Study of Shrinkage and Swelling Phenomena in Clay Soils of Fanaye (Middle Senegal River Valley): Simulation of Water Transfers in a Soil Column

Soil degradation due to shrinkage and swelling of these clay soils is a problem for agriculture. To understand the physical properties of the soils in this agricultural area, we will use an undisturbed soil monolith 60 cm high and 23 cm in diameter in the laboratory. This study quantified the swelling and shrinkage of these soils during a 10-month experiment. The determination of the hydrodynamic parameters of this monolith made it possible to simulate water transfers in a soil of constant volume and a water transfer in a soil of variable volume. The results of this simulation show significant differences between these two cases, hence the need to integrate the variations in soil volume into the simulation processes of water transfers.


Introduction
Drought has generated shrinkage phenomena in many clay soils. These phenomena are mainly translated by the modification of the physical properties of the soil which directly influences agriculture [1] [2] [3] [4]. These physical properties are related to the microporal volume of clay particles and their modeling depends on the size and type of sample [4]- [10].
In the Senegal River valley, simulation tests of water and solute transfers and the study of the hydro-saline functioning of the soils of the delta and the middle valley have been carried out [11] [12] [13]. These authors have shown that shrin-lation of water in these soils.
In recent years, this agricultural area has experienced sodization and alkalinization of the soils, which has led to a decrease in agricultural yields.
In order to understand the shrinkage and swelling phenomena, a simulation of water transfers on a column of undisturbed soil was undertaken.
These physical characteristics of the soil are often unfavorable to cultivation [10] [14] [15] [16] [17]. This is the case in Fanaye, an area known for its agriculture in the middle valley of the Senegal River. In this area, the shrinkage and swelling phenomena would be related to the nature of the soils and the circulation of water in these soils. To better understand the phenomena of shrinkage and swelling of these soils, a simulation of water transfers on a column of undisturbed soil was undertaken in the laboratory.

Presentation of the Study Area
The study area is located in Fanaye, in the middle valley of the Senegal River. This site is located about 165 km from the city of Saint-Louis at 16˚32' North and 15˚12' West. It is drained by the Ngalenka, a defluent of the Senegal River ( Figure 1).

Site Characteristics
The Senegal River Valley is an arid zone where the dry season lasts from November to July and the winter season from July to October. Temperatures vary between 35˚C and 45˚C.
The advance in desertification has led to the formation of shrub and tree steppes composed mainly of Acacia adansonii, Balanites aegyptiaca, Vetiveria nigritana, Chloris prieurii and Schoenefeldia gracilis [18].
The hydrographic network is essentially constituted by the Senegal River and its tributaries: the Bafing and the Bakoy.
The average annual rainfall varies around 200 mm/year [18].
The Senegal River valley belongs to the Senegal-Mauritania Basin. It has undergone numerous climatic and marine variations that have shaped it during the Quaternary period. This valley is characterized by alluvial and colluvial deposits.
The marine transgression of the Nouakchottian period was at the origin of deposits of mud, marine, or lagoon sands but also of the formation of a system of levees and settling basins.
More recent sediments dated from the Post-Nouakchottian period have formed high sandy-silt levees, small sandy-loamy-clay levees, and fluvio-deltaic deposits.
The high parts rarely submerged are levees constituted by not very evolved

Method
The experiment was carried out on a monolith of undisturbed soil taken from Fanaye in the middle valley of the Senegal River. This monolith is 60 cm high and 23 cm in diameter. The experiment was conducted in two phases: a wetting

Experimental Phase
On the sample are placed three types of measuring instruments: • Time Domain Reflectometry (TDR) which measures soil water content; • Pressure sensors which measure the pressure potential of the soil and; • Displacement sensors that measure the displacement in the soil.
• These instruments are placed at −10 cm; −20 cm; −30 cm; −40 cm; −50 cm so that there is one TDR, one pressure sensor, and one displacement sensor for each level.
There are two scales that measure respectively the weight of water that infiltrates and the weight of the soil column. In order to have continuous and regularly distributed measurements in time, all these measuring devices are connected to a data acquisition system consisting of three computers.

