GATE Civil Engineering (CE) 2018 Shift 1 Solved Paper

Question : 52 of 65

Marks: +1, -0

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_________

Solution:

∆ {H}=\;{H_{0} ∆ e}/{1+e_{0}}=\;{H_{0} C_{c}}/{1+e_{0}} \log (\;{σ_{0}+∆ σ}/{σ_{0}})

∆ {H}=H_{0}(\;{0.55-0.40}/{1+0.50})=\;{H_{0} × 0.25}/{1+0.50} \log (\;{140+∆ σ}/{140})

\;{0.15}/{0.25}=\;{3}/{5}=\log (\;{140+∆ σ}/{140})

∆ σ=417.35 {kPa}

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