INTRODUCTION
Soil water repellency (WR) is a physical phenomenon whereby water is
unable to wet the soil surface of mineral particles (Ritsema et al.,
2003; Ritsema et al.,1994). This phenomenon is widely distributed across
the world (Zavala et al., 2014), with higher WR typically occurring in
coarse-textured forest soils (Benito et al., 2019). WR changes the
three-dimensional distribution and dynamic characteristics of soil water
content, resulting in an uneven distribution of soil moisture
(Badía-Villas et al., 2014; S et al., 2015). WR not only affects the
soil wettability (Sepehrnia et al., 2017), but also impacts other
ecological and hydrological processes, e.g., restraining water
infiltration (Sepehrnia et al., 2017), promoting surface runoff (Amiri
et al., 2017; Neris et al., 2013), water and soil erosion (Cawson et
al., 2016; Fox et al., 2007), wind erosion, accelerating fertilizer loss
(Müller et al., 2018a) by influencing preferential flow (Oostindie et
al., 2008; Rye and Smettem, 2017), and increasing soil carbon content
(Muñoz-Rojas et al., 2018), which may lead to a reduction in crop growth
(Li et al., 2019).
The hydraulic properties of water-repellent soil (W-RS) are quite
different from those of hydrophilic soils (HS). Ward et al. (2015)
concluded that, in W-RS, tillage destroys the existing water entry
pathways, and slows the infiltration of water into the soil. Doerr et
al. (2003) found that WR can reduce the soil
∗Corresponding author: Department of Hydraulic and Ecological
Engineering, Nanchang Institute of Technology, Nanchang 330099, China
E-mail address: 971932670@qq.com
infiltration rate (IR) by 10–40%, while DeBano (2000) showed that the
horizontal infiltration of W-RS was 25 times slower than that of HS.
Keizer et al. (2005) reported that soil IR can be decreased by reducing
the potential gradient of the soil matrix. Many studies show that WR is
caused by soil particles and aggregates being coated with hydrophobic
materials, which can originate from plant litter and residues, microbes,
organic fertilizers, or the application of wastewater and artificial
hydrophobic agents (Leelamanie et al., 2009; Subedi
et al.,
2012). The influence of these
factors on the degree of WR reflects the relationship between WR and the
contact angle (CA), which enables measurement of the time dependency of
CA (Leelamanie et al., 2009). The range of CA attained by wettable soils
is less than 90°, whereas W-RS have CA > 90° (Lourenço et
al., 2018). Severe hydrophobicity occurs when the CA is greater than
90°. In this case, water does not spontaneously infiltrate. Subcritical
repellency occurs when the contact angle is less than 90°, whereby the
soil wets spontaneously but with a reduced IR (Tillman et al., 1989).
For the same CA, the matrix suction gradually decreases as the volume of
the liquid bridge increases (Graber et al., 2009; Hamlett et al., 2011).
When the volume of the liquid bridge reaches a certain level, the matrix
suction becomes negative. The WR effect of granules then begins to occur
(Subedi et al., 2012; Subedi et al., 2013). The CA of hydrophobic media
normally decreases with continuous contact with water, eventually
allowing water imbibition (Subedi et al., 2013). Arye et al. (2007)
investigated the main imbibition relationship between water saturation
and capillary pressure using the capillary rise test, and found that
organic matter is likely to detach from the soil particles and be
dissolved into the soil solution. This, in turn, decreases the
equilibrium CA. The effect of WR on infiltration is very complex because
of the unstable wetting fronts, which result in finger-pattern
preferential flow paths (Rye et al., 2017; Wang et al., 2000a) and
hysteresis in soil water retention (Arye et al., 2007). However, WR is a
dynamic property (that generally decreases as the soil wets) and,
therefore, IR is affected during the process itself, resulting in IR
curves that do not correspond to the traditional infiltration theory.
The regulation of surface runoff and infiltration is an important
manifestation of the ecological hydrological function of WR (White et
al., 2017). Because WR can create unstable water flow within the soil
matrix (Jonge et al., 1999), the process of water infiltration is
relatively complex. Current understanding of the infiltration process in
W-RS is limited to the fact that WR can reduce soil IR (Xiao et al.,
2019). In fact, as water infiltration continues, the IR does not
decrease monotonously and, contrary to infiltration in wettable soils,
can increase with time (Ren et al., 2018; Wang et al., 2000b). This
phenomenon generates infiltration curves with a double slope (transient
infiltration curve followed by a steady-state section) (Vogelmann et
al., 2017). For forest soils with strong WR, water infiltration is not
stable (Rye and Smettem, 2017), nor is it strictly in accordance with
the three-stage process of HS infiltration. Instead, with continuous
water infiltration, the WR gradually disappears and the IR appears to
mutate (Burch et al., 1989; Diehl, 2013). The effect of WR is very
evident in cumulative infiltration (CI), which exhibits a double-slope
curve (Vogelmann et al., 2017). Inaccurate fitting indicates that the
Haverkamp model (Haverkamp et al., 1994) should not be applied to such
curves.
Leighton et al. (2007) and Pierson et al. (2008) found that, under WR
conditions, the IR slope gradually increases with continuous rainfall.
Doerr et al. (2000) showed that, during the whole rainfall process, the
IR of W-RS first decreases, then increases, and then decreases to the
lowest value and remains stable. This phenomenon is particularly obvious
in forest soils (Neris et al., 2013; Ritsema et al., 2003). Filipović et
al. (2018) used HYDRUS (2D/3D) to invert the hydraulic properties of
W-RS under drought conditions. They found that the CI of W-RS exhibits a
non-smooth, step-like growth trend, whereas the IR first decreases and
then increases. Rye et al. (2017) believe that including only WR in the
model enables a correct assessment of the hydrological process. Müller
et al. (2018b) considered WR to be an important factor in any
hydrological model.
At present, the phenomenon of increasing IR is being ignored and water
infiltration is generalized as a monotonously decreasing process.
Traditional infiltration models (e.g., those of Green–Ampt, Philip,
Kostiakov, and Horton) and piecewise function models are still used to
fit the double-slope infiltration process (Almeida et al., 2018;
Moret-Fernández et al., 2019) in the model developed by Haverkamp et al.
(1994), and the corresponding infiltration curve indicates that the
traditional model should not be applied to this kind of curve.
A piecewise Kostiakov function
(PKF) has been used to calculate the IR, resulting in a discontinuity at
the inflection point (Ren et al., 2018). This contradicts the physical
phenomenon whereby WR fades away and only one maximum IR exists at the
inflection point. Ren et al.
(2018) used a Gauss function (GF)
and a piecewise Gauss function (PGF) to fit the IR of W-RS. Although the
GF reflects the process of the
increasing and then decreasing IR in W-RS, it is difficult to describe
the gradual decrease in IR after the infiltration
starts.
In this study, water infiltration is analyzed in two types of soil using
the Kostiakov function (KF), PKF,
GF, PGF, Fourier series function (FSF), Gamma
function (GMF),
Beta
function (BF), and
piecewise Beta function (PBF). The
specific objectives of this study are as follows: (1) investigate the
law of W-RS infiltration, and reveal the reasons for the single-peak
curve of IR in W-RS; (2) propose a method of dividing the water
infiltration stages in W-RS; (3) develop a unified model that
demonstrates the monotonous reduction of IR in HS and reflects the
single peak IR curve for W-RS; (4) explore the differences and
relationship between the proposed models (BF and GMF) and traditional
water infiltration models (Philip, Horton, and Kostiakov models).