Hydro-Mechanical Properties of an Unsaturated Frictional Material

8.2. SOIL-WATER CHARACTERISTIC CURVE MODEL 177
Table 8.2: Constitutive parameters for the new SWCC model (calibrated against imbibition
data)
Experimental results β0 β1 β2 β3 s0
Loose specimen, 2 nd imbibition process
TDR/T 70 mm 38.86 −5.91 0.50 −33.12 3.49
TDR/T 160 mm 38.56 −4.63 0.92 −32.62 3.11
TDR/T 260 mm 38.28 −5.05 0.50 −30.42 2.81
TDR/T 360 mm 38.55 −4.37 0.42 −20.92 1.92
- Parameter β2 that also influences the slope of the curve and is in all depth approximately
β2 = 0.5.
An influence according to the initial imbibition suction s0 was found for the scaling param-
eter β3 that influences the minimum volumetric water content θmin. With increasing initial
imbibition suction s0 the parameter β3 is decreasing. Further, it is now tried to replace β3
with a term expression depending on s0, which incorporates the variation of this parameter
for different layers. Simple linear term of s0 instead a constant β3 showed the best fit over
the trial models. The resulting hysteresis model is:
θ(ψ) = β0 + (β 1 3 + β 2 3 · s0) exp(− ψβ1
) (8.3)
where: s0 is the initial imbibition suction measurement that has been recorded using ten-
siometer sensor. Results of the proposed hysteresis model curve fit for both the 1 st and 2 nd
imbibition process are show in Fig. 8.5 for the loose specimen (and in Fig. E.5 for curve fit of
dense specimen in Appendix E). In the 3D plots the initial imbibition suction s0 is introduced
as 3rd dimension on the z-axis. Similar to the curve fit results from the drainage process the
calculated results seem to be in good agreement to the experimental results for loose specimen
(1 st imbibition and 2 nd imbibition process). The identified parameters and the coefficient of
linear regression R 2 are summarized in Tab. 8.3. For drainage as well as imbibition curve
fitting procedure the Levenberg-Marquardt algorithm was used, that is an improvement of
the classical Gauss-Newton method for solving non-linear least-square regression problems.
The plots given in Figs. 8.6 to 8.9 derived from regression analysis of loose specimen
are used to appreciate wether or not the model fits the experimental data well (see also the
results derived from regression analysis of dense specimen in Figs E.6 to E.9 in Appendix E).
Both statistical techniques, coefficient of regression determination and residual analysis were
used to validate the model and to see the adequacy of different aspects of the model. The
statistical results from model validation are shown in Figs. 8.6 and 8.7 for the model fit
of several drainage suction-water content measurements for loose specimens. The model
validation results of the statistical analysis derived from the 1 st as well as 2 nd imbibition
β2