Question

A $3m\times 3m$ square precast reinforced concrete segments to be installed by pushing them through an existing railway embankment for making an underpass as shown in the figure. A reaction arrangement using precast PCC blocks placed on the ground is to be made for the jacks.
At each stage, the jacks are required to apply a force of 1875 kN to push the segment. The jacks will react against the rigid steel plate placed against the reaction arrangement. The footprint area of reaction arrangement on natural ground is 37.5$m^2$. The unit weight of PCC block is 24 $kN/m^3$. The properties of the natural ground are: c = 17 kPa; $\varphi ={25}^{\circ }$ and $\gamma =18kN/m^3$ . Assuming that the reaction arrangement has rough interface and has the same properties that of soil, the factor of safety (round off to 1 decimal place) against shear failure is

• A. 2.0187

Answer 1

The correct option is A 2.0187
FOS against shear failure

$=\frac{Strength}{Appliedload}=\frac{(c+\sigma tan\varphi )A}{P}$



$\sigma =\frac{N}{A}=\frac{24\frac{kN}{m^3}\times 37.5m^2\times 7.5m}{37.5m^2}$

$=24\times 7.5kN/m^2$

$\Rightarrow FOS=\frac{(c+\sigma tan\varphi )A}{P}$

$=\frac{(17+24\times 7.5\times tan{25}^{\circ })\times 37.5}{1875}$

FOS = 2.0187