Fundamentals of Soil and Water Interactions
Fundamentals of Soil and Water Interactions 
6.39 
total pore volume 
Vw Va 
N 
total (bulk) soil volume 
Vs Vw Va 
Note that the bulk soil volume is the sum of the solid, liquid, and air phases. This relationship can then be employed to estimate the volume of air Va from which the soil porosity N may be calculated.
Vb Vs Vw Va 200 ml
Ms 
295 g 
Vs 109.26 ml 
s 
2.7 g/ml 
380 g 295 g
Vw 85 ml 1 g/ml
Therefore, the volume of the air phase Va 200 85 109.265.74 ml. Thus
Vw Va 
85 ml 5.74 ml 
N 
Vs Vw Va 
200 ml 
0.454 (or 45.4 percent)
6.9.1Soil moisture potential
Due to its impact on nutrient and trace element transport, a thorough understanding of the principles governing soil moisture potential is critical for the biosolids landapplication engineer. The importance of soil moisture potential stems from the fact that moisture movement in plantsoil systems is influenced solely by the magnitude of the soil moisture potential difference that exists between locations.
Soil moisture potential is the sum of three individual potentials: gravitational, pressure, and osmotic potential [14]. Gravitational potential is the potential energy of soil moisture due to its elevation relative to some datum. The position of the datum is arbitrary in calculating the contribution of gravitational potential to total potential but is normally chosen so that the gravitational potential is positive.
The pressure potential is related to the energy associated with water pressure. The pressure potential can be either positive or negative depending on whether or not the soil location is at saturated or unsaturated moisture conditions. If the soil location is unsaturated (i.e., the moisture tension is less than atmospheric pressure), the pressure potential is negative. When the soil location is at saturated conditions (i.e., the moisture tension is greater than atmospheric pressure), the pressure potential is positive. Using this convention, the pressure potential at the water table is always zero.
Osmotic potential is a chemical potential resulting from the attraction of moisture to soil locations of higher soluble salt concentrations.
Downloaded from Digital Engineering Library @ McGrawHill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGrawHill Companies. All rights reserved.
Any use is subject to the Terms of Use as given at the website.
Fundamentals of Soil and Water Interactions
6.40Chapter Six
The osmotic potential becomes increasingly negative with increasing salt concentration in the soil solution.
The total potential T is the sum of the individual potentials and is described mathematically by Eq. (6.17). Example 6.9 illustrates the concept of soil moisture potential used in a typical biosolids landappli cation program.

T z p pos 
(6.17) 
where T total potential (ft, kPa, N/m2) 

z 
gravitational potential (ft, kPa, N/m2) 

p 
pressure potential (ft, kPa, N/m2) 

pos 
osmotic potential (ft, kPa, N/m2) 

The direction and rate of moisture movement from one point to another in soil is a function of the magnitude of the difference in total potential. Moisture always moves from a point of higher potential to a point of lower potential. In the absence of roots and when the osmotic potential is negligible, the total potential is equivalent to the piezometric or hydraulic potential Hp [Eq. (6.18)].

Hp z p 
(6.18) 
where Hp 
piezometric potential (ft, kPa, N/m2) 

z 
gravitational potential (ft, kPa, N/m2) 

p 
pressure potential (ft, kPa, N/m2) 

