A multistory building with a basement is to be constructed. The top $4$ m consists of loose silt, below which dense sand layer is present up to a great depth. Ground water table is at the surface. The foundation consists of the basement slab of $6$ m width which will rest on the top of dense sand as shown in the figure. For dense sand, saturated unit weight $=20 \: kN/m^3$, and bearing capacity factors $N_q=40$ and $N_y=45$. For loose silt, saturated unit weight $=18 \: kN/m^3$, $N_q=15$ and $N_{\gamma}=20$. Effective cohesion $c’$ is zero for both soils. Unit weight of water is $10 \: kN/m^3$. Neglect shape factor and depth factor.

Average elastic modulus $E$ and Poisson’s ratio $\mu$ of dense sand is $ 60 \times 10^3 \: kN/m^2$ and $0.3$ respectively.

The foundation slab is subjected to vertical downward stresses equal to net safe bearing capacity derived in the above question. Using influence factor $I_f=2.0$, and neglecting embedment depth and rigidity corrections, the immediate settlement of the dense sand layer will be