Introduction
Determining soil hydraulic properties is of primary importance in various
fields of study such as soil physics, hydrology, ecology, and agronomy.
Information on hydraulic properties is essential to model infiltration and
runoff, to quantify groundwater recharge, to simulate the movement of water
and pollutants in the vadose zone, etc. (Bouwer and Rice, 1984). Most unsaturated
flow studies characterize the hydraulic properties of the fine fraction
(particles smaller than 2 mm in diameter) of supposedly uniform soils only
(Bouwer and Rice, 1984; Buchter et al., 1994; Gusev and Novák, 2007).
Nevertheless, in reality, soils are heterogeneous media and may contain
coarse inclusions (stones) of various sizes and shapes.
Stony soils are widespread across the globe (Ma and Shao, 2008) and represent a
significant part of the agricultural land (Miller and Guthrie,
1984). Furthermore, their usage tends to increase because of erosion and
cultivation of marginal lands (García-Ruiz, 2010). Yet little
attention has been paid to the effects of the coarser
fraction on soil hydraulic characteristics, so that the relevant literature
is still rather scarce (Ma and Shao, 2008; Novák and Šurda, 2010; Poesen and Lavee, 1994).
Many authors consider that the reduction in volume available for water flow
is the only effect of stones on hydraulic conductivity. This hypothesis has
led to models linking the hydraulic conductivity of the fine earth to that
of the stony soils. They predict a decrease in saturated hydraulic
conductivity of stony soil (Kse) with an
increasing volumetric stoniness (Rv) (Bouwer
and Rice, 1984; Brakensiek et al., 1986; Corring and Churchill, 1961;
Hlaváčiková and Novák, 2014; Novák and Kňava, 2012;
Peck and Watson, 1979; Ravina and Magier, 1984).
However, a number of studies do not observe this simple relationship between
the hydraulic conductivity and the stoniness (Zhou et al., 2009; Ma et al.,
2010; Russo, 1983; Sauer and Logsdon, 2002) and suggest that other factors,
mainly changes in pore size distribution and structure, may play a
substantial role in specific situations. Indeed, ambivalent phenomena can
intervene simultaneously, which makes the understanding of the effective
hydraulic properties of stony soils difficult. The reduced volume available
for flow might be partially compensated for by other factors. One compensation
factor might be, as pointed out by Ravina and Magier (1984), the creation of
large pores in the rock fragments' vicinity. Indeed, the creation of new
voids at the stone–fine earth interface could generate preferential flows
and hence increase the saturated hydraulic conductivity (Zhou et
al., 2009; Cousin et al., 2003; Ravina and Magier, 1984; Sauer and Logsdon, 2002).
These statements define the general context in which our study takes place.
The main objectives are (i) to assess the effect of rock fragments on the
saturated and unsaturated hydraulic conductivity of soil and (ii) to test
the validity of the predictive models that have been proposed in the literature.
Material and methods
We studied the effect of Rv on saturated and unsaturated hydraulic
conductivity by means of laboratory experiments (evaporation and
permeability measurements) and numerical simulations involving different
amounts and types of coarse fragments. The latter also serve to further
investigate the effect of the stone size and shape on the Kse.
Models predicting soil hydraulic properties of stony soils
Multiple equations have been proposed to estimate the saturated hydraulic
conductivity of stony soil (Kse) from the one of the fine earth (Ks)
assuming that rock fragments only decrease the volume available
for water flow. The relative saturated hydraulic conductivity (Kr) is
defined as the ratio between the Kse and the Ks. Equations (1)
and (2) were derived by Peck and Watson (1979) based on heat
transfer theory for a homogeneous medium containing non-conductive spherical
and cylindrical inclusions, respectively. Assuming that stones are
non-porous and do not alter the porosity of the fine earth, Ravina
and Magier (1984) approximated the Kr to the volumetric percentage of
fine earth (Eq. 3). Based on empirical relations, Brakensiek et al. (1986) proposed a similar equation, but
involving the mass fraction of the rock fragments instead of the volumetric
fraction (Eq. 4). On the basis of numerical simulations, Novák et al. (2011) proposed to
describe the Kse of stony soils as a linear function of the Rv
and a parameter that incorporates the hydraulic resistance of the stony
fraction (Eq. 5).
