Question

A footing of size 2m $\times$ 2m transferring a pressure of $200kN/m^2$, is placed at depth of 1.5 m below the ground as shown in the figure (not drawn to the scale). The clay stratum is normally consolidated. The clay has specific gravity of 2.65 and compression index of 0.3.


Consideration 2:1 (vertical to horizontal) method of load distribution and ${\gamma }_w=10kN/m^3$ , the primary consolidation settlement (in mm, round off to two decimal places) of the clay stratum is

• A. 74.28

Answer 1

The correct option is A 74.28
Initial effective stress at the mid depth of clay layer

$\left({\sigma }_o\right)=(1.5+0.5)\times 15+0.5\times 18$

$+\frac{1.5}{2}\times 17-(\frac{1.5}{2}+0.5)\times 10$

$=39.25kN/m^2$


Change in effective stress due to surcharge

$=\frac{200\times 2\times 2}{3.75\times 3.75}=56.888kN/m^2$

Initial void ratio of clay $\left(e_o\right)$

${\gamma }_{sat}=\frac{G+e_o}{1+e_o}{\gamma }_w$

$17=\frac{2.65+e_o}{1+e_o}\times 10$

$e_0=1.357$

Primary consoildation settlement $\left(\Delta h\right)$

$\Delta h=\frac{C_{c}H}{1+e_o}log\left(\frac{\overline{{\sigma }_o}+\Delta \overline{\sigma }}{\overline{{\sigma }_o}}\right)$

$=\frac{0.3\times 1.5}{1+1.357}log\left(\frac{39.25+56.888}{39.25}\right)$

= 0.07428 m

= 74.28 mm