Published May 11, 2017

Technical Notes

Analysis of the Hysteretic Hydraulic
Properties of Unsaturated Soil
L. Zhuang, C.R. Bezerra Coelho, S.M. Hassanizadeh,*and M.Th. van Genuchten

Core Ideas• We devised a setup to measure
hydraulic properties using the multistep flux method.
• Results showed good agreementwith the data obtained with thehanging water column.
• However, they deviated slightly fromindependent data obtained with
the HYPROP.

Knowledge of the unsaturated soil hydraulic properties is essential formodeling water flow and solute transport processes in variably saturated
subsurface systems. Various experimental setups have been developed
over the years to measure the hydraulic properties. We devised a relatively
simple setup for simultaneous measurement of the water retention andunsaturated hydraulic conductivity curves using multistep flux (MSF) andhanging water column (HWC) experiments. Our focus was especially on
medium- and coarse-textured sands having relatively narrow particle-size
distributions as reflected by the van Genuchten–Mualem (VGM) hydraulicparameter n. Values of the VGM parameter n for some of the sands we usedwere as high as 15. We also measured the hydraulic properties using the
HYPROP evaporation method. The MSF and HWC results showed excellent
agreement, but deviated slightly from independent data obtained with the
HYPROP measurement system.
Abbreviations: HMS, HYPROP measurement system; HWC, hanging water column method; MSF, multistep flux method; VG, van Genuchten; VGM, van Genuchten–Mualem.

L. Zhuang, S.M. Hassanizadeh, andM.Th. van Genuchten, Dep. of Earth
Sciences, Utrecht Univ., Princetonlaan
9, P.O. Box 80021, 3508 TA, Utrecht, theNetherlands; C.R. Bezerra Coelho,Dep. of Civil Engineering, COPPE,
Federal Univ. of Rio de Janeiro,
UFRJ, Rio de Janeiro, RJ, 21945-970,
Brazil; S.M. Hassanizadeh, Soil and
Groundwater Systems, Deltares, Princetonlaan 6, 3584 CB, Utrecht, theNetherlands; M.Th. van Genuchten,
NIDES Interdisciplinary Center forSocial Development, Federal Univ. of
Rio de Janeiro, UFRJ, Rio de Janeiro,
RJ, 21945-596, Brazil. *Corresponding
author (S.M.Hassanizadeh@uu.nl).

Received 22 Nov. 2016.
Accepted 8 Mar. 2017.
Citation: Zhuang, L., C.R. Bezerra
Coelho, S.M. Hassanizadeh, and M.Th.
van Genuchten. 2017. Analysis of thehysteretic hydraulic properties of
unsaturated soil. Vadose Zone J. 16(5).
doi:10.2136/vzj2016.11.0115

Vol. 16, Iss. 5, 2017
© Soil Science Society of America

5585 Guilford Rd., Madison, WI 53711 USA.
All rights reserved.

Quantifying the unsaturated soil hydraulic properties is essential to understanding andmodeling fluid flow and contaminant transport in the vadose zone, as well as for othervariably saturated multiphase flow systems. The constitutive relationships for air–water
systems generally involve the water content, q, as a function of the pressure head, h, andthe hydraulic conductivity, K, as a function of the pressure head or water content. A rangeof laboratory methods have been developed over the years for estimating the soil hydraulicproperties (cf. van Genuchten and Wierenga, 1986; van Genuchten et al., 1997; Dane andHopmans, 2002; Durner and Lipsius, 2005). This includes not only direct measurementof q and/or K at specific pressure heads or water contents but also the use of inverse procedures to estimate the complete q(h) and/or K(q) curves (Durner et al., 1999; Hopmans
et al., 2002).
Starting with the early studies by Becher (1971) and Wind (1968), the evaporation method
is now widely used to estimate the water retention and the unsaturated hydraulic conductivity curves simultaneously. The method has seen many improvements over the years(e.g., Halbertsma, 1996; Wendroth et al., 1993; Peters and Durner, 2008; Schindler andMüller, 2006; Peters et al., 2015), leading to a semi-automated version (referred to here as
the HYPROP measurement system, HMS) that is now being commercialized by Decagon
Devices and UMS AG. The method uses values of the pressure head measured at two
depths within a 5-cm soil sample, along with the weight of the soil sample during theevaporation process, to estimate the soil hydraulic data. While very reliable results havebeen reported for the HMS approach, one inherent drawback of evaporation methods isthat the results hold only for the drainage branches of the soil hydraulic properties.
An alternative simultaneous direct approach is the multistep flux (MSF) method based onvertically uniform flow (Dirksen and Matula, 1994; Weller et al., 2011; Weller and Vogel,2012; Kumahor et al., 2015). The method allows measurements of K(h) assuming unit gradient conditions during steady-state downward flow in a soil column. Water inflow rates

