沙漠研究 24-1, 77-80 (2014)
Ἃ₍◊✲ 24-1, 77 - 80 (2014)
Journal of Arid Land Studies
Journal of Arid Land Studies－ DT11 Refereed Paper －㸫DT11 Refereed Paper㸫

Hydraulic Properties of Rocky Soils in a Semi-Arid Savannaon the Edwards Plateau, TX
Ieyasu TOKUMOTO*1), James L. HEILMAN2), Kevin J. MCINNES2) and Cristine L.S. MORGAN2)
Abstract: Hydraulic properties of rocky soils, especially the water retention curve (WRC), play an important role in assessing
regional hydrology in terrain such as the karstic Edwards Plateau, TX, USA, where rock occupies a significant fraction of the soilvolume. However, estimation of hydraulic parameters is a challenge because rocky soil makes it difficult to measure the parameters
directly. The objective of this study was to observe the effect of volume fraction of rock on hydraulic properties and to estimate theunsaturated hydraulic properties for rocky soil using the evaporation method. We examined the validity of the van Genuchten (VG)
and the Durner models to express unsaturated hydraulic properties for clay loam containing rock fragments. Hydraulic model
parameters of the VG and the Durner models were inversely optimized over a wide range of pressure heads. The evaporation
measurements showed that small volume fractions of rock can increase evaporation from soils by slowing upward movement of water,
thereby maintaining capillary connectivity to the surface for a longer period of time. Two simulation models, VG and Durner, werecompared with the data from evaporation experiments. Results showed that the Durner model was more appropriate than the VG
model for describing water retention and hydraulic conductivity of rocky soils.
Key Words: Evaporation method, Hydraulic properties, Rocky soils, Water retention curve

1. Introduction
Hydraulic properties of rocky soils, especially the water
retention curve (WRC), play an important role in assessing
regional hydrology in karst ecosystems. Karst areas arelocated widely across the U.S., and soils on karst are generally
shallow and rock occupies a significant fraction of the soilvolume (Schwinning, 2013). Tokumoto et al. (2012) showedthat rock reduces volumetric water content (T). This supports
the idea that volume fraction of rock needs to be included indefining WRC for rocky soils.
The van Genuchten model (VG) (van Genuchten, 1980) is
widely used to estimate WRC, which is adapted for S-shaped
retention curves characteristic of relatively fine-textured soils.
Durner (1994) proposed a modified VG model to predict moreaccurately WRC, especially in low ranges of pressure head (h).
The VG and the Durner models have a pore connectivity
parameter, l, which can represent the tortuosity factor for better
estimating unsaturated hydraulic conductivity based on thestatistical pore-size distribution model of Mualem (1976).
The evaporation method involving monitoring pressure
head and water content during the process of evaporation fromsoil samples has been commonly used to estimate both WRC
and unsaturated hydraulic conductivity.
Wind (1968)
estimated WRC from average Tand h readings at several
depths in a soil column, and determined hydraulic conductivity* Corresponding Author: ieyasu4337@yahoo.co.jp

from measured h profiles and changes in T distribution. With
the evaporation method, unsaturated hydraulic conductivities
can be particularly determined for h ranging fromapproximately -50 cm to -700 cm (ŠimĤnek et al., 1998).
These authors evaluated optimum conditions for predicting
hydraulic parameters for the VG model using the evaporation
method. Studies have assessed the significance of thehydraulic model selection, depending on soil types. Sakaiand Toride (2007) compared the VG and the Durner models,and suggested that the Durner model can express unsaturated
hydraulic conductivity at h lower than -700 cm withappropriate model parameters. Their results highlighted theimportance of proper estimation of l. Mualem (1976)
assumed l = 0.5 based on empirical studies. However l may
be different in rocky soils because tortuosity increases withrock content.
The objective of this study was to observe the effect ofvolume fraction of rock on hydraulic properties and to estimate
the unsaturated hydraulic properties for rocky soil using theevaporation method. We examined the validity of the VG
and the Durner models to express unsaturated hydraulicproperties for clay loam containing rock fragments. Using
the experimental data, hydraulic model parameters of the VG
and the Durner models were inversely optimized over a wide
range of h. We also investigated the relationship between land rock volume fraction. The effect of rock fragments on
unsaturated hydraulic properties was evaluated by comparison
㸦Received, August 10th, 2013; Accepted, January 21st, 2014㸧

1390 Hamasaka, Tottori 680-0001, Japan
1) Arid Land Research Center, Tottori University, Tottori, Japan

2) Department of Soil and Crop Sciences, Texas A&M University, College Station, TX, USA

78of measured and predicted h and T.