Kr=21-Rv2+Rv(PeckandWatson,1979,forsphericalstones)Kr=1-Rv1+Rv(PeckandWatson,1979,forcylindricalstones)Kr=1-Rv(RavinaandMagier,1984)Kr=1-Rw(Brakensieketal.,1986)Kr=1-aRv(Nováketal.,2011)
In the above, Rv is the volumetric stoniness [L3 L-3];
Rw is the mass fraction of the rock fragments (mass of stones divided by the
total mass of the soil containing stones; the stone density is typically
2.5 g cm-3 in this case) [M M-1]; and a is an empirical parameter that
incorporates the hydraulic resistance of the stony fraction considering
shape, size, and orientation of inclusions (the recommended value is 1.32 for
clay soils according to Novák et al., 2011).
Two major characteristics are widely used to describe the hydraulic
properties of unsaturated soil: the water retention curve θ(h) and
the hydraulic conductivity curve K(h). These are both
non-linear functions of the pressure head h. One of the most commonly used
analytical models was introduced by van Genuchten (1980),
based on the pore-bundle model of Mualem (1976), and given by:
Se(h)=θ(h)-θrθs-θr=1+|αh|n-mifh<01ifh≥0,KSe=KsSel1-1-Se1/mm2ifh<0,
in which h is the pressure head [L]; Se(h) is the
saturation state [L3 L-3]; θ(h) is the
volumetric water content [L3 L-3]; θr and θs
respectively represent the residual and saturated water content
[L3 L-3]; Ks is the saturated hydraulic conductivity
[L T-1]; and n [–], l [–], and α [L-1] are empirical shape
parameters (m = 1-1/n, n > 1). To extend the hydraulic
conductivity curves to stony soils, Hlaváčiková and Novák (2014)
propose a simple method assuming that the shape parameters of the
van Genuchten–Mualem (VGM) equations (α, n, and
l) are independent of Rv. However, this
model relies on assumptions that have not been verified. It might be worth mentioning that there are currently no extensive empirical
studies available dealing with the influence of porous inclusions under
unsaturated conditions. This gap in existing literature is probably due to
experimental issues linked with this kind of study: while measuring the
potential and the water content of fine earth has become a standard
procedure, the opposite is true for soil with rock fragments, especially
under transient infiltration processes.
Laboratory experiments
Sample preparation
We performed laboratory experiments on disturbed samples (height: 65 mm;
diameter: 142 mm) containing a mixture of fine earth and coarse inclusions > 10 mm.
Two types of inclusions were used: rock fragments
(granite) with a diameter between 1 and 2 cm (1) and spherical glass beads
with a diameter of 1 cm (2) (see Fig. 1). The fine earth is classified as a
clay (sand: 26 %; silt: 19 %; clay: 55 %).
Before each measurement campaign, the fine earth was first oven-dried for 24 h
at 105 ∘C and passed through a 2 mm sieve. To prepare a
sample without any inclusion, the fine earth was compacted layer by layer to get
an overall bulk density of 1.51 g cm-3 (equal to the mean bulk density
of the fine earth measured in situ; Pichault, 2015). For samples containing
rock fragments, stones were divided over four layers of soil application and
laid on the fine earth bed on their flattest side. The samples were then
compacted layer by layer in a way that maintains the same bulk density of
fine earth as for samples without inclusions (as a result, the global bulk
density of samples varies according to stoniness). Even though the filling
and compaction procedure was conducted with precision, it is probably
impossible to avoid local bulk density heterogeneity as stones can move
and/or soil between stones can be less compacted due to difficult access of
the area close to the stone during compaction. The same procedure was to
prepare samples containing glass balls. Once the specimen was made, it was
placed in a basket containing a thin layer of water for at least 24 h
in order to saturate the soil from below.
Unsaturated hydraulic conductivity
Setup description
We used the evaporation method to determine the unsaturated hydraulic
conductivity and the retention curve of a soil sample. The principle of this
method is to simultaneously measure the matric head at different depths and
the water content of an initially saturated soil sample submitted to evaporation.
Preparation of disturbed samples containing glass balls (left panel) and
gravels (right panel).
The experiments were performed using cylindrical Plexiglas samples of 1 L
(height: 65 mm; diameter: 142 mm), perforated at the bottom to allow
saturation from below and open to the atmosphere on the upper side to allow
evaporation of the soil moisture. Four 24.9 mm long and 6 mm diameter ceramic
tensiometers (SDEC230) were introduced at 10, 25, 40, and 55 mm height,
respectively denoted T1 to T4 (the reference level is located at the bottom
of the sample). Tensiometers are introduced at saturation; a pin with
similar dimensions is used to facilitate their insertion. In order to avoid
preferential flow due to the introduction of the tensiometers on the same
vertical axis, each tensiometer was introduced with a horizontal shift of 12∘ with respect to the centre of the column. The tensiometers are
connected by a tube to a pressure transducer (DPT-100, Deltran). The setup
was filled with degassed water. The variation in pressure of the drying soil
was recorded every 15 min by a CR800 logger (Campbell Scientific). Tensions
beyond the air entry point were not taken into account. The air entry point
refers to the state from which the measured pressure head starts to decrease
as bubbles appear and water vapour accumulates (typically 68 kPa in this case).
