Q21GATE 2006MCQ

The range of void ratio between which quick sand condition occurs in cohesionless granular soil deposits is

📖 Explanation

The specific gravity of cohesionless granular soils (sands) does not vary much and for all practical purposes it is taken to be 2.65. Critical hydraulic gradient should be nearly 1 for quick sand condition. $i.e.\quad i_{cr}=\frac{G-1}{1+e}$ From the above equation, the void ratio range is found to be between 0.6 and 0.7.

Q22GATE 2004MCQ

The figure below shows two flow lines for seepage across an interface between two soil media of different coefficients of permeability. If entrance angle $\alpha _{1}=30^{\circ}$ , the exit angle $\alpha _{2}$ will be

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📖 Explanation

\begin{aligned} \frac{k_{1}}{k_{2}}&=\frac{\tan \alpha_{1}}{\tan \alpha_{2}}\\ \Rightarrow \quad \frac{1.0 \times 10^{-7}}{4.0 \times 10^{-7}}&=\frac{\tan 30^{\circ}}{\tan \alpha_{2}} \\ \Rightarrow \quad \quad \tan \alpha_{2}&=2.309 \\ \Rightarrow \quad \alpha_{2}&=66.59^{\circ} \end{aligned}

Q23GATE 2004MCQ

A unit volume of a mass of saturated soil is subjected to horizontal seepage. The saturated unit weight is 22 kN/ $m^{3}$ and the hydraulic gradient is 0.3. The resultant body force on the soil mass is

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📖 Explanation

\begin{array}{l} \text { Volume of soil }=1 \mathrm{m}^{3} \\ \qquad \gamma_{\text {sat }}=22 \mathrm{kN} / \mathrm{m}^{3} \end{array}

Hydraulic gradient =i=0.3

\begin{aligned} F_{\text {horizontal }} &=i{\gamma}_{w} \cdot \text { volume } \\ &=0.3 \times 9.81 \times 1 \\ &=2.943 \mathrm{kN}\\ F_{\text {verical }} &=\gamma \cdot \text { volume } \\ &=(22-9.81) \times 1 \\ &=12.19 \mathrm{kN} \\ F_{\text {resultant }} &=\sqrt{F_{n}^{2}+F_{v}^{2}} \\ &=12.54 \mathrm{kN} \end{aligned}

Q24GATE 2003MCQ

A masonry dam is founded on previous sand having porosity equal to 45% and specific gravity of sand particles is 2.65. For a desired factor of safety of 3 against sand boiling, the maximum permissible upward gradient will be

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📖 Explanation

Critical hydraulic gradient,

\begin{aligned} \quad \mathrm{i}_{\mathrm{C}}&=\frac{\mathrm{G}-1}{1+\mathrm{e}}=(\mathrm{G}-1)(1-\mathrm{n}) \\ \therefore \mathrm{i}_{\mathrm{C}}&=(2.65-1)(1-0.45)=0.9075 \end{aligned}

Factor of safety $=\frac{\text { Critical hydraulic gradient }}{\text { Maximum permissible gradient }}$ $\Rightarrow$ Maximum permissible gradient $=\frac{0.9075}{3}=0.3025$

Q25GATE 2002MCQ

The specific gravity and insitu void ratio of a soil deposit are 2.71 and 0.85 respectively. The value of the critical hydraulic gradient is

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📖 Explanation

\begin{aligned} i_{c} &=\frac{G-1}{1+e}=\frac{2.71-1}{0.85+1} \\ &=\frac{1.71}{0.85}=0.924 \end{aligned}