Shear Strength of Soil

 Question 1
The most appropriate triaxial test to assess the long-term stability of an excavated clay slope is
 A consolidated drained test B unconsolidated undrained test C consolidated undrained test D unconfined compression test
GATE CE 2021 SET-2   Geotechnical Engineering
Question 1 Explanation:
To assess the long term stability of clayey soil, the results of consolidated drained (CD) test are used.
 Question 2
Based on drained triaxial shear tests on sands and clays, the representative variations of volumetric strain $(\Delta V / V)$ with the shear strain $(\gamma)$ is shown in the figure.

Choose the CORRECT option regarding the representative behaviour exhibited by Curve P and Curve Q.
 A Curve P represents dense sand and overconsolidated clay, while Curve Q represents loose sand and normally consolidated clay B Curve P represents dense sand and normally consolidated clay, while Curve Q represents loose sand and overconsolidated clay C Curve P represents loose sand and overconsolidated clay, while Curve Q represents dense sand and normally consolidated clay D Curve P represents loose sand and normally consolidated clay, while Curve Q represents dense sand and overconsolidated clay
GATE CE 2021 SET-1   Geotechnical Engineering
Question 2 Explanation:

 Question 3
In a drained tri-axial compression test, a sample of sand fails at deviator stress of 150 kPa under confining pressure of 50 kPa. The angle of internal friction (in degree, round off to the nearest integer) of the sample, is ________
 A 78 B 54 C 37 D 44
GATE CE 2020 SET-1   Geotechnical Engineering
Question 3 Explanation:
$\text{Sand }(C=0); \; \sigma _d=150;\; \sigma _3=50;\; \sigma _1=200$
$\sigma _1=\sigma _3 \tan^2\left ( 45+\frac{\phi }{2} \right )+2c\tan \left ( 45+\frac{\phi }{2} \right )$
$200=50 \tan^2 \left ( 45+\frac{\phi }{2} \right )$
$\phi =36.87^{\circ}$
So, the angle of internal friction to the nearest integer is $37^{\circ}$.
 Question 4
The total horizontal and vertical stresses at a point X in a saturated sandy medium are 170 kPa and 300 kPa, respectively. The static pore-water pressure is 30 kPa. At failure, the excess pore-water pressure is measured to be 94.50 kPa, and the shear stresses on the vertical and horizontal planes passing through the point X are zero. Effective cohesion is 0 kPa and effective angle of internal friction is $36^{\circ}$. The shear strength (in kPa, up to two decimal places) at point X is ______
 A 42.23 B 59.45 C 78.82 D 52.52
GATE CE 2018 SET-2   Geotechnical Engineering
Question 4 Explanation:
\begin{aligned} \because\quad \sigma_{n} &=\frac{300+170}{2}+\frac{300-170}{2} \cos 2 \alpha \\ \alpha &=45^{\circ}+\frac{36^{\circ}}{2}=63^{\circ} \\ \Rightarrow\quad \sigma_{n} &=196.79 \mathrm{kPa} \\ \sigma_{n}^{\prime} &=\sigma_{\mathrm{n}}-u=196.79-(30+94.5) \\ \sigma_{n}^{\prime} &=72.29 \mathrm{kPa} \\ \Rightarrow\quad \tau &=c+\sigma_{\mathrm{n}}^{\prime} \tan \phi \\ &=72.29 \text { tan } 36=52.52 \mathrm{kPa} \end{aligned}
 Question 5
A conventional drained triaxial compression test was conducted on a normally consolidated clay sample under an effective confining pressure of 200 kPa. The deviator stress at failure was found to be 400 kPa. An identical specimen of the same clay sample is isotropically consolidated to a confining pressure of 200 kPa and subjected to standard undrained triaxial compression test. If the deviator stress at failure is 150 kPa, the pore pressure developed (in kPa, up to one decimal place) is ______
 A 100 B 125 C 25 D 75
GATE CE 2018 SET-1   Geotechnical Engineering
Question 5 Explanation:
$I^{st}$ Specimen : Drained condition
$\bar{\sigma}_{3}=200 \mathrm{kPa}: \sigma_{\mathrm{d}}=400 \mathrm{kPa}: \bar{\sigma}_{1}=600 \mathrm{kPa}$
$II^{nd}$Specimen : Undrained condition
\begin{aligned} \sigma_{3} &=200 \mathrm{kPa} \\ \sigma_{\mathrm{d}} &=150 \mathrm{kPa} \\ \sigma_{1} &=\sigma_{3}+\sigma_{\mathrm{d}}=350 \mathrm{kPa} \end{aligned}
Let pore pressure developed is u
\begin{aligned} \therefore \quad \bar{\sigma}_{3}&=(200-u)\\ \bar{\sigma}_{1}&=(350-u)\\ \end{aligned}
From stress relationship
$\bar{\sigma}_{1}=\bar{\sigma}_{3} \tan ^{2}\left(45^{\circ}+\frac{\phi}{2}\right)+2 c\tan\left(45^{\circ}+\frac{\phi}{2}\right)$
For clay under drained condition c=0
\begin{aligned} \therefore \quad \bar{\sigma}_{1} &=\bar{\sigma}_{3} \tan ^{2}\left(45^{\circ}+\frac{\phi}{2}\right) \\ 600 &=200 \tan ^{2}\left(45^{\circ}+\frac{\phi}{2}\right) \\ \phi &=30^{\circ} \end{aligned}
For second specimen,
\begin{aligned} \bar{\sigma}_{1}&=\bar{\sigma}_{3} \tan ^{2}\left(45^{\circ}+\frac{\phi}{2}\right)\\ (350-u) &=(200-u) \tan ^{2}\left(45^{\circ}+\frac{30^{\circ}}{2}\right) \\ u &=125 \mathrm{kPa} \end{aligned}
 Question 6
Following are the statements related to the stress paths in a triaxial testing of soils:
P. If $\sigma _{1}=\sigma _{3}$ , the stress point lies at the origin of the p-q plot.
Q. If, $\sigma _{1}=\sigma _{3}$ the stress point lies on the p-axis of the p-q plot.
R. If $\sigma _{1} \gt \sigma _{3}$ , both the stress points p and q are positive.
For the above statements, the correct combination is
 A P - False; Q - True; R - True B P - False; Q - True; R - True C P - False; Q - True; R - False D P - True; Q - False; R - False
GATE CE 2017 SET-2   Geotechnical Engineering
Question 6 Explanation:
On stress path in terms of p-q plot
\begin{aligned} p=\frac{\sigma_{1}+\sigma_{3}}{2} \\ q=\frac{\sigma_{1}-\sigma_{3}}{2} \end{aligned}
If $\sigma_{1}=\sigma_{3}$ then $q=0$ and $p \neq 0$ hence point does not lie at origin, point will lies on the p-axis.
If $\sigma_{1}>\sigma_{3}$, both the stress point will be positive.
 Question 7
A consolidated undrained $\bar{CU}$ triaxial compression test is conducted on a normally consolidated clay at a confining pressure of 100 kPa. The deviator stress at failure is 80 kPa, and the pore-water pressure measured at failure is 50 kPa. The effective angle of internalfriction (in degrees, up to one decimal place) of the soil is _________
 A 26.4 B 48.2 C 58.1 D 45.6
GATE CE 2017 SET-1   Geotechnical Engineering
Question 7 Explanation:
CU test is conducted.
\begin{aligned} \sigma_{3}= 100 &\mathrm{kPa}, \sigma_{a}=80 \mathrm{kPa}, u=50 \mathrm{kPa} \\ \sigma_{1}&=\sigma_{3}+\sigma_{d} =100+80=180 \mathrm{kPa} \\ \bar{\sigma}_{1}&=\sigma_{1}-u= 180-50=130 \mathrm{kPa}\\ \bar{\sigma}_{3}&=\sigma_{3}-u=100-50=50 \mathrm{kPa} \\ \bar{\sigma}_{1}&=\bar{\sigma}_{3} \tan ^{2}\left(45+\frac{\phi^{\prime}}{2}\right)+2 C^{\prime} \tan \left(45+\frac{\phi^{\prime}}{2}\right) \\ \text{Assume }\quad C^{\prime}&=0 \\ \bar{\sigma}_{1}&=\bar{\sigma}_{3} \tan ^{2}\left(45+\frac{\phi^{\prime}}{2}\right) \\ 130&=50 \tan ^{2}\left(45+\frac{\phi^{\prime}}{2}\right) \\ \phi^{\prime}&=26.4^{\circ} \end{aligned}
 Question 8
A soil sample is subjected to a hydrostatic pressure, $\sigma$. The Mohr circle for any point in the soil sample would be
 A a circle of radius $\sigma$ and center at the origin B a circle of radius $\sigma$ and center at a distance $\sigma$ from the origin C a point at a distance $\sigma$ from the origin D a circle of diameter $\sigma$ and center at the origin
GATE CE 2017 SET-1   Geotechnical Engineering
Question 8 Explanation:
Hydrostatic pressure acts equally in all directions.

