Foundation Settlement

Two warehouses each having $2424$ m plan dimensions and $12$ m apart are to be constructed on a very large area with the following soil profile. A very dense coarse sand layer, $8$ m in thickness with a particle specific gravity, Gs$=2\mathrm{.}7$ and porosity, n$=0\mathrm{.}25.$ Underlying this sand layer, a normally consolidated clay layer with the properties given below. Below the clay layer there is bedrock.

Clay layer $($thickness $=2\mathrm{.}0$ m$)$

Compression Index Cc$=0\mathrm{.}5$

Void ratio eo$=0\mathrm{.}50$

Specific Gravity Gs$=2\mathrm{.}70$

Time for $50\%$ consolidation $(25$ mm thick specimen$)$ t$50=5$ min

Initially, the ground water table was at the original ground surface. Before the construction of warehouses, the ground water table was lowered by $6\mathrm{.}0$ m and a $3\mathrm{.}0$ m thick compacted fill composed of sand$-$gravel with a unit weight of $21$ kN$/$m$3$ was constructed over a very large area. Knowing that each warehouse introduces a uniform pressure of $50$ kN$/$m$2$ determine:

$(1)$ The total settlement at the center of the warehouses due to consolidation of the clay layer. Compression of sand will be neglected.

$(2)$ The required time for $50\%$ and $75\%$ settlement of the center point $($plot time$-$settlement curve.

All of the three constructional operations will be completed in three months. Therefore, it is reasonable to assume that the loading is instantaneous. Dense coarse sand

Porosity, $n=0\mathrm{.}25$

Specific gravity, $G_s=2\mathrm{.}7$

$\{\begin{array}{c}\text{:}{C}_c=0\mathrm{.}50\\ e_0=0\mathrm{.}50\\ G_s=2\mathrm{.}7\end{array}$

Bedrock Compacted fill $=21k\frac{N}{m^3}$

Dense coarse sand Porosity, $n=0\mathrm{.}25$ Specific gravity, $G_s=2\mathrm{.}7$

$\{\begin{array}{c}\text{:}{C}_c=0\mathrm{.}50\\ e_0=0\mathrm{.}50\\ G_s=2\mathrm{.}7\end{array}$

Bedrock