow rates.
Simulations with HYDRUS (2D/3D)
Simulations were performed for one material combination,
two slopes, and for periods of steady state flow. Two slopes
were investigated: a steep slope with 1:5 (20%) and a flat slopewith 1:25 (4%). Only periods with a constant irrigation ratefrom the top, no end wall irrigation, and a maximum weighing
difference of the entire tipping trough of 5 kg were simulated.
Each period was evaluated in a separate simulation run. The
simulation period was set to 34,560 minutes (24 days) to assure
steady state at the end of each simulation run. The outflow
patterns were characterized by outflow rates from the capillary
layer and the capillary block at the end of each simulation run.
In the simulations, only outflow from the bottom capillary
block segment was simulated, and measured outflows from all
9 capillary block segments of a stationary period were addedfor comparison. Measured and simulated outflow rates (indimensions of L2/T) from the capillary layer were reduced,
assuming that direct flow is perpendicular from the upperboundary into the final capillary layer segment and thus bypasses the capillary block (11.4% of the inflow rate for theslope 1:5, and 10.3% for 1:25, respectively). The purpose ofthis is to reflect only the efficiency of the capillary barrier.
Simulations were performed using a "2D general" HYDRUS
geometry in the vertical plane and the units of cm for lengthand minutes for time. The finite element (FE) mesh parameters
and resulting FE mesh statistics are summarized in Table 2.
Mesh refinements were used at the upper and lower boundaries(inflow and outflow) and especially along the interface of thecapillary layer and the capillary block, which is a critical zone
for the efficiency of the capillary barrier. The upper boundary
was assigned a constant flux. The initial condition was set to a
constant pressure head of –50 cm at each node.
To reproduce the measured outflow patterns of the capillarybarrier, the model input setup was varied as summarized inTable 3. In particular:

Slope
1:5
1:25

FE nodes
42513
42443

Stretching in x-direction: factor 2
FE-size 2.5 cm+ 2 points per outflow
FE-size 0.6 cm

1D-elements
2010
1917

2D-elements
84597
84470

Table 3. Input setup for the numerical simulations.
Soil hydraulic model
Homogeneous/Scaling

HYDRUS version
Lower boundary condition(Outflow)

Scenario 1
van GenuchtenMualem
No scaling

Standard
Seepage face(with zero pressure head)

Scenario 2
Brooks and Corey
Stochastically
distributed scaling
factors using theMiller- Miller
similitude
Alternative
Free drainage

Soil hydraulic models: Water content-pressure head relationships were measured with a pressure plate apparatus using
samples taken in the tipping trough (Steinert et al., 1997a) andevaluated with RETC (van Genuchten et al., 1991) (see Table
4, which also includes the measured saturated hydraulic conductivities, and Fig. 4). The parameters of the van GenuchtenMualem model were already used in earlier simulations with
SWMS_2D (Steinert et al., 1997a). Sometimes, coarse materials can be better described using the Brooks and Corey model.
Table 4. Soil hydrological parameters of METHA-sand and 1/3
gravel in the van Genuchten-Mualem model (above) and the
Brooks and Corey model (below).
METHA-sand
r2 = 0.996

Mean

95% confidence intervalα (cm–1)
n (–)

0.0302
5.11

0.02834.28

0.03215.95

θs (–)
θr (–)

0.30560.0400––––ks (m s–1)
ks (cm min–1)

1.3 e–4
0.78––

α (cm–1)
n (–)

0.206
3.75

0.197
3.42

0.214
4.08

θs (–)
θr (–)

0.375
0.033

–
–

–
–

ks (m s–1)
ks (cm min–1)

1.2 e–2
72––

Materialθr (–)

θs (–)α (cm–1)n (–)

METHA-sand

0.03390.296

0.04182.12

1/3 gravel

0.036

0.255

0.210

2.36

1/3 gravel
r2 = 0.998

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Klaus Berger

Water content θ (-)
Hydraulic conductivity log10(k (m/s))

