GATE 2023 CE (CE2) – Question 61
A consolidated drained (CD) triaxial test was carried out on a sand sample with the known effective shear strength parameters, c′ = 0 and ϕ′ = 30°. In the test, prior to the failure, when the sample was undergoing axial compression under constant cell pressure, the drainage valve was accidentally closed. At the failure, 360 kPa deviatoric stress was recorded along with 70 kPa pore water pressure. If the test is repeated without such error, and no back pressure is applied in either of the tests, what is the deviatoric stress (in kPa, in integer) at the failure?
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Correct answer: 500
Explanation
**Step 1: strength relation for sand ($c^\prime=0$, $\phi^\prime=30^\circ$).** At failure
$$\frac{\sigma_1^\prime}{\sigma_3^\prime}=\tan^2\!\left(45^\circ+\frac{\phi^\prime}{2}\right)=\tan^2 60^\circ=3 .$$
The deviator stress is $q_f=\sigma_1^\prime-\sigma_3^\prime=3\sigma_3^\prime-\sigma_3^\prime=2\sigma_3^\prime$.
**Step 2: the test with the closed valve.** The deviator stress at failure was 360 kPa and the pore pressure was 70 kPa. The effective confining pressure is $\sigma_3^\prime=\sigma_3-u$, so
$$360=2(\sigma_3-70)\;\Rightarrow\;\sigma_3-70=180\;\Rightarrow\;\sigma_3=250\text{ kPa}.$$
The cell pressure was 250 kPa.
**Step 3: the repeated test with drainage.** The cell pressure is the same, but the pore pressure stays zero (no back pressure), so $\sigma_3^\prime=250$ kPa:
$$q_f=2\times250=\mathbf{500\ kPa}.$$