Question

In terms of compression index and voids ratio for normally consolidated soil, the final settlement is _________

(a) \(ρ_f=Hlog_{10}  \frac{σ’}{σ’_0}\)

(b) \(ρ_f=H \frac{C_c}{1+e_o} log_{10}  \frac{σ’}{σ’_0}\)

(c) \(ρ_f=\frac{C_c}{1+e_o} log_{10}  \frac{σ’}{σ’_0}\)

(d) \(ρ_f=H \frac{1}{1+e_o} log_{10}  \frac{σ’}{σ’_0}\)

This question was posed to me during an interview for a job.

The question is from Consolidation Process topic in section One Dimensional Consolidation of Geotechnical Engineering I

Answer 1

Right answer is (b) \(ρ_f=H \frac{C_c}{1+e_o} log_{10}  \frac{σ’}{σ’_0}\)

Explanation: The final settlement is given by the equation,

\(ρ_f=\frac{e_o-e}{1+e_o}H,\) the relationship between the compression index and voids ratio is  \(C_c=\frac{e_0-e}{log_{10}\frac{σ’}{σ’_0}},\)

Therefore, substituting for compression index,

 We get, \(ρ_f=H \frac{C_c}{1+e_o} log_{10}  \frac{σ’}{σ’_0}.\)