The total water loss as a function of time was monitored by a balance (OHAUS)
with a sensitivity of 0.2 g, an accuracy of ±1 g, and a
time resolution of 15 min. A 50 W infrared lamp was positioned 1 m above the
sample surface to slightly speed up the evaporation process. The light was
turned off for the first 24 h of every experiment, as the evaporation
rate is already high in a saturated sample. A measuring campaign lasted
until three of the four tensiometers ran dry (the tension sharply drops down
to approximately a null value). At the end of the experiment, the sample was
oven-dried for 24 h at 105 ∘C to estimate the θ.
Data processing
A simplified Wind's (1968) method was used to transform matric
potential and total weight data over time into the hydraulic conductivity
curve (Schindler, 1980, cited by Schindler and
Müller, 2006; Schindler et al., 2010). The method is further adapted in
order to take into account the data from four tensiometers. The method
assumes that the distribution of water tension and water content is linear
throughout the soil column. It further linearizes the water tension and the
mass changes over time. The time step chosen to process the data is 1 h.
By calculating the hydraulic conductivity based on measurements of two
tensiometers and linking it to the corresponding mean matric head, one can
evaluate a point of the hydraulic conductivity curve. We used every possible
combination of two tensiometers (six here) to obtain data points for the
hydraulic conductivity curve.
Points of the hydraulic conductivity curve obtained at very small hydraulic
gradients (defined here as ∇H = Δ|h|Δz - 1) were rejected, because large errors occur in the
near-saturation zone due to uncertainties in estimating small hydraulic
gradients (Peters and Durner, 2008; Wendroth, 1993). This highlights in turn the necessity of reliable
tensiometers to estimate the near-saturated hydraulic conductivity. In the
current literature, acceptance limits of the hydraulic gradient vary
between 5 and 0.2 cm cm-1 (Mohrath et al., 1997;
Peters and Durner, 2008; Wendroth, 1993). Using the least restrictive filter
criterion (hydraulic gradient > 0.2) requires fine calibration
and outstanding performance of the tensiometers. Choosing a more restrictive
criterion leads to a larger loss of conductivity points but provides more
reliable and robust data. We decided to use a filter criterion that does not
consider hydraulic conductivity points higher than the evaporation rate
(from 0.1 to 0.2 cm day-1 in this case), resulting in a lower limit of
1 cm cm-1 for the hydraulic gradient.
As pointed out by Wendroth (1993) and Peters and Durner (2008), the main drawback associated with the
evaporation experiment is that no estimates of conductivity in the wet range
can be obtained due to the typically small hydraulic gradients, so that
additional measurements of the Kse should be provided. To do so, we
used constant-head permeability experiments (see below). Except for the Kse
which is fixed using results from the constant-head permeability
experiments, the parameters of the VGM model (1980) (Eq. 7)
are obtained by fitting evaluation points from each combination of
tensiometers using the so-called “integral method” (Peters and Durner, 2006).
Saturated hydraulic conductivity
Constant-head permeability experiments were used to determine the Kse
of saturated cylindrical core samples. The flow through the sample is
measured at a steady rate under a constant pressure difference. The Kse
can thus be derived using the following equation:
Kse=VLAΔHΔt,
in which V is the volume of discharge [L3], L is the length of the
permeameter tube [L], A is the cross-sectional area of the permeameter
[L2], ΔH is the hydraulic head difference across the
length L [L], and Δt is the time for discharge [T].
Parameters of the van Genuchten equations used in the numerical experiments.
θr
θs
α
n
l
Kse
[–]
[–]
[cm-1]
[–]
[–]
[cm day-1]
0.185
0.442
0.0064
2.11
-0.135
2.686
The soil sample used for permeability tests has the same size as the one
from the evaporation experiment (height: 65 mm; diameter: 142 mm). A 2 cm
thick layer of water was maintained on top of the sample thanks to a
Mariotte bottle. Water was collected through a funnel in a burette and the
volume of discharge V was deduced from measurements after 30 and 210 min
after the beginning of the experiment (Δt = 180 min).
