List of top Soil Mechanics and Foundation Engineering Questions on Bearing Capacity asked in GATE CE

A designer used plate load test to obtain the value of the bearing capacity factor $ N_t $. A circular plate of 1 m diameter was placed on the surface of a dry sand layer extending very deep beneath the ground. The unit weight of the sand is 16.66 kN/m$^3$. The plate is loaded to failure at a pressure of 1500 kPa.
Considering Terzaghi's bearing capacity theory, the bearing capacity factor $ N_t $ is ......... (round off to the nearest integer).

A 6 m $\times$ 6 m square footing constructed in clay is subjected to a vertical load of 2500 kN at its centre. The base of the footing is 2 m below the ground surface, as shown in the figure. The footing is made of 2 m thick concrete. The ground water table is at a great depth. Considering Terzaghi's bearing capacity theory, the factor of safety of footing against the bearing capacity failure is ....... (rounded off to 2 decimal places).

A single pile with 450 mm diameter has been driven into a homogeneous clay layer, which has an undrained cohesion ($c_u$) of 20 kPa and unit weight of 18 kN/m³. The ground water table is found to be at the surface of the clay layer. The adhesion factor ($\alpha$) of the soil is 0.95 and bearing capacity factor ($N_c$) is 9. The pile is supporting a column load of 144 kN with a factor of safety of 3.0 against ultimate axial pile capacity in compression. The required embedment depth of the pile (in m) is ......... (rounded off to the nearest integer).

A designer used plate load test to obtain the value of the bearing capacity factor $ N_t $. A circular plate of 1 m diameter was placed on the surface of a dry sand layer extending very deep beneath the ground. The unit weight of the sand is 16.66 kN/m$^3$. The plate is loaded to failure at a pressure of 1500 kPa.
Considering Terzaghi's bearing capacity theory, the bearing capacity factor $ N_t $ is ......... (round off to the nearest integer).

A 6 m $\times$ 6 m square footing constructed in clay is subjected to a vertical load of 2500 kN at its centre. The base of the footing is 2 m below the ground surface, as shown in the figure. The footing is made of 2 m thick concrete. The ground water table is at a great depth. Considering Terzaghi's bearing capacity theory, the factor of safety of footing against the bearing capacity failure is ....... (rounded off to 2 decimal places).
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A single pile with 450 mm diameter has been driven into a homogeneous clay layer, which has an undrained cohesion ($c_u$) of 20 kPa and unit weight of 18 kN/m³. The ground water table is found to be at the surface of the clay layer. The adhesion factor ($\alpha$) of the soil is 0.95 and bearing capacity factor ($N_c$) is 9. The pile is supporting a column load of 144 kN with a factor of safety of 3.0 against ultimate axial pile capacity in compression. The required embedment depth of the pile (in m) is ......... (rounded off to the nearest integer).

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 square footing is to be designed to carry a column load of 500 kN which is resting on a soil stratum having the following average properties: bulk unit weight = 19 kN/m³; angle of internal friction = 0° and cohesion = 25 kPa. Considering the depth of the footing as 1 m and adopting Meyerhof's bearing capacity theory with a factor of safety of 3, the width of the footing (in m) is (round off to one decimal place)}