Correct Answer - Option 1 : 21.3 cm
Concept:
Immediate Settlement:
- This type of settlement is predominant in coarse grained soil (i.e. Sandy Soil) of high permeability an in unsaturated fine grained soils of low permeability.
- Usually this type of settlement is completed during construction period and is called Build in settlement.
- Soil is idealised as an elastic material, Hence theory of elasticity is applied to compute settlement.
- The net elastic settlement beneath the corner of a uniformly loaded flexible surface footing based on theory of elasticity is given by:
\({S_e} = \frac{{{q_n}B\left( {1 - {\mu ^2}} \right){I_f}}}{{{E_s}}},\;m\)
Where, qn = Intensity of contact pressure (kN/m2)
B = Least lateral dimension of loaded area (m),
Es = Modulus of elasticity of soil (kN/m2) and
If = Influence factor which depends on rigidity and the shape of the loaded area.
Note: For clay soils, μ = 0.50 and Es should be considered for undrained condition
- Correction factor is applied immediate settlement to allow for depth of foundation. Hence, final elastic or immediate settlement is given by –
\({S_{ef}} = {S_e}{d_f}\)
Here, df = Depth factor used when footing at some depth from the surface.
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For rigid footing, settlement under flexible footing is reduced by factor Cr = 0.80 (generally) and for calculating settlement at centre superposition theorem can be used.
Calculation:
\({q_n} = \frac{{Load}}{{Area}} = \frac{{600}}{{1 \times 1}} = 600kN/{m^2},\)
\(B = 1m,\;{E_s} = 2000kN/{m^2}\;and\;\mu = 0.50\)
\({S_e} = \frac{{{q_n}B\left( {1 - {\mu ^2}} \right){I_f}}}{{{E_s}}}\)
\({S_e} = 600 \times 1 \times \left( {1 - {{0.5}^2}} \right) \times \frac{{0.95}}{{2000}}\)
∴ \({S_e} = 0.21375m\; \approx 213.75mm\)