Numerical simulations
The HYDRUS-2D software was used to simulate water flow in variably saturated
porous stony soils. HYDRUS-2D solves the two-dimensional Richards equation
using the Galerkin finite-element method.
All the performed simulations assumed that rock fragments were non-porous so
that “no-flux” boundaries conditions were specified along the stones'
limits. Since we mimic the laboratory setup, rock fragments were modelled as
circular inclusions. The soil domain over which simulations were performed
had the same dimensions as the longitudinal section of the sampling ring
used in the laboratory experiments (14 × 6.5 cm). We considered the 2-D
fraction of stoniness equal to the volumetric fraction. The parameters of
fine earth used in the simulations come from the fitting of the hydraulic
conductivity and water retention curves obtained in our laboratory
experiments on stone-free samples (Table 1).
As a general rule, the hydraulic conductivity of a heterogeneous medium
tends to be higher for 3-D than for 2-D simulations (Dagan, 1993). Similarly,
for a same level of heterogeneity, the flow will be more hampered using 1-D
rather than 2-D simulations. In the present study, we performed 2-D
simulations: the quantitative and qualitative conclusions from these
experiments can be only extended to the third dimension for their
corresponding 3-D form with an infinitely long axis.
Unsaturated hydraulic conductivity
We complemented our experimental evaporation results with an equivalent
virtual evaporation experiment. The top boundary of the virtual sample was
submitted to an evaporation rate q of 0.1 cm day-1 over 14 days. No fluxes
were allowed across other boundaries. The calculation method applied to the
output data was similar to the laboratory evaporation experiment, except
that the conductivity and pressure head estimations resulted from two
observation nodes placed at the top and the bottom of the profile instead of
from four tensiometers. We are aware that these choices are debatable: on
the one hand, numerical instabilities are more plausible at the limits of
the sample and, on the other hand, the use of bigger samples than
conventionally used (6.5 cm height) might reduce the accuracy of the
evaporation method (see Peters et al., 2015). However, we did keep the
observation nodes on the edges and the larger sample size for the following
reasons. Firstly, we observed more changes in hydraulic gradient near
stones. As small variations in the hydraulic gradient can lead to
substantial changes in the hydraulic conductivity estimates, we chose to
place observation nodes out of the influence of one specific inclusion. This
difficulty, especially at high stone contents, is the reason why the nodes
are not situated inside of the sample volume but rather at the edges. Secondly, we
checked whether the pressure head was linearly distributed across the soil
profile, which was the case. Finally, as we are studying clayey soils, and
as we are considering a pressure head range between pF 1.5 and 2.5, these
assumptions are likely to be fair (Peters et al., 2015).
As the relative mass balance error was large at the beginning of the
simulations, we only started considering values from the moment when this
relative error was lower than 5 %. This validation criterion was set
arbitrarily, based on the comparison between evaluation points from the
simulation of the evaporation experiment on stone-free samples and the
expected values obtained from the inputs of the simulation. The hydraulic
conductivity curve was obtained fitting the discrete conductivity data plus
the simulated saturated hydraulic conductivity using the integral method (Peters and Durner, 2006), just like we did for the laboratory experiment.
Saturated hydraulic conductivity
The Kse was determined using a numerical constant-head permeability
simulation. We simulated a steady-state water flow of a saturated soil
profile, with a constant head of 10 cm applied on the upper boundary. The
bottom boundary of the column was defined as a “seepage face”, which means
that water starts flowing out as soon as the soil at the boundary reaches
saturation. The calculation method applied to the output data was identical
to the permeability experiment.
Schematic summary of the treatments.
Effect of Rv on
unsaturated hydraulic
Effect of Rv on saturated
conductivity
hydraulic conductivity
Effect of size and shape on saturated hydraulic conductivity
Method
Evaporation experiment
Permeameter (R =5 )1
Permeameter
+ permeameter
Rv2 [%]
0 – 10 – 20 – 30
0 – 20
0 – 20 – 40 – 60
0 – 10 – 20 – 30
Approach
Numerical
Laboratory
Numerical
Laboratory
Numerical
Inclusion
•3 (2-D)
Rock
•3 (2-D)
Glass
Rock
•3 (2-D)
▴3 (2-D)
▾3 (2-D)
▪3 (2-D)
⧫3 (2-D)
type
n4 = 12
fragments
n = 12
spheres
fragments
n = 1, 12, 27
n = 1, 12, 27
n = 1, 12, 27
n = 1, 12, 27
n = 1, 12, 27
1 R = replications;
2 Rv is the volumetric stony fraction;
3 •▴▾▪⧫
stand for shape, i.e. circular, triangular on its longest side,
triangular on its shortest side, rectangular on its shortest side, and rectangular
on its longest side; 4 n is the number of inclusions.
