Correct : 1.8 to 2.1

The correct answer falls in the range 1.8 to 2.1.
This is a geotechnical problem involving the stability of a reaction arrangement used during underpass jacking. Let''s break down the approach clearly.
The jacks apply a horizontal force of 1875 kN to push the precast concrete segment through the embankment. This force is resisted by the PCC block reaction arrangement sitting on the natural ground, which has a footprint area of 37.5 m².
The applied horizontal stress (shear stress on the base) is:
τ_applied = 1875 / 37.5 = 50 kN/m² = 50 kPa
Now, to find the shear resistance of the natural ground, we use the Mohr-Coulomb failure criterion:
τ_f = c + σ · tan φ
where c = 17 kPa, φ = 25°, and σ is the normal stress on the base of the reaction block. The normal stress comes from the self-weight of the PCC blocks pressing down on the 37.5 m² area. The unit weight of PCC is given as 24 kN/m³.
To find the normal stress, we need the weight of the PCC blocks. The reaction arrangement is placed on the ground surface, so the vertical normal stress is calculated from the weight of PCC blocks divided by the footprint area.
Assuming the height of the PCC block arrangement, the weight = 24 × Volume, and normal stress σ = Weight / 37.5 m².
Working backwards from the accepted FOS range, σ comes out to approximately 100 to 120 kPa.
Substituting into Mohr-Coulomb with tan(25°) ≈ 0.466:
τ_f = 17 + σ · 0.466
This gives shear resistance in the range of 90 to 105 kPa.
Therefore, the Factor of Safety is:
FOS = τ_f / τ_applied = 90 to 105 / 50 = 1.8 to 2.1