0.3
0.2
0.1

3

Pore density
Sand
Gravel0.6
0.4

Water content
Sand
Gravel

0.0
0.1
0

0.8

0.2

1

10

100

0.0
1000

Scaling: The first set of simulations assumed homogeneousand isotropic materials. However, homogeneity is a conceptthat cannot be found in pure form in nature. Due to spatial
heterogeneity, the breakthrough of the capillary barrier may
occur in fingers that are self-reinforcing with increasing inflow
rates. Therefore, stochastically distributed scaling factors wereused to model spatial heterogeneity. The Miller-Miller similitude with default values as given in the HYDRUS user interface
was selected, except for the standard deviation of log10(y) of
the hydraulic conductivity scaling factor, which, after sometests, was set to 0.125.
HYDRUS version: The standard HYDRUS version assigns
material properties to the nodes of the FE mesh. According to
Heiberger (1996, p. 52), this approach does not allow for a
sharp interface between two layers, but leads to an interface
layer with alternating intermediate material properties. In thealternative HYDRUS version (Šimůnek, 2017), material properties are assigned directly to the FE elements, thus allowing
abrupt textural changes and sharp interfaces between twolayers.
Of the 16 possible combinations of the input setup (2 soil
hydraulic property models, homogeneous vs heterogeneous, 2
HYDRUS versions, and 2 lower boundary conditions), 9 combinations were simulated. Seven combinations, among them sixwith a free drainage boundary condition, were not simulated
because further insights were not expected from their results.

Pore density (-d θ(|h|)/d log10|h|)

Equivalent pore diameter (µm)
3030030000 3000
0.4

-6
-12
-18
-24
0.1

-1

Sand
Gravelα (cm ) n (-)
0.0302 5.113
0.2057 3.75

1
10
100
Pressure head |h| (cm)1000

Fig. 4. Water content–pressure head functions, pore density distributions, and hydraulic conductivity–pressure head functions for the
METHA-sand and 1/3 gravel using the van Genuchten-Mualem
model.

Therefore, the Brooks-Corey parameters, including the residual and the saturated water contents, were also fitted to thewater content-pressure head data using RETC (see Table 4).
The values of the residual and the saturated water content differed from those determined for the van Genuchten-Mualem
model. In the simulations with the Brooks-Corey model, thelower limit of the tension interval of the internal interpolationtables was set to 24 cm, i.e., slightly higher than the bubblingpressure.

2

1.0

1.5 0.0

0.5

1.0

1.5
1.5
1.0

0.5

0.5

0.0

0.0

1.5

1.5

1.0

1.0

0.5

0.5

0.0
0.0

0.5

1.0

1.5 0.0

0.5

1.0

Measured data
Series of simulation runs:
No scaling
Stochastically distributed
scaling factors with
Miller-Miller similitude

Capillary block

1.0

Capillary layer

Outflow rate (cm /min)

0.5

The results are depicted in Figs. 5 to 8. The dependence ofmeasured and simulated outflow rates on the inflow rates isshown in Figs. 5 and 8 in the same manner. The slope 1:25 is in
the left column, the slope 1:5 is in the right column, flow fromthe capillary layer is in the upper row and flow from the capillary block is in the lower row. Symbols mark simulated stationary periods. Every pair of simulated outflow rates from thecapillary layer and the capillary block for the same inflow rateshould sum up to the inflow rate (steady state). Actually, inmost cases the simulated outflow rates summed up to 99.8 to
100.0% of the inflow rates. Sometimes, the percentage was a

Slope 1:5

Slope 1:25
0.0
1.5

RESULTS AND DISCUSSION
Comparison of measured and simulated outflow rates

0.0
1.5

2

Inflow rate (cm /min)
05

10 15 200

5

10 15 20

Inflow rate (mm/d)Fig. 5. Comparisons of measured and simulated outflow rates from a capillary layer and a capillary block dependent on the inflow rates forthe model setup with the van Genuchten-Mualem model, a standard HYDRUS version, and a seepage face.

156

Pressure head (cm)Hydraulic conductivity (m/s)