Determination of Hydrodynamic Parameters
The knowledge of these parameters is necessary for the simulation of water transfers. They are determined with the help of the curves θ(h) and K(θ).

Tracing the Curves θ(h)
Several equations allow obtaining the hydraulic conductivity curve K(θ) from the retention curve. But the most used are that of [24] and that of [25].
The Brooks and Corey equation gives unreliable results when the soil texture is fine [26], so we chose the Van Genuchten equation.
The curves allow us to better see the relationship between the soil pressure potential and the water contents: these curves were drawn with "Sigma plot", a very practical software for iterative calculations and graphical representations [27] [28].
The relationship h(θ) is one of the most important in the study of water transfers in unsaturated media. In a saturated medium, the total potential remains constant, but in an unsaturated medium, the pressure potential h varies with the water content which allows a better description of the retention curve for water content values close to saturation.
The equation of Van Genuchten was used for the adjustment of the tracing curves because it made it possible to calculate the new values of water contents, and to find the parameters which enter these formulas.
These parameters are constant for each level but they vary from one level to another: Thus, for each level studied, the parameters of the Van Genuchten equation were calculated: θ s = water content at saturation. θ r = residual water content. Open Journal of Soil Science h = pressure potential. n and m = empirical constant the constraints for these calculations are: θ r >0 and θ s > θ r with n > 1.

Drawing of Curves K(θ)
The development of the curves K(θ) requires the values of hydraulic conductivity K and water content θ. The water contents used in the latter calculations are those calculated by the Van Genuchten equation.
The hydraulic conductivity at saturation is given by the formula which is deduced from Darcy's law generalized to one-dimensional flow: Moreover, the continuity equation imposes: ( ) θ θ θ θ K = hydraulic conductivity. K s = hydraulic conductivity at saturation. θ s = saturation water content. θ r =residual water content. m and n are empirical constants.
These curves θ(h) were K(θ) based on the results of water content, pressure potential, displacement, and weight acquired during the drying phase.
These calculations will be carried out with water contents where either a constant or a variable volume of soil is considered.
These operations will allow us to find the hydrodynamic parameters of the sample in these two cases and compare them in the case of a simulation.

Simulation of Water Transfers
The development of numerical modelling in all fields of research is justified because it allows us to anticipate a project, a problem, and consequently avoid it or bring the best solution.
It is with this in mind that soil scientists have been working on modelling water and solute transfers in agricultural environments.

Description of the Hydrus-2D Model
Several models are used to simulate water and solute transfers in soil, but the

Simulation Process
The Hydrus-2D program is provided with the following information necessary

Results and Discussion
The results are presented as curves for the wetting and drying phases.  Figure 3 shows that the height of infiltrated water increases with time. Figure 4 shows that the height of the column varies around 2.75 cm during the first twenty days of wetting and then stabilizes over time. Figure 5 shows that between the surface and 20 cm depth, the water content in

Pressure Potential Variations
The variations of the pressure potential inside the column are shown in Figure 6 below. It shows that the pressure potential varies over the whole column during the drying process, with notable differences when moving from one level to another. The variation of the pressure potential is important at the surface (−900 mb) and very rapid during the drying time. The greater the depth, the smaller this variation is and it tends to stabilise from the surface towards the deep levels from about 330,000 minutes. This stabilization time increases with depth.

