The results of a consolidated drained triaxial test on a normally consolidated clay are shown in the figure. The angle of internal friction is
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In triaxial tests, the angle of internal friction can be found using the Mohr-Coulomb failure criterion, which relates shear stress to normal stress using the internal friction angle.
In a consolidated drained (CD) triaxial test, the relationship between the shear stress \( \tau \) and the effective normal stress \( \sigma \) is given by the Mohr-Coulomb failure criterion:
\[
\tau = \sigma \tan \left( 45^\circ + \frac{\phi}{2} \right),
\]
where \( \phi \) is the angle of internal friction. From the given triaxial test data, we can use the equation:
\[
\sigma_1 = \sigma_3 \tan^2 \left( 45^\circ + \frac{\phi}{2} \right).
\]
Given that \( \sigma_1 = 50 \, {kPa} \) and \( \sigma_3 = 50 \, {kPa} \), we can substitute into the equation for the effective stress:
\[
100 = 50 \left[ 1 + \sin \left( \frac{\phi}{2} \right) \right].
\]
Simplifying:
\[
\sin \left( \frac{\phi}{2} \right) = \frac{1}{3}.
\]
Thus, the angle of internal friction \( \phi \) is given by:
\[
\phi = 2 \sin^{-1} \left( \frac{1}{3} \right).
\]
Hence, the correct angle of internal friction is \( \sin^{-1} \left( \frac{1}{3} \right) \), which corresponds to option (B).
- This equation is derived from the stress and strain relationships in a triaxial test, where we use the Mohr-Coulomb failure criterion to calculate the angle of internal friction.