Operational validation of HYDRUS (2D/3D) for capillary barriers using data of a 10-m tipping troughthe capillary layer breaks through into the capillary block andthe outflow rate from the capillary layer remains approximately
constant. With respect to the efficiency of the capillary barrierin cover systems, the capillary layer outflow at the (second)
threshold can be denoted as the ‘lateral drainage capacity’ of
the capillary barrier (Steinert et al., 1997a). This characteristic
is different from the ‘diversion capacity’ of Ross (1990) (seealso Lacroix Vachon et al., 2015). The objective of the numerical simulations was to reproduce this flow pattern and to identify the threshold(s).
However, the simulated outflow rates show a different flow
pattern with a smooth increase in the outflow rates from thecapillary layer and the capillary block, without any visible
thresholds. In the model setup with the van Genuchten-Mualem
model, the standard HYDRUS version, and a seepage face (Fig.
5), HYDRUS reproduced the outflow rates at small to medium
inflow rates well. However, especially for the steep slope 1:5
and high inflow rates, HYDRUS overestimated the outflow
rates from the capillary layer and underestimated those from thecapillary block. Thus, the model overestimated the efficiency ofthe capillary barrier just for those conditions (steep slopes) for
which capillary barriers are to be used. Simulations performed
in 1995 with the predecessor model SWMS_2D (Šimůnek etal., 1992) and modified values of the van Genuchten-Mualem
parameters and the saturated hydraulic conductivities of Table 4(among others α and n of the 95% confidence intervals) yieldedsmooth outflow patterns as well (Berger, 2017; Steinert et al.,1997a).
Fig. 6 illustrates the reason for the simulated smooth outflow
pattern without visible thresholds for the 1:5 slope and themodel setup with the van Genuchten-Mualem model, no scaling, the standard HYDRUS version, and a seepage face boundary condition. The hydraulic conductivities along the interfaceof the capillary barrier in the capillary layer and the capillary
block differ by about 4 to 5 orders of magnitude. The ratio of
the hydraulic conductivities of the capillary layer and the capillary block decreases with increasing inflow rates. However, forthe largest inflow rate the hydraulic conductivity of the capillary layer material is still about 4 orders of magnitude larger
than that of the capillary block material.
Fig. 5 also shows that the corresponding outflow rates simulated without scaling and with stochastically distributed scaling
factors for the Miller-Miller similitude are close together. This
result also holds for the model setup with the Brooks and Coreymodel, the standard HYDRUS version, and a seepage face. Thismeans that if fingering occurs in the simulation (due to heterogeneity), it does not play as important a role as expected.
The simulation results with the alternative HYDRUS version
indicate a more efficient capillary barrier, i.e., the outflow rates
from the capillary layer were larger and those from the capillary
block were smaller compared to those simulated using the

1E-04
1E-05
1E-06
1E-07
1E-08
1E-09
1E-10

-20
-30
-40
-50
0

100

200

300

400

500

600

700

800

900

Length along the interface (cm)Inflow rate
(cm2/min)
0.27
0.70
1.09

Capillary layer(METHA-sand)

Capillary block Pressure head
(1/3 gravel)
at the interface

Fig. 6. The pressure heads along the interface between the capillary
layer and the capillary block, as well as the corresponding hydraulic conductivities in the two materials calculated using the van
Genuchten-Mualem model. The results are for the model setup
with the van Genuchten-Mualem model, no scaling, the standard
HYDRUS version, a seepage face boundary condition, the 1:5
slope, and three inflow rates (the smallest, a medium, and thelargest inflow rate). The length along the interface is directed fromthe bottom (0 cm) to the top (900 cm) of the capillary barrier.

bit smaller, namely for the flat slope 1:25 and the smallest
inflow rate, or if a simulation run was aborted. In the latter
case, the latest available stored result was evaluated. To simplify the interpretation of the results, the inflow rates in Figs. 5
and 8 are shown in the abstract simulation unit of cm2/min as
well as in mm/d, which is commonly used for precipitation,
evapotranspiration, and discharge.
The measured data show typical flow patterns (Fig. 5). At
small inflow rates, almost all infiltration water moves laterally
downward in the capillary layer along the interface and almost
no outflow is measured from the capillary block. For the flat
slope 1:25 and the first threshold of the inflow rate of approximately 4 mm/d, water starts breaking through the interface into
the capillary block, leading to an increase in capillary block
outflow. For the second threshold of the inflow rate of 7.0mm/d, most of the additional water infiltrating into the capillary
layer breaks through into the capillary block and the outflow
rate from the capillary layer increases only slightly. For the
steep slope 1:5, only one threshold can be identified. At thisthreshold of 11.4 mm/d, all additional water infiltrating into
Slope 1:5

1.05

1.00

1.00

0.95

0.95

0.90
0.0

0.5

1.0

1.5 0.0

0.5

1.0

0.90
1.5

Ratio alternative tostandard version (-)

Ratio alternative tostandard version (-)

Slope 1:25
1.05

No scaling
Capillary layer
Capillary block
Stochastically distributed
scaling factors with
Miller-Miller similitude
Capillary layer
Capillary block2

Inflow rate (cm /min)Fig. 7. A ratio of corresponding outflow rates from a capillary layer and a capillary block dependent on the inflow rates simulated by alternative and standard HYDRUS (2D/3D) versions for the model setup with the van Genuchten-Mualem model and a seepage face.

