SoilUse
and Management
doi: 10.1111/sum.12423

Soil Use and Management, June 2018, 34, 206–215

Numerical analysis of soil water dynamics in a soil column
with an artificial capillary barrier growing leaf vegetables
A. W O N G K A E W 1

I M UN EK3, H. S A I T O 1 , H. F U J I M A K I 2 & J. S

1United Graduate School of Agricultural Science, Tokyo University of Agriculture and Technology, Fuchu, Tokyo 183-8509, Japan,
Arid Land Research Center, Tottori University, Tottori 680-0001, Japan, and 3Department of Environmental Science, Universityof California, Riverside, CA 92521, USA
2

Abstract
An artificial capillary barrier (CB), which consists of two layers of gravel and coarse sand, was used
to improve the soil water retention capacity of the root zone of sandy soil for the cultivation ofJapanese spinach (Brassica rapa var. perviridis). The performance of a CB under specific conditions
can be evaluated using numerical simulations. However, there have been relatively few numericalstudies analyzing soil water dynamics in CB systems during crop growth. The objectives of this study
were (i) to evaluate the performance of a CB during the cultivation of Japanese spinach irrigated at
different rates and (ii) to investigate the effect of the irrigation schedule on root water uptake.
Numerical analysis was performed using HYDRUS-1D after the soil hydraulic properties of the CB
materials were determined. In most cases, the HYDRUS-1D results agreed well with the experimental
soil water content data without any calibration when the dual-porosity model describing soil hydraulicproperties was used for gravel and coarse sand. We found that the dual-porosity model was able toattenuate the unrealistically steep reduction in the unsaturated hydraulic conductivity predicted by thesingle-porosity model. The numerical simulations also showed that the CB played an important rolein maintaining plant-available water in the root zone while maximizing the water use efficiency. The
numerical simulations revealed that the irrigation frequency could be reduced by half during the early
growth stage, and the water use efficiency could be greatly improved with the CB layer installed.

Keywords: Capillary barrier, HYDRUS-1D, irrigation efficiency, drought

Introduction
A capillary barrier (CB) is a layered soil system, which
consists of two layers with contrasting hydrauliccharacteristics. A layer of a finer material usually overlays alayer of a coarser material. Depending upon the difference in
capillary forces, vertical movement of infiltrated water iseither slowed down or temporally paused in the fine layer at
the interface with the coarse layer, as long as the capillary
forces in the fine layer are significantly stronger than thosein the coarse layer, mainly because of the difference in poresizes. CB systems are recognized as alternative systems that
not only control water percolation in landfill covers (Berger
et al., 2005; Abdolahzadeh et al., 2011) but also improve theroot zone water retention capacity. A gravel layer installed

Correspondence: H. Saito. E-mail: hiros@cc.tuat.ac.jp
Received February 2017; accepted after revision May 2018

206

below the root zone was found to both increase watercontents by 20–70%, depending on the soil texture and thedepth of the barrier (Ityel et al., 2011), and to prevent thecapillary rise from an underlying saline soil layer (Rooneyet al., 1998).
In order to improve the performance of a CB under
specific conditions, numerical simulations can be used asthey are recognized as a cost-effective tool to investigate soil
water dynamics. The HYDRUS software package is one of
the most complete packages for simulating soil water
dynamics and has been utilized in a number of hydrological unek et al., 2008, 2016). Ityel et al. (2011)
studies (Simsuccessfully used HYDRUS-2D to simulate the soil watercontent in the root zone with an installed CB, without
accounting for root water uptake. Cheng et al. (2013) also
showed that HYDRUS-1D performed well in simulating theobserved soil water contents in both homogeneous (sandy
soil and silt loam soil) and layered soils (sand overlying silt
loam soil) during Caragana korshinkii Kom cultivation.

© 2018 British Society of Soil ScienceAn artificial capillary barrier

Previously, Miyake et al. (2015) conducted an experimentto evaluate the effects of a two-layered CB system on
cultivating Japanese mustard spinach (Brassica rapa var.
perviridis), a widely grown commercial leaf vegetable inJapan, known for its high nutrient contents. However, thisgenus is highly affected by drought and salinity during plant
growth and development (Zhang et al., 2014; Zhu et al.,2016). The results of Miyake et al. (2015) showed thepotential of the CB system to improve the water retentivity of
the root zone as the average plant height was higher for the
CB system than that for the no-CB standard system when thesame amount of irrigation water was applied. To further
improve the irrigation efficiency, it is necessary to understandsoil water dynamics during the cultivation of Japanesespinach in the soil profile with a CB layer.
The objectives of this study were therefore twofold: (i) toinvestigate the applicability of HYDRUS-1D to predict
observed soil moisture contents and (ii) to evaluate theeffects of different irrigation schedules on root zone moisture
conditions of the cultivation experiment of Miyake et al.
(2015) using HYDRUS-1D.

