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 $18 ~\mathrm{kN} / \mathrm{m}^{3}$ and unit weight of water is $10 ~\mathrm{kN} / \mathrm{m}^{3}$. The maximum vertical load $(P)$ on a column of the proposed building is $2000 \text{ kN}$.
Consider $\sigma_{z} \leq 0.1 \sigma_{v}^{\prime}$ for computation of the minimum depth of soil exploration.
$\sigma_{v}^{\prime}$ 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).
