List of top Geotechnical Engineering Questions asked in GATE CE

In the given figure, Point O indicates the stress point of a soil element at initial non-hydrostatic stress condition. For the stress path (OP), which of the following loading conditions is correct? \includegraphics[width=0.5\linewidth]{image11.png}

An unconfined compression strength test was conducted on a cohesive soil. The test specimen failed at an axial stress of 76 kPa. The undrained cohesion (in kPa, in integer) of the soil is \underline{\hspace{2cm}.}

The reason(s) of the nonuniform elastic settlement profile below a flexible footing, resting on a cohesionless soil while subjected to uniform loading, is/are:

A vertical sheet pile wall is installed in an anisotropic soil having coefficient of horizontal permeability, $k_H$, and coefficient of vertical permeability, $k_V$. In order to draw the flow net for the isotropic condition, the embedment depth of the wall should be scaled by a factor of \underline{\hspace{1cm}, without changing the horizontal scale.}

A soil having the average properties, bulk unit weight $=19\ \text{kN/m^3$, angle of internal friction $=25^\circ$ and cohesion $=15\ \text{kPa}$, is being formed on a rock slope at an inclination of $35^\circ$ with the horizontal. The critical height (in m) of the soil formation up to which it would be stable without failure is \underline{\hspace{2cm}} (round off to one decimal place). [Assume the soil is formed parallel to the rock bedding plane and there is no ground water effect.]}

A smooth vertical retaining wall supporting layered soils is shown in the figure. According to Rankine's earth pressure theory, the lateral active earth pressure acting at the base of the wall is \underline{\hspace{2cm} kPa (rounded off to one decimal place).} \includegraphics[width=0.5\linewidth]{image125.png}

With reference to the compaction test conducted on soils, which of the following is INCORRECT?

A drained direct shear test was carried out on a sandy soil. Under a normal stress of 50 kPa, the test specimen failed at a shear stress of 35 kPa. The angle of internal friction of the sample is \underline{\hspace{3cm} degree (round off to the nearest integer).}

A group of 9 friction piles are arranged in a square grid maintaining equal spacing in all directions. Each pile is of diameter 300 mm and length 7 m. Assume that the soil is cohesionless with effective friction angle $\phi' = 32^\circ$. What is the center-to-center spacing of the piles (in m) for the pile group efficiency of 60%?

A possible slope failure is shown in the figure. Three soil samples are taken from different locations (I, II and III) of the potential failure plane. Which is the most appropriate shear strength test for each sample to identify the failure mechanism? P: Triaxial compression test
Q: Triaxial extension test
R: Direct shear (shear box) test
S: Vane shear test
\includegraphics[width=0.5\linewidth]{image36.png}

The specific gravity of a soil is 2.60. The soil is at 50% degree of saturation with a water content of 15%. The void ratio of the soil is \underline{\hspace{1cm}.}

A group of total 16 piles are arranged in a square grid format. The center-to-center spacing (s) between adjacent piles is 3 m. The diameter (d) and length of embedment of each pile are 1 m and 20 m, respectively. The design capacity of each pile is 1000 kN in the vertical downward direction. The pile group efficiency $ \eta_g $ is given by: \[ \eta_g = 1 - \frac{\theta}{90} \left[ (n-1)m + (m-1)n \right] \frac{1}{mn} \] Where m and n are the number of rows and columns in the plan grid of pile arrangement, and $ \theta = \tan^{-1} \left( \frac{d}{s} \right) $. The design value of the pile group capacity (in kN) in the vertical downward direction is _________ \text{. (round off to the nearest integer)}

A saturated compressible clay layer of thickness h is sandwiched between two sand layers, as shown in the figure. Initially, the total vertical stress and pore water pressure at point P, which is located at the mid-depth of the clay layer, were 150 kPa and 25 kPa, respectively. Construction of a building caused an additional total vertical stress of 100 kPa at P. When the vertical effective stress at P is 175 kPa, the percentage of consolidation in the clay layer at P is _________ \text{. (in integer)}

A soil sample is underlying a water column of height $ h_1 $, as shown in the figure. The vertical effective stresses at points A, B, and C are $ \sigma_A' $, $ \sigma_B' $, and $ \sigma_C' $, respectively. Let $ \gamma_{sat} $ and $ \gamma' $ be the saturated and submerged unit weights of the soil sample, respectively, and $ \gamma_w $ be the unit weight of water. Which one of the following expressions correctly represents the sum $ (\sigma_A' + \sigma_B' + \sigma_C') $?