Vadose Zone Journal | Advancing Critical Zone Scienceare adjusted to achieve the same pressure heads when measured at
two or more vertical positions. The fluid flow rate then becomesequal to K at the measured h. Repeating the measurements at various flow rates and corresponding pressure heads will produce thedesired hydraulic data points.
As part of this study, we constructed a relatively simple experimental setup using a small flow cell for measuring the unsaturated soil
hydraulic properties. We measured the hysteretic properties of two
soil samples having relatively narrow pore-size distributions andcompared the results with the more standard multistep hanging
water column (HWC) approach. The studies were motivated inpart to have reliable soil hydraulic data for more theoretical studies
of hysteresis phenomena using alternative thermodynamics-based
interfacial area approaches (Zhuang, 2017). Moreover, relatively
few experimental and numerical studies have been performed onsands characterized by relatively narrow particle-size distributions(e.g., Weller et al., 2011; Weller and Vogel, 2012; Mahmoodlu etal., 2016; Wang et al., 2016; Zhuang et al., 2016).

66Materials and Methods
Sand Materials

We investigated two types of sands. One sand, S1, was obtained
from a sand mining site (Sibelco) with particles ranging from
0.1 to 0.5 mm. The other sand (S2), having grain sizes between
0.1 and 1 mm, was obtained from a riverbed in the Netherlands.
Prior to use, the two sandy soils were rinsed with deionized waterand then air dried. Saturated hydraulic conductivities of the two
samples were measured using a constant-head method (Reynolds
et al., 2002) with the same sand cell holder as used for the multistep hanging water column and multistep flux experiments (Fig.
1). Selected properties of the two sand samples are shown in Table
1. The particle density was calculated based on the weight andvolume of the sand particles. The sand volume was represented by
the volume of water that overflowed when the sand particles wereplaced in degassed water. The measurements and calculations wererepeated to obtain an average value of the particle density. Valuesof the average porosity were calculated using data from all experiments (HWC, MSF, and HMS).

Hanging Water Column Experiments
Figure 1 shows a schematic of our HWC experimental setup. A
custom-built Plexiglas cell was used for the sand samples. The
dimensions of the cell were 3 cm (height) by 3 cm (length) by 2 cm
(width). A valve at the top of the sandbox (Valve 1) was connected
to a balloon filled with moist air to keep constant atmosphericpressure. At the bottom of the sand cell, a 5-mm hydrophilic nylon
membrane was held by a stainless-steel porous plate to serve as acapillary barrier. The water reservoir at the bottom of the setup
was connected to a small hanging water column, which was used
to control the pressure head at the outlet. Water in the small hanging column could overflow during drainage, while extra water wasadded to keep the water head in the column constant during imbibition. Silicone tape was used at all joints to avoid any leakage.
Two mini-tensiometers (Rhizo Instruments) were installed at depthsof 1 and 2 cm in the sand sample cell. The tensiometers consistedof a ceramic cup, 1 cm long and 4 mm in diameter, and a small porepressure transducer. An air-permeable but water-impermeable plastic hollow fiber was used to connect the ceramic cup to a vacuum
to remove air from the tensiometers. Prior to use, the tensiometers
were saturated with deionized water, while during the experiments,
the tensiometers were always connected to an automatic vacuum
system. This ensured that the tube between the ceramic cup andthe transducer remained filled with water. The pressure transducers were connected to a CR1000 datalogger (Campbell Scientific).
Tensiometer readings were collected every 1 min.
Water contents in the middle of the sand sample were measured
using the g-ray transmission method. When a beam of g radiation passes through a sample of thickness x, the transmission ofphotons can be described using the Beer–Lambert law, which for
an unsaturated soil sample can be written as