Materials and methods
Cultivation experiment
The cultivation experiment was conducted and reported by
Miyake et al. (2015). Japanese spinach was cultivated infour 24 9 36 9 23 cm containers. Three containers with a
two-layered CB and one container without a CB (forreference) were used. The reference container was filledwith Tottori Dune sand (referred to as dune sand in theremainder of the paper). The CB containers additionally
included a 6-cm layer of the CB, which consisted of a 2cm thick coarse sand layer and a 4-cm gravel layer
between a 4-cm dune sand layer at the bottom and a 6-cm
dune sand layer on top of the soil profile (Figure 1).
Fertilizers were mixed into the upper sand layer before
seeding and liquid fertilizers were applied with irrigationwater twice a week.
During the experiment, three different amounts of water
were sprinkled uniformly every day: 0.15, 0.30 and 0.45 cm(referred to as CB15, CB30 and CB45, respectively). The
amount of water sprinkled on the reference container
without a CB layer was 0.30 cm (referred to as REF). The
results showed that the average main root lengths were 2.83,
4.33, 5.77 and 7.20 cm in CB15, CB30, CB45 and REF,
respectively, and that the roots did not penetrate into the CB
layers in any scenario. It was observed that the spinach in
CB30, CB45 and REF grew continuously, while the growthin CB15 was significantly slower than in the other three
scenarios (Figure 2). The average plant height in CB30 was
the highest, while it was slightly smaller in C45 and REF at207

the end of the cultivation (the difference between CB30 and
REF was not statistically significant; P > 0.1).

Soil hydraulic properties
Soil water retention curves of the materials used in thecultivation experiment were determined by measuring watercontents at predetermined matric potential heads ranging
from 0 to 100 cm using a modified suction table method(Dane & Hopmans, 2002). Common retention models werethen fitted to the experimental curves to further evaluate theunsaturated hydraulic conductivity using the pore size
distribution model of Mualem (1976). While the singleporosity (SP) model of van Genuchten (1980) was used forthe dune sand, the dual-porosity (DP) model of Durner(1994) was used for the coarse sand and gravel. As thehydraulic conductivity evaluated with the SP model
intrinsically accounts for capillary-type flow only, it might
not be appropriate for relatively coarse materials, fromwhich water discharges as film-type flow after capillary wateris quickly drained. It is, therefore, necessary to use a modelthat can account for non-capillary type flow, such as film
flow. Although the DP model was originally proposed toaccount for heterogeneity in pore structure, it can be used to
mimic non-capillary flow by suppressing the sharp decreasein the hydraulic conductivity in the dry range. Brunetti et al.
(2016) showed that the DP model outperformed the SP
model in their simulations when the DP model was used forthe hydraulic properties of the green roof substrate, which
consisted mainly of gravel. When the SP model is used forcoarse sand and gravel, the estimated hydraulic conductivity
becomes extremely small even at relatively high pressure
heads, resulting in unstable simulations.
The soil hydraulic properties for the SP model of van
Genuchten (1980) were described as follows:Se ¼

h  hr1¼;
hs  hr ð1 þ ðahÞn Þm

m¼1



m 2
K ðhÞ ¼ K s S0:5
1  1  S1=m
;
e
e

1
n

ð1Þ

ð2Þ

where Se is the effective degree of saturation [], hr and hs
are the residual and saturated water contents [cm3/cm3],
respectively, a [1/cm > 0], n [-, n > 1] and m (=1–1/n,
0 < m < 1) [] are fitting parameters affecting the shape ofthe retention curve, and Ks is the saturated hydraulicconductivity [cm/day].
The soil hydraulic properties for the DP model of Durner(1994) were defined as follows:
Se ¼

k
X
h  hr
1
¼
wi
ni
ð1
þ
ja
hs  hri hj Þmi
i¼1

ð3Þ

© 2018 British Society of Soil Science, Soil Use and Management, 34, 206–215

208 A. Wongkaew et al.

(a)

(b)

6 cm

Tottori Dune sand
2 cm

Coarse sand

16 cm

GravelSoil moisture sensors

4 cm

4 cm

Figure 1 The soil profiles with (a) and without (b) a capillary barrier (CB) layer in the cultivation experiment (Miyake et al., 2015). [Colour
figure can be viewed at wileyonlinelibrary.com]

25
2 weeks
20

3 weeks

Plant height (cm)

4 weeks
15

10

5

0
C15

C30

C45

REF

Figure 2 Average heights of Japanese spinach after 2, 3 and 4 weeks
of cultivation in scenarios C15, C30, C45 and REF. Error bars
indicate standard deviations of measurements (Miyake et al., 2015).

