Flow of Water in the Soil | Soil-Water Relationship | Agronomy

Flow of water in the soil is complex because of various states and direction in which water flows and because of the forces that cause it to flow. Water flows downwards due to gravity. It moves in small pores due to capillarity because of adhesive and cohesive forces. Because of heat, it vapourises and diffuses through soil air.

The rate at which gravitational water moves through soil is determined by the size and continuity of pores. In coarse textured soils, it moves rapidly through large pores. It moves less rapidly through fine textured soils because of resistance to flow in micro pores. Movement is retarded by clay pan or plough pan. A sandy layer temporarily halts percolation, but once water penetrates such layer, it continues to move downwards.

Irrigation water moves as a front from saturated soil layer to an unsaturated layer and movement of the front is unsteady. Movement of water is more uniform in moist soil than in dry soil. Heat vapourises the soil- water, which diffuses through soil air. As soil- water is evaporated from the soil surface, capillary water rises and replaces part of the evaporated water.

Darcy’s Law:

Fig 4.40 shows a horizontal column of soil, through which a steady flow of water is occurring from left to right, from an upper reservoir to a lower one, in each of which the water level is maintained constant.

Experience shows that the discharge rate Q, being the volume V, flowing through the column per unit time, is directly proportional to the cross-sectional area and to the hydraulic head drop ΔH, and inversely proportional to the length of the column L ;

Hydraulic head drop across the system is usually determined by measuring the head at the inflow boundary (H_i) and at the outflow boundary (H_o), relative to some reference level.

Difference between the two heads is ΔH:

ΔH = H_i – H_o

Obviously, no flow occurs in the absence of a hydraulic head difference, i.e., when ΔH = 0.

The head drop per unit distance in the direction of flow (ΔH/L) is the hydraulic gradient, which is in fact the driving force. Simply, hydraulic gradient is the rate of change of hydraulic head with distance. The specific discharge rate, Q/A (i.e. the volume of water flowing through a cross-sectional area A per time t) is called flux density (simply flux) and indicated by q.

Thus, the flux is proportional to the hydraulic gradient:

The proportionality factor K is, generally, designated as the hydraulic conductivity.

This equation is known as Darcy’s law. In other words, hydraulic conductivity is the proportionality factor K in Darcy’s law. The hydraulic conductivity of a soil is a measure of the soil’s ability to transmit water when submitted to a hydraulic gradient.

Where flow is unsteady or the soil is non-uniform; the hydraulic head may not decrease linearly along the direction of the flow. Where the hydraulic head gradient or the conductivity is variable, we must consider the localised gradient, flux and conductivity values rather than overall values for the soil system as a whole. A more generalised expression of Darcy’s law is, therefore, in differential form.

A more exact and generalised expression of Darcy’s law for saturated porous media into a three-dimensional macroscopic system is:

q = -KߜH

Stated verbally, this law indicates that the flow of a liquid through a porous medium is in the direction of, and at a rate proportional to, the driving force (hydraulic gradient) acting on the liquid and also proportional to the property of the conducting medium (conductivity) to transmit the liquid.

In one-dimensional system, the above equation takes the form:

Hydraulic conductivity is one of the hydraulic properties of the soil. These properties determine the behavior of the soil fluid within the soil system under specified conditions. More specifically, the hydraulic conductivity determines the ability of the soil fluid to flow through the soil matrix system under a specified hydraulic gradient; the soil fluid retention characteristics determine the ability of the soil system to retain the soil fluid under a specified pressure condition.

Hydraulic conductivity depends on the soil grain size, the structure of the soil matrix, the type of soil fluid and the relative amount of soil fluid (saturation) present in the soil matrix. Important properties relevant to the solid matrix of the soil include pore size distribution, pore shape, tortuosity, specific surface and porosity. In relation to the soil fluid, the important properties include fluid density and fluid viscosity.

Limitations of Darcy’ Law:

1. It applies only when the flow is laminar and where soil-water interactions do not result in a change of permeability with a change in gradient

2. Since the saturated flow depends on size of pores, management practices like tillage may affect the porosity and hence the flow and hydraulic conductivity of the soil

3. Pore spaces may be entrapped by gases, especially when the soil is under submergence for long time

4. In coarse sands and gravels, hydraulic gradients in excess of unity may result in non-laminar flow conditions where Darcy’ law may not always be applicable.

