2.5 Advantages of Laboratory Methods Over Field Methods
2.6.1.4 Soil Water Characteristic Curve
According to Bear (1979), three different stages of saturation can be distinguished in a soil profile as shown in Figure 2.13. At low degrees of saturation
Figure 2.12 Total, Matric, and Osmotic Suction Measurements on Compacted Regina Clay (Fredlund and Rahardjo, 1993)
the water phase is not continuous except for the very thin film of water around the solids. This stage is called “pendicular” stage.
At higher degrees of saturation, both water and air phases are continuous and water flow is expected to occur. This stage is termed as ‘”Funicular” stage. As the degree of saturation increases, the air in the water turns into small bubbles and the air phase becomes discontinuous. The air bubbles can be transported along with the water, and the soil may reach full saturation, which is “Insular air” stage. As the water content changes in a soil profile, the pore pressure also changes. As the soil is drained, the total or matric suction will increase. Suction will reduce when soil is re- filled with water. By comparing the amount of drained water with the increase in suction, a relationship between the degree of saturation (or volumetric water content) and the matric suction of the soil can be established. This relationship is called the soil water characteristic curve of a soil.
Figure 2.13 Possible Water Saturation Stages (Bear, 1979)
The soil-water characteristic curve can be obtained by performing tests using pressure plate device in the laboratory by following the axis-translation technique (Hilf, 1956). In the late 1950’s, soil-water characteristic curve was commonly used to predict the coefficient of permeability at specific water content in terms of matric
suction (Mashall, 1958, Millington and Quirk, 1961). This soil-water characteristic curve is also required in the determination of water volume changes in the soil respect to matric suction change. The coefficient of water volume change with respect to matric suction is given by the slope of the soil-water characteristic curve.
For these applications, it is more useful if soil-water characteristic curve can be expressed as an equation. Over the last few decades, a number of equations have been suggested based on shape of the curve. These equations can be grouped into the number of curve-fit parameters that have to be determined (unknown parameters) as follows:
The two-parameter equations Williams Model (1996):
b w
a θ
ψ ln
ln = + (unknowns: a, b) (2.15) where θw is volumetric water content and ψ is soil suction.
The three-parameter equations Gardner Model (1956):
+ + −
= r s rb
w θ θ aψθ
θ 1 (unknowns: θr, a and b) (2.16) where θw is volumetric water content; θs is saturated volumetric water content; θr is residual volumetric water content; and ψ is soil suction.
Brooks and Corey Model (1964):
b r s r w
a
− +
=θ θ θ ψ
θ ( ) (unknowns: θr, a and b) (2.17)
where θw is volumetric water content; θs is saturated volumetric water content; θr is residual volumetric water content; and ψ is soil suction.
Note: equation 2.17 is valid for ψ greater than or equal to a (air-entry value). For ψ less than a, θw is equal to θs. For larger values of ψ, 2.17 will give similar values as 2.16.
McKee and Bumb Model (1984):
−
− +
= b
a
r s r
w θ θ θ ψ
θ ( )exp (unknowns: θr, a and b) (2.18) where θw is volumetric water content; θs is saturated volumetric water content; θr is residual volumetric water content; and ψ is soil suction.
McKee and Bumb Model (1984):
−
+ + −
=
b a
r r s
w θ θ ψθ
θ
exp 1
)
( (unknowns: θr, a and b) (2.19)
where θw is volumetric water content; θs is saturated volumetric water content; θr is residual volumetric water content; and ψ is soil suction.
Fredlund and Xing Model (1994) with correction factor C(ψ) =1:
c
b s w
e a
+
=
ψ θ θ
ln
(unknowns: a, b and c) (2.20)
where θw is volumetric water content; θs is saturated volumetric water content; θr is residual volumetric water content; ψ is soil suction; and e is void ratio.
Fredlund and Xing (1994) had mentioned that C(ψ) is approximately equal to 1 at low suctions as the curve at the low suction range is not significantly affected by C(ψ). With C(ψ) =1, θw is not zero when ψ is 1,000,000 kPa.
The four-parameter equations Van Genuchten Model (1980):
( s br)c
r
w aψ
θ θ θ
θ +
+ −
= 1 (unknowns: θr, a, b and c) (2.21) where θw is volumetric water content; θs is saturated volumetric water content; θr is residual volumetric water content; and ψ is soil suction.
Fredlund and Xing Model (1994):
b c s
r r w
e a
+
+
+ +
= ψ
θ ψ
ψ ψ θ
ln 000 , 000 , 1 1 ln
1 ln
1 (2.22)
(unknowns: θr, a, b and c)
where θw is volumetric water content; θs is saturated volumetric water content; ψ is soil suction; ψr is soil suction in residual condition that can be computed or assumed to be a value such as 15000 kPa or 3000 kPa; and e is void ratio
Fredlund and Xing Model (1994), if the residual water content θr is required:
b c r s r
w
e a
+ + −
=
ψ θ θ θ
θ
ln
(unknowns: θr, a, b and c) (2.23)
where θw is volumetric water content; θs is saturated volumetric water content; θr is residual volumetric water content; ψ is soil suction; and e is void ratio.
These equations have been developed to describe the soil-water characteristic curves of control samples. However, the variations in constant parameters can be used to explain void ratio distribution and particle size distribution in soils. A summary of the equations and applications of these equations are reported in Sillers et al. (2001). The equation 2.20 was proposed to be used in this research since it can easily provide the general soil suction properties effects of sandy and clayey soil samples.
In the present work, an attempt has been made to assess soil-water characteristic curves under two different K0 stress state conditions: controlled radial confinement approach and controlled anisotropic stress state approach.