In stress distribution in soil, the approximate method in which the vertical stress at any point due to any loaded area is calculated by dividing the area into small parts is:
Try it first: pick an option, then read the explanation.
Asked in SSC JE 28/10/2020 (Evening)
Detailed Explanation
Boussinesq's equation gives the vertical stress under a single point load. Real loads are spread over areas of any shape. The simplest approximate way to handle them is the equivalent point load method.
\[ \sigma_z \approx \sum \frac{3Q_i}{2\pi z^2}\left[\frac{1}{1+(r_i/z)^2}\right]^{5/2} \]
Why “Equivalent point load method” Is Correct
The loaded area is divided into small squares; the load on each is treated as a point load at its centre. The stress at the point is the sum of the Boussinesq stresses from all these point loads. It is approximate (accuracy improves when the squares are small compared with the depth) and works for any shape of area.
Why the Other Options Are Wrong
- A. Newmark's influence chart: Newmark's chart is a graphical method based on the exact uniformly loaded circle solution; it uses influence areas rather than equivalent point loads.
- B. Boussinesq's method: Boussinesq's method is the exact elastic solution for a point load; the approximate area method is built from it.
- D. Westergaard's method: Westergaard's method is an exact solution for layered (anisotropic) soils, not an approximation for areas.
Key Point
Equivalent point load: split area → point loads at centroids → sum Boussinesq stresses.
Key Concepts for Students
- Rule of thumb: keep each square smaller than about one third of the depth z.
- 2:1 dispersion method is another quick approximation.
- Newmark's chart: σz = n × I × q, with I = 0.005 for the usual chart.
Practice more: this is question 30 in Shear Strength of Soils MCQs – Part 2. Try the whole set and check every answer instantly.