A river is 2 m deep. The river bed consists of a depth of sand of saturated unit weight 20 kN/m³. What is the effective vertical stress 5 m below the top of the sand ?
- A68·6 kN/m²
- B119·6 kN/m²
- C51 kN/m²Correct
- D10·2 kN/m²
Solution
Concept
Effective stress below water
Formula
σ′ = γ′ z = (γsat − γw) z
Step-by-step solution
1. Water above the sand adds equal amounts to the total stress and the pore pressure, so it cancels. 2. σ′ = (20 − 9.81) × 5 = 50.95 ≈ 51 kN/m².
Explanation
Effective stress depends only on the submerged weight of the soil above the point. The depth of the river does not change the effective stress.
Why the other options are wrong
119.6 kN/m² would add the weight of water above; 68.6 kN/m² and 10.2 kN/m² come from wrong depths or unit weights.
Shortcut
σ′ = γ′ × depth (water depth cancels).
Common mistake
Adding the 2 m of water.
Correct answer: C) 51 kN/m²