K ðhÞ ¼ Ks

fashion to the experimental retention curve. The fitting
parameters of the DP model were determined so that thegeneral shape of the measured soil water retention curve waswell reproduced.
The saturated hydraulic conductivity (Ks) of dune sandand coarse sand was measured using the constant head
method. In the case of gravel, the seepage rate was too highto measure Ks accurately using the constant head method; it
was therefore estimated using available empirical models.
The Kozeny (1927)-Carman (1937), Hazen (1892), Slichter(1899) and Terzaghi (1925) equations were compared toestimate Ks. The measured Ks of sand and coarse sand werecompared with the Ks estimated using the above equations
to find the best estimator for Ks. As the Hazen (1892)
equation resulted in the minimum error for Ks of sand andcoarse sand, it was also used to estimate Ks of gravel in thisstudy.
According to the Hazen (1892) equation, Ks [cm/s] can be
estimated as follows:




m1 


m2 2
1
2
þ w2 a2 1  1  S1=m
ðw1 Se1 þ w2 Se2 Þl w1 a1 1  1  S1=me1e2

where wi is the weighting factor for the overlapping regions,l is the pore-connectivity parameter (0.5), and ai, ni and mi(=1–1/ni) are fitting parameters of the sub-curves. While the
SP model was fitted using the SWRC Fit program (Seki,2007), the DP model was manually fitted in a trial-and-error

ðw1 a1 þ w2 a2 Þ2

Ks ¼ CH D10 2 ;

;

ð4Þ

ð5Þ

where CH is an empirical coefficient [1/(cm/s)], which ranges
from 1 to 1000 (Carrier, 2003) and D10 is the effective
particle size in cm, for which 10% of the soil particles are© 2018 British Society of Soil Science, Soil Use and Management, 34, 206–215

An artificial capillary barrier

finer. CH was set to 1 because it is suitable for the estimationof Ks for uniformly graded soils from very fine sand togravel. As a result of the particle size distribution analysis,
the D10 of gravel used in this study was estimated to be
between 0.475 cm and 0.485 cm. The Ks was then computed
as a geometric mean of ten different D10 values ranging from
0.475 cm and 0.485 cm.

Numerical simulations
 unek et al., 2008, 2016) was used to
HYDRUS-1D (Simsimulate soil water contents in soil containers with a CB
layer installed during the cultivation of Japanese spinach(Miyake et al., 2015). In HYDRUS-1D, water flow invariably saturated soil is simulated by numerically solving
the following Richards equation:



@h
@
@h
¼
K ðhÞ
þ 1  S;
@t @z
@z

ð6Þ

where h is the soil water pressure head [cm], h is thevolumetric water content (VWC) [cm3/cm3], t is time [day], z
is the vertical coordinate that is positive upward [cm], K(h) is
the unsaturated hydraulic conductivity [cm/day], and S is thesource/sink term [cm3/cm3/day]. The sink term, S, is definedas the volume of water removed from a unit volume of soil
per unit time because of plant water uptake. In HYDRUS1D, a model proposed by Feddes et al. (1978) is used toevaluate S:
S ¼ aðhÞRðzÞT p ;ð7Þ

where R(z) is the normalized water uptake distributionfunction as a function of depth z [1/cm], Tp is the potential
transpiration rate [cm/day] and a(h) is the stress response
function [-], which is a prescribed dimensionless function of
the soil water pressure head h (0 ≤ a ≤ 1). The a(h) function
is defined using a piecewise linear function introduced
by Feddes et al. (1978):8 0;><ðh  h1 Þ=ðh2  h1 Þ;aðhÞ ¼>: 1;
ðh  h4 Þ=ðh3  h4 Þ;

h  h4 ; h [ h1h2  h\h1
h3 \h  h2
h4 \h  h3

ð8Þ

where h1, h2, h3 and h4 are the threshold parameters. Rootwater uptake is assumed to be zero when h < h4 or h > h1,
to be at its potential value when the pressure head is
between h2 and h3, and to increase (or decrease) linearly withh when h1 > h > h2 or h4 < h < h3. In this study, the Feddes
parameters for lettuce, as morphology of this leafy vegetable
was similar to Japanese spinach, were chosen from the unek et al., 2008), anddatabase in HYDRUS-1D (Sim
modified to stabilize numerical solutions as explained later.
Although the wilting point h4 is usually set in the range of209

80 to 150 m, at which the water content of coarse soil isalmost equal to the residual water content, h4 should beselected so that the corresponding water content is at least
0.005 greater than the residual water content for a numericalreason. Table 1 lists the threshold pressure heads, h1 to h4,of the stress response function used in this study.
Because soil water dynamics were simulated from seeding
to final cultivation, the root growth module implemented in
HYDRUS was used to obtain the rooting depth, lr [cm], at
any given time. The rooting depth was assumed to be
proportional to the Surface Cover Fraction (SCF). A linear
interpolation was used to obtain lr at a given time from theobserved SCF. The trapezoidal function of Hoffman & van
Genuchten (1983) that is implemented in HYDRUS wasused as a normalized water uptake distribution function R(z). The simulation domain was 16 cm deep and discretized
into 120 finite elements of equal sizes. While the 6-cm-thick
CB layer was positioned at a depth of 6 cm for the CB
profiles, the reference profile consisted of a 16-cm dune sandlayer without a CB layer. In all simulations, two observation
points at depths of 3 and 14 cm were used to compare
simulated and observed VWC.
A constant pressure head of 200 cm was assigned to thewhole domain as an initial condition. The atmosphericboundary condition with surface run off was used as theupper boundary condition. This boundary condition requires
potential evapotranspiration and irrigation fluxes as input.
The actual evapotranspiration rate obtained from Miyake
et al. (2015) was split into the potential transpiration andevaporation rates using SCF. SCF values during thecultivation period were proportional to the SCF values
estimated at the end of the cultivation using photographimages taken from above. The irrigation fluxes were
determined by assuming that irrigation water was applied
over the duration of 30 min. The depth of the root zone wasdetermined based on the root depth data obtained by
Miyake et al. (2015). A no-flux boundary condition was
assigned at the lower boundary. The simulation period was
28 days. In HYDRUS, the time step is automaticallyadjusted between the minimum and maximum time steps
specified by the user. In this study, they were 107 and103 days, respectively.

