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GATE 2017 CE (CE2) – Question 45

Geotechnical Engineering · Shear strength, Mohr circle, stress-strain characteristics, stress paths · 2 marks · Multiple choice

Consider triaxial stress-path statements: P. If $\sigma_1=\sigma_3$, the stress point lies at the origin of the p–q plot. Q. If $\sigma_1=\sigma_3$, it lies on the p-axis. R. If $\sigma_1>\sigma_3$, both p and q are positive. Which combination is correct?

  1. P false, Q true, R true
  2. P true, Q false, R true
  3. P false, Q true, R false
  4. P true, Q false, R false

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Show answer and explanation

Correct answer: (A) P false, Q true, R true

Explanation

Using $p=(\sigma_1+\sigma_3)/2$ and $q=(\sigma_1-\sigma_3)/2$, equal principal stresses give q = 0 but generally nonzero p. Thus P is false and Q true. For the conventional compressive state $\sigma_1>\sigma_3\ge0$, p and q are positive, so R is true. Answer A.