List of top Geotechnical Engineering Questions asked in GATE CE

An uncompacted heap of soil has a volume of 10000 m$^3$ and void ratio of 1. If the soil is compacted to a volume of 7500 m$^3$, then the corresponding void ratio of the compacted soil is $\underline{\hspace{2cm}}$ (round off to one decimal place).

A concentrated vertical load of 3000 kN is applied on a horizontal ground surface. Points P and Q are at depths 1 m and 2 m below the ground, respectively, along the line of application of the load. Considering the ground to be a linearly elastic, isotropic, semi-infinite medium, the ratio of the increase in vertical stress at P to the increase in vertical stress at Q is $\underline{\hspace{2cm}}$ (in integer).

At a site, Static Cone Penetration Test was carried out. The measured point (tip) resistance $ q_c $ was 1000 kPa at a certain depth. The friction ratio ($ f_r $) was estimated as 1 % at the same depth.
The value of sleeve (side) friction (in kPa) at that depth was $\underline{\hspace{2cm}}$ . (in integer)

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?

Let $ \sigma_{\nu}' $ and $ \sigma_{h}' $ denote the effective vertical stress and effective horizontal stress, respectively. Which one of the following conditions must be satisfied for a soil element to reach the failure state under Rankine's passive earth pressure condition?

Four different soils are classified as CH, ML, SP, and SW, as per the Unified Soil Classification System. Which one of the following options correctly represents their arrangement in the decreasing order of hydraulic conductivity?

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)}

Match the following in Column X with Column Y:

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') $?

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).

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).

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?

An unsupported slope of height 15 m is shown in the figure (not to scale), in which the slope face makes an angle of 50° with the horizontal. The slope material comprises purely cohesive soil having undrained cohesion 75 kPa. A trial slip circle KLM, with a radius 25 m, passes through the crest and toe of the slope and it subtends an angle 60° at its center O. The weight of the active soil mass (W, bounded by KLMN) is 2500 kN/m, which is acting at a horizontal distance of 10 m from the toe of the slope. Consider the water table to be present at a very large depth from the ground surface.

Considering the trial slip circle KLM, the factor of safety against the failure of the slope under undrained condition (rounded off to two decimal places) is $\underline{\hspace{1cm}}$.

A combined trapezoidal footing of length $ L $ supports two identical square columns $ P_1 $ and $ P_2 $ of size $ 0.5 \, \text{m} \times 0.5 \, \text{m} $, as shown in the figure. The columns $ P_1 $ and $ P_2 $ carry loads of 2000 kN and 1500 kN, respectively.

If the stress beneath the footing is uniform, the length of the combined footing L (in m, round off to two decimal places) is $\underline{\hspace{1cm}}$.

A retaining wall of height 10 m with clay backfill is shown in the figure (not to scale). Weight of the retaining wall is 5000 kN per m acting at 3.3 m from the toe of the retaining wall. The interface friction angle between base of the retaining wall and the base soil is $ 20^\circ $. The depth of clay in front of the retaining wall is 2.0 m. The properties of the clay backfill and the clay placed in front of the retaining wall are the same. Assume that the tension crack is filled with water. Use Rankine's earth pressure theory. Take unit weight of water, $ \gamma_w = 9.81 \, \text{kN/m}^3 $.

The soil profile at a construction site is shown in the figure (not to scale). Ground water table (GWT) is at 5 m below the ground level at present. An old well data shows that the ground water table was as low as 10 m below the ground level in the past. Take unit weight of water, $ \gamma_w = 9.81 \, \text{kN/m}^3 $.

The overconsolidation ratio (OCR) (round off to two decimal places) at the mid-point of the clay layer is $\underline{\hspace{1cm}}$.

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.

The cohesion ($ c $), angle of internal friction ($ \phi $) and unit weight ($ \gamma $) of a soil are 15 kPa, 20°, and 17.5 kN/m$^3$, respectively. The maximum depth of unsupported excavation in the soil (in m, rounded off to two decimal places) is $\underline{\hspace{2cm}}$.

In an Oedometer apparatus, a specimen of fully saturated clay has been consolidated under a vertical pressure of 50 kN/m² and is presently at equilibrium. The effective stress and pore water pressure immediately on increasing the vertical stress to 150 kN/m², respectively, are:

A partially-saturated soil sample has natural moisture content of 25% and bulk unit weight of 18.5 kN/m³. The specific gravity of soil solids is 2.65 and unit weight of water is 9.81 kN/m³. The unit weight of the soil sample on full saturation is

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

A clay layer of thickness $ H $ has a preconsolidation pressure $ p_c $ and an initial void ratio $ e_0 $. The initial effective overburden stress at the mid-height of the layer is $ p_0 $. At the same location, the increment in effective stress due to applied external load is $ \Delta p $. The compression and swelling indices of the clay are $ C_c $ and $ C_s $, respectively. If $ p_0 < p_c < (p_0 + \Delta p) $, then the correct expression to estimate the consolidation settlement $ s_c $ of the clay layer is