Hydro-Mechanical Properties of an Unsaturated Frictional Material

7.2. SOIL-WATER CHARACTERISTIC CURVE 139
In Fig. 7.1 a) to d) the overall impression is that the points are close to the bisection
line in the diagrams of observed and predicted values. As closer the points to the bisection
line f(x) = x in the diagrams of observed versus predicted values as better the result of the
curve fit. Using Brooks and Corey’s (1964) power-law relationship saturated volumetric water
contents are not considered in the best-fit procedure and statistical analysis. This equation is
not valid in the saturated zone and is only applicable for suctions larger than air-entry value
(ψ > ψaev), that corresponds to volumetric water contents smaller than saturated volumetric
water content (θ < θs). Due to sudden increase in volumetric water content after reaching the
air-entry value up to the residual water content, points are concentrated mainly at low values
(see Fig 7.1 a) to d)) as well as high values (see Fig 7.1 b) to d)) that corresponds to volumetric
water contents in the residual zone and respectively to saturated volumetric water contents.
For low volumetric water contents good agreement between observed and predicted values
was found for all model functions. At larger volumetric water contents between θ = 7% to
20% for the most results the observed values are overestimated by the predicted values when
using Brooks and Corey’s (1964) model function and van Genuchten’s (1980) model including
m = 1 − 1/n. Except two points that are far underestimated by all model functions. Best
agreement in the range of θ = 7% to 20% was found for van Genuchten’s (1980) and Fredlund
and Xing’s (1994) model. Using Brooks and Corey’s (1964) equation for volumetric water
content between θ = 20% to 46 the most experimental values are underestimated by the
predicted values. Even the points are closer to the bisection line in Fig 7.1 this trend can be
observed also when using van Genuchten’s (1980) equation considering m = 1 − 1/n. In this
range best agreement between observed and predicted values was found for van Genuchtens
(1980) as well as Fredlund and Xing’s (1994) model function. At all the results are closest to
the bisection line using Fredlund and Xing’s (1994) model, which means that the observed
values are similar to predicted values. This is also expressed by the coefficient of regression
determination R 2 = 0.996. The plot of residuals versus predicted values should be randomly
distributed above and below the line of f(x) = 0. The diagrams are given in Fig. 7.1 e) to h)
respectively. The diagrams in Fig. 7.1 e) to h) show that for low volumetric water contents
θ = 0% to θ = 10% the points are best scattered, when using Brooks and Corey’s (1964)
and Fredlund and Xing’s (1994) model for fitting procedure. Mainly when using both van
Genuchten’s (1980) equations vertical orientation of points was found in the residual zone. In
the range of θ = 10% to θ = 46% the results are randomly distributed.
Results derived from statistical analysis of fitting procedure from imbibition data (see
Fig 7.2) show that observed and predicted values are in good agreement for fitting procedure
using both van Genuchten’s (1980) and Fredlund and Xing’s (1994) model functions. This is
also reflected in the coefficient of regression determination R 2 = 0.993. Results are randomly
distributed in the plot of residual versus predicted values for all model functions. But for
volumetric water contents θ = 20% to 46% most points are located above the line of f(x) = 0
when using Brooks and Corey’s (1964) function. This is also reflected in the underestima-