I = I 0 exp(-m s x s -m w x w )[1]

where I and I0 are the measured and corresponding reference intensities, respectively, m s and m w are the soil and water attenuation
coefficients, respectively, and xs and x w denote path lengths ofthe g-ray beam through soil and water, respectively. Values of theTable 1. Properties of the two sands used in the experiments.

Fig. 1. Schematic view of the experimental setup for the hanging watercolumn (HWC) experiments.

VZJ | Advancing Critical Zone Science

Properties

S1

S2

Mean particle diameter (d50), mm

0.20

0.28

Uniformity coefficient (Cu)†

2.3

3.3

Particle density (ρs), g cm−3

2.56

2.55

Saturated conductivity (Ks), cm h−1

61.2

75.6

Average porosity (j)

0.39

0.36

† Cu is the ratio of d60 to d10.

p. 2 of 9porosity (j) of the sand and its water content (q) can be calculated
from xs and xw usingj=x - xs
x

and

q=

xw
x

[2]

respectively, where x is the total thickness of the soil sample (i.e.,
2 cm, being the width of our experimental setup).
For our study we used a dual-energy g-ray system. The g-ray
sources consisted of 241Am, with an energy peak of 59 keV, and137Cs, with an energy peak of 662 keV. The diameter of the g-ray
beam was 6 mm. Measured intensities hence were average values
across the cross-section of the beam and the sample thickness x.
The attenuation coefficients m s and m w for both 241Am and 137Cs
were measured and calculated beforehand. Details of the calibration procedures and the dual g-ray system were given by Fritz(2012). We chose the intensities of the empty cell as the reference I0
for both 241Am and 137Cs. Intensities for 241Am and 137Cs can becollected simultaneously for each g-ray transmission measurement,
while xs and xw can be calculated from Eq. [1], written for Am andCs separately. Once xs and xw are known, the sand porosity (j) andwater content (q) can be calculated for every g-ray transmission
measurement. Water contents were measured after equilibrationof the soil sample at each imposed water level (and hence pressure head). During primary drainage, the total amount of waterfrom the outlet at equilibrium was recorded every two or threeelevations. The resulting average water contents were essentially
identical to the measured water contents using g-ray transmission.
The experimental setup was first mounted with the bottom reservoir
and the cell full of water and without the top lid. Deionized anddegassed water was used to minimize air entrapment. The cell was
packed by pouring dry sand continuously into the water-filled cellthrough a funnel and regularly tapping the sand. A small comb wasused to mix the sand in the water to avoid layering. The top cover
was installed after packing the sand uniformly. All experiments wereconducted in a constant-temperature room at 21 ± 0.5°C.

changing the inflow rate and the height of the hanging watercolumn (and thus of h).
A sketch of the MSF experimental setup is shown in Fig. 2. Six
injection needles (two in the lateral direction and three in the longitudinal direction) were used to obtain a spatially uniform water
inflow rate to the top of the cell. Each needle was connected toa tube with an inner diameter of 2 mm. The six tubes were connected to a peristaltic pump that controlled the injected flow rate.
The tips of needles were put in contact with a 200-mm hydrophilic
nylon membrane (Hydrophilic Membrane 1 in Fig. 2) to establish
a homogenous water flow rate into the sand sample.
A series of continuous water flow conditions were establishedduring the various experiments, i.e., starting from primary drainage, to scanning imbibition, and then to main drainage. After
packing the saturated sand samples into the cell, a water flow rate,
slightly smaller than the measured saturated hydraulic conductivity (as obtained with the constant-head method), was applied tothe top of the sample. The hanging water column was then kept
at the same level as the bottom of the sand sample.
Readings of the two tensiometers were collected continuously,
while outflow was measured when the readings of the two tensiometers became identical, in which case the measured outflow wasassumed to be equivalent to the value of the hydraulic conductivity
at the pressure head obtained from the tensiometer readings. The
process was reversed when the water flow rate became too small forthe peristaltic pump. The level of the hanging column after eachstep was moved to a new elevation prior to decreasing the flow rateusing the pump during drainage, while moving in the opposite
manner during imbibition using higher flow rates. The level of thehanging column at each step was first estimated from the HWC
experiments and then adjusted every 0.5 or 1 cm based on the difference between the two tensiometer readings. The water content

