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GATE Civil Engineering (CE) 2020 Shift 1 Solved Paper

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Question : 44 of 65

Marks: +1, -0

The soil profile at a site up to a depth of

10\ \mathrm{m}

is shown in the figure (not drawn to the scale). The soil is preloaded with a uniform surcharge (q) of

70\ \mathrm{kN}/\mathrm{m}^{2}

at the ground level. The water table is at a depth of

3\ \mathrm{m}

below ground level. The soil unit weight of the respective layers is shown in the figure. Consider unit weight of water as

9.81\ \mathrm{kN}/\mathrm{m}^{3}

and assume that the surcharge (q) is applied instantaneously.

Immediately after preloading, the effective stresses (in kPa) at points P and Q. respectively, are

54 and 95
36 and 90
36 and 126
124 and 204

Solution:

Surcharge is applied instantaneous

\therefore

Extra pore water pressure of

7\ \mathrm{kPa}

is develated.

\overline{\sigma_{p}} = \sigma_{p} - v_{p}

\sigma_{p} = 70 + 18 \times 3 = 124

u_{p} = 0 + 70 = 70

\overline{\sigma_{p}} = 124 - 70 = 54

\overline{\sigma_{q}} = \sigma_{q} - v_{q}

\sigma_{q} = 70 + 18 \times 3 + 20 \times 4 = 204

v_{q} = 9.81 \times 4 + 70 = 109.24

\overline{\sigma_{p}} = 204 - 109.24 = 94.76\ \mathrm{kPa}

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