Table 1 The threshold parameters of the Feddes model used in the
HYDRUS simulations for spinach
Threshold parameters of
the Feddes model
h1
h2
h3
h4

Initial parameters(lettuce) (cm)Modifiedparameters (cm)

10
25
400
600

10
25
190
200

© 2018 British Society of Soil Science, Soil Use and Management, 34, 206–215

210 A. Wongkaew et al.

0.40

Alternative irrigation scheduleθ (cm3/cm3)

0.30
Tottori Dune sand experiment

0.20

Coarse sand experiment

Gravel experiment
Tottori Dune sand (SP model)
Coarse sand (SP model)

0.10

Gravel (SP model)
Coarse sand (DP model: n2 = 3)
Gravel (DP model: n2 = 3)

0.00
0.1

1
10
Pressure head (cm)100

Figure 3 Measured and fitted retention curves of Tottori Dune sand,coarse sand and gravel. Single-porosity (SP) and dual-porosity (DP)models were used in fitting.

100

Pressure head (-cm)

0.001 0

20

40

60

80

100

Gravel (DP)1E-08
K(h) (cm/hour)

Figure 2 shows the plant height of the Japanese spinachfrom the cultivation experiment of Miyake et al. (2015). The
plant growth rate was 1.54, 7.21, 5.78 and 6.71 cm per week
for CB15, CB30, CB45 and REF, respectively. This showsthat the spinach growth was at maximum for CB30.
However, it is not obvious whether the daily application of
0.3 cm of water indeed maximized root water uptake and thetranspiration rate of the Japanese spinach under theapplication of a liquid fertilizer twice a week with a CB at a6-cm depth. To investigate if the water use efficiency (WUE)
could be improved during spinach cultivation in the CB
profile, a numerical analysis was performed with different
irrigation schedules for the same simulation setup used for
CB30 in the previous section.
Two different irrigation schedules were compared. The sameamount of water (0.5 cm) was applied during the first twodays after seeding in both irrigation schedules. In the firstirrigation schedule, 0.3 cm of water was applied every otherday (every 2 days) during the first stage of plant growth (fromday 4 to day 14) when only small leaves were grown, instead ofirrigating every day. This resulted in 7 cm of irrigation waterin total, which is 1.5 cm less than the 8.5 cm of water applied
during the CB30 experiment. In the second irrigation schedule,
the amount of applied water was reduced by irrigating every
other day during the entire cultivation period. This resulted in
the application of only 4.9 cm of water. The effect of theirrigation schedule was evaluated by comparing the actualroot water uptake (RWU) rate.

1E-13

Tottori (SP)Coarse sand (DP)Tottori (SP model)

1E-18
1E-23

Gravel (SP)Coarse sand (SP model)
Gravel (SP model)
Coarse sand (DP model: n2 = 3)

1E-28

Gravel (DP model: n2 = 3)

1E-33
Coarse sand (SP)

1E-38

Results and discussion
Soil hydraulic properties
Observed soil water retention curves for the materials usedin this study are plotted along with the fitted water retention
model curves in Figure 3. Figure 4 then shows the predictedunsaturated hydraulic conductivity functions that correspondto those retention curves. Both the SP and DP models werefitted to the coarse sand and gravel retention data. All threeexperimental retention curves clearly show the air-entry
point (Figure 3). The SP model fits well with the dune sandretention data. The experimental retention data for coarse
sand and gravel showed that the residual water content was
already reached at pressure heads larger than 10 cm.
Although the SP model fits well with the experimental
retention curves of coarse sand and gravel, thecorresponding unsaturated hydraulic conductivity functions
shown in Figure 4 unrealistically predict small conductivity
values at lower pressure heads.
The DP model was fitted in a trial-and-error fashion to
the experimental retention curves of coarse sand and gravel.
The hydraulic conductivity in the dry range was not as low

Figure 4 Estimated hydraulic conductivity functions of Tottori
Dune sand, coarse sand and gravel calculated using the SP modeland the DP model when n2 was set to 3.

as predicted by the SP model, although it was still
significantly lower than for dune sand. Parameters w2, w1, a2
and n2 were set to 0.01, 0.99, 0.25 and 3, respectively. The
difference between the fitted SP and DP retention models
was almost imperceptible because w2 is very small (Figure 3).
On the other hand, the K(h) predicted by the DP model inthe dry range was much larger than that predicted by the
SP model. Table 2 lists the basic soil hydraulic parametersof the materials used in the following HYDRUS-1D
simulations.