Multistep Flux Experiments
We modified the HWC setup to enable also MSF experiments.
This allowed us to measure unsaturated conductivities and thewater retention curve directly. Water flow in the porous medium
was described using the standard Darcy–Buckingham equation:æ ¶h ö
q =-K ( q )ççç -1÷÷÷è ¶z ø

[3]

where q is the fluid flux and z is vertical spatial coordinate. For
unit gradient flow in the vertical direction (i.e., when ¶h/¶z =0), the flux becomes equal to the hydraulic conductivity, K(h).
Different hydraulic conductivity values can be obtained by

VZJ | Advancing Critical Zone ScienceFig. 2. Schematic view of the experimental setup for the multistep flux
(MSF) experiments.

p. 3 of 9

in the middle of the sample was measured once the tensiometerreadings had stabilized.

HYPROP Experiments
We used the HYPROP commercial device (UMS AG) to carry out
the HMS evaporation experiments. Saturated soil samples (250cm3, 5 cm in height) were prepared for this purpose following
the HYPROP manual. Dry sand was first placed in the sample
rings, which were then put into distilled and degassed water. The
soil samples were saturated with water from the bottom througha porous plate. Once saturated, the soil samples were sealed at thebottom and exposed at the top for evaporation. Values of the pressure head were monitored continuously at two depths (1.25 and3.75 cm). The weight loss of the sample was measured simultaneously so that values of the water content could be calculated
volumetrically. At any given time, values of the water content, thepressure head, and the unsaturated hydraulic conductivity were
calculated using the HYPROP-FIT software as documented by
Pertassek et al. (2015). The software uses geometric mean valuesof the pressure heads measured with the two tensiometers.

Soil Hydraulic Functions
Measured soil water retention and unsaturated conductivity data
were analyzed in terms of the van Genuchten–Mualem (VGM)
equations (van Genuchten, 1980):

q( h ) = q r +(q s -q r

1+ ah

n m

)

m ù2
l é
K ( q ) = K s ( S e ) ê1-(1- S e1/ m ) ú
ëê
ûú

[4]

[5]

Se =

q-q r
q s -q r[6]

where q s and q r are the saturated and residual water contents,
respectively; S e is the effective saturation, Ks is the saturated
hydraulic conductivity; a, n, and l are fitting parameters; and m= 1 − 1/n. All optimizations of the retention data were performed
using the RETC software (van Genuchten et al., 1991).

66Results and Discussion

Three replicates were conducted for all experiments. Because of
the very close overlap of the replicates, only one measurement set
is shown here for each sand.

Hanging Water Column Experiments
While the HWC experiments for Sands S1 and S2 each lasted
approximately 2 wk, the exact duration depended on the numberof elevations and the times needed to reach equilibrium. Typicalequilibration times at early and later stages for primary drainage
for Sand S1 are shown in Fig. 3. The top of the soil sample wastaken as a reference for the level of the hanging water column. As
can be seen, the equilibration times were very short initially but
then increased because of lower conductivities when the sample
dried out.
Water retention data for the two sands as obtained with the HWC
experiments are shown in Fig. 4a and 4b. The different symbols represent the HWC measured retention data during primary drainage,
main imbibition, and main drainage. The shapes of the retention
curves are consistent with the particle-size distribution ranges of thetwo sands: the retention curve of Sand S1 with its narrow particle-size
distribution range is flatter for both drainage and imbibition.