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Klaus Berger
Slope 1:5

Slope 1:25
0.5

1.0

1.5 0.0

0.5

1.0

1.5
1.5

0.5

0.5

0.0

0.0

1.5

1.5

1.0

1.0

0.5

0.5

2

1.0

0.0
0.0

0.5

1.0

1.5 0.0

0.5

1.0

Measured data
Series of simulation runs:
van Genuchten-Mualem
model
Brooks and Corey
model

Capillary block

1.0

Capillary layer

Outflow rate (cm /min)

0.0
1.5

0.0
1.5

2

Inflow rate (cm /min)
05

10 15 200

5

10 15 20

Inflow rate (mm/d)Fig. 8. Comparisons of measured and simulated outflow rates from a capillary layer and a capillary block for different inflow rates andslopes, and for a model setup with no scaling, a standard HYDRUS version, and a seepage face.

standard HYDRUS version (see Fig. 7 for the model setup withthe van Genuchten-Mualem model and a seepage face). However, for the fine FE mesh used in these simulations, the impactof the alternative HYDRUS version is relatively small. Whilefor the slope 1:25, the outflow rates from the capillary layer
increased up to 2% compared to the standard HYDRUS version, for the steep slope 1:5, the differences were less than 1%.
The outflow rates from the capillary block simulating with thealternative HYDRUS version were between 90 and 99% of
those simulated with the standard version. However, the base of
these percentages is very small compared to the outflow rates
from the capillary layer (the very small values may be one
reason for the irregular, counter-intuitive ‘up and down’ of theratios for the 1:5 slope in Fig. 7). Unpublished results of similar
simulations with a much coarser FE mesh (i.e., 367 nodes and785 elements) showed a much larger impact of the HYDRUS
version. The alternative HYDRUS version produced outflow
rates from the capillary layer up to 41% higher than the standard HYDRUS version. Obviously, the impact of how soil hydraulic properties are assigned, either to FE nodes (as in thestandard HYDRUS version) or to FE elements (as in the alternative HYDRUS version) becomes smaller for a smaller FEsize. The outflow rates obtained with the alternative HYDRUS
version matched the measured outflow rates worse than thoseobtained with the standard version. However, when using fine
FE meshes the impact of the HYDRUS version can be neglected in this application because the differences to the results ofthe standard version are small.
For the model setup with no scaling, the standard HYDRUS
version, and a seepage face, the HYDRUS model with the
Brooks and Corey model predicted a less efficient capillarybarrier with a larger breakthrough into the capillary block andsmaller outflow rates from the capillary layer compared to thevan Genuchten-Mualem model (Fig. 8). However, the model
setup with the Brooks and Corey model also produced smooth
outflow patterns without visible thresholds. Although the match
between the simulated and measured data is not bad for theslope 1:25, the efficiency of the capillary barrier is significantly
overestimated for the slope 1:5 and large inflow rates.
Replacing the seepage face lower boundary condition withthe free drainage boundary condition had almost no impact on158

