GATE Papers >> Civil >> 2019 >> Question No 135

Question No. 135 Civil | GATE 2019

Construction of a new building founded on a clayey soil was completed in January 2010. In January 2014, the average consolidation settlement of the foundation in clay was recorded as 10 mm. The ultimate consolidation settlement was estimated in design as 40 mm. Considering double drainage to occur at the clayey soil site, the expected consolidation settlement in January 2019 (in mm, round off to the nearest integer) will be ________


Answer : 15 to 15


Solution of Question No 135 of GATE 2019 Civil Paper

January-2014

Time=4years

Consolidation settlement (S) = 10mm

Ultimate settlement (Sf) = 40mm

Degree of consolidation $ \left(\mathrm U\right)=\frac{\mathrm S}{{\mathrm S}_{\mathrm f}}\times100=\frac{10}{40}\times100=25\% $

January-2019

Time = 9years

Drainage is double drainage

$ \begin{array}{l}\mathrm U\leq60\Rightarrow{\left({\mathrm T}_{\mathrm v}\right)}_1=\frac{\mathrm\pi}4\left(\mathrm U\right)^2={\left({\mathrm T}_{\mathrm v}\right)}_1=\frac{\mathrm\pi}4\left(0.25\right)^2=0.0491\\{\mathrm T}_{\mathrm v}=\frac{{\mathrm C}_{\mathrm v}.\mathrm t}{\mathrm H^2}=\frac{\mathrm\pi}4\mathrm U^2\Rightarrow\mathrm U^2\propto\mathrm t\\\frac{\mathrm U_1^2}{\mathrm U_1^2}=\frac{{\mathrm t}_1}{{\mathrm t}_2}=\frac{\left(0.25\right)^2}{\mathrm U_2^2}=\frac49\Rightarrow\mathrm U_2^2=\frac94\times0.25^2\\{\mathrm U}_2=\sqrt{\frac94\times0.25^2}=0.375\\\mathrm{Total}\;\mathrm{consolidation}=40\times0.375=15\mathrm{mm}\end{array} $

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