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GATE 2020 CE (CE1) – Question 44

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

The shown total-stress paths start from isotropic consolidation O, with $p=(\sigma_1+2\sigma_3)/3$, $q=\sigma_1-\sigma_3$. Loading conditions: I compression loading ($\sigma_1$ increasing, $\sigma_3$ fixed); II compression unloading ($\sigma_1$ fixed, $\sigma_3$ decreasing); III extension unloading ($\sigma_1$ decreasing, $\sigma_3$ fixed); IV extension loading ($\sigma_1$ fixed, $\sigma_3$ increasing). Match the paths.

Diagram for GATE 2020 CE (CE1) question 44
  1. OP–I, OQ–II, OR–IV, OS–III
  2. OP–IV, OQ–III, OR–I, OS–II
  3. OP–III, OQ–II, OR–I, OS–IV
  4. OP–I, OQ–III, OR–II, OS–IV

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Show answer and explanation

Correct answer: (B) OP–IV, OQ–III, OR–I, OS–II

Explanation

Use $p=(\sigma_1+2\sigma_3)/3$, $q=\sigma_1-\sigma_3$. Increasing σ1 gives (+p,+q), OR–I. Decreasing σ3 gives (−p,+q), OS–II. Decreasing σ1 gives (−p,−q), OQ–III. Increasing σ3 gives (+p,−q), OP–IV. **B**.