Numerical analysis
The observed VWCs (Figure 5) were averaged from hourly
observed VWCs. The HYDRUS-1D simulation reproduced
the soil water contents above (at a depth of 3 cm) and below(at a depth of 14 cm) the CB layer reasonably well for CB15

© 2018 British Society of Soil Science, Soil Use and Management, 34, 206–215

An artificial capillary barrier

211

Table 2 Soil hydraulic parameters for the single-porosity (SP) and dual-porosity (DP) models for Tottori Dune sand, coarse sand and gravel
used in HYDRUS-1D
Materials
Tottori Dune sandCoarse sandGravelhsa (1/cm)n

Ks (cm/s)

w1

w2

a2 (1/cm)

n2

0.016
0.004
0.005

0.384
0.371
0.274

0.030
0.133
0.204

6.665
20.77215.524

0.020
0.081
0.230

0.99
0.99

0.01
0.01

0.25
0.25

3
3

0.5

Simulated VWC at –3 cm
Simulated VWC at –14 cm

0.4
θ (cm3/cm3)(b) 0.5

Observed VWC at –3 cm

0.3

Observed VWC at –14 cm
0.2

0.4
θ (cm3/cm3)

(a)

hr

0.3
0.2
0.1

0.1

0

0
0

7

14

21

0

28

7

Time (day)

21

28

21

28

Time (day)

(c)

(d)
0.5

0.5

0.4

0.4
θ (cm3/cm3)

θ (cm3/cm3)

14

0.3
0.2
0.1

0.3
0.2
0.1

0

0
0

7

14

21

28

0

7

14
Time (day)Time (day)Figure 5 A comparison of observed (symbols) and simulated (lines) volumetric water contents (VWC) for experiments with different irrigation
rates. Results for the soil containers with the CB and irrigation rates of 0.15, 0.30 and 0.45 cm/day are shown in (a), (b) and (c), respectively.
Results for the soil container without a CB and the irrigation rate of 0.30 cm/day are in (d). It should be noted that the first values of VWC ata depth of 3 cm in (d) were observed after additional water was applied during the seedling day.

and CB45, although the timing of a sudden increase in thewater content at a depth of 14 cm was not well reproduced
for CB45 (Figure 5). In CB45, the simulated water contentsof the top layer reached almost full saturation and water
held above the interface leaked into the bottom layer
through the CB layer. An accurate prediction of the breaktime may require detailed characterization of the spatial
distribution of pore sizes at the interface, which isimpractical. Also, it is more important to know whether theamount of applied water was too high for a CB to keepfunctioning than to know when the break occurs.

For CB30, the simulated values were higher than observed
values at a depth of 3 cm and lower at a depth of 14 cm(Figure 5). Although the simulation results showed thatvertically infiltrated water stopped at the interface, the watercontent in the bottom layer also increased continuously
during the experiment. This may be caused by waterreaching the bottom layer along the container walls during
the experiment, which is common in lysimeter experiments(Corwin, 2000). In addition to sidewall flow, water
vaporization and condensation may occur near the container
walls because of changes in temperature between nighttime© 2018 British Society of Soil Science, Soil Use and Management, 34, 206–215

212 A. Wongkaew et al.
and daytime, although all containers were insulated withstyrene foams.
For REF, while the simulated values overestimated theobserved values at a depth of 3 cm, the observed andsimulated VWCs corresponded well. Given that none of thesoil hydraulic parameters were calibrated, the results give us
confidence that the HYDRUS-1D model can be used tosimulate soil VWCs in the CB profile during Japanesespinach cultivation.
The simulation results for CB15 and CB30 showed thatwater accumulated at the interface between dune sand andcoarse sand (Figure 6a and b). For CB45, as the top layer
almost reached full saturation, the first capillary barrier ofcoarse sand was broken after a few days and the second
barrier of gravel after about a week (Figure 6c). Although
the VWC in the gravel layer did not increase much, it was
sufficient to conduct water from the coarse sand layer to thedune sand layer. As a result, the VWCs in all layers
increased. The simulated profile for REF showed that

(a)

0.2

0.3

0.4

θ (cm3/cm3)
0

0.5

–4

–4
Depth (cm)

0

0

–8

–12

–16

–16
(d)

θ (cm3/cm3)
0

0.1

0.2

0.3

0.4

0.2

0.3

0.4

0.5

0.4

0.5

θ (cm3/cm3)

0.5

0

0

0

–4

–4

–8

0.1

–8

–12

Depth (cm)Depth (cm)

0.1

(c)

Depth (cm)(b)

