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GATE 2023 CE (CE1) – Question 42

Geotechnical Engineering · Shallow foundations: bearing capacity, combined footing, raft, settlement · 2 marks · Multiple choice

A square footing of size 2.5 m × 2.5 m is placed 1.0 m below the ground surface on a cohesionless homogeneous soil stratum. Considering that the groundwater table is located at the base of the footing, the unit weights of soil above and below the groundwater table are 18 kN/m$^3$ and 20 kN/m$^3$, respectively, and the bearing capacity factor $N_q$ is 58, the net ultimate bearing capacity of the soil is estimated as 1706 kPa (unit weight of water = 10 kN/m$^3$).
Earlier, a plate load test was carried out with a circular plate of 30 cm diameter in the same foundation pit during a dry season, when the water table was located beyond the plate influence zone. Using Terzaghi's bearing capacity formulation, what is the ultimate bearing capacity (in kPa) of the plate?

  1. 110.16
  2. 61.20
  3. 204.00
  4. 163.20

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Correct answer: (A) 110.16

Explanation

For the square footing, Terzaghi's net capacity is $q_{nu} = \gamma D_f(N_q - 1) + 0.4\gamma'BN_\gamma = 18 \times 1 \times 57 + 0.4 \times 10 \times 2.5 \times N_\gamma = 1026 + 10N_\gamma = 1706$, so $N_\gamma = 68$. The plate was tested at the bottom of the foundation pit, so there is no surcharge on it, and the capacity of the circular plate in dry soil is $q_u = 0.3\gamma BN_\gamma = 0.3 \times 18 \times 0.3 \times 68 = 110.16$ kPa.