GATE Civil Engineering (CE) 2020 Shift 2 Solved Paper

Question : 53 of 65

Marks: +1, -0

A footing of size

2 {m} × 2 {m}

transferring a pressure of

200 {kN} {/} {m}^{2}

, is placed at a depth of

1.5 {m}

below the ground as shown in the figure (not drawn to the scale). The clay stratum is normally consolidated. The clay has specific gravity of

2.65

and compression index of

0.3 .

Considering

2: 1

(vertical to horizontal) method of load distribution and

γ_{ {v}}=10 {kN} {/} {m}^{3}

, the primary consolidation settlement (in

{mm}

, round off to two decimal places) of the clay stratum is____________.

Solution:

For CLAY

⇒ {y}_{ {SAT}}=(\;{ {G}+ {e}}/{1+ {e}}) {y}_{ {W}}=(\;{2.65+ {e}}/{1+ {e}}) × 10

=17 {kw} {/}{/} {m}^{3}

{eo}=1.357

{Ho}=1.5 {m}

σ_{0} {AT} × {x}=24 {d}+0.54 {sant}+0.754 {SAT}-1.25 {y}_{ {w}}=39.25 {kN} {/} {m}^{2}

∆ \ov{σ}=\;{ {qB}^{2}}/{( {B}+2 {n} 2)^{2}}=\;{\;\text " force "\;}/{\;\text " Area "\;}=\;{200 × 2 × 2}/{(2+2 × \;{1}/{2} × 1.75)^{2}} ∆ \ov{σ}=56.88 {kN} {/} {m}^{2}

∆ {H}=\;{ {C}_{ {C}} {H}_{0}}/{1+ {e}_{0}} \log (\;{\ov{σ_{0}}+\ov{∆ σ}}/{\ov{σ_{0}}})

=\;{1.5 × 0.3}/{1+1.357} \log (\;{39.25+56.88}/{39.25})

∆ {H}=74.27 {mm}

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