Question

The Boussinesq’s vertical pressure σz under a uniformly loaded circular area is given by ________

(a) \(σ_z=q\left[1-\left[\frac{1}{1+(\frac{a}{z})^2}\right]^{\frac{3}{2}}\right] \)

(b) \(σ_z=q\left[1+\left[\frac{1}{1+(\frac{a}{z})^2}\right]^{\frac{3}{2}}\right] \)

(c) \(σ_z=q\left[\frac{1}{1+(\frac{a}{z})^2}\right]^{\frac{3}{2}} \)

(d) \(σ_z=q\left[1-\left[\frac{1}{1+(\frac{a}{z})^2}\right]^{\frac{5}{2}}\right] \)

I had been asked this question in an internship interview.

The question is from Stress Distribution in portion Stress Distribution of Geotechnical Engineering I

Answer 1

Correct choice is (a) \(σ_z=q\left[1-\left[\frac{1}{1+(\frac{a}{z})^2}\right]^{\frac{3}{2}}\right] \)

Explanation: The Boussinesq’s vertical pressure σz under a uniformly loaded circular area is given by,

\(σ_z=q\left[1-\left[\frac{1}{1+(\frac{a}{z})^2}\right]^{\frac{3}{2}}\right] \)  

where, q=load intensity per unit area

a=radius of circle

z= depth of point.