Consider the following statements 1.Coulomb earth pressure theory does not take the roughness of wall into consideration 2.Active earth pressure on a retaining wall decreases due to increase in wall friction 3.Rankine theory of earth pressure assumes that back of wall is vertical and smooth Of these statements,
- A1 and 2 are correct
- B3 and 1 are correct
- C2 and 3 are correctCorrect
- D1, 2 and 3 are correct
Solution
Concept
Rankine's earth pressure theory assumes a frictionless (smooth) and vertical wall back, while Coulomb's wedge theory accounts for both wall friction and inclined back of the wall. Wall friction reduces active earth pressure and increases passive earth resistance.
Step-by-step solution
1. Analyze Statement 1: 'Coulomb earth pressure theory does not take the roughness of wall into consideration' - Incorrect, Coulomb's theory specifically accounts for wall roughness via the wall friction angle δ. 2. Analyze Statement 2: 'Active earth pressure on a retaining wall decreases due to increase in wall friction' - Correct, friction acts upward along the wall face during downward movement of the active wedge, supporting part of the soil weight and reducing total active thrust. 3. Analyze Statement 3: 'Rankine theory of earth pressure assumes that back of wall is vertical and smooth' - Correct, Rankine assumed a semi-infinite, homogeneous soil mass bounded by a vertical, smooth wall face. 4. Therefore, only statements 2 and 3 are correct.
Explanation
Statement 1 is incorrect because Coulomb's wedge theory explicitly considers friction between the retaining wall and backfill soil (wall friction angle δ). Statement 2 is correct because the inclusion of wall friction decreases the total active earth pressure compared to a smooth wall. Statement 3 is correct because Rankine's theory assumes the back face of the retaining wall to be vertical and perfectly smooth.
Why the other options are wrong
A: Statement 1 is false because Coulomb's theory includes wall friction. B: Statement 1 is false because Coulomb's theory considers wall friction. D: Statement 1 is false, so all three cannot be correct.
Shortcut
Remember: Rankine = Smooth (no wall friction); Coulomb = Rough (includes wall friction δ). This immediately eliminates Statement 1.
Common mistake
Confusing Rankine's and Coulomb's assumptions regarding wall friction, or forgetting whether wall friction increases or decreases active earth pressure (it decreases active and increases passive).
Correct answer: C) 2 and 3 are correct