Question

For a Poisson’s ratio of 0.5, the elastic strain ∆ in terms of Boussinesq settlement factor is __________

(a) \(∆=\frac{pa}{E} F_B\)

(b) \(∆=\frac{3pa^2}{2E} F_B\)

(c) \(∆=\frac{a^2}{2E} F_B\)

(d) \(∆=\frac{pa^2}{2E} F_B\)

The question was asked in an interview.

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

Answer 1

Right choice is (a) \(∆=\frac{pa}{E} F_B\)

Best explanation: When the Poisson’s ratio is 0.5, the elastic strain ∆ is given by,

\(∆=\frac{3pa^2}{2E(a^2+z^2)^\frac{1}{2}},\) the Boussinesq settlement factor is \(F_B=\frac{3}{2}  \frac{1}{(1+(\frac{z}{a})^2)^\frac{1}{2}},\)

∴ substituting in the equation,

 \(∆=\frac{pa}{E} F_B.\)