# Properties of Soils

 Question 1
A standard penetration test (SPT) was carried out at a location by using a manually operated hammer dropping system with $50 \%$ efficiency. The recorded SPT value at a particular depth is 28 . If an automatic hammer dropping system with $70 \%$ efficiency is used at the same location, the recorded SPT value will be
 A 28 B 20 C 40 D 25
GATE CE 2023 SET-2   Geotechnical Engineering
Question 1 Explanation:
We know that,
Efficiency of blow $\alpha \frac{1}{\text { SPT value }}$
$\Rightarrow \quad \eta_{1} \mathrm{~N}_{1}=\eta_{2} \mathrm{~N}_{2}$
Hence,
$0.50 \times 28=0.70 \times \mathrm{N}_{2}$
or $\quad \mathrm{N}_{2}=\frac{0.50 \times 28}{0.7}=20$
Option (B) is correct
 Question 2
A soil having the average properties, bulk unit weight $=19 \mathrm{kN} / \mathrm{m}^{3}$; angle of internal friction $=25^{\circ}$ and cohesion $=15 \mathrm{kPa}$, is being formed on a rock slope existing at an inclination of $35^{\circ}$ with the horizontal. The critical height (in $\mathrm{m}$ ) of the soil formation up to which it would be stable without any failure is _____ (round off to one decimal place).
 A 2.1 B 3.6 C 5.1 D 8.2
GATE CE 2023 SET-1   Geotechnical Engineering
Question 2 Explanation:
Given,
$\quad \gamma_{\mathrm{t}}=19 \mathrm{kN} / \mathrm{m}^{3}$
$\phi=25^{\circ}$
$C= 15 \mathrm{kPa}$
$\beta=35^{\circ}$
For $\mathrm{C}-\phi$ soil
$\mathrm{FOS}=\frac{\mathrm{C}+\gamma_{\mathrm{t}} z \cos ^{2} \beta \tan \phi}{\gamma_{\mathrm{t}} z \cos \beta \sin \beta}$

For critical height FOS=1
\begin{aligned} \text { FOS } & =\frac{\mathrm{C}+\gamma_{\mathrm{t}} \mathrm{z} \cos ^{2} \beta \tan \phi}{\gamma_{\mathrm{t}} \mathrm{zcos} \beta \sin \beta}=1 \\ & =19 \times \mathrm{H}_{\mathrm{C}} \times \cos 35^{\circ} \sin 35^{\circ} \\ & =15+19 \times \mathrm{H}_{\mathrm{C}} \times \cos ^{2} 35 \tan 25 \\ \mathrm{H}_{\mathrm{C}} & =5.03 \mathrm{~m} \end{aligned}

 Question 3
Let $\psi$ represent soil suction head and $K$ represent hydraulic conductivity of the soil. If the soil moisture content $\theta$ increases, which one of the following statements is TRUE?
 A $\psi$ decreases and K increases. B $\psi$ increases and K decreases. C Both $\psi$ and K decrease. D Both $\psi$ and K increase.
GATE CE 2022 SET-1   Geotechnical Engineering
Question 3 Explanation:
$h_c\propto \frac{1}{R}$
$K\propto S$
Water content $\uparrow \rightarrow R\uparrow \rightarrow h_c \downarrow \rightarrow \psi \downarrow$
Water content $\uparrow \rightarrow S\uparrow \rightarrow K \uparrow$
 Question 4
In an aggregate mix, the proportions of coarse aggregate, fine aggregate and mineral filler are 55%, 40% and 5%, respectively. The values of bulk specific gravity of the coarse aggregate, fine aggregate and mineral filler are 2.55, 2.65 and 2.70, respectively. The bulk specific gravity of the aggregate mix (round off to two decimal places) is ____________
 A 2.6 B 3.21 C 5.64 D 6.25
GATE CE 2021 SET-2   Geotechnical Engineering
Question 4 Explanation:
$G_{m}=\frac{55+40+5}{\frac{55}{2.55}+\frac{40}{2.65}+\frac{5}{2.70}}=2.596$
 Question 5
A partially-saturated soil sample has natural moisture content of 25% and bulk unit weight of $18.5 \mathrm{kN} / \mathrm{m}^{3}$. The specific gravity of soil solids is 2.65 and unit weight of water is $9.81 \mathrm{kN} / \mathrm{m}^{3}$. The unit weight of the soil sample on full saturation is
 A $21.12 \mathrm{kN} / \mathrm{m}^{3}$ B $19.03 \mathrm{kN} / \mathrm{m}^{3}$ C $20.12 \mathrm{kN} / \mathrm{m}^{3}$ D $18.50 \mathrm{kN} / \mathrm{m}^{3}$
GATE CE 2021 SET-1   Geotechnical Engineering
Question 5 Explanation:
\begin{aligned} \mathrm{w} &=0.25, \gamma_{\mathrm{t}}=18.5 \mathrm{kN} / \mathrm{m}^{3} \\ \mathrm{G}_{\mathrm{s}} &=2.65, \gamma_{\mathrm{w}}=9.81 \\ \gamma_{\mathrm{t}} &=\frac{G_{\mathrm{S}} \gamma_{W}(1+w)}{1+e} \\ \Rightarrow \qquad \qquad \qquad \qquad \mathrm{e} &=\frac{2.65 \times 9.81 \times 1.25}{18.5}-1\\ \Rightarrow \qquad \qquad \qquad \qquad e&=0.756\\ \text{At full saturation}, \quad \mathrm{S}&=1\\ \Rightarrow \qquad \qquad \qquad \quad \gamma_{\mathrm{sat}}&=\frac{\left(G_{\mathrm{S}}+e\right) \gamma_{\mathrm{W}}}{1+e}\\ \gamma_{\text {sat }} &=\frac{(2.65+0.756) \times 9.81}{1.756} \\ &=19.03 \mathrm{kN} / \mathrm{m}^{3} \end{aligned}

There are 5 questions to complete.

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