Example 6.9 As shown in the figure on the next page, two points in a soil are to be monitored for their moisture potential. If the measured pressure potentials at point A and B were 30 and 45 cmH2O, respectively, determine the following:
1.The total potential at points A and B (ignore osmotic potential).
2.The direction of moisture flow, i.e., is moisture moving from point A to B or the reverse?
3.Is point A or B at saturated moisture conditions?
solution
Step 1. The total potential of points A and B can be estimated as follows:
Total potential at point A z p 75 cm ( 30 cm) 45 cm
Total potential at point B z p 300 cm ( 45 cm) 255 cm
Step 2. Moisture always flows from a point of higher potential to a point of lower potential. Therefore, moisture is flowing from point B to point A.
Downloaded from Digital Engineering Library @ McGrawHill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGrawHill Companies. All rights reserved.
Any use is subject to the Terms of Use as given at the website.
Fundamentals of Soil and Water Interactions
Fundamentals of Soil and Water Interactions 
6.41 
75 cm
A.
300 cm
B.
Step 3. Since the pressure potential at both points is negative, both locations are at unsaturated conditions.
Under unsaturated moisture conditions, a tensiometer (or equivalent) is used to measure the hydraulic potential of a soil. Under saturated moisture conditions, a device called a piezometer can be used to measure the hydraulic potential and to evaluate the vertical direction and rate of moisture flow. A piezometer is essentially an openended tube placed at a given depth in a saturated soil. The difference in water heights between two piezometers placed at different depths reflects the variation in hydraulic potentials between the two depths. Example 6.10 illustrates the use of piezometers to estimate the direction of moisture flow.
Example 6.10 The Tubman County Water Reclamation Plant is considering a potential site for biosolids land application. To fully characterize the site, the regulatory agency has required that the publicly owned treatment works (POTW) evaluate the hydraulics of groundwater flow. If two piezometers are installed in the same vicinity but at different depths (as shown in figure on the next page), estimate the hydraulic potentials of the two points and the vertical direction of water flow. (Ignore osmotic potential.)
Downloaded from Digital Engineering Library @ McGrawHill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGrawHill Companies. All rights reserved.
Any use is subject to the Terms of Use as given at the website.
Fundamentals of Soil and Water Interactions
6.42Chapter Six
solution
Step 1. Estimate the hydraulic potential at points A and B.
hA z p 0.8 m 5.0 m 5.8 m
hB z p 3.0 m 2.4 m 5.4 m
Step 2. Since the hydraulic potential at point A is larger than at point B, moisture is flowing upward (i.e., from point A to point B).
NOTE: This is an example of artesian conditions.
6.9.2 Measurement of soil water potential
In all landapplication systems, biosolids are applied to unsaturated soils. Soil water potential in unsaturated soils is measured in the
Downloaded from Digital Engineering Library @ McGrawHill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGrawHill Companies. All rights reserved.
Any use is subject to the Terms of Use as given at the website.
Fundamentals of Soil and Water Interactions
Fundamentals of Soil and Water Interactions 
6.43 
Figure 6.13 Typical soil water characteristic curve. (Adapted by permission from ref. [14].)
field by installation of tensiometers or resistance meters (e.g., gypsum blocks). Tensiometers measure the suction pressure (or tension) of the soil, whereas resistance meters read an electrical resistance that is correlated with tension by means of a calibration curve. detailed instructions for the installation and measurement of tension using tensiometers and resistance meters are provided in standard soil testing handbooks [6,14].
The relationship between soil water content and the soil water potential is termed the soil water characteristic curve. Knowledge of the soil water characteristic curve is important in the design and management of biosolids landapplication systems because it is necessary to convert tension readings to a soil moisture content. Figure 6.13 provides an illustration of a soil water characteristic curve.
It should be noted that soil types made up of fine particles (e.g., clays) have a higher moisture content at the same tension as soils with coarser particles (e.g., sands).
6.9.3 Hydraulic conductivity
The velocity of moisture through a soil profile is proportional to the difference in total potential between two points. This difference in potential measured over some defined distance is termed the hydraulic
Downloaded from Digital Engineering Library @ McGrawHill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGrawHill Companies. All rights reserved.
Any use is subject to the Terms of Use as given at the website.
Fundamentals of Soil and Water Interactions
6.44Chapter Six
TABLE 6.15 Estimation of Hydraulic Gradient in a SoilWater System*
Step 1. Assuming that the magnitude of the osmotic potential between two points is negligible, the total potential is equal to the piezometric potential:
Piezometric potential at point 1 z1 p1 h1
Piezometric potential at point 2 z2 p2 h2
Step 2. Using these definitions, the potential for moisture flow (i.e., hydraulic gradient) may be defined by the following equation:
dh 
h1 
h2 
(z1 
p1) (z2 
p2) 
Hydraulic gradient 
ds 
s1 
s2 