2.2.2. Durner model
For conductivity estimation in heterogeneous pore systems,Durner (1994) modified the water retention curve of the VG
model as:2. Theory
2.1. Water flow model for rocky soils
The water content of rock, and flow of water between soil
and rock are assumed to be negligible. Bulk volumetric watercontent includes the impact of rock, and is estimated as:ߠ ൌ ሺͳ െ ܴ ሻߠ‫݈݅݋ݏ‬(1)
Where RV is the volumetric fraction of rock (cm3 cm-3), andTsoil is volumetric water content of the soil (cm3 cm-3). The
prediction of water flow requires functions for the water
retention curve and hydraulic conductivity so that accurate
determination of proper hydraulic functions and estimation of
the function parameters for rocky soils are important. In thispaper, we used the evaporation method (ŠimĤnek et al., 1998)
to examine the van Genuchten (1980) and the Durner (1994)
models for obtaining the water retention curve and hydraulicconductivity.
To calculate water flow in rocky soil numerically, we used
Hydrus 1D, a simulation model for analysis ofsaturated-unsaturated water flow, developed by ŠimĤnek et al.
(2005).
2.2. Water retention curve models
2.2.1. van Genuchten (VG) model
The van Genuchten (1980) model describes water contentand hydraulic conductivity in unsaturated soil using theequationsandܵ݁ ൌߠെߠ‫ݎ‬ߠ‫ ݏ‬െߠ‫ݎ‬݊ െ݉ൌ ሾͳ ൅ ߙ݄ ሿ(2)ͳ‫ܭ‬ሺܵ݁ ሻ ൌ  ‫ ݈ܵ ܭ‬ሾͳ െ ሺͳ െ ܵ݉ ሻ݉ ሿሺ͵ሻWhere Se is the effective water content, Ks is the saturated
hydraulic conductivity (cm d-1), Tr and Ts are residual andsaturated water contents (cm3 cm-3), respectively, n, m (=1-1/n)
andD (cm-1) are empirical parameters, and l is a poreconnectivity parameter related to pore tortuosity. We
assumed that Ts and Tr, calculated by Eq. (2), decreased as Rv
increased. The VG model uses a predictive K(Se) model
based on the statistical pore-size distribution model of Mualem(1976) in conjunction with Eq. (3) (ŠimĤnek et al., 1998).
The pore connectivity, l in the hydraulic conductivity function,is considered as 0.5 for many soils (Mualem, 1976).
However, l can vary and be used to optimize the other model
parameters with the evaporation method (Sakai and Toride,2007). For rocky soils, l could be affected by the volumetricfraction of rock and rock size.

ܵ݁ ൌߠെߠ‫ݎ‬ߠ‫ ݏ‬െߠ‫ݎ‬ൌ σ݇݅ൌͳ ‫ ݅ݓ‬ሾͳ ൅ ሺߙ݅ ȁ݄ȁ݊ ݅ ሻሿെ݉ ݅(4)

