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Question

A footing of size 2m × 2m transferring a pressure of 200kN/m2, is placed at 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.

Consideration 2:1 (vertical to horizontal) method of load distribution and γw=10kN/m3 , the primary consolidation settlement (in mm, round off to two decimal places) of the clay stratum is

Consideration 2:1 (vertical to horizontal) method of load distribution and γw=10kN/m3 , the primary consolidation settlement (in mm, round off to two decimal places) of the clay stratum is

- 74.28

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Solution

The correct option is **A** 74.28

Initial effective stress at the mid depth of clay layer

(σo)=(1.5+0.5)×15+0.5×18

+1.52×17−(1.52+0.5)×10

=39.25 kN/m2

Change in effective stress due to surcharge

=200×2×23.75×3.75=56.888kN/m2

Initial void ratio of clay (eo)

γsat=G+eo1+eoγw

17=2.65+eo1+eo×10

e0=1.357

Primary consoildation settlement (Δh)

Δh=CcH1+eolog(¯¯¯¯¯σo+Δ¯¯¯σ¯¯¯¯¯σo)

=0.3×1.51+1.357log(39.25+56.88839.25)

= 0.07428 m

= 74.28 mm

Initial effective stress at the mid depth of clay layer

(σo)=(1.5+0.5)×15+0.5×18

+1.52×17−(1.52+0.5)×10

=39.25 kN/m2

Change in effective stress due to surcharge

=200×2×23.75×3.75=56.888kN/m2

Initial void ratio of clay (eo)

γsat=G+eo1+eoγw

17=2.65+eo1+eo×10

e0=1.357

Primary consoildation settlement (Δh)

Δh=CcH1+eolog(¯¯¯¯¯σo+Δ¯¯¯σ¯¯¯¯¯σo)

=0.3×1.51+1.357log(39.25+56.88839.25)

= 0.07428 m

= 74.28 mm

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