Displacement Variations in the Column
These variations can be vertical as well as lateral.
1) The vertical displacement

The Variation of the Weight of the Column
The weight of the column was monitored throughout the drying process and its evolution is shown in Figure 9 below. This figure shows that the weight of the column has strongly decreased from 75 kg at the beginning of the experiment to 71.3 kg at the end of the experiment; that is to say a weight loss of 3.7 kg which allows calculating the evaporation flux. More than weight loss, water content, and pressure potential are important data in that a relationship can be established between these two parameters by plotting the θ(h) curves for each level

Determination of Hydrodynamic Parameters Without volume variation
Curves h(θ) and K(θ) at 10 and 20 cm depth ( Figure 10 and Figure 11) The parameters in Table 1 were obtained by curve fitting ( )    With volume variation Curves h(θ) and K(θ) at 10 and 20 cm depth ( Figure 12 and Figure 13) The hydrodynamic parameters of the soil column (Table 1 and Table 2) show    a difference between the two cases considered. They will be used for the numerical modelling of water transfers in the soil column. Our results give higher hydraulic conductivities at saturation when the variation in soil volume is taken into account. The modeling was done with the drying data of the first two levels.

The Results of the Simulation A constant soil volume
If we consider a constant volume over time (Figures 14-19), the curves obtained by the Hydrus-2D model show a decrease in the pressure potential which stabilizes and is cancelled out from the thirtieth day of infiltration at the surface and around the thirty-fifth day for the deeper levels ( Figure 14).      The retention curves show that the reduction of the pressure potential in the soil ( Figure 14) is related to an increase in the water content.
Water content increases during infiltration and stabilizes when the sample is saturated from day 30 onwards (Figure 15). The cumulative fluxes during the 45 days of infiltration are 55 cm 2 and 8.5 cm 2 respectively for the inflow and outflow (Figure 18 and Figure 19).
If we consider a variable volume of soil, which is more reflective of reality, we also have a decrease in pressure potential ( Figure 20) accompanied by an increase in water content ( Figure 21). However, the time required for the stabilization of the system is shorter; it is 20 days for the saturation of the sample which is manifested by very low to zero pressure potentials and high water contents ( Figure 20 and Figure 21).
The values of the inflow are larger (of the order of 90 cm 2 ) for the whole duration of the simulation (Figure 22 and Figure 24). This is also the case for the outlet flows which are not only more important (with values of 25 cm 2 ) but also the drainage time which is shorter. In fact, we note an outlet flow from the twentieth day of infiltration (Figure 23 and Figure   25).
The analysis of the simulation results shows a difference in the time required for the saturation of the soil sample, a difference in the start of drainage, and a      These errors are not negligible, hence the need to take into account the variation in soil volume when simulating water transfers, as recommended by authors such as [29] in the modelling, not of water transfers, but of the shrinkage curve.
The studies carried out, therefore, show the importance of soil shrinkage and swelling phenomena in the simulation of water transfers in this agricultural area.
These results confirm [9] who showed that a high soil swelling shrinkage capacity makes it difficult to grow plants because their roots can break.
The interest of our study is also illustrated by [30], who shows that the taking into account the phenomena of shrinkage-swelling and cracking, at the time of the infiltration of water in clayey soils, makes it possible to improve the prediction of the water balance in this type of soil. [11] showed that the hydraulic conductivity decreased when the clay content increased in depth.
This experiment on an undisturbed soil monolith of this size confirmed the variability of soil volume and hydrodynamic parameters along the profile.

Conclusions
The exploitation of the data acquired in the laboratory showed the relationships between the variations of water content, pressure potential, and displacement.
Thus, the volume variation of the soil sample occurs both vertically and laterally during infiltration and during drying. It takes place at the surface as well as at depth and ultimately the calculated hydrodynamic parameters change from one level to another in the soil column.
The analysis of the curves of variations in water content, pressure potential, weight, and horizontal and vertical displacement shows the relationship between the variation in water content and the variation in the volume of the soil sample.
This loss of water during drying is a very slow process and only affects the first three levels. It is accompanied by an increase in the pressure potential of the soil which is felt at all levels of the soil column. The resulting shrinkage occurs both vertically and horizontally. For a correct determination of the hydrodynamic parameters necessary for a numerical simulation, it is important to integrate the volume variations of the soil.