Measurement of Saturated Hydraulic Conductivity:

The saturated hydraulic conductivity of water in soil (or the intrinsic permeability of the soil) can be measured by both field and laboratory experiments. Either way, the experimental measurement of K (or k) consists in determining the numerical value for the coefficient in Darcy’s equation.

Laboratory Methods:

In the laboratory, the value of K can be determined by several different instruments and methods such as the permeameter, pressure chamber and consolidometer. A common feature of all these methods is that a soil sample is placed in a small cylindrical receptacle representing a one-dimensional soil configuration through which the circulating liquid is forced to flow.

Depending on the flow pattern imposed through the soil sample, the laboratory methods for measuring hydraulic conductivity are classified as either a constant head test with a steady-state flow regimen or a falling head test with an unsteady state flow regimen.

Constant head methods are primarily used in samples of soil materials with an estimated K above 1.0 x 10² m yr^-1, which corresponds to coarse-grained soils such as clean sands and gravels. Falling head methods, on the other hand, are used in soil samples with estimated values of K below 1.0 x 10² m yr^-1.

Constant Head method:

The constant head test with the permeameter is one of the most commonly used methods for determining the saturated hydraulic conductivity of coarse grained soils in the laboratory. The test operates in accordance with the direct application of Darcy’s law to a soil liquid configuration representing a one-dimensional, steady flow of a percolating liquid through a saturated column of soil from a uniform cross- sectional area.

In this method, a cylindrical soil sample of cross-sectional area A and length L is placed between two porous plates that do not provide any extra hydraulic resistance to the flow (Fig 4.41).

A constant head difference, H₂ – H₁, is then applied across the test sample.

By measuring the volume V of the test fluid that flows through the system during time t, the saturated hydraulic conductivity K of the soil can be determined directly from Darcy’s equation:

Falling Head methods:

The falling head test with the permeameter is primarily used for determining the K (or k) value of fine grained soils in the laboratory. Like the constant head method, the falling head test also operates in accordance with direct application of Darcy’s law to a one-dimensional, saturated column of soil with a uniform cross sectional area.

The falling head method differs from the constant head method in that the liquid that percolates through the saturated column is kept at an unsteady state flow regimen in which both the head and the discharged volume vary during the test (Fig 4.42).

In the falling head test method, a cylindrical soil sample of cross-sectional area A and length L is placed between two highly conductive plates. The soil sample column is connected to a standpipe of cross-sectional area a, in which the percolating fluid is introduced into the system.

Thus, by measuring the change in head in the standpipe from H₁ to H₂ during a specified interval of time t, the saturated hydraulic conductivity can be determined as follows:

The lower limit of K, which can be measured in a falling head permeameter, is about 1 x 10^-2 m yr^-1. This value corresponds approximately to the lower limit of conductivity of silts and coarse clays.

A common problem encountered in using either the constant head or falling head test with the permeameter is related to the degree of saturation achieved within the soil samples during the test. Air bubbles are usually trapped within the pore space and although they tend to disappear slowly by dissolving into the de-aerated water, their presence in the system may alter the measured results.

Therefore, after using these instruments to measure K, it is always recommended that the degree of saturation of the sample be verified by measuring the sample’s volumetric water content and comparing the result with the total porosity calculated from the particle density.

Ranges of hydraulic conductivity for different soils are given in Table 4.7:

Field Methods:

Many in situ methods have been developed for determining the saturated hydraulic conductivity of soils within a groundwater formation under unconfined and confined conditions.

Auger-hole method or Hooghoudt’s method:

Auger-hole method is the field procedure most commonly used for in situ determination of saturated hydraulic conductivity of soils. In its simplest form, it consists of the preparation of a cavity partially penetrating the aquifer, with minimal disturbance of the soil. After preparation of the cavity, water in the hole is allowed to equilibrate with the groundwater; that is, the level in the hole becomes coincident with the water table level. Actual test starts by removing the entire amount of water from the hole and by measuring the rate of rise of water level within the cavity (Fig 4.43).

