GATE 2019 CE (CE1) – Question 64
Precast 3 m × 3 m square reinforced-concrete segments are pushed through a railway embankment to form an underpass. Jacks react against a rigid steel plate and a precast PCC-block stack on natural ground, as shown. Each stage requires 1875 kN. Stack footprint is 37.5 m², height 7.5 m and unit weight 24 kN/m³. Natural soil has c = 17 kPa, φ = 25° and unit weight 18 kN/m³. Assume the stack is rough and has the soil’s shear properties at its base. Find safety factor against shear failure, to one decimal place.
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Correct answer: 1.8 to 2.1
Explanation
Stack weight is $W=37.5(7.5)(24)=6750$ kN. Base shear resistance is $cA+W\tan\phi=17(37.5)+6750\tan25^\circ=3785.08$ kN. Safety factor is $3785.08/1875=2.0187$: **2.0**.