θ (cm3/cm3)0

without a CB, water infiltrated all the way to the bottom of
the container.
This study shows that HYDRUS simulations withappropriate hydraulic models predict soil water dynamics
well in a soil profile with a CB at a column scale. Similarly,
Ityel et al. (2011) performed HYDRUS (2D/3D) simulations
to investigate the soil water content in the root zone of aplot experiment with an installed CB. While they did notaccount for RWU, they found that HYDRUS (2D/3D)
performed well in simulating soil water dynamics inside theCB system. Our results, taken together with those reported
by Ityel et al. (2011) thus demonstrate that HYDRUS is agood tool to simulate the performance of the CB system.
Additionally, HYDRUS has also been successfully used tosimulate soil water dynamics in systems with other types ofphysical barriers (e.g. El-Nesr et al., 2014; Guber et al.,2015. El-Nesr et al. (2014) showed with the HYDRUS (2D/
3D) model that the 1-cm-thick impermeable physical barriersignificantly changed the wetting pattern and the distribution

0.1

0.2

0.3

Day 0
–8

Day 7
Day 14

–12

–12

–16

–16

Day 21
Day 28Figure 6 Simulated volumetric soil water contents at different times. Results for the soil containers with the CB and irrigation rates of 0.15, 0.30
and 0.45 cm/day are shown in (a), (b) and (c), respectively. Results for the soil container without a CB and the irrigation rate of 0.30 cm/day
are in (d).

© 2018 British Society of Soil Science, Soil Use and Management, 34, 206–215

An artificial capillary barrierof nutrients in the root zone by preventing downward
movement of water and nutrients. Guber et al. (2015) usedthe HYDRUS (2D/3D) model to evaluate the effects of the
shape, installation depths and alignment of the polyethylene
membrane barriers on reducing leaching water losses fordifferent soil textures.

The role of CB on an increase in water use efficiency
Simulated cumulative RWUs for CB15, CB30, CB45 and
REF were 0.13, 4.48, 6.03 and 4.76 cm, respectively, while
simulated cumulative evaporations were 4.48, 2.98, 2.99 and2.76 cm, respectively (Figure 7 and Table 3). These results
reflect the fact that the spinach growth was similar for CB30,
CB45 and REF. They also reveal that more than 90% of
irrigated water in CB15 and more than 30% of irrigatedwater in CB30 and REF evaporated from the soil surface.
Stormont & Morris (1998) also showed that a significant
amount of water stored near the surface in the CB system
could be lost by evaporation. This means that controllingthe evaporation rate is also important for improving the
WUE during spinach cultivation in the CB profile. For

CB45, only about 25% of water was lost because ofevaporation as a significant amount of water infiltrated
below the CB layer.

Alternative irrigation schedules
Figure 8 shows computed cumulative RWU rates fordifferent irrigation schedules during the cultivation with andwithout a CB. The one without a CB was obtained by using
an 80-cm-long domain where the bottom boundary
condition was set to free drainage (i.e. the pressure headgradient was forced to zero). The irrigation schedule for the
non-CB profile was the same as for CB30. When theirrigation frequency was reduced by half during the initialstage of plant growth, the cumulative RWU was almost thesame as for the original CB30 and much greater than for the
non-CB profile. With a CB, the spinach roots can uptake
water almost at the same rate as in CB30 even though theirrigation frequency is reduced during the early stage of thecultivation because applied water is stored in the root zone
above a CB. This means that by reducing the irrigation
frequency during the early growth stage, water loss by(b)
15

Cumulative infiltration

Cummulative water flux (cm)Cummulative water flux (cm)(a)
Cumulative RWU

12Cumulative evaporation
9
Cumulative soil water accumulation
6
3
0

15
12
9
6
3
0

0

7

14

21

28

0

7

Time (day)

14

21

28

21

28

Time (day)

(c)

(d)
Cummulative water flux (cm)15
Cummulative water flux (cm)

213

12
9
6
3
0

15
12
9
6
3
0

0

7

14
Time (day)

21

28

0

7

14
Time (day)Figure 7 Simulated cumulative infiltration, root water uptake (RUW), evaporation and soil water accumulation at different times. Results forthe soil containers with a CB and irrigation rates of 0.15, 0.30 and 0.45 cm/day are shown in (a), (b) and (c), respectively. Results for the soil
container without a CB and the irrigation rate of 0.30 cm/day are displayed in (d).

© 2018 British Society of Soil Science, Soil Use and Management, 34, 206–215

214 A. Wongkaew et al.

Cumulative fluxes (cm)Infiltration
Root water uptake (RWU)
Evaporation
Water storage

CB15
4.75
0.13
4.48
0.14

CB30
8.50
4.48
2.98
1.04

CB45
12.25
6.03
2.99
3.23

REF
8.50
4.76
2.76
0.98

5.0
Cumulative RWU (cm)

Table 3 Simulated cumulative infiltration, root water uptake (RWU)
and evaporation for each simulated scenario