Match the following in Column X with Column Y:

In a triaxial unconsolidated undrained (UU) test on a saturated clay sample, the cell pressure was 100 kPa. If the deviatoric stress at failure was 150 kPa, then the undrained shear strength of the soil is _________ \text{ kPa}. (in integer)

The inside diameter of a sampler tube is 50 mm. The inside diameter of the cutting edge is kept such that the Inside Clearance Ratio (ICR) is 1.0% to minimize the friction on the sample as the sampler tube enters into the soil. The inside diameter (in mm) of the cutting edge is _________ (round off to two decimal places).

A concentrically loaded isolated square footing of size 2 m $\times$ 2 m carries a concentrated vertical load of 1000 kN. Considering Boussinesq’s theory of stress distribution, the maximum depth (in m) of the pressure bulb corresponding to 10% of the vertical load intensity will be _________ (round off to two decimal places).

Stresses acting on an infinitesimal soil element are shown in the figure (with $ \sigma_z>\sigma_x $). The major and minor principal stresses are $ \sigma_1 $ and $ \sigma_3 $, respectively. Considering the compressive stresses as positive, which one of the following expressions correctly represents the angle between the major principal stress plane and the horizontal plane?

Read the following statements:
(P) While designing a shallow footing in sandy soil, monsoon season is considered for critical design in terms of bearing capacity.
(Q) For slope stability of an earthen dam, sudden drawdown is never a critical condition.
(R) In a sandy sea beach, quicksand condition can arise only if the critical hydraulic gradient exceeds the existing hydraulic gradient.
(S) The active earth thrust on a rigid retaining wall supporting homogeneous cohesionless backfill will reduce with the lowering of water table in the backfill.
Which one of the following combinations is correct?

The internal $d_i$ and external $d_o$ diameters of a Shelby sampler are 48 mm and 52 mm, respectively. The area ratio ($A_r$) of the sampler (in %, round off to two decimal places) is

The soil profile at a road construction site is as shown in figure (not to scale). A large embankment is to be constructed at the site. The ground water table (GWT) is located at the surface of the clay layer, and the capillary rise in the sandy soil is negligible. The effective stress at the middle of the clay layer after the application of the embankment loading is 180 kN/m$^2$. Take unit weight of water, $ \gamma_w = 9.81 \, \text{kN/m}^3 $.

A rectangular footing of size 2.8 m $\times$ 3.5 m is embedded in a clay layer and a vertical load is placed with an eccentricity of 0.8 m as shown in the figure (not to scale). Take Bearing capacity factors: $ N_c = 5.14 $, $ N_q = 1.0 $, and $ N_\gamma = 0.0 $; Shape factors: $ s_c = 1.16 $, $ s_q = 1.0 $ and $ s_\gamma = 1.0 $; Depth factors: $ d_c = 1.1 $, $ d_q = 1.0 $ and $ d_\gamma = 1.0 $; and Inclination factors: $ i_c = 1.0 $, $ i_q = 1.0 $ and $ i_\gamma = 1.0 $.

Using Meyerhoff's method, the load (in kN, round off to two decimal places) that can be applied on the footing with a factor of safety of 2.5 is $\underline{\hspace{1cm}}$.

The void ratio of a clay soil sample M decreased from 0.575 to 0.510 when the applied pressure is increased from 120 kPa to 180 kPa. For the same increment in pressure, the void ratio of another clay soil sample N decreases from 0.600 to 0.550. If the ratio of hydraulic conductivity of sample M to sample N is 0.125, then the ratio of coefficient of consolidation of sample M to sample N (round off to three decimal places) is $\underline{\hspace{1cm}}$.

From laboratory investigations, the liquid limit, plastic limit, natural moisture content and flow index of a soil specimen are obtained as 60%, 27%, 32% and 27, respectively. The corresponding toughness index and liquidity index of the soil specimen, respectively, are