Geology Reference
In-Depth Information
[C] Stress-Strain Graph
A stress-strain graph should be prepared by plotting unit axial load
(deviator stress) (ordinate) versus axial strain (abscissa). From this graph,
the unit axial load at failure can be determined by taking the maximum
unit axial load or the unit axial load at 15% axial strain, whichever occurs
first. The unit axial load (deviator stress) at failure is denoted by
p
.
Δ
[D] Shear Diagram (Mohr Circles for Triaxial Compression)
The minor and major principal stresses must be determined in order to
plot the required shear diagram (Mohr circle for triaxial compression),
from which values of the shear strength parameters (cohesion
c
and
angle of internal friction
) can be obtained.
The minor principal stress is equal to the chamber pressure and is
denoted by
The major principal stress at failure, denoted by
σ
1
,is
σ
3
.
equal to the sum of unit axial load at failure,
p
, and minor principal
Δ
stress. That is,
s
1
¢
p
(22-1)
s
3
After the minor and major principal stresses and unit axial loads at
failure have been determined for each specimen tested, the required
shear diagram may be prepared with shear stresses plotted along the
ordinate and normal stresses on the abscissa. From results of one of the
triaxial tests, a point is located along the abscissa at a distance
σ
3
from
the origin. This point is denoted by
A
in Figure 22-5 and is indicated as
being located along the abscissa at a distance (
3
)
1
from the origin. It is
also necessary to locate another point along the abscissa at a distance
1
from the origin, by measuring either the distance
1
from the origin or the
distance
3
from the ori-
gin). This point is denoted by
B
in Figure 22-5 and is noted as being
located along the abscissa at a distance (
p
from point
A
(the point located at a distance
Δ
p
)
1
from point
A
. With
AB
as a
diameter, a semicircle known as the
Mohr circle
is then constructed. This
entire procedure is repeated using data obtained from the triaxial test of
another specimen of the same soil sample at a different chamber pres-
sure. In such manner, point
C
is located along the abscissa at a distance
(
p
)
2
from point
C
. With
CD
as a diameter, another semicircle is then constructed. The next step is
to draw a straight line tangent to the two semicircles, as shown in Figure
22-5. The angle between this straight line and a horizontal line (
3
)
2
from the origin and point
D
at a distance (
in the
figure) gives the angle of internal friction, and the value of stress where
the straight line intersects the ordinate (
c
in the figure) is the cohesion.
The same scale must be used along abscissa and ordinate.
In theory, it is adequate to have only two Mohr circles to define the
straight-line relationship of Figure 22-5. In practice, however, it is bet-
ter to have three (or more) such semicircles that can be used to draw the
best straight line. That is why the test procedure calls for three or more
separate tests to be performed on three or more specimens from the same
soil sample.
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