s1 s2 

where s1 s2 is the distance between points 1 and 2.
*Adapted from ref. [14].
gradient. Table 6.15 illustrates the approach for estimating the hydraulic gradient in a soil system.
Estimating the hydraulic gradient between two points in a soil is illustrated in Example 6.11. The proportionality constant that relates velocity to the hydraulic gradient is termed the hydraulic conductivity K. Equation (6.19), which is known as Darcy’s law, illustrates the functional relationship between soil moisture velocity, hydraulic gradient, and the hydraulic conductivity.
Example 6.11 In order to increase the depth of the unsaturated zone at a biosolids landapplication site, the biosolids engineer decides to install a well to lower the groundwater table. If the steadystate drawdown from the well is given in the figure on the next page, estimate the hydraulic gradient between points A and B. Assume that the following data apply: s1 25 ft, s215 ft, hA 12.5 ft, and hB 11 ft.
solution
Step 1. Estimate the piezometric potential at heights hA and hB. Note that since both points are at the water table, their pressure potentials are equal to zero. Therefore, the piezometric potential for points A and B are given as follows:
hA 12.5 m hB 11.0 m
Step 2. The distance between points A and B is 10 m. Therefore, the hydraulic gradient is calculated as follows:
dh 
hA 
hB 
12.5 m 11.0 m 

ds 
s1 
ss 
25 m 15 m 



0.15 m 
m
Downloaded from Digital Engineering Library @ McGrawHill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGrawHill Companies. All rights reserved.
Any use is subject to the Terms of Use as given at the website.
Fundamentals of Soil and Water Interactions
Fundamentals of Soil and Water Interactions 
6.45 

Velocity (v) K 
dh 
(6.19) 




ds 

where v moisture velocity (cm/s, ft/s) 


K hydraulic conductivity (cm/s, ft/s) 

dh 
hydraulic gradient (dimensionless) 



ds 



NOTE: The minus sign in Eq. (6.19) is required because water flow is always from a point of higher to lower total potential.
The volumetric moisture flow rate (ft3/s, m3/min, gal/day, etc.) in soil can be obtained by multiplying the moisture velocity by the crosssec tional area. The approach used to estimate moisture flow rate in soil is illustrated in Example 6.12.
Hydraulic conductivity K is a function of a number of parameters, including texture, temperature, porosity, and soil water content. It should be noted that Eq. (6.19) defines the Darcy velocity as the velocity perpendicular to a crosssectional area between two points. Since water moves only through the pore space, the pore velocity will always be higher than the Darcy velocity. The pore velocity is defined by Eq. (6.20):
v 
(6.20) 
Pore velocity (vp) 
N 