CB30
Irrigation schedule (1)4.0

Irrigation schedule (2)3.0

Non-CB

2.0
1.0
0.0
0

evaporation can be greatly reduced. In other words, thewater use efficiency can be improved without sacrificing root
water uptake much.
The irrigation frequency during the later stage was also
further reduced by half. Cumulative RWU, in this case,could not keep up with that of CB30, especially after day 14(Figure 8). It was shown that the amount of irrigation water
could be reduced by half during the early growth stage.
However, during the later stage when plant growth is at its
maximum, reducing the irrigation frequency by half may
inhibit plant growth. Simulated cumulative evaporation foralternative irrigation scenarios was 2.64 and 2.48 cm,
respectively, while that for CB30 was 2.99 cm. Although theamount of applied water was significantly reduced, thesimulated amount of water evaporated from the soil surface
did not decrease much. The water loss by evaporation needs
to be taken into account when deciding the irrigation
schedule even when the CB layer is installed to improve thewater retention of the root zone. In addition to maximizing
the water use efficiency, all possible irrigation schedules
would have to be examined. That was, however, beyond thescope of this study.
This study numerically demonstrates the role of a CB in
improving root zone conditions and maximizing the WUE.
Semi-commercial
scale
experiments
conducted
ingreenhouses during cultivation of a horticultural crop by
Ityel et al. (2012) showed that the installation of a CB
increased the soil water content by 60% and the fruit yieldby 25% for green peppers, and increased the matric headby 80% and the biomass yield by 36% for lettuce.
However, although the CB system can be installed on alarge commercial field scale, there are some challenges
associated with the maintenance of a CB. For example,
soil management activities such as tillage and seedbed
preparation can cause the movement of the top soil, during
which finer soil particles can penetrate and fill the larger
pores of the coarser layer, resulting in a break of a CB
layer. To minimize such risk, Ityel et al. (2011) installed asheet material to keep the gravel layer separate from thelayer above. Alternatively, Miyake et al. (2015) proposed a
two-layered CB system where a thin 2-cm coarse sandlayer was installed between the top sand layer and thelower gravel layer. The 2-cm coarse sand layer intercepts

714Time (day)21

28

Figure 8 Cumulative root water uptake (RWU) for different
irrigation strategies based on CB30. The irrigation schedule (1)involves the soil container with a CB in which 0.30 cm of water wasapplied every other day during the first stage of plant growth (fromday 4 to day 14). The irrigation schedule (2) involves the soil
container with a CB where 0.30 cm of water was applied every
2 days during the entire growing period. The non-CB scenario
represents the soil profile without a CB.

fine sand particles penetrating from the top sand layer sothat pores of the gravel layer are kept open. However, ashallow CB layer can be easily damaged by machinery,
which is necessary in large-scale farming. The installationof a CB system of the design used in this study in a largescale field thus may not be appropriate. The CB systemneeds to be carefully designed for large-scale farming.
While the installation of a CB in the root zone can avoid
excess nutrients or pesticides leaching to groundwater, it may
result in accumulation in the root zone. Without appropriate
treatment, such farmland can then be damaged for further
cultivation. For the long-term utilization of CB systems forcultivation, a CB layer that can be directly installed in theroot zone and easily displaced for soil maintenance needs tobe further developed.

Conclusions
A numerical analysis of soil water dynamics in a dune sandprofile with a capillary barrier layer installed at a depth of
6 cm during leaf vegetable cultivation was performed in thisstudy using HYDRUS-1D. In most cases, the simulated soilvolumetric water contents were in good agreement with theobserved results when the dual-porosity model describing
hydraulic properties was used for gravel and coarse sand.
The numerical simulations of alternative irrigation schedules
showed that when a CB is installed, the irrigation frequency
can be reduced by half during the early growth stage and thewater use efficiency can be improved. These results
demonstrate that a CB system can be a practical tool for
leafy vegetable cultivation in sandy soil.

© 2018 British Society of Soil Science, Soil Use and Management, 34, 206–215

An artificial capillary barrier

Acknowledgements
This study was partially supported by the Arid Land ResearchCenter (Tottori University) Joint Research Program and the
Leading Graduate School of Tokyo University of Agriculture
and Technology. The authors greatly acknowledge
constructive and critical comments by two anonymous
reviewers and the editor to improve this manuscript.