Fig. 3. Hanging water column experiments: typical trajectories of the two tensiometer readings for primary drainage for Sand S1.

VZJ | Advancing Critical Zone Sciencep. 4 of 9

Fig. 4. Hanging water column (HWC) experiments: water retention data for Sands S1 and S2, together with the fitted van Genuchten (VG) water
retention curves.

Figure 4 also includes the van Genuchten (VG) retention functions (dashed lines) as fitted to the experimental data. The fitted
parameter values are listed in Table 2. The residual water content
q r was fitted iteratively, using RETC, to the same value for eachsand for all HWC experiments. The fitted value of the saturated
water content q s for the main drainage and imbibition curves wasless than the porosity due to air entrapment (leading to a non-zero
residual air content).

Table 2. Values of the fitted van Genuchten–Mualem hydraulic parameters for the different experiments.
Experiment†

a

n

cm−1

qr

qs
3
—cm cm−3 —Ks

Multistep Flux Experiments
The MSF experiments for the two sands each lasted about 10 d.
Typical pressure head changes from one uniform condition toanother uniform condition for primary drainage during the MSF
experiments are shown in Fig. 5. The level of the hanging column
was always kept lower than the tensiometer readings during primary drainage. When the inflow rate was reduced, initially a
relatively large difference between the two tensiometer readings
could be observed. After stabilization of the tensiometer readings,
the level of the hanging column was lowered carefully in small
steps (every 0.5 cm) until the readings of two tensiometers became
the same, thus reflecting steady-state conditions.

l

cm
h−1

Sand S1
Primary drainage, HWC

0.0284

14.5

0.086

0.385

–

–

Main imbibition, HWC

0.0451

14.8

0.086

0.340

–

–

Main drainage, HWC

0.0288

13.5

0.086

0.340

–

–

Primary drainage, MSF

0.0315

15.1

0.087

0.385

61.2

0.81

Scanning imbibition, MSF 0.0553

8.0

0.110

0.340

41.0

0.40

Main drainage, MSF

0.0322

10.0

0.086

0.340

41.0

0.82

Primary drainage, HMS

0.0219

10.0

0.068

0.410

61.2

0.20

Primary drainage, HWC

0.0442

12.2

0.065

0.345

–

–

Main imbibition, HWC

0.1003

3.9

0.065

0.300

–

–

Main drainage, HWC

0.0453

11.1

0.065

0.300

–

–

Primary drainage, MSF

0.0460

12.2

0.065

0.338

75.6 4.50

Scanning imbibition, MSF 0.1007

4.0

0.141

0.300

22.0 −0.50

Main drainage, MSF

0.0480

10.0

0.065

0.300

22.0 2.00

Primary drainage, HMS

0.0421

5.9

0.044

0.363

75.6 0.66

Sand S2† H WC, hanging water column; MSF, multistep flux; HMS, HYPROP
measuring system.

VZJ | Advancing Critical Zone ScienceFig. 5. Multistep flux (MSF) experiments: typical trajectories of thetwo tensiometer readings for primary drainage for Sand S1: (A) inflow
rate of 13.7 cm h−1 and a hanging water level of −37 cm; (B) inflow
rate of 6.8 cm h−1 and a hanging water level of −37 cm; (C) inflow rateof 6.8 cm h−1 and a hanging water level of −37.5 cm.