Downloaded from Digital Engineering Library @ McGrawHill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGrawHill Companies. All rights reserved.
Any use is subject to the Terms of Use as given at the website.
Fundamentals of Soil and Water Interactions
6.46Chapter Six
where v Darcy velocity N soil porosity
In most biosolids landtreatment applications, it is the Darcy velocity rather than the pore velocity that is of concern. The pore velocity is an important parameter in the analysis of subsurface contaminant transport.
Example 6.12 A proposed biosolids landapplication area is approximately 1000 m by 200 m in aerial size. The depth to the water table is 1.5 m. If the unsaturated soil has an average tension of 200 cmH2O and the hydraulic conductivity of the soil is approximately 10 5 cm/s, estimate the vertical volumetric flow rate of groundwater through the landapplication area. Assume that the depth to the water table remains constant and that the osmotic potential can be neglected.
solution
Step 1. Determine the hydraulic potential at the soil surface and at water table. Choose the water table as the datum.
hp (soil surface) z p 1.5 m ( 2.0 m) 0.5 m
hp (water table) z p 0 m 0 m 0.0 m
Step 2. Estimate the hydraulic gradient:
dh 
0.5 m 
0.33 m/m 
ds 
1.5 m 
Step 3. Estimate the flow velocity:
dh
Velocity K ds
10 5 cm/s 0.33 m/m 1 m/100 cm 3600s/h
1.188 10 4 m/h
Step 4. Estimate the volumetric flow rate through the biosolids landappli cation site in cubic meters per day:
Volumetric flow rate Q velocity area
1.188 10 4 m/h (1000 m 200 m) 24 h/day
570 m3/day
6.9.4Measurement of hydraulic
conductivity
Hydraulic conductivity typically is measured in the laboratory using undisturbed soil cores or in the field under saturated soil conditions.
Downloaded from Digital Engineering Library @ McGrawHill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGrawHill Companies. All rights reserved.
Any use is subject to the Terms of Use as given at the website.
Fundamentals of Soil and Water Interactions
Fundamentals of Soil and Water Interactions 
6.47 
Figure 6.14 Laboratory permeameter for measurement of hydraulic conductivity. (Adapted by permission from F. Fernandez and R. M. Quigly (1985), Canadian Geotechnical Journal, 22:205–214.)
Values of saturated hydraulic conductivity vary over a wide range under field conditions. Figure 6.14 depicts a typical laboratory permeameter used to measure hydraulic conductivity.
Typical ranges of hydraulic conductivity as a function of soil texture are given in Table 6.16.
6.10 Infiltration
Infiltration is the process by which water passes through the soil surface and enters the subsoil. The units of infiltration are normally depth of water per unit time (e.g., inches per hour, feet per day, etc.). The rate at which infiltration can be maintained in a particular soil is an important parameter in the design of biosolids landapplication systems. Infiltration will affect not only irrigation scheduling but also surface and subsurface drainage requirements. The permissible range in biosolids moisture content for a given biosolids landapplication program is often governed by the infiltration characteristics of the soil. For example, application of liquid biosolids would be undesirable on soils with low or marginal infiltration rates [68].
In the agricultural literature, there are various infiltration terms with which the biosolids landapplication engineer should become familiar. Cumulative infiltration refers to the depth of moisture that has penetrated the soil surface after a particular amount of time. Figure 6.15 depicts the differences in cumulative infiltration versus time for various soil types.
Downloaded from Digital Engineering Library @ McGrawHill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGrawHill Companies. All rights reserved.
Any use is subject to the Terms of Use as given at the website.
Fundamentals of Soil and Water Interactions
6.48Chapter Six
TABLE 6.16 Hydraulic Conductivity as a Function
of Soil Texture*
Soil type 
Hydraulic conductivity (m/day) 
Coarse gravel 
150 
Coarse sand 
45 
Medium sand 
12 
Fine sand 
2.5 
Silt 
0.08 
Clay 
0.0002 


*Adapted from ref. [14].
Figure 6.15 Cumulative infiltration versus time in typical agricultural soils. (Adapted by permission from ref. [14].)
Infiltration rate refers to the slope of the cumulative infiltration curve and represents the rate of change of infiltration. Instantaneous and average infiltration rates normally decrease with time. It should be noted that the rate of infiltration is a function of the initial soil moisture content, with drier soils demonstrating a significantly greater instantaneous infiltration rate.
Numerous approaches and empirical equations have been developed to represent observed infiltration data. An early equation used to model infiltration was the Kostiakov equation, which is still used in many agricultural crop production applications [Eq. (6.21)]:
Downloaded from Digital Engineering Library @ McGrawHill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGrawHill Companies. All rights reserved.
Any use is subject to the Terms of Use as given at the website.