Geotechnical Engineering

DHARM

308 GEOTECHNICAL ENGINEERING

Graphical method:

f= 30°

s

Normal stress, kN/m^2

t

C

Strength envelop

e

A

300

200

100

(^0) 100 200 300 400 500 600 700 800 810
B^850
Fig. 8.56 Mohr’s circle and strength envelope (Ex. 8.13)
The strength envelope is drawn at 37° to σ-axis, through the origin. The minor principal
stress 200 kN/m^2 is plotted as OA on the σ-axis to a convenient scale. With the centre on the σ-
axis, draw a circle to pass through A and be tangential to the strength envelope by trial and
error. If the circle cuts σ-axis at B also, OB is scaled-off to give the major principal stress, σ 1.
(Fig. 8.56).
The result in this case is 810 kN/m^2 which compares favourably with the analytical
value.
Example 8.14: In a drained triaxial compression test, a saturated specimen of cohesionless
sand fails under a deviator stress of 535 kN/m^2 when the cell pressure is 150 kN/m^2. Find the
effective angle of shearing resistance of sand and the approximate inclination of the failure
plane to the horizontal. Graphical method is allowed. (S.V.U.—B.E., (R.R.)—Nov., 1972)
The cell pressure will be the minor principal stress and the major principal stress will
be got by adding the deviator stress to it. These principal stresses are plotted as OA and OB to
a convenient scale on the σ-axis. C, the mid-point of AB, is the centre of the circle. The Mohr
circle is completed with radius as CA or CB. Since this is pure sand, the strength envelope is
drawn as the tangent to the circle passing through the origin. Angles DOC and angle BCD are
measured with a protractor to give φ and 2θcr, respectively. The values in this case are:
Graphical method:
f=
40°
s
Normal stress, kN/m^2
t
A C
4
3
2
1
(^0100200300400500600700)
Shear stress, kN/m B
2
150
2 qcr= 130°
685
Fig. 8.57 Mohr’s circle and strength envelope (Ex. 8.14)