p. 5 of 9

Figures 6a and 6b show observed water retention data for the twosands as measured using the MSF experiments. Different symbols
are used for the primary drainage, scanning imbibition, and main
drainage data points. Fitted VGM curves for the MSF experiments
are shown as solid lines. Also included for comparison are the fitted
VG curves of the HWC experiments (dashed lines; the same curves
as in Fig. 4). Both sands showed reasonable consistency in terms of
the HWC and MSF retention data, especially considering that the
imbibition branches of the HWC data presented main imbibition,
while the MSF imbibition branch represented a scanning curve.
The retention curves of Sand S1 obtained with the MSF method
is situated slightly below the HWC data for both drainage andimbibition. A minor rearrangement of small sand particles during
the MSF experiments may have contributed to the discrepancies, as
perhaps the presence of some nonequilibrium dynamic effects (e.g.,
Weller et al., 2011; Diamantopoulos and Durner, 2012).
Unsaturated hydraulic conductivities obtained using the MSF
method are shown in Fig. 6c and 6d. The conductivity vs. watercontent data showed very little or no hysteresis between the main
drainage, primary wetting, and main wetting branches, consistent
with previous studies (e.g., Poulovassilis, 1969; Tzimas, 1979). The
unsaturated conductivities of the two sands at high water contents
were close to the saturated conductivity as measured with the constant-head method.
We used the VGM model to obtain a simultaneous fit of the MSF
measured water retention and unsaturated conductivity data. The
resulting curves are shown as solid lines in Fig. 6. Values of theresidual water content, q r, for primary and main drainage were
fixed at those obtained with the HWC experiments, while its
value was fitted for the scanning imbibition curve. The value ofthe saturated conductivity Ks for primary drainage was taken to
be the value measured using the constant-head method. The valueof Ks for primary drainage was taken to be the value measured
using the constant-head method, while Ks for the scanning andmain drainage branches was fixed at the largest measured value
obtained for these two branches. The estimated values are shown

Fig. 6. Multistep flux (MSF) experiments: water retention data, including the fitted van Genuchten–Mualem (VGM) curve for the MSF experiments
and the fitted van Genuchten (VG) curve for the hanging water column (HWC) experiments for comparison (top), and unsaturated hydraulic conductivities, including the saturated hydraulic conductivity (Ksat) and the fitted VGM curve (bottom) for Sands S1 and S2.

VZJ | Advancing Critical Zone Science

p. 6 of 9

in Table 2. Small differences in the fitting parameter values existed
between the HWC and MSF data points for primary and main
drainage. Values of the pore connectivity parameter l showed somevariation among the various curves. However, fixing the value at
0.5 as suggested by Mualem (1976) did not have a major effecton the plotted curves, except for the MSF primary drainage andscanning imbibition curves of Sands S1 and S2 (results not further
shown here). This was not overly surprising because many (notall) of the soils used in the analysis by Mualem were also relatively
coarse-textured disturbed porous media as in our study. Values ofl for other soils often deviate significantly from 0.5 (e.g., Yates etal., 1992; Schaap and Leij, 2000).

Comparison with HYPROP Evaporation Data
We compared some of the HWC and MSF primary drainage datawith the HYPROP (HMS) evaporation experiments. Figures 7aand 7b show that the HMS setup produced very well-definedsmooth retention curves but with somewhat higher saturated
water contents than the HWC data, as well as lower residual

water contents. The primary drainage curve for Sand S1 obtainedwith the HMS evaporation method was situated above the curve
obtained with the HWC method throughout the entire watercontent range (Fig. 7a), while the data for Sand S2 showed only
slight differences, mostly in the drier water content range. Similar
discrepancies between HMS data and especially pressure plate
data were also noted by Schelle et al. (2013) for their coarse-textured samples. They offered three possible explanations for thedeviations. One could be the different saturated water contents ofthe sand samples used for the two methods. Another possibility
may be cooling effects during the evaporation experiments. The
tensiometer readings are temperature dependent, which could
have caused the measured retention curve to be shifted slightly
upward (to larger absolute pressure head values). A third explanation could be possible dynamic nonequilibrium effects during
the evaporation experiments, as discussed by Hassanizadeh et al.
(2002) and Diamantopoulos and Durner (2012), among others.
We conclude that more studies of the observed differences may
be needed.

Fig. 7. Hanging water column (HWC) and HYPROP measuring system (HMS) experiments: measured and fitted van Genuchten–Mualem (VGM)and van Genuchten (VG) water retention data (top) and unsaturated hydraulic conductivity (bottom) curves during primary drainage of the HWC
and multistep flux (MSF) experiments for Sands S1 (left) and S2 (right).

