GATE CE 2019 Set 1 — Question 64
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Geotechnical Engineering → Shear Strength of Soils → Mohr-Coulomb Criterion
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Question
A 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 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 . The unit weight of PCC block is . The properties of the natural ground are: ; and . 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 ________

Correct answer
1.8 to 2.1
Solution
The factor of safety against shear failure of the reaction arrangement is the ratio of the ultimate shear resistance to the applied horizontal force.
Rounding off to 1 decimal place, the factor of safety is .
1.Calculate the vertical load () from the PCC blocks:
The height of the PCC blocks is given as in the figure.2.Calculate the ultimate shear resistance () at the interface:
Using the Mohr-Coulomb failure criterion: 3.Calculate the Factor of Safety ():
The applied horizontal force .Rounding off to 1 decimal place, the factor of safety is .
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