5. A vertical point load of 250 kN is applied at the surface of a homogeneous, elastic soil mass. The point load is located at a depth of 6 meters. Calculate the vertical stress at a depth of 6 meters directly beneath the point load and at a horizontal distance of 4 meters away from the point load.

To calculate the vertical stress at a depth of 6 meters directly beneath the point load, you can use the point load stress formula, which is given by σ = P/(A) where P is the point load and A is the area of influence. At a depth equal to the load's depth (6 m), the vertical stress directly beneath the load would be σ = 250 kN. At a horizontal distance of 4 meters away, you’ll apply the Boussinesq equation for vertical stress in soil masses, which involves the load and empirical factors for radial distance. You’d consider the distance and depth to compute the stress. The stress can be calculated as σ = P * (z / (z^2 + r^2)^(3/2)), where z is the depth (6 m) and r is the horizontal distance (4 m). Plugging in the values gives a more nuanced understanding of stress distribution in the soil mass. Remember, the stress decreases with distance, so the value at 4 meters will be less than directly beneath the load!