VZJ | Advancing Critical Zone Sciencep. 7 of 9

Unsaturated conductivities obtained with the MSF and HMS
evaporation experiments are shown in Fig. 7c and 7d. Values of
the unsaturated conductivity in this case are presented using alogarithmic scale. Results indicate a several orders of magnitudedifference between the measured unsaturated hydraulic conductivities using the two methods. Unsaturated conductivity data
points obtained with the evaporation method were mainly in thedry range, while MSF experiments measured unsaturated conductivities mainly in the wet range. Our results are consistent withother studies showing that HMS applications to soils having very
narrow pore-size distributions (as reflected by van Genuchten nvalues above 5 or even 10) may still produce reliable results forwater retention but not for near-saturated hydraulic conductivity
values (Peters et al., 2015).
Figure 7 includes the fitted VGM curves for the MSF and HMS
measured soil water retention and hydraulic conductivity data.
Fitted parameter values are reported in Table 2. Values of thesaturated conductivity, Ks, of the two sands were fixed at thosemeasured using the constant-head method. The fitted curves for
the HMS data are indicated by solid lines in Fig. 7. They showed
excellent agreement with the retention data but not with theunsaturated conductivity measurements. The HWC experiments
produced mostly higher values of the parameters a, n, and q r thanthe HMS experiments. We have included the measured file of oneof the sands (S1) as supplemental material.
We conclude by noting that some of the differences between the
HWC, MSF, and evaporation experiments may have been due todifferences in the measured water contents caused by different
averaging volumes. Water contents during the HWC and MSF
experiments were measured using g transmission, in which casethey were calculated based on the average volume of the g source
opening area (6 mm in diameter) and the sample width (2 cm).
By comparison, water contents during the evaporation experiments were averaged based on the entire volume of the sample
rings (250 cm 3, 5 cm in depth). Moreover, due to the narrow
particle-size distributions (especially for Sand S1), the moisture
front during evaporation becomes very sharp, leading to large differences between the water contents in the upper and lower partsof the sample. This may cause the measured retention curve to be
shifted slightly rightward at lower water contents. Such a situation
may compromise the linearization assumptions inherent in the
HMS evaporation approach (Peters et al., 2015).

66Concluding Remarks

In this study, we used three laboratory methods to characterize theunsaturated soil hydraulic properties of two sands having relatively
narrow particle-size distributions. A small custom-built cell or box
was developed to conduct HWC and MSF experiments, while thecommercial HYPROP system was used for the evaporation experiments. Both drainage and imbibition curves could be obtained

VZJ | Advancing Critical Zone Scienceusing the HWC and MSF methods. The HMS method, on theother hand, provides only primary drainage curves. The hysteretic
retention data obtained with the HWC and MSF experiments
showed good agreement with each other for the primary drainage
and main imbibition processes. The MSF-measured unsaturated
conductivities did not show distinct hysteretic behavior as a function of water content in that values for primary drainage, scanning
imbibition, and main drainage all showed very little difference
when plotted vs. the water content.
We also compared the HWC- and MSF-measured hydraulicdata with the HMS evaporation results. Some discrepancies were
found between the HWC and HMS retention data, presumably
because of the assumed linear distribution of the water content
vs. depth in the HMS approach. This assumption may not bevalid for our porous media with very narrow particle-size distributions. Unsaturated conductivities using the HMS evaporation
experiments were furthermore confined to the very dry range.
Independent saturated conductivity measurements hence may be
critical to obtain a good description of the complete hydraulic conductivity curve. Additional numerical and experimental studies
may be needed to further clarify these issues.

Acknowledgments

Author L. Zhuang would like to thank the China Scholarship Council (no. 201206380076)
for financial support; S.M. Hassanizadeh has received funding from the European ResearchCouncil under the European Union’s Seventh Framework Program (FP/2007-2013)/ERC
Grant Agreement no. 341225. We would like to thank Associate Editor Peter Lehmann andtwo anonymous reviewers for providing constructive comments to the manuscript.

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