Q21GATE 2014MCQ

For a saturated cohesive soil, a triaxial test yields the angle of internal friction ( $\phi$ ) as zero. The conducted test is

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Q22GATE 2012MCQ

The effective stress friction angle of a saturated, cohesionless soil is 38 $^{\circ}$ . The ratio of shear stress to normal effective stress on the failure plane is

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📖 Explanation

\begin{aligned} \therefore \quad \tau&=c+\bar{\sigma}_{a} \tan \phi \\ \text{For sands,} \quad c&=0 \\ \Rightarrow \quad \tau&=\bar{\sigma}_{n} \tan \phi \\ \therefore \quad \frac{\tau}{\sigma_{n}}&=\tan \phi=\tan 38^{\circ}=0.781 \end{aligned}

Q23GATE 2011MCQ

A field vane shear testing instrument (shown in figure) was inserted completely into a deposit of soft, saturated silty clay with the vane rod vertical such that the top of the blades were 500 mm below the ground surface. Upon application of a rapidly increasing torque about the vane rod, the soil was found to fail when the torque reached 4.6 Nm. Assuming mobilization of undrained shear strength on all failure surfaces to be uniform and the resistance mobilized on the surface of the vane rod to be neglibible, what would be the peak undrained shear strength (rounded off to the nearest integer value of kPa) of the soil?

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📖 Explanation

When the top end of the vane completely shear the soil, Then the torque at failure is given by

\begin{aligned} T&=c_{u} \pi\left(\frac{d^{\prime} h}{2}+\frac{d^{3}}{6}\right)\\ \Rightarrow \frac{4.6}{1000}&=c_{u} \times \pi \times \left(\frac{(0.05)^{2} \times 0.1}{2}+\frac{(0.05)^{3}}{6}\right) \\ \Rightarrow \quad c_{u}&=10 \mathrm{kPa} \end{aligned}

Q24GATE 2011MCQ

A soil is composed of solid spherical grains of identical specific gravity and diameter between 0.075mm and 0.0075mm. If the terminal velocity of the largest particle falling through water without flocculation is 0.5mm/s, that for the smallest particle would be

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📖 Explanation

According to Stoke s law

\begin{aligned} v&= D \\ \Rightarrow \frac{v_{1}}{v_{2}}&=\left(\frac{D_{1}}{D_{2}}\right)^{2} \Rightarrow \frac{0.5}{v_{2}}=\left(\frac{0.075}{0.0075}\right)^{2} \\ \Rightarrow \quad v_{2}&=\frac{0.5}{100} \quad \Rightarrow \quad v_{2}=0.005 \mathrm{mm} / \mathrm{s} \end{aligned}

Q25GATE 2011MCQ

Two geometrically identical isolated footings, X (linear elastic) and Y (rigid), are loaded identically (shown below). The soil reactions will

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Q26GATE 2011MCQ

For a sample of dry, cohesionless soil with friction angle, $\phi$ , the failure plane will be inclined to the major principal plane by an angle equal to

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📖 Explanation

Angle between major principal plane and failure plane is $\theta_{1}$ , from Mohr's circle

\begin{array}{r} 2\theta_{1}=90^{\circ}+\phi \\ \theta_{1}=45^{\circ}+\frac{\phi}{2} \end{array}

Q27GATE 2008MCQ

A direct shear test was conducted on a cohesion less soil (c=0) specimen under a normal stress of 200 kN/ $m^{2}$ . The specimen failed at a shear stress of 100 kN/ $m^{2}$ . The angle of internal friction of the soil (degree) is

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📖 Explanation

\begin{aligned} t&=c+\bar{\alpha} \tan \theta &\left[\because c=0 \right]\\ \therefore \quad 100&=0+200 \tan \theta \\ \Rightarrow \quad \phi&=\tan ^{-1}(0.5) \\ \Rightarrow \quad \phi&=26.6^{\circ} \end{aligned}

Q28GATE 2007MCQ

A clay soil sample is tested in a triaxial apparatus in consolidated-drained conditions at a cell pressure of 100 kN/ $m^{2}$ . What will be the pore water pressure at a deviator stress of 40 kN/ $m^{2}$ ?

