**Part 1: Calculate Stresses**

Point | Depth (m) | Total Stress (kN/m²) | Pore Water Pressure (kN/m²) | Effective Stress (kN/m²) |
---|---|---|---|---|

a | 0 | 0 | 0 | 0 |

b | 4 | 40 | 20 | 20 |

c | 8 | 80 | 30 | 50 |

d | 12 | 120 | 40 | 80 |

**Part 2: Calculate Stresses with Dropped Water Table**

Point | Depth (m) | Total Stress (kN/m²) | Pore Water Pressure (kN/m²) | Effective Stress (kN/m²) |
---|---|---|---|---|

a | 0 | 0 | 0 | 0 |

b | 4 | 40 | 15 | 25 |

c | 8 | 80 | 15 | 65 |

d | 12 | 120 | 15 | 105 |

**Part 3: Calculate Increase in Vertical Stress**

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

**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`

**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.