Geoscience Reference
In-Depth Information
A soil sample is usually saturated and the pore pressure
u
plays a role. The
corresponding effective stresses become, using Terzaghi's effective stress principle
(4.1b):
=
' + u
, leading to
q' = q =
1
' -
2
'
and
p' =
(
1
' +
2
3
'
)/3
= p - u
(7.9)
In a Mohr-circle representation the effective stress circle is shifted over
u
with
respect to the total stress circle, while the deviator (radius) does not change (Fig
7.5). Since soil failure is related to effective stresses, the influence of pore pressure
has to be accounted for with regard to total stress. It confirms that criterion (7.2)
refers to effective stress. In terms of total stresses (7.2) the failure state reads
|
s
| = c +
(
s
- u
) tan
(7.10)
A typical undrained triaxial compression test includes two steps: an isotropic
consolidated loading stage (until excess pore pressure
u
= 0) at
1
=
2
=
3
,
giving
p
0
= p
0
' =
1
and
q =
0, and an undrained loading stage increasing
1
,
giving
p =
(
3
. This relation gives a straight
line under a slope of 1/3 as a total stress path in a
p-q
diagram (path DC in Fig 7.6).
Since during loading the pore pressure may change due to volume change under
shear deformation, while the undrained condition prevents pore water pressure
dissipation, the effective stress path will follow the total stress path by horizontally
subtracting this pore pressure change (
u
). For positive pore pressure generation
(path DU)
p' < p
and
q' = q
(normal clay, contractant sand). For negative pore
pressure generation (path DU')
p' > p
and
q' = q
(overconsolidated clay, dilatant
sand), as shown in Fig 7.6.
The changes in the
K
0
value can be measured in the triaxial cell from
dq/dp'
,
using equation (7.8), taking
1
+
2
3
)/3
=
(
1
-
3
+
3
3
)/3
=
q +
1
'
=
v
'
,
2
'
=
3
'
=
h
'
, and
K
0
=
h
'
/
v
'
, it follows
that
dq
3
'
'
)
3
K
)
dq
dq
v
h
0
K
0
= (3
-
)/(3 + 2
)
(7.11)
dp
'
'
2
'
1
2
K
dp
'
dp
'
v
h
0
failure surface
q
q
M
Y
E
yield surface
Y
U
p'
u
Y
C
U
C
U'
q
p
p
D
a
O
Y
D
p
o
(a) (b)
Figure 7.6 Triaxial cell test in a p-q diagram, and a yield surface
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