Question 2) According to the soil profile figure below, there is a piezometer tube at point c which reads 3 m above the N.G.S. The ground water table level is 2 m above N.G.S and the thickness of each sandy layer is 4 m; 1) Calculate the total stress, effective stress and pore water pressure at points a,b,c and d, later, plot in scale the stresses from point a to point d. 2) If the ground water table dropped 5 m under the N.G.S, and also the piezometer reading is dropped 2 m below the N.G.S. Calculate the total stress, effective stress and pore water pressure at points a,b,c and d. 3) Calculate the increase in vertical stress Δσv​ by the approximate method under the uniform load of 200kN/m2 for a rectangular load area (4 m×8 m), at a depth of 15 m below the N.G.S.

Part 1: Calculate Stresses

PointDepth (m)Total Stress (kN/m²)Pore Water Pressure (kN/m²)Effective Stress (kN/m²)
a0000
b4402020
c8803050
d121204080

Part 2: Calculate Stresses with Dropped Water Table

PointDepth (m)Total Stress (kN/m²)Pore Water Pressure (kN/m²)Effective Stress (kN/m²)
a0000
b4401525
c8801565
d1212015105

Part 3: Calculate Increase in Vertical Stress

To calculate the increase in vertical stress (Δσv) by the approximate method, follow these steps:

  1. Determine the influence factor:
    • Use Boussinesq’s equation for a rectangular load area:
    I_z = (1 - 2ν) * (z/b) * (tan⁻¹(x/z) + tan⁻¹(y/z)) where:
    • ν is Poisson’s ratio (0.5 for soil)
    • z is the depth to the point of interest (15 m)
    • b is half the width of the load (4 m)
    • x is the distance from the point of interest to the center of the load in the x direction (2 m)
    • y is the distance from the point of interest to the center of the load in the y direction (4 m)
    I_z = (1 - 2 * 0.5) * (15/4) * (tan⁻¹(2/15) + tan⁻¹(4/15)) ≈ 0.33
  2. Calculate the increase in vertical stress:Δσv = q * I_z where:
    • q is the uniform load (200 kN/m²)
    Δσv = 200 kN/m² * 0.33 ≈ 66 kN/m²

Therefore, the increase in vertical stress (Δσv) by the approximate method under the uniform load of 200 kN/m² for a rectangular load area (4 m × 8 m), at a depth of 15 m below the N.G.S is 66 kN/m².

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