Question

A square footing of size $2.5\, \text{m} \times 2.5\, \text{m}$ is placed $1.0\, \text{m}$ below the ground surface on a cohesionless soil. The water table is at the base of the footing. Above and below the water table, $\gamma=18$ and $\gamma_{\text{sat}}=20~ \text{kN/m}^3$ (thus $\gamma' = 20-10 = 10~ \text{kN/m}^3$). Given $N_q=58$, the net ultimate bearing capacity for the soil is $q_{nu}=1706~ \text{kPa}$. Earlier, a plate load test with a circular plate of diameter $0.30$ m was carried out in the same pit during dry season (WT below influence zone). Using Terzaghi's formulation, find the ultimate bearing capacity of the plate (in kPa). 

• A. 110.16
• B. 61.20
• C. 204.00
• D. 163.20

Hint:

In plate load tests at foundation level, take $D_f=0$ (no surcharge). For Terzaghi's $N_\gamma$ term, use $0.5$ (strip), $0.4$ (square) and $0.3$ (circular).

Answer 1

The Correct Option is A

Step 1: Back–calculate $N_\gamma$ from the given square footing data.
For $c=0$, Terzaghi (square footing) net ultimate capacity \[ q_{nu}=\gamma D_f\,(N_q-1)+0.4\,\gamma' B\,N_\gamma . \] With $D_f=1$ m, $B=2.5$ m, $\gamma=18$, $\gamma'=10$, $N_q=58$: \[ 1706=18(58-1)+0.4(10)(2.5)N_\gamma =1026+10N_\gamma \Rightarrow N_\gamma=68. \]

Step 2: Ultimate capacity of the circular plate during dry season.
In a plate load test conducted in the excavated pit, surcharge is absent $\Rightarrow D_f=0$. For a circular footing (Terzaghi): \[ q_u= \gamma D_f N_q + 0.3\,\gamma\,B\,N_\gamma =0 + 0.3(18)(0.30)(68)=110.16~\text{kPa}. \] \[ \boxed{q_u=110.16~\text{kPa}} \]