Because of the three-dimensional aspect of the flow pattern of the water near the cavity, there is no simple equation for accurately determining the conductivity. Numerous available semi-empirical expressions, however, can be used for approximating the saturated hydraulic conductivity for different soil configurations.

The formula to use in the case where the auger-hole does not terminate on a impermeable layer is:

When the auger-hole terminates on an impermeable layer:

In both equations, S is given by the relation:

S = 0.19 a x d

where, y₁ = Water level in the auger-hole (cm) below groundwater level at the start of measurement

y₂ = Water level in the auger-hole (cm) at the end of measurement

Δt = Rise of water level in the auger-hole between t₂ and t₁

2R = Auger-hole diameter

d = Depth of auger-hole (cm) below groundware level

S = Depth of impermeable layer (cm) below auger-hole.

Hoodghoudt determined that the constant S is dependent of a, d and s expressed with the above equation.

Advantages:

1. Use the soil-water for the measurement

2. Sample used for the measurement is large

3. Measurement is not greatly affected by the presence of rocks, and or root holes adjacent to the hole

4. Measurement reflects the horizontal component of K_sat.

Auger-hole method is applicable to an unconfined aquifer with homogeneous soil properties and a shallow water table. In its simplest form, this method provides an estimate of the average horizontal component of the saturated hydraulic conductivity of the soil within the aquifer.

Enhanced variations of the method have been developed to account for layered soils and for the determination of either horizontal or vertical components of saturated hydraulic conductivity.

Results obtained by the auger-hole method are not reliable for cases in which:

1. The water table is above the soil surface

2. Artesian conditions exist

3. Soil structure is extensively layered

4. Occurrence of highly permeable small strata.

Piezometer Method:

Kirkham (1946) proposed a method in which a tube is inserted into the auger hole below a water table with or without a cavity at the end of the tube.

Pipes or tubes are driven in to the soil below the water table either with or without a cavity at the end. Soil is removed from the pipe or tube. Water table is allowed to get its level and then water is pumped out. Rise of water level in the pump is recorded with time (Fig 4.44).

Movement of Water in the Soil:

Water movement in soils is quite simple and easy to understand in some ways and quite complex and difficult to grasp in others. An object that is free to move tends to move spontaneously from a state of higher potential energy to one of lower potential energy. So it is with water. A unit volume or mass of water tends to move from an area of higher potential energy to one of lower potential energy (Fig 4.45).

Movement of Water under Saturated Conditions:

Poiseuille’s law forms the basis for a number of different equations which have been developed for determining the hydraulic conductivity of the soil for knowledge of its pore size distribution. Pore size is of outstanding significance, as its fourth power is proportional to the rate of saturated flow. This indicates that saturated flow under otherwise identical conditions decreases as the pore size decreases.

Generally, the rate of flow in soils of various textures is in the following sequence:

Sand > loam > clay

Saturated flow occurs when the soil pores are completely filled with water. This water moves at water potentials larger than – 33 kPa. Saturated flow is water flow caused by gravity’s pull. It begins with infiltration, which is water movement into soil when rain or irrigation water is on the soil surface. When the soil profile is wetted, the movement of more water flowing through the wetted soil is termed percolation.

Factors affecting movement of water include:

1. Texture

2. Structure

3. Amount of organic matter

4. Depth of soil to hard pan

5. Amount of water in the soil

6. Temperature

7. Pressure.

Moisture Movement under Unsaturated Conditions:

It is flow of water held with water potentials lower than -1/3 bar. Water will move toward the region of lower potential (towards the greater “pulling” force). In a uniform soil this means that water moves from wetter to drier areas. The water movement may be in any direction.

The rate of flow is greater as the water potential gradient (the difference in potential between wet and dry) increases and as the size of water filled pores also increases. The two forces responsible for this movement are the attraction of soil solids for water (adhesion) and capillarity. Under field conditions this movement occurs when the soil macro pores (non-capillary) are filled with air and the micro-pores (capillary) pores with water and partly with air.

As drainage proceeds in a soil and the larger pores are emptied of water, the contribution of the hydraulic head or the gravitational component to total potential becomes progressively less important and the contribution of the matric potential ψ_m becomes more important.