Where wi is a weighting factor for the water retention curves,
subject to 0 < wi < 1 and 6 wi = 1, and i, ni and mi are
curve-shape parameters. The Durner model can define awater retention function for bimodal pore-size distributions (i d2) in soils containing inter- and intra-aggregated pores. A
hypothetical Se water retention curve was used based on theDurner model in which the stepwise shape of the curve
indicates intra-aggregate pores are depleted of water at high hand inter-aggregate pores at lower h (Sakai and Toride, 2007).
Thus, Se is expressed as the sum of intra-aggregate moisture(first curve) and inter-aggregate moisture (second curve).
Although the Durner model is typically used for aggregatedsoils, we applied it to water retention curves for rocky soil.
When the relative hydraulic conductivity is coupled to Eq. (4)by the predictive K(Se) model of Mualem (1976), it gives theunsaturated hydraulic conductivity for aggregated soils (i d 2)
(Priesack and Durner, 2006) as݇‫ ܭ‬ሺܵ݁ ሻ ൌ ‫ ܭ‬ሾ෍ ‫ ݅ݓ‬ሾͳ ൅ ሺߙ݅ ȁ݄ȁ݊ ݅ ሻሿെ݉ ݅ ሿ݈݅ൌͳൈͳ݉ቌσൌͳ ‫  ߙ  ݓ‬቎ͳെሺͳെ   ሻ݉  ቏ቍሺσൌͳ ‫  ߙ  ݓ‬ሻʹʹ(5)3. Materials and Methods
3.1. Evaporation experiments
Soil sample was rumple gravelly clay loam
(Clayey-skeletal, mixed, active, thermic Typic Argiustolls) withchert fragments above 1.0 m deep on the Edwards Plateau, TX(Tokumoto et al., 2012). The soil was screened by a 2 mmsieve. The particle density of the clay loam and the density ofchert were 2.5 g cm-3 and 2.4 g cm-3, respectively. The shapeof chert fragments in this study was blocky, and the longest
length was less than 7 cm. The average volumetric watercontent of chert (n = 72) was 0.01 cm3 cm-3. Additionally,spherical-shaped gravel (diameter < 1 cm and density = 2.6 gcm-3) was used to compare with the effect of different rocksizes on hydraulic properties.
The evaporation method was carried out with two different
size columns: a 7.9-cm i.d. u 15-cm long cylindrical soilcolumn for non-rocky soil, gravel, and small chert (longest
length < 4 cm and thickness < 2 cm), and a 10-cm i.d. u 30-cm

2.0Evaporation (cm d-1)

64SoilGravel
Small rock
Large rock20051015Time (d)Fig. 1. Observed cumulative evaporation of soil + gravel (Rv = 0.20
cm3 cm-3), soil + small rock (Rv = 0.12 cm3 cm-3) and soil +large rock (Rv = 0.24 cm3 cm-3).

long soil column for large chert (longest length < 7 cm andthickness < 4 cm). Initially, the evaporation method used clay
loam without chert. The air-dried soil sample was packed
uniformly to a bulk density of 1.15 g cm-3 in the 15-cm soilcolumn. The soil water pressure head was monitored with 5mm diam. and 10 mm long tensiometers inserted horizontallyat depths of 3, 8 and 13 cm in the smaller soil column. In thelarger column, tensiometers were inserted horizontally at
depths of 5 cm and 10 cm. The tensiometers were connected
to pressure transducers, and soil samples were saturated using amariotte bottle that provided water from the bottom of thecolumn for 3 days. Saturated hydraulic conductivity Ks of theclay loam was measured with a constant hydraulic pressure
head at the top of the soil column. Then, the bottom inlet wasclosed and the soil surface on the top of column was exposed
to air to allow evaporation. A small fan circulated air over thesoil surface. The soil column was placed on a digital scale,and the water loss was measured to calculate the average
evaporation flux for a given time interval. After theexperiment was completed, average volumetric water content
in the entire soil column, Tave and bulk density, Ub wereobtained gravimetrically.

4. Results and Discussion
4.1. Observed evaporation and pressure head
Figure 1 shows temporal changes in observed cumulative
evaporation and pressure head of soil, gravel (Rv = 0.20 cm3cm-3), small rock (Rv = 0.12 cm3 cm-3) and large rock (Rv =0.24 cm3 cm-3). Initially, evaporation was highest for the soil
alone and soil with gravel, but over time, cumulative
evaporation with soil and small rocks reached values similar tothe other two cases. Evaporation was lowest for soil with thelarger rock. Saturated hydraulic conductivity was estimatedat 20 cm d-1 for soil, 13 cm d-1 for gravel and 14 cm d-1 for soil
with small rock. Gravel and small rock maintained a higher hthan soil alone (not shown). These results suggest that graveland small rocks slowed upward movement of water, thereby

(a)

Obs.
Durner
VG

1.5
1.0
0.5
0.00

Pressure head (cm )Cumulative evaporation (cm)

79

13 cm

-200

8 cm

-400
3 cm(b)-600

051015Time (d)Fig. 2. Comparison of Durner and VG model simulation ofevaporation (a) and pressure head (b) with measured values
for soil + small rock (Rv = 0.12 cm3 cm-3).

