Environmental Engineering Reference
In-Depth Information
Figure 13.15
Relationship of the volume-mass volumetric deformation moduli to one another
for an initially saturated soil subjected to total stress changes or soil suction changes.
The
a
m
coefficient is approximately equal to the
a
t
coef-
ficient when the degree of saturation is near 100% or when
the matric suction goes to zero (Fig. 13.10a). At saturation
(i.e., on the plane of zero matric suction), the
a
t
coeffi-
cient becomes the coefficient of compressibility
a
v
for a
saturated soil.
The
a
t
coefficient becomes greater than the
a
m
coefficient
as degree of saturation decreases. This shows that a change
in total stress is more effective in changing void ratio than is
a change in matric suction. It can be observed that the void
ratio corresponding to the shrinkage limit of a soil is the
minimum void ratio that can be attained under unconfined,
maximum soil suction conditions.
The
b
m
coefficient approaches the
b
t
coefficient as the
degree of saturation approaches 100%. At lower degrees of
saturation, the
b
m
coefficient will generally be greater than
the
b
t
coefficient (Fig. 13.10b). In other words, a change in
matric suction is more effective in changing the water con-
tent of the soil than is a change in total stress. This occurs
because the matric suction is applied directly to the water
phase. The
b
t
coefficient can be related to
a
t
or
a
v
coeffi-
cients when the soil is on the saturation plane (i.e., matric
suction is equal to zero). The
b
t
coefficient is related to
a
t
or
a
v
coefficients using the basic volume-mass relationship (i.e.,
Se
=
net normal stress. The pore-air pressure approaches the pore-
water pressure for the saturated condition.
If the same soil is subjected to increasing matric suction,
the volume change will be the same as long as the soil
remains saturated. Once the soil commences to desaturate,
a matric suction change will not be as effective as a total
stress change in producing a volume change. This behavior
is reflected by curve
B
(i.e.,
e
versus
u
a
−
u
w
) in Fig. 13.15,
which shows less volume change than curve
A
(i.e.,
e
versus
σ
−
u
a
).
A matric suction increase, on the other hand, is more
effective than a net normal stress increase in removing water
from the soil. This behavior is illustrated by the water con-
tent curve (i.e.,
wG
s
versus
u
a
−
u
w
), which shows greater
changes in water content than curve
A
. Unlike curve
A
,the
void ratio-matric suction curve (i.e., curve
B
) starts to devi-
ate from the water content-matric suction curve (i.e., curve
C
) as the soil begins to desaturate. The separation of the two
curves is due to the decreasing degree of saturation as the
matric suction increases. On the other hand, there is essen-
tially a constant degree of saturation during the total stress
increment (i.e.,
wG
s
=
e
on curve
A
). The ratio of the ordi-
nates for curves
C
and
B
indicates the degree of saturation
(i.e.,
S
=
wG
s
/e
).
Curve
C
eventually reaches zero water content or zero
degree of saturation. Zero water content corresponds to a soil
suction of approximately 10
6
kPa for all soils, as explained
in Chapter 5.
wG
s
where
G
s
is the specific gravity of the soil solids).
When the degree of saturation is 100%, the following basic
relationship exists between the soil moduli:
a
t
=
b
t
G
s
.
A two-dimensional plot of the constitutive surfaces allows
the above-mentioned coefficients to be compared (i.e.,
a
t
versus
a
m
and
b
t
versus
b
m
; Fig. 13.10). The relationship
among the four coefficients can also be illustrated using
a single plot (Fig. 13.15). Consider initially saturated silt
that is subjected to isotropic consolidation by increasing the
total normal stress. The soil remains saturated during the
consolidation process. Consolidation curve
A
in Fig. 13.15
represents the relationship between the void ratio and net
normal stress
σ
−
u
a
as well as the water content
wG
s
13.5.2 Relationship of Volumetric Deformation
Coefficients for Volume-Mass Form of Constitutive
Surfaces
The volumetric deformation coefficients used for the com-
pressibility form of the constitutive surfaces can be defined
in a manner similar to that described above. The soil structure
and water phase constitutive surfaces are shown in Fig. 13.8.
and
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