Environmental Engineering Reference
In-Depth Information
b
b
′
′
B
Failure
envelope
c
u
τ
ff
A
σ
ff
(
σ
-
u
a
)
f
Mohr circle at failure
(
σ
ff
-
u
a
)
f
= 0
c
′
0
Net normal stress,
σ
-
u
a
Figure 12.67
Typical stress path followed during unconfined compression test on unsaturated
soil with soil suction.
ure envelope:
in Eq. 12.69. There will also be a change in the ultimate
bearing capacity,
q
f
(i.e.,
N
c
c
u
), and the final bearing
capacity can be written as the sum of the initial capacity and
the change in capacity (i.e.,
q
f
c
+
u
a
)
f
tan
φ
+
u
w
)
f
tan
φ
b
c
u
≈
(σ
f
−
(u
a
−
(12.68)
q
f
).
Figure 12.68 illustrates the possible variation in the ulti-
mate bearing capacity of clay due to matric suction changes.
The clay had an initial measured undrained shear strength
c
u
0
of 50 kPa and a
φ
b
angle of 15
◦
. The initial computed
bearing capacity of the clay,
q
f
0
, was 285 kPa for a strip
footing or 342 kPa for a square footing. An average change
in matric suction is assumed in order to compute the changes
in the ultimate bearing capacity of the clay. The
φ
b
angle
is assumed to remain constant. Figure 12.68 shows that an
increase in soil matric suction increases bearing capacity,
while a decrease in matric suction reduces bearing capacity.
The percent change in the ultimate bearing capacity can
be related to the change in matric suction as follows:
=
q
f
0
+
where:
c
u
=
undrained shear strength.
The in situ matric suction can later increase or decrease in
response to changes in the climatic conditions such as evapo-
ration, precipitation, and lawn watering. The undrained shear
strength of the soil will also change and its change can be
expressed as follows:
u
w
)
tan
φ
b
c
u
=
(u
a
−
(12.69)
where:
c
u
=
change in undrained shear strength due to
matric suction change and
q
f
q
f
0
=
(u
a
−
u
w
)
tan
φ
b
(12.70)
c
u
0
(u
a
−
u
w
)
=
change in matric suction due to drying and
wetting.
where:
The bearing capacity of clayey soil is often computed
using the undrained shear strength
c
u
in accordance with
the total stress approach (i.e., the
φ
q
f
/q
f
0
=
percent change in the ultimate bearing
capacity and
=
0 approach). Applying
(u
a
−
u
w
)/c
u
0
=
percent change in the matric suction
with respect to the initial undrained
shear strength.
the
φ
0 condition to Eq. 12.68 gives the ultimate bearing
capacity of the clay in terms of its undrained shear strength
(i.e.,
q
f
=
c
u
N
c
).
Let us consider a clay with an initially measured undrained
shear strength of
c
u
0
and an initial ultimate bearing capacity
of
q
f
0
(i.e.,
N
c
c
u
0
). A change in matric suction in the field,
(u
a
−
=
Results of the above equation are plotted in Fig. 12.69
for various
φ
b
values. The relationship is applicable to all
shapes of footings since the analysis does not depend on
N
c
. For a
φ
b
value of 15
◦
, the ultimate bearing capacity
will increase or decrease by 27% when the matric suction
u
w
)
(i.e., an increase or decrease), will result in a
change in the undrained shear strength,
c
u
, as expressed
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