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GATE 2021 CE (CE2) – Question 55

Geotechnical Engineering · Compaction and one-dimensional consolidation · 2 marks · Numerical answer

A 2 m sand layer (γ=18.5 kN/m³) overlies 6 m saturated clay, with GWT at the clay top. Clay Gs=2.65, water content=45%, Cc=0.25. Final effective stress at clay midpoint is 180 kPa. With γw=9.81, find primary settlement in m to two decimals.

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Correct answer: .32 to .34

Explanation

For saturated clay e₀=wGs=0.45(2.65)=1.1925. Submerged unit weight is $(G_s-1)\gamma_w/(1+e_0)=7.38255$ kN/m³; initial midpoint effective stress is $2(18.5)+3(7.38255)=59.1477$ kPa. For normally consolidated clay, $S=C_cH\log_{10}(180/59.1477)/(1+e_0)=\mathbf{0.33}$ m.