GATE Papers >> Civil >> 2018 >> Question No 56

Question No. 56 Civil | GATE 2018
The void ratio of a soil is 0.55 at an effective normal stress of 140 kPa. The compression index of the soil is 0.25. In order to reduce the void ratio to 0.4, an increase in the magnitude of effective normal stress (in kPa, up to one decimal place) should be ______

Answer : 416.0 to 420.0

Solution of Question No 56 of GATE 2018 Civil Paper

Given, intial void ratio, e = 0.55

intial effective normal stress, ${\overline{\mathrm\sigma}}_1$ = 140 kPa

Compression index, Cc = 0.25

Final void ratio, ef = 0.4

Increase in effective normal stress, $\triangle\overline{\mathrm\sigma}=?$ We know,

$\begin{array}{l}{\mathrm C}_\mathrm c=\frac{\triangle\mathrm e}{\log_{10}\left({\displaystyle\frac{{\overline{\mathrm\sigma}}_1+\triangle\mathrm\sigma}{{\overline{\mathrm\sigma}}_1}}\right)}\\0.25=\left(\frac{0.55-0.4}{\log_{10}\left({\displaystyle\frac{140+\triangle\mathrm\sigma}{140}}\right)}\right)\\\triangle\mathrm\sigma=417.35\;\mathrm{kPa}\end{array}$

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