GATE 2024 CE (CE2) – Question 55
A drained triaxial test was conducted on a saturated sand specimen using a stress-path triaxial testing system. The specimen failed when the axial stress reached a value of 100 kN/m$^2$ from an initial confining pressure of 300 kN/m$^2$.
The angle of shearing plane (in degrees) with respect to horizontal is ________________ (rounded off to the nearest integer).
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Correct answer: 30
Explanation
The axial stress was reduced from 300 to 100 kN/m² while the confining pressure stayed at 300 (a triaxial extension path). At failure the major principal stress is the radial one, $\sigma_1 = 300$, and the minor principal stress is the axial one, $\sigma_3 = 100$. So $\sin\phi = \frac{300 - 100}{300 + 100} = 0.5$ and $\phi = 30°$. The failure plane makes $45° + \frac{\phi}{2} = 60°$ with the major principal plane. The major principal stress acts radially, so the major principal plane is vertical, and the failure plane is at $90° - 60° = 30°$ to the horizontal.