GATE 2026 CE (CE2) – Question 58
A building is proposed in an area having thick deposit of silty clay. The water table is at the ground surface. The saturated unit weight of soil is 18 kN/m$^3$ and unit weight of water is 10 kN/m$^3$. The maximum vertical load ($P$) on a column of the proposed building is 2000 kN.
Consider $\sigma_z \le 0.1\,\sigma'_v$ for computation of the minimum depth of soil exploration. $\sigma'_v$ is the effective vertical overburden stress. $\sigma_z$ is the increase in the vertical stress at depth $z$ below load $P$ as per the Boussinesq's stress theory.
Based on above, the minimum depth (in m) of soil exploration required for the foundation design is ________ (*rounded off to two decimal places*).
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Correct answer: 10.56 to 10.66
Explanation
The effective unit weight is $18 - 10 = 8$ kN/m$^3$, so $\sigma'_v = 8z$. Directly below a point load Boussinesq's theory gives $\sigma_z = \frac{3P}{2\pi z^2} = \frac{3 \times 2000}{2\pi z^2} = \frac{954.9}{z^2}$. The condition $\sigma_z \le 0.1\sigma'_v$ becomes $\frac{954.9}{z^2} \le 0.8z$, so $z^3 \ge 1193.7$ and $z \ge 10.61$ m.