Question

When the pre-consolidation pressure σp‘ is greater than initial effective pressure σ’0 but smaller than effective pressure σ’, then the final settlement is calculated on the basis of equation _________

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

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

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

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

The question was asked in semester exam.

I need to ask this question from Consolidation Process topic in portion One Dimensional Consolidation of Geotechnical Engineering I

Answer 1

Right option is (d) \(ρ_f=H\frac{C_S}{1+e_o}log_{10}\frac{σ_p’}{σ’_0}+H \frac{C_c}{1+e_o}log_{10}  \frac{σ’}{σ_p’}\)

The best I can explain: In the determination of the final settlement by voids ratio, when the pre-consolidation pressure σp‘ is greater than initial effective pressure σ’0 but smaller than effective pressure σ’, then the final settlement is calculated using the two parts:

 settlement due to σ’0 to σp‘ using CS

 settlement due to σp‘ to σ’ using Cc.

Therefore, the final settlement is given by the equation,

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