Correct Answer - Option 3 : 22 mm
Concept:
For sandy soil or cohesionless soil, we know that
\(\frac{{{S_f}}}{{{S_p}}} = \;{\left\{ {\frac{{{B_f}\left( {{B_p}\; + \;0.3} \right)}}{{{B_p}\left( {{B_f}\; + \;0.3} \right)}}} \right\}^2}\)
Where, Bp = Width of plate, Sp = Settlement of plate, Bf = Width of foundation, and Sf = Settlement of foundation
Calculation:
Given, Bp = 30 cm, Sp = 8 mm, Bf = 1.5 m
\(\frac{{{S_f}}}{8} = {\left\{ {\frac{{1.5\left( {0.3\; + \;0.3} \right)}}{{0.3\left( {1.5\; + \;0.3} \right)}}} \right\}^2}\)
∴ Sf = 22.22 mm ≈ 22 mm
Note:
For clay of cohesive soils, the relation between Settlement of foundation and plate is:
\(\frac{{{S_f}}}{{{S_p}}} = \frac{{{B_f}}}{{{B_p}}}\)