Treatments
Table 2 presents a scheme of all the performed experiments. We duplicated
each laboratory experiment with similar numerical simulations.
We first studied the effect of Rv on unsaturated hydraulic properties
using laboratory experiments and numerical simulations. In the laboratory
approach, we performed evaporation experiments on samples containing (i) fine
earth only and (ii) on others with rock fragments (1) at a Rv of
20 %. Two replications per treatment were performed (four measurement
campaigns in total). For the numerical approach, simulations of the
evaporation experiment were done on homogeneous soil (without stones) and on
soil with a Rv of 10, 20, and 30 %. Having fewer time and practical
constraints in the numerical simulation, we added an increasing Rv to
observe the evolution of the hydraulic conductivity curve. Simulations were
performed on soil samples containing 12 regularly distributed stones. One
can notice that no investigations of the unsaturated properties with coarse
fragments above 30 % of Rv were performed. Indeed, given that small
variations in the hydraulic gradient can lead to substantial changes in the
hydraulic conductivity estimates, the tensiometers should be ideally
positioned out of the direct influence of one particular stone in order to
obtain generalizable results. This implies the need for relatively low stone
contents (< 30 % according to Zimmerman and Bodvarsson, 1995).
Then, to study the relationship between saturated hydraulic conductivity,
Kse, and Rv, we performed five replications of four volumetric
stone fractions (0, 20, 40, and 60 %) with rock fragments (1). We also
tested a second type of inclusions, glass spheres (2), with a Rv of
20 % (1 replication). The first setup with rock fragments was concomitant
with the one with glass spheres. Then, the four supplementary replications
with rock fragments were processed for the different volumetric fractions
altogether: between replications the soil was oven-dried for 24 h at
105 ∘C and passed through a 2 mm sieve. Numerical permeability
simulations were also performed involving 12 circular regularly distributed
inclusions for the same Rv (0, 20, 40, and 60 %).
Finally, we used supplementary numerical simulations to investigate the
effect of the inclusion shape and size on Kse. To do so, simulations
of the permeability test were performed on soil containing stones of five
different shapes: circular, upward equilateral triangle, downward
equilateral triangle, rectangle on its shortest side (L × 1.5 L), and
rectangle on its longest side (1.5 L × L) with an Rv of 10, 20, and
30 %. We first performed simulations on soil containing only one centred
inclusion. We also performed permeability simulations on soil containing
12 and 27 regularly distributed inclusions (for each Rv).
Results and discussion
In the following, results from laboratory experiments and numerical
simulations will be compared to the predictions of the different models
presented in Sect. 2.1. The Kse will be represented by the median
value predicted by the five models linking the properties of fine earth to
the ones of stony soil (Eqs. 1 to 5). This will be referred to as
“results from the Kse predictive models” in the following and will
be graphically represented by dotted lines. The same predictive models
assume that the shape parameters of the VGM equations (n, l, and α) do
not depend on the stoniness, as suggested by Hlaváčiková and
Novák (2014). As mentioned above, unsaturated functions of stony soils
have been barely studied. We will compare results from unsaturated
experiments and numerical simulations to predictive models results following
this assumption.
Kse depending on Rv obtained from laboratory
experiments, numerical simulations with 12 circular inclusions, and the
predictive models (the bars show the maximum and minimum intervals around
the median predicted by these models).
Effect of stones on saturated hydraulic conductivity
Figure 2 shows the relationship between the saturated hydraulic conductivity (Kse)
and the volumetric stone content (Rv) obtained from the
constant-head permeability tests for laboratory experiments and numerical
simulation (12 circular inclusions). The figure also depicts the median
Kse of the predictive models (dashed line) and the bars show the 95 %
intervals around the median predicted by these models.
