- Construct a tangent to the circle
Draw a line through H tangent to the circle. Let F denote the point of intersection of the
tangent and the vertical line through O. - Measure OF and the angle of inclination of the tangent
The results are OF=C = 688 Ib/ft^2 (32.9 kPa); <£ = 22°.
In general, in an unconfmed compression test,
c = Y 2 (T 1 = cot 0-' 0 = 20'-90° (9)where S' denotes the angle between the plane of failure and the plane on which Cr 1 occurs.
In the special case where frictional resistance is negligible, </> = O; c = VxT 1.
APPRAISAL OF SHEARING CAPACITY OF
SOIL BY TRIAXIAL COMPRESSION TEST
Two samples of a soil were subjected to triaxial compression tests, and it was found that
failure occurred under the following principal stresses: sample 1, (T 1 = 6960 lb/ft
2
(333.2
kPa) and cr 3 = 2000 lb/ft
2
(95.7 kPa); sample 2, (T 1 = 9320 lb/ft
2
(446.2 kPa) and V 3 =
3000 lb/ft
2
(143.6 kPa). Find the cohesion and angle of internal friction of this soil, both
trigonometrically and graphically.
Calculation Procedure:
- State the equation for the angle
Trigonometric method: Let S and D denote the sum and difference, respectively, of the
stresses (T 1 and (T 3. By referring to Fig. 6<z, develop this equation:
D - S sin (f> = 2c cos (f> (10)Since the right-hand member represents a constant that is characteristic of the soil, D 1 - S 1
sin (/) = — S 2 sin </>, or
sin<£=^-^ (11)
O 2 -O 1where the subscripts correspond to the sample numbers.
- Evaluate
and c
By Eq. 11, S 1 = 8960 lb/ft^2 (429.0 kPa); D 1 = 4960 lb/ft^2 (237.5 kPa); S 2 = 12,320 lb/ft^2
(589.9 kPa); D 2 = 6320 lb/ft^2 (302.6 kPa); sin <£ = (6320 - 4960)/(12,320 - 8960); <£ =
23°53'. Evaluating c, using Eq. 10, gives c = Y 2 (D sec ^-Stan </>) = 729 lb/ft^2 (34.9 kPa). - For the graphical solution, use the Mohr's circle
Draw the Mohr's circle associated with each set of principal stresses, as shown in Fig. 7. - Draw the envelope; measure its angle of inclination
Draw the envelope (common tangent) FHH', and measure OF and the angle of inclination
of the envelope. In practice, three of four samples should be tested and the average value
of 0 and c determined.