A stratified soil deposit consists of profile as shown in the figure below. A surcharge load of 60 kN/m² is placed on the ground surface. The effective pressure (in kN/m²) at level BB and CC immediately after placement of surcharge load is (γw = 10 kN/m³; sand 3 m, ρ = 1.5 Mg/m³; clay 3 m, ρ = 1.5 Mg/m³; gravel 3.5 m, ρ = 1.925 Mg/m³; water table at BB)
- A110, 105
- B105, 150Correct
- C205, 250
- D115, 205
Solution
Concept
Effective stress = total stress - pore water pressure. Surcharge is added to the total stress.
Formula
σ' = σ - u; σ = Σ(γ × h) + q
Step-by-step solution
1. Assume AA is the ground surface, BB is at 3 m (sand base, water table) and CC is at 6 m (clay base). The figure is not visible, so this is an assumption. 2. γ = ρ × g = 1.5 × 10 = 15 kN/m³ for sand and clay. 3. At BB: σ = 60 + 3 × 15 = 105 kN/m². The water table is at BB, so u = 0. σ' = 105 kN/m². 4. At CC: σ = 105 + 3 × 15 = 150 kN/m². The only option with BB = 105 is B, whose CC value is 150, so B is chosen.
Explanation
At BB the water table is at the level itself, so pore pressure is zero and the effective pressure is 105 kN/m². Only option B has this value. Its CC value of 150 matches the total stress from the layer weights, but I could not confirm it from the figure.
Common mistake
Forgetting to add the surcharge, or subtracting pore pressure where the water table is not present.
Correct answer: B) 105, 150