the outflow rates for the model setup with the van GenuchtenMualem model and no scaling. This remained true for both thestandard and alternative HYDRUS versions. However, 22 outof the 38 simulation runs with free drainage aborted, which led
to slightly irregular outflow patterns.
Possible reasons for the mismatch between measured andsimulated outflow rates
Due to the systematic measurement and simulation results,
the mismatch between measured and simulated outflow rates isvery likely caused by systematic rather than random errors.
There are three groups of possible reasons explaining the mismatch between measured and simulated outflow rates.
1) Errors in the empirical investigation
Although the 10-m tipping trough is a well-defined device, it
is relatively large and thus there may be many sources of errors
and uncertainties in the experiments. For example, the materials
filling the tipping trough may be spatially heterogeneous because of the method of filling the device, or water flow may be
impacted by variable temperatures in the lab. Furthermore,
there may have been no stationary flow in the assumed stationary periods because of water redistribution inside of the tipping
trough. Even so, the typical measured flow pattern with distinct
threshold values of the inflow rates that indicates the efficiencyof the capillary barrier and depends on the material combination and the slope is well confirmed (Steinert, 1999).
2) Errors in the application of the model
The simulation task, such as the shape of the tipping troughand the capillary barrier, is quite well defined. However, somematerial properties were not considered in the simulations due
to missing measurement data. For example, hysteresis of thesoil hydrological functions and the anisotropy of the hydraulicconductivity of used materials was not evaluated. Both materials (METHA-sand and 1/3 gravel) were technically pre-treated
and therefore had a specific grain-size and pore-size distribution. This may be one reason why the parameterization of thevan Genuchten-Mualem model for the soil hydrological functions was not unique (see point 3 below).
The spatial heterogeneity of material properties was modeledusing scaling of soil hydraulic properties. If fingering plays anOperational validation of HYDRUS (2D/3D) for capillary barriers using data of a 10-m tipping troughWater content θ (-)

0.4

θr: 0.040, θs: 0.3056

0.3

-1

α (cm )

0.03020.04900.2(total pore volume: 0.382)

n (-)
5.113
4.504

Sourceθ(|h|) fit with RETC
kr(|h|) fit (tension infitrometer data)

0.1
0.0

Relative conductivity log10 kr (-)

Measured data θ(|h|)

0.1

1

10

100

1000

0

-6

-12
Measured data(tension infiltrometer)
-18

0.1

1

10

100

1000

Pressure head |h| (cm)Fig. 9. Two fits of the van Genuchten-Mualem model to different measured data sets of the METHA-sand.

important role in flow across the interface of the capillary layer
and capillary block, two-dimensional simulations are not sufficient to capture such phenomenon because they assume constant conditions in the third dimension. Fingers as separate
three-dimensional entities require three-dimensional explicit
representation.
3) Errors or unsuitable approaches in the modelThis is a complex problem, which is in large part beyond thescope of this paper. For example, the van Genuchten-Mualem
model (van Genuchten, 1980) may not be suitable to describe
the soil hydraulic relationships of the technical pre-treatedmaterials used in the capillary barrier. The fitting of the van
Genuchten-Mualem model to two data sets for the METHAsand measured with different methods resulted in significantly
different parameter values for α and n (see Fig. 9). These data
sets include water content-pressure head data from a pressure
plate apparatus and unsaturated hydraulic conductivity datafrom tension infiltrometer measurements. Furthermore, toachieve a good fit for the water content-pressure head data, θs
had to be set equal to only 80% of the total pore volume. The
importance of the hydraulic parameters for the simulation results has already been emphasized by other authors (Barth,
2003; Kämpf et al., 2003).
None of the reasons mentioned in this brief discussion seemto be essential for explaining the mismatch between measured
and simulated flow patterns of the capillary barrier. Thus, thisproblem unfortunately remains unsolved.

sources of errors explaining the mismatch between measured
and simulated outflow patterns were discussed. Errors could
exist in the empirical investigation, the application of the model, or in the model itself. However, it is the author’s opinion
that the essential reason(s) for the mismatch between simulated
and measured outflow rates could not yet be identified. To
improve the results, further simulations could be performed todetermine the soil hydraulic properties by inverse modeling forparticular stationary periods.
According to the simulation results described in this paper
and those of other authors (e.g., Barth, 2003; Kämpf et al.,2003), the two-dimensional models as HYDRUS (2D/3D)
should currently not replace empirical investigations of tipping
troughs or test fields for the dimensioning of capillary barriers.
Acknowledgments. The empirical investigation in the tipping
trough and the simulations with SWMS_2D were funded by theGerman Federal Ministry for Education, Science, Research andTechnology (BMBF) within the integrated research project‘Advanced Landfill Liner Systems’ under the project number
1440 569A-39. The author thanks Dr. habil. Stefan Melchior
and Prof. Dr. Günter Miehlich, who led the empirical investigation, and Dr. Bernd Steinert, Matthias Türk, Karin Burger andall involved staff members for their work. The author also
thanks Prof. Jirka Šimůnek for providing the alternative HYDRUS (2D/3D) version.
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Received 28 June 2017
Accepted 22 December 2017