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Stress Path

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NPTEL- Advanced Geotechnical Engineering Dept. of Civil Engg. Indian Institute of Technology, Kanpur 1
Module 6 Lecture 40 Evaluation of Soil Settlement - 6 Topics 1.5
STRESS-PATH METHOD OF SETTLEMENT CALCULATION
1.5.1
Definition of Stress Path
1.5.2
Stress and Strain Path for Consolidated Undrained Undrained Triaxial Tests
1.5.3
Calculation of Settlement from Stress Point
1.5
STRESS-PATH METHOD OF SETTLEMENT CALCULATION
Lambe (1964) proposed a technique for calculation of settlement in clay which takes into account both the immediate and the primary consolidation settlements. This is called the
stress-path method.
1.5.1 Definition of Stress Path
In order to understand what a stress path is, consider a normally consolidated clay specimen subjected to a consolidated drained triaxial test (
Figure 6.31a
). At any time during the test, the stress condition in the specimen can be represented
by a Mohr’s circle (
Figure 6.31b
). Note here that, in a drained test, total stress is equal to effective stress. So,
3
=
′
3
(minor principal stress)
1
=
3
+
∆
=
′
1
(major principal stress)
NPTEL- Advanced Geotechnical Engineering Dept. of Civil Engg. Indian Institute of Technology, Kanpur 2
At failure, the Mohr’s circle will touch a line that is the Mohr
-Coulomb failure envelope; this makes an angle
∅
with the normal stress axis (
∅
is the soil friction angle). We now consider another concept; without drawing the M
ohr’s circles, we may represent each one by a
point defined by the coordinates
′
=
′
1
+
′
3
2
(59) And
′
=
′
1
−′
3
2
(60) This is shown in
Figure 6.31b
for the smaller of the Mohr’s circles. If the points with
′
′
coordinates
of all the Mohr’s circles are joined, this will result in the line
AB
. This line is called a
stress path
. The straight line joining the srcin and the point
B
will be defined here as the
line. The
line makes an angle
with the normal stress axis. Now,
tan
=
=
(
′
1
−
′
3
)/2(
′
1
+
′
3
)/2
(61) Where
′
1
and
′
3
are the effective major and minor principal stresses at failure. Similarly,
sin
∅
=
=
(
′
1
−
′
3
)/2(
′
1
+
′
3
)/2
(62) From equations (61 and 62), we obtain
tan
α
=
sin∅
(63)
Figure 6. 31
Definition of stress path
NPTEL- Advanced Geotechnical Engineering Dept. of Civil Engg. Indian Institute of Technology, Kanpur 3
Again let us consider a case where a soil specimen is subjected to an oedometer (one-dimensional consolidation) type of loading (
Figure 6.32
). For this case, we can write
′
3
=
′
1
(64) Where
is the at-rest earth pressure coefficient and can be given by the expression (Jaky, 1944)
=1
−
sin
∅
(65)
For the Mohr’s circle shown in
Figure 6. 32
, the coordinates of point
E
can be given by
′
=
′
1
−′
3
2
=
′
1
(1
−
)2
′
=
′
1
+
′
3
2
=
′
1
(1+
)2
Thus,
=
−
1
′′
=
−
1
1
−
1+
(66) Where ,
is the angle that the line
(
line)
makes with the normal stress axis. For purposes of comparison, the
line
is also shown in
Figure 6. 31b
. In any particular problem, if a stress path is given in a
′
.
′
plot, we should be able to determine the values of the major and minor principal stresses for any given point on the stress path. This is demonstrated in
Figure 6. 33
, in which
ABC
is an effective stress path.
Figure 6.32
Determination of the slope of
line
NPTEL- Advanced Geotechnical Engineering Dept. of Civil Engg. Indian Institute of Technology, Kanpur 4
1.5.2 Stress and Strain Path for Consolidated Undrained Triaxial Tests
Consider a clay specimen consolidated under an isotropic stress
3
=
′
3
in a triaxial test. When a deviator stress
∆
is applied on the specimen and drainage is not permitted there will be an increase in the pore water pressure,
∆
(
Figure 6. 34a
).
∆
=
∆
(67)
Figure 6. 33
Determination of major and minor principal stresses for a point on a stress path
Figure 6. 34
Stress path for consolidation undrained triaxial test

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