Question

The stress σz at any point (r,z) below the pavement is __________

(a) \(σ_z=\frac{3P}{2πz^2}\left[\frac{1}{1+(\frac{r}{z})^3}\right]^\frac{5}{2}\)

(b) \(σ_z=\frac{3P}{2πz^2}\left[\frac{1}{(\frac{r}{z})^2}\right]^\frac{5}{2}\)

(c) \(σ_z=\left[\frac{1}{1+(\frac{r}{z})^2}\right]^\frac{5}{2}\)

(d) \(σ_z=\frac{3P}{2πz^2}\left[\frac{1}{1+(\frac{r}{z})^2}\right]^\frac{5}{2}\)

I got this question in an interview.

Enquiry is from Stresses in Flexible Pavements topic in portion Design of Flexible & Rigid Pavement of Geotechnical Engineering II

Answer 1

The correct choice is (d) \(σ_z=\frac{3P}{2πz^2}\left[\frac{1}{1+(\frac{r}{z})^2}\right]^\frac{5}{2}\)

For explanation I would say: The stress σz at any point (r,z) below the pavement is given by,

\(σ_z=\frac{3P}{2πz^2}\left[\frac{1}{1+(\frac{r}{z})^2}\right]^\frac{5}{2},\)

Where, σz is the vertical stress

P is the point load acting at the ground surface

r is the radial horizontal distance

z is the vertical distance.