Environmental Engineering Reference
In-Depth Information
from Eq. 13.53 using the above-measured values of m 1 and
m 2 (from Eqs. 13.60 and 13.61). The actual volume change
can then be measured and compared with the computed value.
A close agreement between the measured and predicted vol-
ume changes indicates uniqueness of the constitutive surface
near a stress point. The above example illustrates a possible
uniqueness test for the soil structure constitutive surface. The
water phase constitutive surface could also be verified if water
volume change measurements were made for the computation
of the m 1 and m 2 coefficients.
The above test for uniqueness can be approximated by
an even simpler procedure using a single soil specimen sub-
jected to a series of small stress changes (Fredlund and Mor-
genstern, 1976). The procedure is illustrated in Fig. 13.13b.
Consider a single unsaturated soil specimen that is first
subjected to a small increase in net normal stress (i.e., an
increase in the total stress) along a constant-matric-suction
plane (i.e., 0-1 loading path in Fig. 13.13b). The measured
volume changes are used to compute the m 1 and m 1 coef-
ficients, respectively.
The specimen can then be subjected to an increase in
its matric suction while maintaining a constant net normal
stress (i.e., 1-2 loading path in Fig. 13.13b). The matric suc-
tion is increased by decreasing the pore-water pressure. The
measured volume changes can be used to compute the m 2
and m 2 coefficients, respectively. The m 1 , m 1 and m 2 , m 2
coefficients can then be used to predict the overall volume
change and the water volume change of the soil specimen
during any subsequent loadings. The coefficients can be
assumed to approximate a single stress point on the con-
stitutive surface even though the first and second loadings
are performed at slightly differing initial volume-mass prop-
erties,. This assumption is reasonable for small changes in
the stress state variables.
The next step is to apply a small increment in both the net
cell was used for isotropic loading. The total, pore-air, and
pore-water pressures were controlled during the experiments.
Thewater pressurewas isolated from the air pressure bymeans
of a high-air-entry disk placed at the bottom of the specimen.
After equalization at a selected stress point, each specimen
was subjected to several loading stages in order to test the
uniqueness of the constitutive surface. The predicted andmea-
sured volume changes were assessed by plotting the predicted
volume changes versus the measured volume changes.
Good agreement was observed between the measured and
predicted volume changes for undisturbed Regina clay, as
shown in Fig. 13.14. The specimen was tested under K 0 load-
ing. The volume changes at two elapsed times (e.g., 1000
and 5000 min) are considered for each specimen. Uniqueness
implies a slope of unity and an intercept of zero for the plot
of measured versus predicted volume change. Figure 13.14a
demonstrates that all points obtained at two elapsed times
essentially fall along the 45 line, indicating virtually perfect
correlation. This agreement supports the uniqueness of the
soil structure constitutive surface.
The agreement between the predicted and measured water
volume changes (Fig. 13.14b) is not as consistent as that
normal stress d σ u a and matric suction d u a u w
(i.e., 2-3 loading path in Fig. 13.13b). This path is adhered
to by increasing the total normal stress and decreasing
the pore-water pressure. The anticipated overall volume
change and change in volume of water as a result of the
third loading can be predicted from Eqs. 13.53 and 13.54,
respectively, while using the coefficients of volume change
obtained from the previous two loadings. The measured
overall and water volume changes can then be compared
with the predicted values. The constitutive surface at a
point is considered unique if the measured and predicted
deformations are essentially equal. This procedure can be
repeated at various state points on the constitutive surface.
Fredlund and Morgenstern (1976) experimentally tested
constitutive surfaces of two unsaturated soils for uniqueness
by using small changes in stress state variables. Four series of
experiments were conducted using three specimens of undis-
turbed Regina clay and one specimen of compacted kaolin.
The specimens were tested using a modified oedometer (i.e.,
K 0 loading) and a modified triaxial cell. The modified triaxial
(a)
(b)
Figure 13.14 Comparison of predicted and measured volume
changes for undisturbed Regina clay undergoing K 0 loading: (a)
soil structure constitutive surface; (b) water phase constitutive sur-
face (from Fredlund and Morgenstern, 1976).
 
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