maintaining flow of liquid water to the surface for a longer
period of time.
4.2. Optimization with the Durner and VG models
We optimized the six unknown parameters defined by Eqs.
(2) through (5): Tr, TS, D1, D2, n1, n2, w1, w2, Ks, and l.
Estimated l (d 0.03) was lower than 0.5, the value
recommended by Mualem (1976). Figure 2 comparesmeasured and modeled evaporation and h for soil with volume
fraction of small rock using the optimized Durner and VG
model parameters.
Both models underestimated evaporation for small rock but
the Durner model optimized h better than the VG model (Fig.
2b). As rock content increased, the Durner model performed
well (Fig. 3). It may seem contradictory that the simulationsof evaporation using with small rocks in the soil were notbetter (Fig. 2a), because simulated h was in good agreementwith measured h (Fig. 2b). These results imply an uncertainty
about the influence of rock size and Rv on unsaturated
hydraulic conductivity K(h). In unsaturated conditions, rocky
soil with Rv (< 0.2 cm3 cm-3) maintained a stable evaporation
flux longer than the non-rocky soil. However, simulations
with the larger rocks (higher Rv) matched observations quite
well (Fig. 3b). It is likely that higher rock volume disrupted
capillary connections with the surface, creating regions ofhigher water content beneath the rocks.
Estimated water retention curves for the gravel, the smallrocks, and the large rocks with the Durner model are shown inFigure 4. The measured retention curve for the non-rocky
soil is also shown for comparison. To optimize the Durnermodel parameters, we assumed that the air entry value of the
rocky soil would be similar to the value for the clay loam andPressure head (cm )Evaporation (cm d-1)

80

1.5

obtain reasonable water retention curves for rocky soil. These
results confirmed our hypothesis that tortuosity increases withrock content, while most of earlier studies did not optimize thel (Sakai and Toride, 2007), which implied that hydraulicproperties for rocky soil would be adjusted mainly by Ks.
Our finding was that estimating K(h) due to the parameter l,which represents the tortuosity factor, is the key for modelinghydraulic properties of rocky soil.

(a)Obs.
DurnerVG

1.0
0.5
0.0010 cm-200

5. Conclusions-400(b)

-600

05 cm

102030Time (d)4050

Water content (cm3 cm-3)

Fig. 3. Comparison of Durner and VG model simulation ofevaporation (a) and pressure head (b) with measured values
for soil + the large rocks (Rv = 0.24 cm3 cm-3).
0.6Obs. soil
GravelSmall rock
Large rock0.40.20.00.1

1101001000 10000 100000-Pressure head (cm)Fig. 4. Water retention curves for the gravel (Rv = 0.20 cm3 cm-3), thesmall rock (Rv = 0.12 cm3 cm-3) and the large rocks (Rv = 0.24
cm3 cm-3) using the Durner model.

the second curve would dominate the water retention curve forrocky soil. Our results showed that the difference between
the optimized Ts and the Ts estimated by Eq. (1) were less than
0.03 cm3 cm-3. This suggests that the air entry values of therocky soil were similar to the value for the clay loam. Thisdiffers from results of Fiés et al. (2002) that showed the air
entry value of mixtures of soils and glass fragments (< 6 mm)increased with volume fraction of glass (> 30%) even though
Ts and Tr decreased as glass volume increased.
This might have occurred because of increasing air gaps
between glass fragments. However, if large air gaps do notexist, as was likely the case in our study, the impact of change
in the air entry value due to larger air-filled porosity may beignored. Evaluating whether the second curve can dominate
a water retention curve for rocky soil is difficult, but the initial
w2 value (t 0.5) led to an increase in the flexibility of theDurner model in describing retention and hydraulic data acrossthe range of h. For example, if initial w2 value was lower than0.4, it resulted in overestimated Ks (> 30 cm d-1) and Ts (> 0.50
cm3 cm-3). Thus, the initial w2 value (t 0.5) was helpful toTwo simulation models, the VG and Durner, wereevaluated for estimating hydraulic properties of rocky soils.
Estimated l (d 0.03), representing tortuosity was lower than 0.5,
which improved simulation performance for both models.
Results showed that the Durner model was more appropriate
than the VG model for describing water retention andhydraulic conductivity of rocky soils across the wide range ofpressure heads.

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