The effect of pressure is, generally, negligible because of the continuous nature of the air space. The solute potential (osmotic potential) ψ_s does not affect the potential gradient unless there is unusual concentration of salt at some point in the soil. The negligible effect of solute potential is due to the fact that both solutes and water are moving. Thus, in moisture moment under unsaturated conditions, the potential ψ is the sum of the matric potential (ψ_m) and to some extent the gravitational potential (ψ_g). In horizontal movement, only ψ_m applies. Under conditions of downward movement, capillary and gravitational potentials act together. In upward capillary movement ψ_m and ψ_g oppose one another.

For unsaturated flow the equation can be rewritten as:

The direction of I is the path of greatest change in (ψ_m + ψ_g).

Under unsaturated conditions, Darcy’s is still applied but with some modifications. It is applicable to unsaturated flow if K is regarded as a function of water content, i.e K (θ) in which θ is the soil moisture content.

As the soil moisture content and soil moisture potential decreases, the hydraulic conductivity decreases very rapidly, so that ψ_soil is – 15 bars, K is only 10^-3 of the value at saturation. Rapid decrease in conductivity occurs because the larger pores are emptied first, which greatly decreases the cross-section available for liquid flow. When the continuity of the films is broken, liquid flow no longer occurs.

In unsaturated soil moisture movement, also called capillary movement, k is often termed as capillary conductivity, though the term hydraulic conductivity is also frequently used. The unsaturated conductivity is a function of soil moisture content as well as number, size and continuity of soil pores.

At moisture contents below field capacity, the capillary conductivity is so low that capillary movement is of little or no significance in relation to plant growth. Many investigations have shown that capillary rise from a free water table can be an important source of moisture for plants only when free water is within 60 or 90 cm of the root zone.

Movement of unsaturated flow ceases in sand at a lower tension than in finer textured soils, as the water films lose continuity sooner between the larger particles. The wetter the soil, the greater is the conductivity for water.

In the ‘moist range’, the range of unsaturated flow in soils of various textures is in the following order:

Sand < loam < clay

It may be noticed that this is the reverse of the order encountered in saturated flow. However, in the ‘wet range’ the unsaturated conductivity occurs in the same or similar order as saturated conductivity.

Water Vapour Movement:

The movement of water vapour from soils takes place in two ways:

1. Internal movement — the change from the liquid to the vapour state takes place within the soil, that is, in the soil pores and

2. External movement — the phenomenon occurs at the land surface and the resulting vapour is lost to the atmosphere by diffusion and convection.

Movement of water vapour through the diffusion mechanism takes place from one area to other soil area depending on the vapour pressure gradient (moving force). This gradient is simply the difference in vapour pressure of two points, a unit distance apart. The greater this difference, the more rapid the diffusion and the greater is the transfer of water vapour during a unit period.

Movement of soil-water in unsaturated soils involves both liquid and vapour phases. Although, vapour transfer is insignificant in high soil-water contents, it increases as void space increases. At a soil moisture potential of about -15 bars, the continuity of the liquid films is broken and water moves only in the form of vapour.

Diffusion of water vapour is caused by a vapour pressure gradient as the driving force. The vapour pressure of soil moisture increases with the increase in soil moisture content and temperature, it decreases with the increase in soluble salt content.

Water vapour movement is significant only in the ‘moist range’. In the ‘wet range’ vapour movement is negligible because there are few continuous open pores. In the ‘dry range’ water movement exists, but there is so little water in the soil that the rate of movement is very small.

Water vapour movement goes on within the soil and also between soil and atmosphere, for example, evaporation, condensation and adsorption. The rate of diffusion of water vapour through the soil is proportional to the square of the effective porosity, regardless of pore sizes. The finer the soil pores, the higher is the moisture tension under which maximum water vapour movement occurs.

In a coarse textured soil, pores become free of liquid water at relatively low tensions and when the soil dries out there is little moisture left for vapour transfer. But a fine textured soil retains substantial amounts of moisture even at high tensions, thus permitting vapour transfer. It is interesting to note that maximum water vapour movement in soils is of greatest importance for the growth and survival of plants.