References
Abdolahzadeh, A.M., Lacroix Vachon, B. & Cabral, A.R. 2011.
Evaluation of the effectiveness of a cover with capillary barrier
effect to control percolation into a waste disposal facility.
Canadian Geotechnical Journal, 48, 996–1009.
Berger, J., Fornes, L.V., Ott, C., Jager, J., Wawra, B. & Zanke, U.
2005. Methane oxidation in a landfill cover with capillary barrier.
Waste Management, 25, 369–373.
 unek, J. & Piro, P. 2016. A comprehensive analysis
Brunetti, G., Simof the variably saturated hydraulic behavior of a green roof in a
Mediterranean climate. Vadose Zone Journal, 15, doi:10.2136/
vzj2016.04.0032
Carman, P. 1937. Fluid flow through a granular bed. Transactions of
the Institution of Chemical Engineers, 15, 150–167.
Carrier, W.D. 2003. Goodbye, Hazen; Hello, Kozeny-Carman.
Journal of Geotechnical and Geoenvironmental Engineering, 129,
1054–1056.
Cheng, X., Huang, M., Si, B.C., Yu, M. & Shao, M. 2013. The
differences of water balance components of Caragana korshinkii
grown in homogeneous and layered soils in the desert–Loess
Plateau transition zone. Journal of Arid Environments, 98, 10–19.
Corwin, D.L. 2000. Evaluation of a simple lysimeter-designmodification to minimize sidewall flow. Journal of ContaminantHydrology, 42, 35–49.
Dane, J.H. & Hopmans, J. 2002. Methods of soil analysis, Part 4;
Physical methods; Laboratory determination of water retention. Soil
Science Society of America, Inc., Madison, WI.
Durner, W. 1994. Hydraulic conductivity estimation for soils withheterogeneous pore structure. Water Resources Research, 30, 211–223.
 unek, J. 2014. HYDRUS
El-Nesr, M.N., Alazba, A.A. & Sim
simulations of the effects of dual-drip subsurface irrigation and aphysical barrier on water movement and solute transport in soils.
Irrigation Science, 32, 111–125.
Feddes, R.A., Kowalik, P.J. & Zaradny, H. 1978. Simulation of fieldwater use and crop yield. Wiley, New York.
van Genuchten, M.T. 1980. A closed-form equation for predicting
the hydraulic conductivity of unsaturated soils. Soil Science
Society of America Journal, 44, 892–898.
Guber, A.K., Smucker, A.J.M., Berhanu, S. & Miller, J.M.L. 2015.
Subsurface water retention technology improves root zone water
storage for corn production on coarse-textured soils. Vadose Zone
Journal, 14, 2–13.

215

Hazen, A. 1892. Some physical properties of sands and gravels, withspecial reference to their use in filtration. In: 24th Annual Rep,
Massachusetts State Board of Health. pp. 539–556.
Hoffman, G.J. & van Genuchten, M.T. 1983. Soil properties andefficient water use: Water management for salinity control. In:
Limitations to efficient water use in crop production (eds H.M.
Taylor, W.R. Jordan & T.R. Sinclair), pp. 73–85. ASA-CSSASSSA, Madison, WI.
Ityel, E., Lazarovitch, N., Silberbush, M. & Ben-Gal, A. 2011. An
artificial capillary barrier to improve root zone conditions forhorticultural crops: physical effects on water content. Irrigation
Science, 29, 171–180.
Ityel, E., Lazarovitch, N., Silberbush, M. & Ben-Gal, A. 2012. An
artificial capillary barrier to improve root-zone conditions forhorticultural crops: response of pepper, lettuce, melon, andtomato. Irrigation Science, 30, 293–301.
Kozeny, J. 1927. Uber kapillare leitung des wassers in boden.
Sitzungsber. Akad. Wiss. Wien, 136, 271–306.
Miyake, M., Otsuka, M., Fujimaki, H., Inoue, M. & Saito, H. 2015.
Evaluation of an artificial capillary barrier to control infiltrationand capillary rise to root zone areas. Journal of Arid Land Studies,25, 117–120.
Mualem, Y. 1976. A new model for predicting the hydraulicconductivity of unsaturated porous media. Water Resources
Research, 12, 513–522.
Rooney, D.J., Brown, K.W. & Thomas, J.C. 1998. The effectivenessof capillary barriers to hydraulically isolate salt contaminatedsoils. Water, Air, and Soil Pollution, 104, 403–411.
Seki, K. 2007. SWRC fit &ndash; a nonlinear fitting program with awater retention curve for soils having unimodal and bimodal pore
structure. Hydrology and Earth System Sciences Discussions, 4,
407–437.
 unek, J., van Genuchten, M.T. & Sejna,Sim
M. 2008. Development
and applications of the HYDRUS and STANMOD software
packages and related codes. Vadose Zone Journal, 7, 587–600.
 unek, J., van Genuchten, M.T. & Sejna,Sim
M. 2016. Recent
developments and applications of the HYDRUS computer
software package. Vadose Zone Journal, 15, 1539–1663.
Slichter, C.S. 1899. Theoretical investigation of the motion ofground waters. In. US Geological Survey 19th Annual Report, pp.
322.
Stormont, J.C. & Morris, C.E. 1998. Method to estimate water
storage capacity of capillary barriers. Journal of Geotechnical andGeoenvironmental Engineering, 124, 297–302.
Terzaghi, C. 1925. Principles of soil mechanics. Engineering NewsRecord, 95, 832.
Zhang, X., Lu, G., Long, W., Zou, X., Li, F. & Nishio, T. 2014.
Recent progress in drought and salt tolerance studies in Brassica
crops. Breeding Science, 64, 60–73.
Zhu, M., Monroe, J.G., Suhail, Y., Villiers, F., Mullen, J., Pater,
D., Hauser, F., Jeon, B.W., Bader, J.S., Kwak, J.M., Schroeder,
J.I., McKay, J.K. & Assmann, S.M. 2016. Molecular and systems
approaches towards drought-tolerant canola crops. New
Phytologist, 210, 1169–1189.

© 2018 British Society of Soil Science, Soil Use and Management, 34, 206–215