The models predict a decreasing Kse for an increasing Rv. The
numerical simulations show a decrease in Kse with an increasing Rv,
similar to the predictive models. Looking at the average curve
obtained with our five replications (Fig. 2), we observe an overall increase
between a Rv of 0 and 60 %, with this global trend being
observed for each replication individually (Fig. 3). Statistically speaking,
there are significant differences between Kse at a
Rv of 0 and 60 % and between Kse at a
Rv of 20 and 60 %. However, at low stone content,
we observe a local decrease in Kse for some replications. For example,
for the first replication (Gravels 1, Fig. 3) Kse decreases until a
Rv of 20 % and then Kse begins to increase. For the second
replication (Gravels 2, Fig. 3), the Kse increases from a
Rv of 0 to 20 % and then decreases at a
Rv of 40 %. Analogous permeability tests conducted
by Zhou et al. (2009) showed a similar
behaviour: the Kse initially decreases at low rock content to a minimum
value at Rv = 22 %, and then at higher Rv Kse tends to
increase with Rv. Other laboratory tests carried out by Ma et al. (2010) displayed a
larger Kse at Rv = 8 % than the one of the fine earth alone. While carrying out in situ
infiltration tests, Sauer and Logsdon (2002) measured higher Kse with
increasing Rv but decreasing K with increasing Rv under
unsaturated conditions (and particularly at h = -12 cm). These
considerations suggest that the relationship between Kse and Rv
proposed by the predictive models simplifies reality to a great extent.
These contradictory results suggest that the variation in Kse
depends on different factors that can counteract the reduction in the volume
available for water flow. One possible explanation of our observations has
been pointed out by Ravina and Magier (1984), who directly observed large
voids by cutting across a stony clay soil sample after its compaction,
presumably due to translational displacement of densely packed fragments.
This compaction of a saturated sample creates voids near the stone surface
and hence increases Kse with an increasing Rv. Our packing
procedure, demanding the compaction of the sample layer by layer, could lead
to the same kind of phenomena observed by Ravina and Magier (1984). Moreover,
we have to keep in mind that these elements are very likely to have a
different impact depending on soil texture, which was clay for both studies.
Kse depending on Rv obtained from laboratory
experiments with gravels (five replications) and glass balls (one replication).
Glass beads were used to check the influence of rock characteristics on our
conclusions about Kse. Since results with glass beads show a trend
similar to the five replications with rock fragments, we infer that it is
not the rock fragment itself that produces bigger Kse but rather the
presence of a certain volume of inclusions. In addition, the variation observed
between the trends of the curves with rock fragments and glass beads could
be due to the inner variation in the hydraulic properties of samples, but it
could suggest as well that Kse depends on the shape and the roughness
of the inclusions. Nevertheless, we can only see the combined effect of
these factors in this experiment. This leaves the understanding of the major
drivers of the Kse and their relative importance unclear. These
elements are further investigated through numerical simulations.
Results from the investigation of the inclusion size and shape with regard to the
saturated hydraulic conductivity by means of numerical simulations (n is the
number of inclusions simulated in the profile for the corresponding Rv).
Rv
Shape
Relative saturated
hydraulic conductivity
n = 1
n = 12
n = 27
10 %
▪
0.88
0.88
0.88
•
0.84
0.83
0.82
▴
0.80
0.79
0.78
0.80
0.79
0.78
⧫
0.84
0.83
0.82
20 %
▪
0.76
0.71
0.68
•
0.73
0.69
0.65
▴
0.67
0.63
0.54
▾
0.67
0.63
0.54
⧫
0.66
0.61
0.54
30 %
▪
0.70
0.60
0.55
•
0.64
0.58
0.48
▴
0.59
0.50
0.46
▾
0.59
0.50
0.47
⧫
0.56
0.48
0.31
Besides the observed increase in Kse with rock content, we can also
observe a decrease in Kse between replications (see Fig. 3). In fact,
as mentioned above, the global trend of increasing Kse is observed
for each replication individually, but packing procedure seems to have a
large impact on results too. There are significant differences (p < 0.05)
between replication 2 and replication 5, the last one presenting lower Kse.
The drying and wetting cycles and/or the sieving influence the
hydrodynamic behaviour of soil fraction since the effect decreases when
Rv increases. This underlines the effect of soil texture and is an
important aspect to take into account in future studies.
Effect of the stone size and shape on the saturated hydraulic conductivity
To investigate the effect of the size of the inclusions and their shape
on Kse separately from other factors of variation, we performed
constant-head permeability simulations on samples containing 1, 12, and
27 inclusions of various shapes, for a Rv of 10, 20, and 30 %. Table 3
illustrates the tendency of the effects and their respective factors.
Relationship between minimum surface area and Kr for different Rv.