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Q29GATE 2006MCQ

A sample of saturated cohensionless soil tested in a drained triaxial compression test showed an angle of internal friction of $30^{\circ}$ . The deviatoric stress at failure for the sample at a confining pressure of 200 kPa is equal to

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📖 Explanation

\begin{aligned} \sigma_{1} &=\sigma_{3} \tan ^{2}\left(45+\frac{9}{2}\right)+2 \mathrm{c} \tan \left(45+\frac{\phi}{2}\right) \\ \Rightarrow \sigma_{1} &=200 \tan ^{2}\left(45+\frac{30}{2}\right)+2 \times 0 \times \tan \left(45+\frac{30}{2}\right) \\ \Rightarrow \sigma_{1} &=600 \mathrm{kN} / \mathrm{m}^{2} \end{aligned}

$\therefore$ Deviatoric stress at failure

\begin{aligned} &=\sigma_{1}-\sigma_{3}=600-200 \\ &=400 \mathrm{kPa} \end{aligned}

Q30GATE 2005MCQ

For a tri-axial shear test conducted on a sand specimen at a confining pressure of 100 kN/ $m^{2}$ under drained conditions, resulted in a deviator stress ( $\sigma_{1} - \sigma _{3}$ ) at failure of 100 kN/ $m^{2}$ . The angle of shearing resistance of the soil would be

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📖 Explanation

We know that

\begin{aligned} \frac{\sigma_{1}}{\sigma_{1}}&=\frac{1+\sin \theta}{1-\sin \theta} \\ \Rightarrow \quad \sin \theta&=\frac{\sigma_{1}-\sigma_{2}}{\sigma_{1}+\sigma_{3}} \\ \Rightarrow \quad \sin \phi&=\frac{100}{\sigma_{1}+\sigma_{3}-\sigma_{3}+\sigma_{3}} \\ \Rightarrow \quad \sin \phi&=\frac{100}{\left(\sigma_{1}-\sigma_{3}\right)+2 \sigma_{3}}\\ \Rightarrow \quad \sin \theta &=\frac{100}{100+2 \times 100} \\ \Rightarrow \quad \theta &=\sin ^{-1}\left(\frac{1}{3}\right) \\ \Rightarrow \quad &=19.47^{\circ} \end{aligned}

Q31GATE 2004MCQ

In an undrained triaxial test on a saturated clay, the Poisson's ratio is

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📖 Explanation

In undrained triaxial test on saturated clay, the volume change due to confining pressure is zere

\begin{aligned} \Rightarrow \quad \varepsilon_{3}&=0 \\ \frac{\sigma_{3}}{E}-\frac{\mu \sigma_{1}}{E}-\frac{\mu \sigma_{2}}{E} &=0 \\ \mu &=\frac{\sigma_{3}}{\sigma_{1}+\sigma_{3}} \end{aligned}

Q32GATE 2002MCQ

In a triaxial test carried out on a cohesionless soil sample with a cell pressure of 20 kPa, the observed value of applied stress at the point of failure was 40 kPa. The angle of internal friction of the soil is

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📖 Explanation

\begin{aligned} \text{Given,}\quad \sigma_{1} &=\sigma_{a}+\sigma_{3} \\ &=40+20=60 \mathrm{kPa} \\ \text{Now,}\quad \sigma_{1} &=\sigma_{3} N_{0}+2 \mathrm{c} \sqrt{\mathrm{N}_{2}}\\ \text{Where }\quad c&=0\\ \frac{\sigma_{1}}{\sigma_{3}} &=N_{0}=\frac{60}{20}=3 \\ &=\tan ^{2}\left(45^{\circ}+\frac{\phi}{2}\right)\\ \tan \left(45^{\circ}+\frac{\phi}{2}\right)&=\sqrt{3}=1.732 \\ 45^{\circ}+\frac{\phi}{2}&=60^{\circ} \\ \text{or }\quad \frac{\phi}{2}&=60^{\circ}-45^{\circ} \\ \phi&=30^{\circ} \end{aligned}\\

Q33GATE 2002MCQ

If the effective stress strength parameters of a soil are c'=10 kPa and ${\phi}' =30^{\circ}$ , the shear strength on a plane within the saturated soil mass at a point where the total normal stress is 300 kPa and pore water pressure is 150 kPa will be

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📖 Explanation

\begin{aligned} \tau &=c+\bar{\sigma}_{s} \tan \phi^{\prime} \\ &=10+(150) \tan 30^{\circ} \\ &=96.6 \mathrm{kPa} \end{aligned}