Question

The final settlement in terms of voids ratio is given by ____________

(a) \(ρ_f=\frac{e_o-e}{e_o}H\)

(b) \(ρ_f=\frac{e}{1+e_o}H\)

(c) \(ρ_f=\frac{e_o-e}{1+e_o}\)

(d) \(ρ_f=\frac{e_o-e}{1+e_o}H\)

The question was asked during an interview.

This intriguing question comes from Consolidation Process in portion One Dimensional Consolidation of Geotechnical Engineering I

Answer 1

Correct answer is (d) \(ρ_f=\frac{e_o-e}{1+e_o}H\)

For explanation I would say: Since the final settlement is equal to the change in thickness, and the change in thickness is given by,

\(\frac{∆H}{H_0} = \frac{e_o-e}{1+e_o},\)

∴ \(ρ_f = ∆H = \frac{e_o-e}{1+e_o}H.\)