Table 3 presents the Kr for different sizes of circular inclusions and
increasing overall stone content (Rv). When the size of the
inclusions decreases (when the number of inclusions increases for a same Rv),
the Kr tends to decrease. An interaction between the Rv
and the size of inclusion can be observed: the effect of size is
more marked with a higher Rv. For example, the decrease in Kr
between 1 and 27 circular inclusions is limited to 2 % for a Rv of
10 % but rises up to 25 % for a Rv of 30 %. A similar behaviour
is observed with simulations for different shapes of inclusions. One could
think that this observation is directly related to change in the minimal
cross section for water flow. Figure 4 plots Kr as a function of the
ratio between minimal surface area and total surface area. Minimal surface
area was calculated as the sample width minus the maximal bulk of stones.
Even if we observe a linear trend between these two variables, the
relationship is not perfect as we could expect with numerical simulations,
supporting the hypothesis that the reduction in the cross section is not the
only factor for Kr variations. These statements support the findings
of Novák et al. (2011): the smaller the stones, the higher the resistance to flow at a given stoniness.
We suggest the decrease in Kse is due to a combination of the two
following phenomena. The first one is the overlapping of the influence zone
of each inclusion, causing further reduction in Kr. The concept of
overlapping influence zones was first proposed by Peck and
Watson (1979) to explain higher decrease in the hydraulic conductivity of
stones very close to each other in comparison to isotropically distributed
stones. The second phenomenon could be that, for a given Rv, the
contact area between stones and fine earth is higher for small stones than
for bigger ones. Hence, a higher tortuosity can be responsible for a lower flow rate.
The shape of the inclusions also has a visible impact on Kr. For a
fixed number of inclusions, the Kr is higher with rectangular
inclusions on their shortest side and smaller with rectangular inclusions on
their longest side. Circular inclusions provoke a smaller reduction than
triangular inclusions. The orientation of the triangles does not have a
pronounced effect on Kr. Here again, we observe a stronger effect
of the size for higher stoniness. As an illustration, the decrease in Kr
between circular and triangular inclusions is limited to 5 % for
a Rv of 10 % but rises up to 14 % for a Rv of 30 %. A
similar behaviour is observed with simulations including either 1 or 27 fragments.
Considering a fixed Rv of 20 % (see Table 3), the effect of the
shape of the inclusions depends on their size. For example, the decrease
in Kr between rectangular inclusions positioned on their longest and
shortest sides is limited to 13 % for samples containing one inclusion
only, while it is as high as 21 % for samples containing 27 inclusions.
Inversely, the effect of the size of inclusions also depends on their shape.
This effect is higher for triangular and rectangular inclusions positioned
on their longest side, with a Kr decrease between 1 and 27 inclusions
of 23 and 18 %, respectively. This effect is less significant for circular
inclusions, as well as for rectangular inclusions positioned on their shortest
sides. The associated Kr decrease between 1 and 27 inclusions is
11 and 10 %, respectively.
The median value of Kr predicted by the models for a Rv of
20 % (0.73) is similar to the simulated Kr for samples containing
only one spherical inclusion (Table 3). The Kr predicted by the
models is always higher than the Kr determined by the simulations,
except for soils containing one inclusion on its shortest side. This can be
a side effect of 2-D simulations versus 3-D measurements. Nevertheless, the
numerical simulations show that the shape and the size of inclusions may
have an effect on Kse, which is usually neglected by the current
predictive models. In general there is a concordance between models and
simulations, whatever the shape and orientation of stones. This strengthens our
hypothesis that macropore creation or heterogeneity of bulk density close to
the stones can occur and influence Kse. Indeed, numerical simulations
cannot simulate the creation of voids, unless we create them manually and
subjectively in the domain.
Eventually, we hypothesize that, from a certain Rv
onwards (the exact Rv value depending on the
sampling procedure and the shape and roughness of inclusions, as well as soil
texture), stoniness is at the origin of a modification of pore size
distributions and of a more continuous macropore system at the stone
interface. This macropore system could overcome the other drivers reducing Kse.
Effect of stones on unsaturated hydraulic conductivity
Figure 5 represents the hydraulic conductivity curves obtained from the
permeability and evaporation simulations for different stoniness (Rv = 0,
10, 20 and 30 %) as well as results predicted by the models for
the corresponding Rv. The hydraulic conductivity curves from the
predictive models and from the numerical simulations match hydraulic
conductivity decreases for increasing Rv. According to these
simulations, hydraulic conductivity in the unsaturated zone is well defined
using a correct Kse and shape parameters do not depend on the
stoniness. But this is not surprising since predictive models and numerical
simulations rely on the same assumptions, i.e. imperviousness of stones and an
identical porosity distribution of fine earth. As a result, these elements
do not prove that shape parameters do not depend on the stoniness.