 Question 9
A drained triaxial compression test on a saturated clay yielded the effective shear strength parameters as ${c}'=15\, kPa \: \, and \: {\phi }'=22^{\circ}.$ Consolidated Undrained triaxial test on an identical sample of this clay at a cell pressure of 200 kPa developed a pore water pressure of 150kPa at failure. The deviator stress (expressed in kPa) at failure is _________ .
 A 104.38 B 50.25 C 154.39 D 160.22
GATE CE 2016 SET-1   Geotechnical Engineering
Question 9 Explanation:
Cell pressure,
$\sigma_{3}=200 \mathrm{kPa}$
Pore water pressure.
\begin{aligned} u &=150 \mathrm{kPa} \\ \therefore \bar{\sigma}_{3} &=\sigma_{3}-U=200-150=50 \mathrm{kPa} \end{aligned}
Effective shear parameters $\left(c^{\prime}=150 \mathrm{kPa}\text{ and } \phi^{\circ}=22^{\circ}\right)$ is given
\begin{aligned} \therefore \quad \bar{\sigma}_{1} &=\bar{\sigma}_{3} \tan ^{2}\left(45+\frac{\varphi^{\prime}}{2}\right)+2 c^{\prime} \tan \left(45+\frac{\phi^{\prime}}{2}\right) \\ \bar{\sigma}_{1} &=50+\tan ^{2}\left(45+\frac{22}{2}\right)+2 \times 15 \tan \left(45+\frac{22}{2}\right) \end{aligned}
$\bar{\sigma}_{1}=154.376 \mathrm{kPa}$
Now
$\begin{array}{l} \vec{\sigma}_{1}=\bar{\sigma}_{3}+\sigma_{\sigma} \\ \sigma_{d}=\bar{\sigma}_{1}-\bar{\sigma}_{3}=154.376-50 \end{array}$
$\text{Deviator stress, }\sigma_{\sigma}=104.376 \mathrm{kPa}$
 Question 10
In the consolidated undrained triaxial test on a saturated soil sample, the pore water pressure is zero
 A during shearing stage only B at the end of consolidation stage only C both at the end of consolidation and during shearing stages D under none of the above conditions
GATE CE 2016 SET-1   Geotechnical Engineering
There are 10 questions to complete.

1 thought on “Shear Strength of Soil”

1. Question 17 is not of soil but of environmental
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