The GATE Grind

GATE 2022 CE (CE1) – Question 18

Geotechnical Engineering · Earth pressure theories: Rankine and Coulomb, sheet piles · 1 mark · Multiple choice

Let $\sigma_v\prime$ and $\sigma_h\prime$ denote effective vertical and horizontal stress. Which condition must be satisfied at Rankine passive failure?

  1. $\sigma_v\prime<\sigma_h\prime$
  2. $\sigma_v\prime>\sigma_h\prime$
  3. $\sigma_v\prime=\sigma_h\prime$
  4. $\sigma_v\prime+\sigma_h\prime=0$

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Correct answer: (A) $\sigma_v\prime<\sigma_h\prime$

Explanation

Passive pressure develops when a wall pushes into the backfill and increases horizontal effective stress. At failure the horizontal stress is the major principal stress, while vertical stress is the minor one.

Thus $\mathbf{\sigma_v\prime<\sigma_h\prime}$, **A**. In the active state the ordering is reversed.