Figure 6 represents the hydraulic conductivity curves obtained from laboratory
experiments on stone-free samples and on samples with a Rv of 20 %
as well as the results predicted by the models for a Rv of 20 %.
Even though the data points are dispersed, those coming from the evaporation
experiments measured on stony samples are globally lower and slightly more
flattened than the ones measured on stone-free samples. This suggests that
stones decrease unsaturated hydraulic conductivity. However, it must be
noted that we do not have unsaturated K data for higher stone contents,
whereas for Kse the effect of stoniness becomes more obvious for
Rv > 20 %. In order to draw final conclusions, it might be necessary to find a way to conduct evaporation experiments for higher stone contents.
Hydraulic conductivity curves obtained from numerical experiments
(data and fit for Rv = 0, 10, 20, 30 %) and results predicted
by the models for the corresponding Rv.
In the numerical simulations, the presence of stones reduces the hydraulic
conductivity in the same way as predicted by the models, regardless of what the
suction was. Similarly, the laboratory experiments suggest that stones
reduce the unsaturated hydraulic conductivity, while laboratory experiments
in saturated conditions indicated that stones content might increase the Kse.
These elements support the hypothesis of the macropore creation:
according to the well-known law of Jurin (1717), pores
through which water will flow depend on both the pore size distribution and
the effective saturation. Consequently, flow in the macropore system will
only be “activated” in the near-saturation zone, while small pores will
only be drained at high suction. Therefore, we could hypothesize that stones
are always expected to decrease the hydraulic conductivity at low effective
saturation states. However, under saturated conditions, the relationship
between Rv and Kse seems to be less trivial and requires further
investigations considering soil texture and stone characteristics.
Conclusion
Determining the effect of rock fragments on soil hydraulic properties is a
major issue in soil physics and in the study of fluxes in
soil–plant–atmosphere systems in general. Several models aim at linking the
hydraulic properties of fine earth to those of stony soil. Many of them
assume that the only effect of stones is to reduce the volume available for
water flow. We tested the validity of such models with various complementary experiments.
Hydraulic conductivity curves obtained from laboratory experiments
(data and fit for Rv = 0 and 20 %) and results predicted by
the models for a Rv of 20 % (dotted line). Triangles are saturated
hydraulic conductivity: closed is measured with black for the stony and grey
for the fine earth, and open is predicted by the model (median value of the models).
Our results suggest that it may be ill-founded to consider that stones only reduce the volume
available for water flow. First, we observed that,
contradictory to the predictive models, the saturated hydraulic conductivity
of the clayey soil of this study increases with stone content. Furthermore, we
pointed out several other potential drivers influencing Kse which are
not considered by these Kse predictive models. We observed that, for
a given stoniness, the resistance to flow is higher for smaller inclusions
than for bigger ones. We explain this tendency by an overlap of the
influence zones of each stone combined with a higher tortuosity of the flow
path. We also pointed out the shape of stones as a factor affecting the
hydraulic conductivity of the soil. We showed that the effect of the shape
depends on the inclusion size and inversely that the effect of inclusion
size depends on its shape. Finally, our results converge to the assumption
that this contradictory variation in Kse could find its origin at the
creation of voids at the stone–fine earth interface as pointed out by
Ravina and Magier (1984). Even if the very mechanisms behind these
observations remain unclear, they seem to strongly depend on Rv,
shape,
and roughness of inclusions. However, as we conducted these experiments on a
specific clay soil only, and given the fact that structural modifications
are textural dependent, our results cannot be extrapolated to other soil
textures without similar experiments. Finally, as we worked with disturbed
samples, our results do not include quantification of natural phenomena
such as swelling and shrinking that occur naturally for clay soils.
These findings suggest that the aforementioned predictive models are not
appropriate in all cases, particularly under saturated conditions. Models
should take into account the counteracting factors, notably size and shape
of stones. However, further investigations are required in order to explore
the hydraulic properties of stony soils and to develop new models or adapt
the existing ones. The direct observation of the porosity of undisturbed stony samples using X-ray computed tomography or magnetic resonance imaging could
firstly confirm and then help to better understand the mechanism of
supposed voids' creation at the stone–fine earth interface. However, under
unsaturated conditions, these considerations should be more nuanced, as both
numerical simulations and laboratory experiments corroborate the general
trends from the predictive models. Finally, similar analyses should be
conducted in view of determining the effect of the fine earth texture on the
drivers of hydraulic properties as pointed out throughout our research.