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GATE 2019 CE (CE1) – Question 26

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

A retaining wall of height H with a smooth vertical back supports cohesionless backfill inclined at β to horizontal. The soil friction angle is φ and active thrust is $P_a$. Which statement is true?

  1. $P_a$ acts at H/2 above the base and at β to horizontal.
  2. $P_a$ acts at H/2 above the base and at φ to horizontal.
  3. $P_a$ acts at H/3 above the base and at β to horizontal.
  4. $P_a$ acts at H/3 above the base and at φ to horizontal.

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Show answer and explanation

Correct answer: (C) $P_a$ acts at H/3 above the base and at β to horizontal.

Explanation

The appended key uses the Rankine sloping-backfill idealization. Triangular pressure gives a resultant at H/3, parallel to the backfill at β to horizontal: **C**. There is a source-model inconsistency: a literally smooth vertical wall transmits no tangential traction, so its resultant would be horizontal. The keyed direction requires the Rankine interpretation rather than that literal boundary condition.