Q41GATE 2005MCQ

A strip footing (8 m wide) is designed for a total settlement of 40 mm. The safe bearing capacity (shear) was 150 kN/ $m^{2}$ and safe allowable soil pressure was 100 kN/ $m^{2}$ . Due to important of the structure, now the footing is to be redesigned for total settlement of 25 mm. The new width of the footing will be

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📖 Explanation

Load per metre length of footing $P=B \times$ { Minimum of bearing capacity and allowable soil pressure}

\begin{array}{l} =8 \times \text { Minimum of }[150,100] \\ =8 \times 100=800 \mathrm{kN} / \mathrm{m} \end{array}

Allowable pressure for 25mm settlement $=\frac{100 \times 25}{40}=62.5 \mathrm{kN} / \mathrm{m}^{2}$ Load resisted = Width x Allowable pressure

\begin{array}{rr} & 800=B \times 62.5 \\ \Rightarrow \quad & B=12.8 \mathrm{m}\end{array}

Q43GATE 2004MCQ

The figure given below represents the contact pressure distribution underneath a

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Q44GATE 2004MCQ

Two circular footings of diameters $D_{1}$ and $D_{2}$ are resting on the surface of the same purely cohesive soil. The ratio of their gross ultimate bearing capacities is

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📖 Explanation

We know that $a_{u}=1.3 \mathrm{cN}_{\mathrm{c}}+\mathrm{qN}_{\mathrm{q}}+0.3 \gamma \mathrm{DN}_{\mathrm{y}}$ where D is the diameter of the circular footing Now, for purely cohesive soils, $\phi=0$ $N_{c}=5.7, N_{q}=1, N_{\gamma}=0$ Therefore, the gross ultimate bearing capacity of a footing (of any shape) resting on the surface of a purely cohesive clay is constant irrespective of its size. Thus, the ratio of gross ultimate bearing capacities of the two circular footings will be 1.0.

Q45GATE 2003MCQ

In a plate load test conducted on cohesion less soil, a 600 mm square test plate settles by 15 mm under a load intensity of 0.2 $N/mm^{2}$ . All conditions remaining the same, settlement of a 1 m square footing will be

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📖 Explanation

Settlement of footing in a cohesionless soil is given by

\begin{aligned} \quad S_{1}&=S_{p}\left[\frac{B_{1}\left(B_{p}+30\right)}{B_{p}\left(B_{1}+30\right)}\right]^{2} \\ \Rightarrow \quad S_{f}&=15\left[\frac{100(60+30)}{60(100+30)}\right]^{2} \\ \Rightarrow \quad S_{f}&=19.97 \mathrm{mm} \end{aligned}

Q46GATE 2002MCQ

The observed value of the standard penetration number (N) at 10 m depth of a silty sand deposit is 13. The unit weight of the soil is 16 $kN/m^3$ . The N value after correcting for the presence of fines will be

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📖 Explanation

Given SPT number $N=13(\lt 15)$ Correction of fines is not required as N is not greater than 15 $N_{\text {corrected }}=13$

Q47GATE 2001MCQ

A plate load test was conducted in sand on a 300 mm diameter plate. If the plate settlement was 5 mm at a pressure of 100 kPa, the settlement (in mm) of a 5mx8m rectangular footing at the same pressure will be

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📖 Explanation

For cohesionless soil

\begin{aligned} S_{t} &=S_{\mathrm{p}}\left[\frac{\mathrm{B}_{\mathrm{t}}\left(\mathrm{B}_{\mathrm{p}}+0.3\right)}{\mathrm{B}_{\mathrm{p}}\left(\mathrm{B}_{\mathrm{t}}+0.3\right)}\right]^{2} \\ &=5\left[\frac{5(0.3+0.3)}{0.3(5+0.3)}\right]^{2}=17.8 \mathrm{mm} \end{aligned}

Q48GATE 2001MCQ

The following two statements are made with reference to the calculation of net bearing capacity of a footing in pure clay soil ( $\phi =0$ ) using Terzaghi's bearing capacity theory. Identify if they are TRUE or FALSE. I. Increase in footing width will result in increase in bearing capacity. II. Increase in depth of foundation will result in higher bearing capacity.

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📖 Explanation

$q_{u}=c N_{c}+\gamma D_{i} N_{q}+0.5 \gamma B N_{\gamma}$ For pure clay,

\begin{aligned} \phi &=0, N_{c}=5.7, N_{q}=1, N_{\gamma}=0 \\ \therefore \quad a_{u} &=c N_{c}+\gamma D_{t} \\ q_{n u} &=c N_{c}+\gamma D_{t}-\gamma D_{t}=c N_{c} \end{aligned}

Q49GATE 2001MCQ

The width and depth of a footing are 2 and 1.5m respectively. The water table at the site is at a depth of 3m below the ground level. The water table correction factor for the calculation of the bearing capacity of soil is

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📖 Explanation

\begin{aligned} W_{y} &=0.5+0.5 \frac{\mathrm{D}_{t}}{\mathrm{B}} \\ &=0.5+0.5 \times \frac{1.5}{2}=0.875 \end{aligned}